diff --git a/lib/doc/Math.lyx b/lib/doc/Math.lyx index 3947cd25f4..76801d362b 100644 --- a/lib/doc/Math.lyx +++ b/lib/doc/Math.lyx @@ -1,38450 +1,38450 @@ -#LyX 2.0 created this file. For more info see http://www.lyx.org/ -\lyxformat 413 -\begin_document -\begin_header -\textclass scrartcl -\begin_preamble -% DO NOT ALTER THIS PREAMBLE!!! -% -% This preamble is designed to ensure that the file prints -% out as advertised. If you mess with this preamble, -% parts of this document may not print out as expected. 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-\graphics default -\default_output_format default -\output_sync 0 -\bibtex_command default -\index_command default -\paperfontsize 12 -\spacing single -\use_hyperref true -\pdf_title "LyX's Math Manual" -\pdf_author "LyX Team, Uwe Stöhr" -\pdf_subject "LyX-documentation about math" -\pdf_keywords "LyX, Mathed" -\pdf_bookmarks true -\pdf_bookmarksnumbered true -\pdf_bookmarksopen true -\pdf_bookmarksopenlevel 1 -\pdf_breaklinks false -\pdf_pdfborder false -\pdf_colorlinks true -\pdf_backref false -\pdf_pdfusetitle false -\pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false" -\papersize a4paper -\use_geometry false -\use_amsmath 2 -\use_esint 1 -\use_mhchem 1 -\use_mathdots 1 -\cite_engine basic -\use_bibtopic false -\use_indices false -\paperorientation portrait -\suppress_date false -\use_refstyle 0 -\notefontcolor #0000ff -\index Index -\shortcut idx -\color #008000 -\end_index -\secnumdepth 4 -\tocdepth 3 -\paragraph_separation skip -\defskip medskip -\quotes_language english -\papercolumns 1 -\papersides 2 -\paperpagestyle plain -\bullet 1 0 6 -1 -\bullet 2 2 35 -1 -\bullet 3 2 7 -1 -\tracking_changes false -\output_changes false -\html_math_output 0 -\html_css_as_file 0 -\html_be_strict false -\end_header - -\begin_body - -\begin_layout Title -LyX's detailed Math manual -\end_layout - -\begin_layout Author -by the LyX Team -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -\noindent -If you have comments or error corrections, please send them to the LyX Documenta -tion mailing list: -\family typewriter - -\begin_inset CommandInset href -LatexCommand href -name "lyx-docs@lists.lyx.org" -target "lyx-docs@lists.lyx.org?subject=LyX's Math manual" -type "mailto:" - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -author: Uwe Stöhr -\end_layout - -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\family sans -Version 2.0.x -\end_layout - -\begin_layout Standard -\begin_inset CommandInset toc -LatexCommand tableofcontents - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Note -status open - -\begin_layout Plain Layout -To export this document to PDF, PS or DVI the LaTeX-packages -\series bold -braket, cancel, eurosym, mathdots, mhchem -\series default - and -\series bold -was -\series default - should be installed. - If they are not installed the document can be exported anyway but the sections - where the packages are required will not appear in the output. - An exception is -\series bold -mhchem -\series default -; if it is not installed, this file cannot be exported. -\end_layout - -\begin_layout Plain Layout -The latest PDF-version of this document can be found here: -\begin_inset Newline newline -\end_inset - - -\series bold -http://wiki.lyx.org/LyX/DocumentationDevelopment#Math -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -Introduction -\end_layout - -\begin_layout Standard -This document explains LyX's math features and is furthermore a collection - of LaTeX-commands used for mathematical characters and constructs. - The explanations are designed for the usage of commands. - It is therefore required that you have read the section -\family typewriter -Mathematical -\begin_inset space ~ -\end_inset - -Formulas -\family default - of the User's Guide. -\end_layout - -\begin_layout Standard -Most of the characters and many constructs explained in this manual are - also accessible via the menu -\family sans -Insert -\series bold -\SpecialChar \menuseparator - -\series default -Math -\family default - or the -\family sans -math -\family default -\series bold - -\family sans -\series default -toolbar -\family default -. - But everybody who has to write lots of formulas will notice that it is - much faster to use commands instead of the math toolbar. - Therefore this manual is focused on commands but also mentions the correspondin -g toolbar buttons when available. -\end_layout - -\begin_layout Standard -If not specially mentioned the commands are only available within formulas. - To be able to use all commands explained in this document, the option -\family sans -Use AMS math package -\family default - must be checked in the document settings (menu -\family sans -Document\SpecialChar \menuseparator -Settings\SpecialChar \menuseparator -Math -\begin_inset space ~ -\end_inset - -Options -\family default -). -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -The option -\family sans -Use AMS math package automatically -\family default - only uses -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -AmS -\end_layout - -\end_inset - --math when math constructs are found that are supported by LyX. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -This document doesn't list all -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -AmS -\end_layout - -\end_inset - --math commands -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -A list with all -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -AmS -\end_layout - -\end_inset - --math commands is in the file -\family sans - -\begin_inset CommandInset href -LatexCommand href -name "amsguide.ps" -target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps" - -\end_inset - - -\family default -, which is part of every LaTeX standard installation. -\end_layout - -\end_inset - - for lucidity reasons. -\end_layout - -\begin_layout Section -General Instructions -\end_layout - -\begin_layout Standard -To create an inline formula -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! inline -\end_layout - -\end_inset - - that is embedded into a text line, use one of the shortcuts -\begin_inset Info -type "shortcuts" -arg "math-mode" -\end_inset - - or the toolbar button -\begin_inset Graphics - filename ../images/math-mode.png - scale 85 - -\end_inset - -. -\begin_inset Newline newline -\end_inset - -To create a display style formula -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! display style -\end_layout - -\end_inset - - which will appear bigger, has a different format, and will be in a separate - paragraph, use one of these shortcuts: -\begin_inset Info -type "shortcuts" -arg "math-display" -\end_inset - -. -\end_layout - -\begin_layout Standard -To change a display style formula to an inline formula, set the cursor into - the formula and use one of the shortcuts -\begin_inset Info -type "shortcuts" -arg "math-mode" -\end_inset - - or the menu -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Change formula type -\family default -. - The same way is used to change an inline formula to a display style formula. -\end_layout - -\begin_layout Standard -To display parts of an inline formula in the size of a display style formula, - enter the command -\series bold - -\backslash -displaystyle -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -displaystyle -\end_layout - -\end_inset - - to a formula. - Then a new blue box appears in which the desired formula part is inserted. -\end_layout - -\begin_layout Standard -Only inline formulas are allowed inside tables. -\end_layout - -\begin_layout Standard -The -\family sans -math toolbar -\family default - can be turned on in the menu -\family sans -View\SpecialChar \menuseparator -Toolbars -\family default -. - When you click there on -\begin_inset Quotes eld -\end_inset - -Math -\begin_inset Quotes erd -\end_inset - - the toolbar will be shown permanently at the bottom; this state is visualized - in the -\family sans -Toolbars -\family default - menu with a checkmark. - When you click in this state again on -\begin_inset Quotes eld -\end_inset - -Math -\begin_inset Quotes erd -\end_inset - - in the -\family sans -Toolbars -\family default - menu, the -\family sans -math toolbar -\family default - is only shown when the cursor is within a formula; this state is visualized - by the renaming of the menu entry from -\begin_inset Quotes eld -\end_inset - -Math -\begin_inset Quotes erd -\end_inset - - to -\begin_inset Quotes eld -\end_inset - -Math -\begin_inset space ~ -\end_inset - -(auto) -\begin_inset Quotes erd -\end_inset - -. -\end_layout - -\begin_layout Standard -The TeX-mode -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -T@TeX-mode -\end_layout - -\end_inset - - is invoked by pressing the toolbar button -\begin_inset Graphics - filename ../images/ert-insert.png - scale 85 - -\end_inset - - or by using the menu -\family sans -Insert\SpecialChar \menuseparator -Te -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{} -\end_layout - -\end_inset - -X Code -\family default - (shortcut -\begin_inset Info -type "shortcut" -arg "ert-insert" -\end_inset - -). -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -In LyX there are three -\begin_inset Quotes eld -\end_inset - -proper names -\begin_inset Quotes erd -\end_inset - - that appear in the output with sub- and superscript letters: TeX, LaTeX - and LyX -\end_layout - -\begin_layout Plain Layout -To avoid that these names are recognized as proper names, a TeX-brace pair - is inserted. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To change the LaTeX-preamble -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -L@LaTeX-preamble -\end_layout - -\end_inset - -, use the menu -\family sans -Document\SpecialChar \menuseparator -Settings\SpecialChar \menuseparator -LaT -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{} -\end_layout - -\end_inset - -eX -\family default - -\family sans -Preamble -\family default -. -\end_layout - -\begin_layout Standard -To edit matrices, case differentiations and multiline formulas subsequently, - use the menus -\family sans -Edit\SpecialChar \menuseparator -Math -\family default - and -\family sans -Edit\SpecialChar \menuseparator -Rows -\begin_inset space \thinspace{} -\end_inset - -& -\begin_inset space \thinspace{} -\end_inset - -Columns, -\family default - or the -\family sans -table toolbar -\family default -. - When lines and columns are swapped via the menu, the column or line where - the cursor is in is exchanged with the column to the right or the line - below, respectively. - Is the cursor in the last column or row, the exchange is done with the - column to the left or the line above. -\end_layout - -\begin_layout Standard -To write text in formulas -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -For multiline formulas the command -\series bold - -\backslash -intertext -\series default - is used, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Text-in-multiline" - -\end_inset - -. -\end_layout - -\end_inset - - -\emph on -mathematical text -\emph default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Text ! in formulas -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Mathematical text -\end_layout - -\end_inset - - is used. - This mode is invoked with the shortcut -\begin_inset Info -type "shortcut" -arg "font-default" -\end_inset - - or by the insertion of the command -\series bold - -\backslash -text -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -text -\end_layout - -\end_inset - -. - The text appears black in LyX and can therefore be distinguished from the - other formula parts which appear blue. - In the output mathematical text is set upright, in contrary to other formula - parts. -\end_layout - -\begin_layout Subsection* -Command Scheme -\end_layout - -\begin_layout Standard -Most of the LaTeX-commands for math constructs have the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -commandname[optional -\series default - -\series bold -argument]{required -\series default - -\series bold -argument} -\end_layout - -\begin_layout Standard -A command always starts with a backslash -\begin_inset Quotes gld -\end_inset - - -\series bold - -\backslash - -\series default - -\begin_inset Quotes grd -\end_inset - -. - To omit optional arguments, also omit the associated brackets. - The braces around the required arguments are named in this document as - TeX-braces -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -T@TeX-braces -\end_layout - -\end_inset - -. - If you add in a formula a left brace to a command name, LyX automatically - creates a TeX-brace. - In all other cases TeX-braces are created in formulas with the command - -\series bold - -\backslash -{ -\series default -. - TeX-braces appear red in LyX, in contrary to normal braces which appear - blue. - In TeX-mode no command is needed to get TeX-braces. - TeX-braces don't appear in the output. -\end_layout - -\begin_layout Standard -When commands without arguments, like commands for symbols are entered in - TeX-mode, a space character must -\emph on -always -\emph default - be behind the command to end it. - This space doesn't appear in the output. - When the space should appear in the output, the space must be followed - by a protected space in normal text. -\end_layout - -\begin_layout Standard -A protected space is inserted with -\begin_inset Info -type "shortcuts" -arg "command-alternatives space-insert protected ; math-space" -\end_inset - -. -\end_layout - -\begin_layout Subsection* -\begin_inset Newpage newpage -\end_inset - -Syntax Explanation -\end_layout - -\begin_layout Itemize -The symbol -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -This visible space character can be created with the command -\series bold - -\backslash -textvisiblespace -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -textvisiblespace -\end_layout - -\end_inset - -, inserted in TeX-mode. -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset space ~ -\end_inset - -denotes a space character to be input. -\end_layout - -\begin_layout Itemize -An arrow like -\begin_inset Formula $\to$ -\end_inset - - denotes the usage of the corresponding arrow key on the keyboard. - The -\family sans -Tab -\family default - key can often be used instead of -\begin_inset Formula $\to$ -\end_inset - - and -\begin_inset Formula $\downarrow$ -\end_inset - -, and -\family sans -Shift+Tab -\family default - instead of -\begin_inset Formula $\leftarrow$ -\end_inset - - and -\begin_inset Formula $\uparrow$ -\end_inset - -. -\end_layout - -\begin_layout Subsection* -Available units -\end_layout - -\begin_layout Standard -\align center -\begin_inset Float table -placement H -wide false -sideways false -status open - -\begin_layout Plain Layout -\align center -\begin_inset Caption - -\begin_layout Plain Layout -\begin_inset CommandInset label -LatexCommand label -name "tab:Available-units" - -\end_inset - -Available units -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Plain Layout -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Unit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Name / Description -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -mm -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Millimeter -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -cm -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Centimeter -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -in -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Inch (1 -\begin_inset space \thinspace{} -\end_inset - -in = 2,54 -\begin_inset space \thinspace{} -\end_inset - -cm) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -pt -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Point (72.27 -\begin_inset space \thinspace{} -\end_inset - -pt = 1 -\begin_inset space \thinspace{} -\end_inset - -in) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -pc -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Pica (1 -\begin_inset space \thinspace{} -\end_inset - -pc = 12 -\begin_inset space \thinspace{} -\end_inset - -pt) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -sp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -scaled point (65536 -\begin_inset space \thinspace{} -\end_inset - -sp = 1 -\begin_inset space \thinspace{} -\end_inset - -pt) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -bp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -big point (72 -\begin_inset space \thinspace{} -\end_inset - -bp = 1 -\begin_inset space \thinspace{} -\end_inset - -in) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -dd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Didot (1 -\begin_inset space \thinspace{} -\end_inset - -dd -\begin_inset Formula $\approx$ -\end_inset - - 0.376 -\begin_inset space \thinspace{} -\end_inset - -mm) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -cc -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Cicero (1 -\begin_inset space \thinspace{} -\end_inset - -cc = 12 -\begin_inset space \thinspace{} -\end_inset - -dd) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -ex -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Height of letter -\emph on - -\begin_inset Quotes eld -\end_inset - -x -\emph default - -\begin_inset Quotes erd -\end_inset - - in the current font -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -em -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -width of letter -\begin_inset Quotes eld -\end_inset - - -\emph on -M -\emph default - -\begin_inset Quotes erd -\end_inset - - in the current font -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -mu -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -math unit (1 -\begin_inset space \thinspace{} -\end_inset - -mu = -\begin_inset Formula $\nicefrac{1}{18}$ -\end_inset - - -\begin_inset space \thinspace{} -\end_inset - -em) -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -Basic Functions -\end_layout - -\begin_layout Subsection -Exponents -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Exponents -\end_layout - -\end_inset - - and Indices -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Indices -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Superscripts|see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Exponents -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Subscripts|see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Indices -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Indices are created with an underscore -\begin_inset Quotes eld -\end_inset - -_ -\begin_inset Quotes erd -\end_inset - - or via the math toolbar button -\begin_inset Graphics - filename ../images/math-subscript.png - scale 85 - -\end_inset - -, exponents with a caret -\begin_inset Quotes eld -\end_inset - -^ -\begin_inset Quotes erd -\end_inset - - or via the math toolbar button -\begin_inset Graphics - filename ../images/math-superscript.png - scale 85 - -\end_inset - -. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -B_V -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $B_{V}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -B^V -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}B^{V}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -B^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}B^{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -As the caret is in some languages an accent, vowels will be accentuated - in this case and not set as exponents -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -Depending on the used keyboard settings this can also happen for characters - other than vowels. -\end_layout - -\end_inset - -. - To get exponents in this case, press -\family sans -Space -\family default - after the caret as in the last example. -\end_layout - -\begin_layout Subsection -Fractions -\begin_inset CommandInset label -LatexCommand label -name "sub:Fractions" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Fractions -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Fractions are generated with the command -\series bold - -\backslash -frac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! F ! -\backslash -frac -\end_layout - -\end_inset - - or via the math toolbar button -\begin_inset Graphics - filename ../images/math/frac.png - scale 50 - -\end_inset - -. - The font size is adjusted automatically, depending on whether the fraction - is in an inline or display style formula. - With the math toolbar button -\begin_inset Graphics - filename ../images/math/frac-square.png - scale 85 - -\end_inset - - you can select different fraction types. -\end_layout - -\begin_layout Standard -With the command -\series bold - -\backslash -dfrac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dfrac -\end_layout - -\end_inset - - a fraction can be created that always has the size of a display style formula. - With -\series bold - -\backslash -tfrac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -tfrac -\end_layout - -\end_inset - - the fraction appears always with the size of an inline formula. - An example: -\end_layout - -\begin_layout Standard -A line with the fraction -\begin_inset Formula $\frac{1}{2}$ -\end_inset - - that was created with the command -\series bold - -\backslash -frac -\series default -. -\end_layout - -\begin_layout Standard -A line with the fraction -\begin_inset Formula $\dfrac{1}{2}$ -\end_inset - - that was created with the command -\series bold - -\backslash -dfrac -\series default -. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -frac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dfrac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dfrac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e^ -\backslash -frac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -1 -\begin_inset Formula $\downarrow$ -\end_inset - -2 -\begin_inset Formula $\downarrow\downarrow$ -\end_inset - -3 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - - -\begin_inset Newpage newpage -\end_inset - -For nested fractions the command -\series bold - -\backslash -cfrac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -cfrac -\end_layout - -\end_inset - - can be used. - Here is an example: -\begin_inset VSpace -3mm -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Formula -\begin{align*} -\textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\ -\frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}} -\end{align*} - -\end_inset - - -\end_layout - -\begin_layout Standard -The command for the example above is: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -cfrac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B+ -\backslash -cfrac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C+ -\backslash -cfrac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -E -\begin_inset Formula $\downarrow$ -\end_inset - -F -\begin_inset Formula $\downarrow$ -\end_inset - -D -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - - -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -cfrac -\series default - sets the fraction always in the size of a displayed formula, also when - it is part of another fraction. -\end_layout - -\begin_layout Standard -It is possible to specify the alignment of the numerator. - The command -\series bold - -\backslash -cfracleft -\series default - is used to left align it, the command -\series bold - -\backslash -cfracright -\series default - to right-align it. - -\series bold - -\backslash -cfrac -\series default - centers the numerator. - These fractions demonstrate the different alignments: -\end_layout - -\begin_layout Standard - -\series bold -\begin_inset Formula -\[ -\cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - -\series bold - -\backslash -cfracleft -\series default - and -\series bold - -\backslash -cfracright -\series default - are no real LaTeX commands but represent the command -\series bold - -\backslash -cfrac[alignment]{numerator}{denominator} -\series default - . - Therefore you cannot use them in TeX code. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -It is often advantageous to combine -\series bold - -\backslash -cfrac -\series default - and -\series bold - -\backslash -frac -\series default -: -\begin_inset Formula -\[ -\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -For inline fractions with a sloped fraction stroke you can use the command - -\series bold - -\backslash -nicefrac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! N ! -\backslash -nicefrac -\end_layout - -\end_inset - -: -\begin_inset Formula $\nicefrac{5}{31}$ -\end_inset - - or -\series bold - -\backslash -unitfrac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -unitfrac -\end_layout - -\end_inset - -: -\begin_inset Formula $\unitfrac{5}{31}$ -\end_inset - - There is furthermore the command -\series bold - -\backslash -unitfracthree -\series default - that offers to write a fraction in combination with a number: -\begin_inset Formula $\unitfrac[2]{1}{3}$ -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - -\series bold - -\backslash -unitfracthree -\series default - is not a real LaTeX command but the command -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -unitfrac[number]{numerator}{denominator} -\series default - . - Therefore you cannot use it in TeX code. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -How to define own fractions where the fraction stroke can be changed, is - explained in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Self-defined-Fractions" - -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Subsection -Roots -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Roots -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Square roots are created with -\series bold - -\backslash -sqrt -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -sqrt -\end_layout - -\end_inset - - or the math toolbar button -\begin_inset Graphics - filename ../images/math/sqrt.png - scale 85 - -\end_inset - -, all other roots with the command -\series bold - -\backslash -root -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -root -\end_layout - -\end_inset - - or with the math toolbar button -\begin_inset Graphics - filename ../images/math/root.png - scale 85 - -\end_inset - -. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqrt -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A-B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -root -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -3 -\begin_inset Formula $\downarrow$ -\end_inset - -A-B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -A square root can also be created with -\series bold - -\backslash -root -\series default - when the root index field is left empty. -\end_layout - -\begin_layout Standard -With certain indices the distance to the root is too small, like in this - formula: -\begin_inset Formula $\sqrt[\beta]{B}$ -\end_inset - - -\begin_inset Newline newline -\end_inset - -The -\begin_inset Formula $\beta$ -\end_inset - - touches the root. - To avoid this, the commands -\series bold - -\backslash -leftroot -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -leftroot -\end_layout - -\end_inset - - and -\series bold - -\backslash -uproot -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -uproot -\end_layout - -\end_inset - - are used with the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -leftroot{distance} -\series default - and -\series bold - -\backslash -uproot{distance} -\end_layout - -\begin_layout Standard -Distance is the number of Big Points (unit bp; -\begin_inset Formula $\mathrm{72\, bp=1\, inch}$ -\end_inset - -), that the index should be moved to the left or top, resp.. - The commands are written to the index. - This way the command -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -root -\backslash -leftroot{-1 -\begin_inset Formula $\to$ -\end_inset - - -\backslash -uproot{2 -\begin_inset Formula $\to$ -\end_inset - - -\backslash -beta -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset Formula $\to$ -\end_inset - -B -\begin_inset Newline newline -\end_inset - - -\series default -produces a correct typeset formula: -\begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$ -\end_inset - - -\end_layout - -\begin_layout Subsection -Binomial Coefficients -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Binomial coefficients -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Binomial coefficients are inserted with the command -\series bold - -\backslash -binom -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -binom -\end_layout - -\end_inset - - or with the submenu of the math toolbar button -\begin_inset Graphics - filename ../images/math/frac-square.png - scale 85 - -\end_inset - -. - As with fractions ( -\series bold - -\backslash -frac -\series default -) in addition to -\series bold - -\backslash -binom -\series default - there are the commands -\series bold - -\backslash -dbinom -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dbinom -\end_layout - -\end_inset - - and -\series bold - -\backslash -tbinom -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -tbinom -\end_layout - -\end_inset - -. - For other brackets around binomial coeficients there are the commands -\series bold - -\backslash -brace -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -brace -\end_layout - -\end_inset - - and -\series bold - -\backslash -brack -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -brack -\end_layout - -\end_inset - -. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -binom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dbinom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -tbinom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -brack -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -brace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Subsection -Case Differentiations -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Case differentiations -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cases -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\to$ -\end_inset - -B>0 -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -cases -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\begin{cases} -A & B>0\end{cases}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cases -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\begin{cases} -A & \textrm{for }x>0\\ -B & \textrm{for }x=0 -\end{cases}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -After inserting -\series bold - -\backslash -cases -\series default - or pressing the math toolbar button -\begin_inset Graphics - filename ../images/math/cases.png - scale 85 - -\end_inset - - you can create new lines with the shortcut -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - - or the table toolbar button -\begin_inset Graphics - filename ../images/tabular-feature_append-row.png - scale 85 - -\end_inset - -. -\end_layout - -\begin_layout Standard -The command -\series bold - -\backslash -cases -\series default - is also available via the menu -\family sans -Insert\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Cases-Environment -\family default -. -\end_layout - -\begin_layout Subsection -Negations -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Negations -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -By inserting -\series bold - -\backslash -not -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! N ! -\backslash -not -\end_layout - -\end_inset - - every character can be displayed canceled. - The characters are quasi accentuated by a slash. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not= -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\not=$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not -\backslash -le -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\not\le$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not -\backslash -parallel -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\not\parallel$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -The last example shows that not all negations look good. - Therefore there are special commands for some negations (see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Mathematical-Symbols" - -\end_inset - - and -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Relations" - -\end_inset - -). -\end_layout - -\begin_layout Subsection -Placeholders -\begin_inset CommandInset label -LatexCommand label -name "sub:Placeholders" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Placeholders -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Chemical characters ! Isotopes -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Isotopes|see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Chemical characters -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -When displaying e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -isotopes -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -Typesetting isotopes and chemical symbols is described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Chemical-Symbols-and" - -\end_inset - -. -\end_layout - -\end_inset - - the following problem occurs: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Indices created with sub- and superscripts: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -correct indices: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The shorter index is by default placed below or above the first character - of the longer index. - To avoid this there is the command -\series bold - -\backslash -phantom -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! P ! -\backslash -phantom -\end_layout - -\end_inset - - or the math toolbar button -\begin_inset space \thinspace{} -\end_inset - - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -can be found in the submenu of the toolbar button -\begin_inset Graphics - filename ../images/math/space.png - scale 85 - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Graphics - filename ../images/math/phantom.png - scale 85 - -\end_inset - - that creates one or more phantom characters. - When inserting -\series bold - -\backslash -phantom -\series default - a small blue box appears that is superposed with two red arrows. - The arrows indicate that the complete width and height of the box content - will be created as placeholder. - Phantom characters are accordingly placeholders with the size of the characters. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -^19 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -_ -\backslash -phantom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -1 -\begin_inset Formula $\to$ -\end_inset - -9 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -F -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -^235 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -_ -\backslash -phantom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -23 -\begin_inset Formula $\to$ -\end_inset - -9 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -F -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Lambda^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -phantom -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -ii -\begin_inset Formula $\to$ -\end_inset - -t -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -_MMt -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -Furthermore there are the commands -\series bold - -\backslash -vphantom -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! V ! -\backslash -vphantom -\end_layout - -\end_inset - - (toolbar button -\begin_inset space ~ -\end_inset - - -\begin_inset Graphics - filename ../images/math/vphantom.png - scale 85 - -\end_inset - -) and -\series bold - -\backslash -hphantom -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hphantom -\end_layout - -\end_inset - - (toolbar button -\begin_inset space ~ -\end_inset - - -\begin_inset Graphics - filename ../images/math/hphantom.png - scale 85 - -\end_inset - -). - -\series bold - -\backslash -hphantom -\series default - creates only space for the maximal height of the characters in the box - but not for its width. - -\series bold - -\backslash -vphantom -\series default - creates only space for the width of the box content. - Therefore the boxes of both commands have only one red arrow. -\end_layout - -\begin_layout Standard -For example the command -\series bold - -\backslash -vphantom -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold -a -\backslash -int -\series default - creates space for the height of the integral sign, -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -The command -\series bold - -\backslash -int -\series default - creates an integral sign, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Big-Operators" - -\end_inset - -. -\end_layout - -\end_inset - - because this is the larger character. - An example application is in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Multiline-Brackets" - -\end_inset - -. -\end_layout - -\begin_layout Standard -Placeholders can also be used for text when they are inserted via the menu - -\family sans -Insert\SpecialChar \menuseparator -Formatting\SpecialChar \menuseparator -Phantom -\family default -: -\end_layout - -\begin_layout Standard -This is a sentence. -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom Phantom -status open - -\begin_layout Plain Layout -This -\end_layout - -\end_inset - - is a sentence. -\end_layout - -\begin_layout Subsection -Lines -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Lines -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! underlined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overline -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! O ! -\backslash -overline -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -underline -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -underline -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overline -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -underline -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -In the last example it doesn't matter if first -\series bold - -\backslash -overline -\series default - or -\series bold - -\backslash -underline -\series default - is inserted. -\end_layout - -\begin_layout Standard -To double underline use -\series bold - -\backslash -underline -\series default - twice. -\end_layout - -\begin_layout Standard -It is possible to place up to 6 lines above or below characters. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -Custom lines can be created using the command -\series bold - -\backslash -rule -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -rule -\end_layout - -\end_inset - - which has the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -rule[vertical offset]{length}{thickness} -\end_layout - -\begin_layout Standard -The optional vertical offset shifts the line upwards (or downwards, when - the value is negative). - The units listed in -\begin_inset CommandInset ref -LatexCommand ref -reference "tab:Available-units" - -\end_inset - - can be used for the values. - Here are two example lines created with the commands -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -rule[-2ex]{3cm}{2pt} -\series default - and -\series bold - -\backslash -rule{2cm}{1pt} -\series default -: -\end_layout - -\begin_layout Standard -This is a sentence -\begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$ -\end_inset - - with two lines. -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -rule -\series default - can also be used for text when a line is inserted via the menu -\family sans -Insert\SpecialChar \menuseparator -Formatting\SpecialChar \menuseparator -Horizontal -\begin_inset space ~ -\end_inset - -Line -\family default -: -\end_layout - -\begin_layout Standard -This is a sentence -\begin_inset CommandInset line -LatexCommand rule -offset "0.5ex" -width "3cm" -height "1pt" - -\end_inset - - with one line. -\end_layout - -\begin_layout Subsection -Ellipses -\begin_inset CommandInset label -LatexCommand label -name "sub:Ellipses" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Ellipses -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -There are different types of ellipses available. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -In the math toolbar in the submenu of the button -\begin_inset Graphics - filename ../images/math/ldots.png - scale 85 - -\end_inset - - -\end_layout - -\end_inset - - For listings dots at the baseline are used ( -\series bold - -\backslash -ldots -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -ldots -\end_layout - -\end_inset - -), while for operations dots are needed that are on the same height as the - operators ( -\series bold - -\backslash -cdots -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -cdots -\end_layout - -\end_inset - -). - When using the command -\series bold - -\backslash -dots -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dots -\end_layout - -\end_inset - -, LaTeX decides on the basis of the next character what type is used. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A_1 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -, -\backslash -dots -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -,A_n -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A_{1},\dots,A_{n}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A_1 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+ -\backslash -dots -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+A_n -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A_{1}+\dots+A_{n}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A_1 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -, -\backslash -ldots -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -,A_n -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A_{1},\ldots,A_{n}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A_1 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+ -\backslash -cdots -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+A_n -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A_{1}+\cdots+A_{n}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vdots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\vdots$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ddots$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -iddots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\iddots$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -3×3 -\begin_inset space \thinspace{} -\end_inset - -matrix with the different dots -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\begin{array}{ccc} -A_{11} & \cdots & A_{1m}\\ -\vdots & \ddots & \vdots\\ -A_{n1} & \cdots & A_{nm} -\end{array}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -The ellipses available in menu -\family sans -Insert\SpecialChar \menuseparator -Special -\begin_inset space ~ -\end_inset - -Character -\family default - are -\series bold - -\backslash -ldots -\series default -. -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -To use -\series bold - -\backslash -iddots -\series default -, one of the options -\family sans -Use mathdots package (automatically) -\family default - must be set in the document settings under -\family sans -Math -\begin_inset space ~ -\end_inset - -Options -\family default -. -\begin_inset Newline newline -\end_inset - -Using the option -\family sans -Use mathdots package -\family default - will improve the appearance of all dots in the documents if their font - style or size is not the default. -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -Specially for matrices there are ellipses that span over several columns. - They are created with the command -\series bold - -\backslash -hdotsfor -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hdotsfor -\end_layout - -\end_inset - -, that has the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -hdotsfor[distance]{number of columns} -\end_layout - -\begin_layout Standard -The number of columns specifies how many columns should be spanned. - Distance is a factor for the distance between the dots. -\end_layout - -\begin_layout Standard -In the following matrix the command -\series bold - -\backslash -hdotsfor[2]{4} -\series default - was inserted in the first box of the second line, to get an ellipsis with - a dot distance twice as long as with the command -\series bold - -\backslash -dots -\series default -: -\begin_inset Formula -\[ -\left(\begin{array}{cccc} -A & B & C & D\\ -\hdotsfor[2]{4}\\ -q & w & e & r -\end{array}\right) -\] - -\end_inset - -Note that the matrix fields that should be spanned must be empty, otherwise - you get LaTeX-errors. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -Furthermore you can fill with the command -\series bold - -\backslash -dotfill -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dotfill -\end_layout - -\end_inset - - the rest of a line with dots. - The effect of these commands is the same as with -\series bold - -\backslash -hfill -\series default -, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Variable-Space" - -\end_inset - -. -\end_layout - -\begin_layout Standard -For example the command -\series bold -A -\backslash -dotfill -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -B -\series default - produces -\end_layout - -\begin_layout Standard -\begin_inset Formula $A\dotfill B$ -\end_inset - - -\end_layout - -\begin_layout Standard -Similar to -\series bold - -\backslash -dotfill -\series default - there is for a line the command -\series bold - -\backslash -hrulefill -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hrulefill -\end_layout - -\end_inset - -: -\end_layout - -\begin_layout Standard -\begin_inset Formula $A\hrulefill B$ -\end_inset - - -\end_layout - -\begin_layout Standard -To use the commands for text, they have to be inserted in TeX-mode. -\end_layout - -\begin_layout Section -Matrices -\begin_inset CommandInset label -LatexCommand label -name "sec:Matrices" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Matrices -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Matrices can be inserted via the math toolbar button -\begin_inset Graphics - filename ../images/dialog-show_mathmatrix.png - scale 85 - -\end_inset - - or the menu -\family sans -Insert\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Matrix -\family default -. - In the matrix dialog you can specify the number of columns and rows, the - alignment and the decoration. - The vertical alignment is only of importance for matrices in inline formulas: -\end_layout - -\begin_layout Standard -The first matrix is top -\begin_inset Formula $\begin{array}[t]{cccc} -A & D & G & J\\ -B & E & H & K\\ -C & F & I & L -\end{array}$ -\end_inset - -, the second middle -\begin_inset Formula $\begin{array}{cccc} -A & D & G & J\\ -B & E & H & K\\ -C & F & I & L -\end{array}$ -\end_inset - - and the third bottom -\begin_inset Formula $\begin{array}[b]{cccc} -A & D & G & J\\ -B & E & H & K\\ -C & F & I & L -\end{array}$ -\end_inset - - aligned. -\end_layout - -\begin_layout Standard -The horizontal alignment specifies how the column entries should be aligned. - It is set by entering a letter for every column. - -\emph on -l -\emph default - denotes left aligned, -\emph on -c -\emph default - centered and -\emph on -r -\emph default - right aligned. - To create for example a 4 -\series bold -× -\series default -4 -\begin_inset space ~ -\end_inset - -matrix where the first column is left aligned, the second and third are - centered and the last one is right aligned, one enters for the horizontal - alignment -\series bold -lccr -\series default -. - Normally in a matrix all columns are centered, therefore the default for - every column is a -\series bold -c -\series default -. -\end_layout - -\begin_layout Standard -Horizontal alignment: -\end_layout - -\begin_layout Standard - -\series bold -lll -\series default - : -\begin_inset Formula $\begin{array}{lll} -10000 & D & G\\ -B & 10000 & H\\ -C & F & 10000 -\end{array}$ -\end_inset - - , -\series bold -ccc -\series default - : -\begin_inset Formula $\begin{array}{ccc} -10000 & D & G\\ -B & 10000 & H\\ -C & F & 10000 -\end{array}$ -\end_inset - - , -\series bold -rrr -\series default - : -\begin_inset Formula $\begin{array}{rrr} -10000 & D & G\\ -B & 10000 & H\\ -C & F & 10000 -\end{array}$ -\end_inset - - -\end_layout - -\begin_layout Standard -To add or delete rows and columns subsequently, the math toolbar buttons - -\begin_inset Graphics - filename ../images/tabular-feature_append-row.png - scale 85 - -\end_inset - -, -\begin_inset Graphics - filename ../images/tabular-feature_delete-row.png - scale 85 - -\end_inset - -, etc. -\begin_inset space \thinspace{} -\end_inset - -, or the menu -\family sans -Edit\SpecialChar \menuseparator -Rows & Columns -\family default - can be used. - New rows can also be created with -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -The -\family sans -Decoration -\family default - adds parentheses in the selected style around the matrix. - Alternatively, parentheses can can either be created with the commands - -\series bold - -\backslash -left -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -left -\end_layout - -\end_inset - - and -\series bold - -\backslash -right -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -right -\end_layout - -\end_inset - - (shortcut -\family sans -Alt+M -\begin_inset space ~ -\end_inset - -Parenthesis -\family default -), see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Automatic-Bracket-Size" - -\end_inset - -, or by using the following commands: -\begin_inset VSpace medskip -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bmatrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc} -0 & \textrm{-}\mathrm{i}\\ -\mathrm{i} & 0 -\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Bmatrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc} -0 & \textrm{-}\mathrm{i}\\ -\mathrm{i} & 0 -\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -pmatrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc} -0 & \textrm{-}\mathrm{i}\\ -\mathrm{i} & 0 -\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vmatrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc} -0 & \textrm{-}\mathrm{i}\\ -\mathrm{i} & 0 -\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Vmatrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc} -0 & \textrm{-}\mathrm{i}\\ -\mathrm{i} & 0 -\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -matrix -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2 -\series bold -× -\series default -2 -\begin_inset space \thinspace{} -\end_inset - -matrix -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc} -0 & \textrm{-}\mathrm{i}\\ -\mathrm{i} & 0 -\end{array}\end{matrix}\raisebox{-5.3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -When e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - - -\series bold - -\backslash -vmatrix -\series default - is inserted, a blue box appears between two vertical lines where the matrix - is inserted. -\begin_inset Newline newline -\end_inset - -Note that decorated matrices ignore the vertical alignment. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -As all multiline formulas are matrices, the length -\series bold - -\backslash -arraycolsep -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -arraycolsep -\end_layout - -\end_inset - - that is described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Column-Separation" - -\end_inset - - can also be used to change the column separation of matrices. -\end_layout - -\begin_layout Standard -To change the row separation, the command -\series bold - -\backslash -arraystretch -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -arraystretch -\end_layout - -\end_inset - - is used. - It is used as follows: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -renewcommand{ -\backslash -arraystretch}{stretch factor} -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -renewcommand -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The command -\series bold - -\backslash -renewcommand -\series default - assigns the stretch factor to the predefined command -\series bold - -\backslash -arraystretch -\series default -. - To double e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -the row separation, use the factor 2. - This is then used for all following matrices. - To go back to the original separation, assign the factor 1 to -\series bold - -\backslash -arraystretch -\series default -. -\end_layout - -\begin_layout Standard -To set matrices into a text line, the command -\series bold - -\backslash -smallmatrix -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -smallmatrix -\end_layout - -\end_inset - - is used. - When it is inserted a blue box with two dashed lines appears. - In this box the matrix is inserted. -\end_layout - -\begin_layout Standard -This is a matrix -\begin_inset Formula $\left(\begin{smallmatrix}A & B\\ -C & D -\end{smallmatrix}\right)$ -\end_inset - - in a text line. -\end_layout - -\begin_layout Section -Brackets and Delimiters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Brackets -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Delimiters -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Vertical Brackets and Delimiters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Brackets ! vertical -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -( -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $($ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -{ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\{$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -[ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $[$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -langle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\langle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lceil -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\lceil$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lfloor -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\lfloor$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -/ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $/$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -| -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $|$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $)$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -] -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $]$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rangle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rceil -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rceil$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rfloor -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rfloor$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash - -\backslash - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\backslash$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -| -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\|$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard - -\series medium -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - In TeX-mode the command -\series bold - -\backslash -textbackslash -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -textbackslash -\end_layout - -\end_inset - - must be used for the backslash, because the command -\series bold - -\backslash - -\backslash - -\series default - produces a line break there. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -For all characters listed above the size can be adjusted with the commands - described in the following two subsections. - When using these commands, the characters < and > can directly be used - instead of the commands -\series bold - -\backslash -langle -\series default - and -\series bold - -\backslash -rangle -\series default -. -\end_layout - -\begin_layout Subsubsection -Manual Bracket Size -\begin_inset CommandInset label -LatexCommand label -name "sub:Manual-Bracket-Size" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Bracket size ! manual -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The bracket size can be specified manually by the LaTeX-commands -\series bold - -\backslash -big -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -big -\end_layout - -\end_inset - -, -\series bold - -\backslash -Big -\series default -, -\series bold - -\backslash -bigg -\series default - and -\series bold - -\backslash -Bigg -\series default -. - -\series bold - -\backslash -big -\series default - denotes the smallest and -\series bold - -\backslash -Bigg -\series default - the largest bracket size. -\end_layout - -\begin_layout Standard -These commands are used to emphasize levels of brackets: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -all brackets in the same size: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -this looks better: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -For the second formula the command -\series bold - -\backslash -Big((A+B)(A-B) -\backslash -Big)^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C -\series default - has been used. -\end_layout - -\begin_layout Standard -Here is an overview about all bracket sizes: -\end_layout - -\begin_layout Standard -\align center - -\backslash -Bigg( -\backslash -exp -\backslash -bigg< -\backslash -Big[ -\backslash -big{ -\backslash -ln(3x) -\backslash -big}^2 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -sin(x) -\backslash -Big]^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -bigg> -\backslash -Bigg)^0,5 -\end_layout - -\begin_layout Standard -\align center -\begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$ -\end_inset - - -\end_layout - -\begin_layout Standard -Besides the -\series bold - -\backslash -big -\series default --commands there is the variant -\series bold - -\backslash -bigm -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -bigm -\end_layout - -\end_inset - - that adds a bit more space between the bracket and its content, and the - variant -\series bold - -\backslash -bigl -\series default -- -\series bold - -\backslash -bigr -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -bigl - -\backslash -bigr -\end_layout - -\end_inset - -, that don't add additional space. - The -\emph on -l -\emph default - at the end of the command -\series bold - -\backslash -bigl -\series default - is for a left bracket; for a right bracket this will be replaced by an - -\emph on -r -\emph default -. - A left or right bracket can each be an opening or closing bracket. -\end_layout - -\begin_layout Standard -In the following table is a comparison of the variants: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Bigm( -\backslash -bigm( -\backslash -ln(3x) -\backslash -bigm)^2 -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default - -\backslash -Bigm) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Big( -\backslash -big( -\backslash -ln(3x) -\backslash -big)^2 -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default - -\backslash -Big) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Bigl( -\backslash -bigl( -\backslash -ln(3x) -\backslash -bigr)^2 -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default - -\backslash -Bigr) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigl) -\backslash -ln(3x) -\backslash -bigr( -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Subsubsection -Automatic Bracket Size -\begin_inset CommandInset label -LatexCommand label -name "sub:Automatic-Bracket-Size" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Bracket size ! automatic -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Brackets with variable size can be inserted with the commands -\series bold - -\backslash -left -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -left -\end_layout - -\end_inset - - and -\series bold - -\backslash -right -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -right -\end_layout - -\end_inset - - or via the math toolbar button -\begin_inset Graphics - filename ../images/dialog-show_mathdelimiter.png - scale 85 - -\end_inset - -. - Directly behind -\series bold - -\backslash -left -\series default - and -\series bold - -\backslash -right -\series default - the wanted bracket must be inserted. - The bracket size will then automatically be calculated for the output. -\end_layout - -\begin_layout Standard -\align center -normal bracket: The command -\series bold - -\backslash -ln( -\backslash -frac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -C -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -) -\series default - creates -\begin_inset Formula -\[ -\ln(\frac{A}{C}) -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -multiline bracket: The command -\series bold - -\backslash -ln -\backslash -left( -\backslash -frac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -C -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -right) -\series default - creates -\begin_inset Formula -\[ -\ln\left(\frac{A}{C}\right) -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -Instead of -\series bold - -\backslash -left -\series default - and -\series bold - -\backslash -right -\series default - the shortcut -\family sans -Alt+M -\begin_inset space ~ -\end_inset - -Bracket -\family default - can be used. - This has the advantage that you can see in LyX immediately the real bracket - size and that the matching right bracket will be created too. -\begin_inset Newline newline -\end_inset - -The command for the last example would then be: -\series bold - -\backslash -ln Alt+M -\series default - -\series bold -( -\backslash -frac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -C -\end_layout - -\begin_layout Standard -To omit a left or right bracket, a dot is inserted for the omitted bracket. - For example the command -\series bold - -\backslash -left. -\backslash -frac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -right} -\series default - creates: -\series bold - -\begin_inset Formula -\[ -\left.\frac{A}{B}\right\} -\] - -\end_inset - - -\series default -The commands -\series bold - -\backslash -left -\series default - and -\series bold - -\backslash -right -\series default - will be converted by LyX to brackets in the right size when the document - is reloaded and an omitted bracket will appear as dashed line. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX, - the command -\series bold - -\backslash -middle -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -middle -\end_layout - -\end_inset - - is additionally available for all brackets and limits. - With this command the height of the following character is adapted to the - one of the surrounding brackets, what is e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -needed for physical vectors: -\begin_inset Formula -\[ -\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle -\] - -\end_inset - -For physical vectors there is a special LaTeX-package, described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Physical-Vectors" - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Horizontal Brackets -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Brackets ! horizontal -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -raisebox{2.3mm}{ -\end_layout - -\end_inset - - -\backslash -overbrace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -3 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! O ! -\backslash -overbrace -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\overbrace{A+B}^{3}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -raisebox{-2.2mm}{ -\end_layout - -\end_inset - - -\backslash -underbrace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -_5 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -underbrace -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\underbrace{A+B}_{5}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overbrace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -underbrace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A+B_w -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -_7 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -In the last example it doesn't matter if -\series bold - -\backslash -overbrace -\series default - or -\series bold - -\backslash -underbrace -\series default - is inserted at first. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -When brackets are needed that overlap each other, multiline formulas, as - described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Multiline-Formulas" - -\end_inset - -, must be used: -\begin_inset Formula -\begin{eqnarray*} -A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\ - & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s} -\end{eqnarray*} - -\end_inset - -In the first row the formula is inserted together with the first brace. - It is hereby important that the space command -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -Space commands are explained in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Predefined-Space" - -\end_inset - -. -\end_layout - -\end_inset - - -\series bold - -\backslash -: -\series default - is inserted before the first -\begin_inset Formula $d$ -\end_inset - -, because the brace that ends behind the -\begin_inset Formula $q$ -\end_inset - - prevents that the following -\begin_inset Quotes eld -\end_inset - -+ -\begin_inset Quotes erd -\end_inset - - is surrounded by space. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -because a bracket is not handled as a character, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Binary-Operators" - -\end_inset - - -\end_layout - -\end_inset - - In the second row the second brace is inserted. - As it should begin before the -\begin_inset Formula $b$ -\end_inset - -, first the command -\series bold - -\backslash -hphantom{gggg+ -\backslash -:} -\series default - is inserted. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -more about -\series bold - -\backslash -hphantom -\series default - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Placeholders" - -\end_inset - - -\end_layout - -\end_inset - - This space is needed because the -\begin_inset Quotes eld -\end_inset - -+ -\begin_inset Quotes erd -\end_inset - - is also surrounded by space in the formula. - The brace is placed under the command -\series bold - -\backslash -hphantom{bbqq+dddd} -\series default -. -\end_layout - -\begin_layout Standard -It gets more complicated when brackets overlap each other, like in the following - example: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -setlength{ -\backslash -jot}{-6pt} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{eqnarray*} - & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\ -A & = & \underbrace{gggg+bbqq}_{r}+\: dddd -\end{eqnarray*} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -setlength{ -\backslash -jot}{3pt} -\end_layout - -\end_inset - -The first formula row is the same as the second row of the previous example, - with the difference that the brace is above. - The second row contains the formula together with the second brace. - To avoid that there is space between the upper brace in the first row and - the formula, the row spacing needs to be reduced. - This is not easily possible due to a bug in LyX -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #1505" -target "http://www.lyx.org/trac/ticket/1505" - -\end_inset - - -\end_layout - -\end_inset - -. - As a solution for the problem, the global formula row separation -\series bold - -\backslash -jot -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! J ! -\backslash -jot -\end_layout - -\end_inset - - must be changed to -6 -\begin_inset space \thinspace{} -\end_inset - -pt before the formula with the command -\series bold - -\backslash -setlength{ -\backslash -jot}{-6pt} -\series default - in TeX-mode. - -\series bold - -\backslash -jot -\series default - is set back after the formula to the standard value of 3 -\begin_inset space \thinspace{} -\end_inset - -pt using the same command. - More about the row separation in formulas is explained in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Line-Separation" - -\end_inset - -. -\end_layout - -\begin_layout Section -Arrows -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Arrows -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Arrows can be inserted via the math toolbar button -\begin_inset Graphics - filename ../images/math/leftarrow.png - scale 85 - -\end_inset - - or the commands listed in the following subsections. -\end_layout - -\begin_layout Subsection -Horizontal Arrows -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Arrows ! horizontal -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -gets -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\gets$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Leftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Leftarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -longleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\longleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Longleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Longleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leftharpoonup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\leftharpoonup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leftharpoondown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\leftharpoondown$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hookleftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\hookleftarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -to -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\to$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Rightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Rightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -longrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\longrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Longrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Longrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rightharpoonup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rightharpoonup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rightharpoondown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rightharpoondown$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hookrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\hookrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\leftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Leftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Leftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -longleftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\longleftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Longleftrightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Longleftrightarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rightleftharpoons -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rightleftharpoons$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hspace{} -\length 25pt -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mapsto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mapsto$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -longmapsto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\longmapsto$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leadsto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\leadsto$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dasharrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\dasharrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -Arrows used as accents like e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -vector arrows are listed in -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Accents" - -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -Furthermore there are the labeled arrows -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Arrows ! labeled -\end_layout - -\end_inset - - -\series bold - -\backslash -xleftarrow -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! X ! -\backslash -xleftarrow -\end_layout - -\end_inset - - and -\series bold - -\backslash -xrightarrow -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! X ! -\backslash -xrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - -. - When inserting one of these commands in a formula, an arrow with two blue - boxes appear where the label can be inserted. - The length of the arrow adapts to the label width. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -F(a) -\backslash -xleftarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -x=a -\begin_inset Formula $\downarrow$ -\end_inset - -x>0 -\begin_inset Formula $\to$ -\end_inset - -F(x) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -F(x) -\backslash -xrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -x=a -\begin_inset Formula $\downarrow$ -\end_inset - -x>0 -\begin_inset Formula $\to$ -\end_inset - -F(a) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Subsection -Vertical and diagonal Arrows -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Arrows ! diagonal -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Arrows ! vertical -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -uparrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\uparrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Uparrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Uparrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -updownarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\updownarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Updownarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Updownarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Downarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Downarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -downarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\downarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nearrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nearrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -searrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\searrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -swarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\swarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nwarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nwarrow$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -Vertical arrows can be used also as delimiters together with the commands - described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Manual-Bracket-Size" - -\end_inset - - and -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Automatic-Bracket-Size" - -\end_inset - -. -\end_layout - -\begin_layout Section -Accents -\begin_inset CommandInset label -LatexCommand label -name "sec:Accents" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Accents -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Accents can be inserted via the math toolbar button -\begin_inset Graphics - filename ../images/math/hat.png - scale 85 - -\end_inset - - or the commands listed in the following subsections. -\end_layout - -\begin_layout Subsection -Accents for one Character -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -texorpdfstring{ -\end_layout - -\end_inset - - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -accents in text see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Accents-in-Text" - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -}{} -\end_layout - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -texorpdfstring -\series default - is used to avoid that the footnote appears in the PDF-bookmark. -\end_layout - -\begin_layout Plain Layout -More about -\series bold - -\backslash -texorpdfstring -\series default - is in section -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Formulas-in-Section" - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset CommandInset label -LatexCommand label -name "sub:Accents-for-one" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Accents ! for one character -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dot -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\dot{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddot -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dddot -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddddot -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vec -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Vectors -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\vec{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bar -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\bar{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathring -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -tilde -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hat -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\hat{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -check -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\check{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -acute -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\acute{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -grave -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\grave{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -breve -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\breve{A}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - - -\end_layout - -\begin_layout Standard -You can directly insert accents like é to formulas. - LyX will transform them to the corresponding accent command. - For umlauts -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Umlauts -\end_layout - -\end_inset - - it is better to insert a quotation mark before the vowel. - These two characters are then treated by LaTeX as -\emph on -one -\emph default - character when the formula part with the umlaut is marked as German. - In contrary to -\series bold - -\backslash -ddot -\series default -, with this method -\begin_inset Quotes eld -\end_inset - -real -\begin_inset Quotes erd -\end_inset - - umlauts are created as demonstrated in the following example: -\end_layout - -\begin_layout Standard -\begin_inset VSpace -2mm -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - and the 0 -\begin_inset space \thinspace{} -\end_inset - -pt space are only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\lang ngerman -\begin_inset Quotes grd -\end_inset - -i -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset space \hspace{} -\length 0pt -\end_inset - - -\lang ngerman - -\begin_inset Formula $"i$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddot -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -i -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\ddot{i}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -Another advantage to -\series bold - -\backslash -ddot -\series default - is that umlauts can directly be converted to mathematical text because - the accent commands above are -\emph on -not allowed -\emph default - -\emph on -in mathematical text -\emph default -. - To convert an accented character to mathematical text, only the character - under the accent may be converted. - This applies also for all other conversions, e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -to italic or bold. -\end_layout - -\begin_layout Standard -In mathematical text, umlauts and other accented characters can directly - be inserted. -\end_layout - -\begin_layout Subsection -Accents for several Characters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Accents ! for several characters -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overleftarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -underleftarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overleftrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -underleftrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -overrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -underrightarrow -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -widetilde -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -widehat -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -With these commands as many characters as you like can be accented. - But the accents -\series bold - -\backslash -widetilde -\series default - and -\series bold - -\backslash -widehat -\series default - will only be set in the output with a length of three characters, as shown - in the following example: -\begin_inset Formula -\[ -\widetilde{A+B=C-D} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -With the commands -\series bold - -\backslash -overset -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! O ! -\backslash -overset -\end_layout - -\end_inset - - and -\series bold - -\backslash -underset -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -underset -\end_layout - -\end_inset - - described in the previous subsection it is also possible to accent several - characters. - The command -\series bold - -\backslash -underset -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\begin_inset Formula $\downarrow$ -\end_inset - -*** -\series default - creates: -\begin_inset Formula -\[ -\underset{***}{A=B} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -Space -\begin_inset CommandInset label -LatexCommand label -name "sub:Space" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Space ! horizontal -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Predefined Space -\begin_inset CommandInset label -LatexCommand label -name "sub:Predefined-Space" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Space ! horizontal ! predefined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Sometimes it is necessary to insert horizontal space into a formula. - This is done by inserting a protected space (shortcut -\begin_inset Info -type "shortcut" -arg "command-alternatives space-insert protected ; math-space" -\end_inset - -). - A -\begin_inset Quotes eld -\end_inset - - -\color blue - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\color inherit - -\begin_inset Quotes erd -\end_inset - - appears and by pressing -\family sans -Space -\family default - several times one can select one of eight different space sizes. - The spaces can also be inserted using the math toolbar button -\begin_inset Graphics - filename ../images/math/space.png - scale 85 - -\end_inset - - or special commands. - Independent from the inserted command, one can select the size again by - pressing -\family sans -Space -\family default - afterwards. -\end_layout - -\begin_layout Standard -\noindent -\align center -\begin_inset VSpace -5mm -\end_inset - - -\begin_inset Tabular - - - - - - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -, -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -; -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -quad -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -qquad -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -! -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -Number of -\family sans -Space -\family default - keystrokes after inserting the protected space -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -0 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -1 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -2 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -3 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -4 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -5 -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\, B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\: B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\; B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\quad B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\qquad B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\! B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -The last size seem to produce no space. - It is displayed red in LyX contrary to the other sizes, because it is a - negative space. - There are two more negative spaces: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -negmedspace -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -negthickspace -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -Number of -\family sans -Space -\family default - keystrokes after inserting the protected space -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -6 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -7 -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\negmedspace B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\negthickspace B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -Negative spaces can lead to characters overlapping each other. - Thus they can be used to enforce ligatures, which are e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -useful for summation operators: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sum -\backslash -sum -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -f_kl -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sum -\backslash -negmedspace -\backslash -sum -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -f_kl -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -Relations like for example equal signs, are always surrounded by space. - To suppress this, the equal sign is placed into a TeX-brace. - The following example demonstrates this: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -normal equation -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A=B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\begin_inset Formula $\raisebox{5mm}{}$ -\end_inset - -equation without space -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A{=}B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\noindent -The command for the last formula is: -\series bold -A -\backslash -{= -\begin_inset Formula $\to$ -\end_inset - -B -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -Spaces are needed for physical units, because the space between the value - and the unit is the smallest one and not a normal space. - For units in text, the smallest space is inserted via the menu -\family sans -Insert\SpecialChar \menuseparator -Formatting\SpecialChar \menuseparator -Thin -\begin_inset space ~ -\end_inset - -Space -\family default - (shortcut -\begin_inset Info -type "shortcut" -arg "space-insert thin" -\end_inset - -). -\end_layout - -\begin_layout Standard -An example to visualize the difference: -\end_layout - -\begin_layout Standard -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -24 kW -\begin_inset Formula $\cdot$ -\end_inset - -h -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -space between value and unit -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -24 -\begin_inset space \thinspace{} -\end_inset - -kW -\begin_inset Formula $\cdot$ -\end_inset - -h -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -smallest space between value and unit -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Subsection -Variable Space -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -texorpdfstring{ -\end_layout - -\end_inset - - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -for vertical space in formulas see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Line-Separation" - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -}{} -\end_layout - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\backslash -texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. -\end_layout - -\begin_layout Plain Layout -More about -\backslash -texorpdfstring is in section -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Formulas-in-Section" - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset CommandInset label -LatexCommand label -name "sub:Variable-Space" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Space ! horizontal ! variable -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Space with a defined length can be inserted with the command -\series bold - -\backslash -hspace -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hspace -\end_layout - -\end_inset - -. - Then a long -\begin_inset Quotes eld -\end_inset - - -\color blue - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\color inherit - -\begin_inset Quotes erd -\end_inset - - appears. - The length can be specified by left-clicking on the -\begin_inset Quotes eld -\end_inset - - -\color blue - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\color inherit - -\begin_inset Quotes erd -\end_inset - -. - The length may also be negative. - To insert as much space as is available, the command -\series bold - -\backslash -hfill -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hfill -\end_layout - -\end_inset - - is used. -\end_layout - -\begin_layout Standard -\begin_inset VSpace -1mm -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command ( -\backslash -hspace length) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A=B -\backslash -hspace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset Formula $\to$ -\end_inset - -A -\backslash -not=C (3 -\begin_inset space \thinspace{} -\end_inset - -cm) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A=B\hspace{3cm}A\not=C$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A -\backslash -hspace -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset Formula $\to$ -\end_inset - -A -\backslash -not=A (-1 -\begin_inset space \thinspace{} -\end_inset - -mm) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\hspace{-1mm}A\not=A$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A=A -\backslash -hfill -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -B=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A=A\hfill B=B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -In the last example the available space is given by the longest column entry - of the table. - In an inline formula the space depends on the length of the line in which - -\series bold - -\backslash -hfill -\series default - is inserted. - Thus, when the line uses the full width, no space will be created. - -\series bold - -\backslash -hfill -\series default - only has an effect on displayed formulas when the formula style -\series bold -Indented -\series default - is used. - (Formula styles are explained in -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - -.) -\end_layout - -\begin_layout Standard -Besides -\series bold - -\backslash -hfill -\series default -, there are the commands -\series bold - -\backslash -dotfill -\series default - and -\series bold - -\backslash -hrulefill -\series default - that fill the space with a pattern, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Ellipses" - -\end_inset - - for an example. -\end_layout - -\begin_layout Standard -For text, variable space can be inserted via the menu -\family sans -Insert\SpecialChar \menuseparator -Formatting\SpecialChar \menuseparator -Horizontal -\begin_inset space ~ -\end_inset - -Space -\family default -: -\end_layout - -\begin_layout Standard -This is a line with -\begin_inset space \hspace{} -\length 2cm -\end_inset - -2 -\begin_inset space \thinspace{} -\end_inset - -cm space. -\end_layout - -\begin_layout Standard -This is a line with -\begin_inset space \hfill{} -\end_inset - -maximum space. -\end_layout - -\begin_layout Subsection -Space besides inline Formulas -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Space ! besides inline formulas -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The space that surrounds inline formulas can be adjusted with the length - -\series bold - -\backslash -mathsurround -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -mathsurround -\end_layout - -\end_inset - -. - The value of a length is set with the command -\series bold - -\backslash -setlength -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -setlength -\end_layout - -\end_inset - - which has the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -setlength{length name}{value} -\end_layout - -\begin_layout Standard -To set -\series bold - -\backslash -mathsurround -\series default - to the value 5 -\begin_inset space \thinspace{} -\end_inset - -mm, the command -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -setlength{ -\backslash -mathsurround}{5mm} -\end_layout - -\begin_layout Standard -is inserted in TeX-mode. - 5 -\begin_inset space \thinspace{} -\end_inset - -mm space will now be set around all inline formulas: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -setlength{ -\backslash -mathsurround}{5mm} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -This is a line with an inline formula -\begin_inset Formula $A=B$ -\end_inset - - with 5 -\begin_inset space \thinspace{} -\end_inset - -mm surrounding space. -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -setlength{ -\backslash -mathsurround}{0pt} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To return to the predefined value, -\series bold - -\backslash -mathsurround -\series default - is set to the value 0 -\begin_inset space \thinspace{} -\end_inset - -pt. -\end_layout - -\begin_layout Section -Boxes and Frames -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Boxes -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Frames | see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Boxes -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Boxes for text are described in chapter -\family typewriter -Boxes -\family default - in the -\family typewriter -Embedded -\begin_inset space ~ -\end_inset - -Objects -\family default - manual. -\end_layout - -\begin_layout Subsection -Boxes with Frame -\begin_inset CommandInset label -LatexCommand label -name "sub:Boxes-with-Frame" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Boxes ! with frame -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -It is possible to frame a formula or part of one with the commands -\series bold - -\backslash -fbox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! F ! -\backslash -fbox -\end_layout - -\end_inset - - and -\series bold - -\backslash -boxed -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -boxed -\end_layout - -\end_inset - -. -\end_layout - -\begin_layout Standard -When one of these commands is inserted in a formula, a blue box appears - within a frame to enter formula parts. - For -\series bold - -\backslash -fbox -\series default - an additional formula has to be created by -\family sans -Ctrl+M -\family default - within this box, because the box content will otherwise be treated as mathemati -cal text. - When -\series bold - -\backslash -boxed -\series default - is used, a new formula is automatically created inside the frame. -\end_layout - -\begin_layout Standard -The command -\series bold - -\backslash -fbox -\series default - is not suitable to frame displayed formulas because the formula will always - be set in the size of the text. - -\series bold - -\backslash -boxed -\series default - is in contrary not suitable to frame inline formulas, because the formula - will always be set in the size of a displayed formula. -\end_layout - -\begin_layout Standard -An extension to -\series bold - -\backslash -fbox -\series default - is the command -\series bold - -\backslash -framebox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! F ! -\backslash -framebox -\end_layout - -\end_inset - - where additionally the frame width and the alignment can be specified. - -\series bold - -\backslash -framebox -\series default - is used in the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -framebox[frame width][position]{box content} -\end_layout - -\begin_layout Standard -The position can either be -\emph on -l -\emph default - or -\emph on -r -\emph default -. - -\emph on -l -\emph default - left aligns, -\emph on -r -\emph default - right aligns the formula in the box. - When no position is given, the formula will be centered. -\begin_inset Newline newline -\end_inset - -If no width is given, also no position can be given. - In this case the frame width is adjusted to the box content like for -\series bold - -\backslash -fbox -\series default -. -\end_layout - -\begin_layout Standard -When the command -\series bold - -\backslash -framebox -\series default - is inserted, a box appears containing three blue boxes. - The first two boxes are surrounded by brackets and denote the two optional - arguments. - The third box is for formula parts like for -\series bold - -\backslash -fbox -\series default -. -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -fbox -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\family sans -Ctrl+M -\family default - -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -boxed -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A+ -\backslash -fbox -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -framebox -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -20mm -\begin_inset Formula $\to$ -\end_inset - - -\begin_inset Formula $\to$ -\end_inset - - -\family sans -Ctrl+M -\family default - -\backslash -frac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\downarrow$ -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}$ -\end_inset - - -\begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$ -\end_inset - - -\begin_inset Formula $\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -The frame thickness can also be adjusted. - To do this the following commands have to be inserted in TeX-mode before - the formula -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -fboxrule -\series default - -\series bold - -\begin_inset Quotes eld -\end_inset - -thickness -\begin_inset Quotes erd -\end_inset - - -\series default - -\series bold - -\backslash -fboxsep -\series default - -\series bold - -\begin_inset Quotes eld -\end_inset - -distance -\begin_inset Quotes erd -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Quotes eld -\end_inset - -distance -\begin_inset Quotes erd -\end_inset - - specifies the minimal distance between the frame and the first character - in the box. - An example for this is the following framed formula: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fboxrule 2mm -\backslash -fboxsep 3mm -\end_layout - -\end_inset - - -\begin_inset Formula -\[ -\boxed{A+B=C} -\] - -\end_inset - -Before this formula the commands -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -fboxrule -\series default - -\series bold -2mm -\series default - -\series bold - -\backslash -fboxsep -\series default - -\series bold -3mm -\end_layout - -\begin_layout Standard -were inserted in TeX-mode. - The given values are used for all following boxes. -\end_layout - -\begin_layout Standard -To return to the standard frame size, the command -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -fboxrule -\series default - -\series bold -0.4pt -\series default - -\series bold - -\backslash -fboxsep -\series default - -\series bold -3pt -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fboxrule 0.4pt -\backslash -fboxsep 3pt -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -is inserted in TeX-mode before the next formula. -\end_layout - -\begin_layout Subsection -Boxes without Frame -\begin_inset CommandInset label -LatexCommand label -name "sub:Boxes-without-Frame" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Boxes ! without frame -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -For boxes without a frame there are the following box commands: -\series bold - -\backslash -mbox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -mbox -\end_layout - -\end_inset - -, -\series bold - -\backslash -makebox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -makebox -\end_layout - -\end_inset - - and -\series bold - -\backslash -raisebox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -raisebox -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -With -\series bold - -\backslash -raisebox -\series default - a box can be super- or subscripted. - But in contrary to normal super- and subscripting, the characters in the - box keep their font size. - -\series bold - -\backslash -raisebox -\series default - is used in the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -raisebox{height}{box content} -\end_layout - -\begin_layout Standard -When the box should contain a formula, an extra formula is needed like for - -\series bold - -\backslash -fbox -\series default -. - -\series medium - -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - For -\series bold - -\backslash -raisebox -\series default - this extra formula is created by pressing -\family sans -Ctrl+M -\family default - twice instead of once because LyX doesn't yet support -\series bold - -\backslash -raisebox -\series default - directly. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -H -\backslash -raisebox{2mm -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{al -\begin_inset Formula $\to$ -\end_inset - - lo -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $H\raisebox{2mm}{al}lo$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -H -\backslash -raisebox{-2mm -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{al -\begin_inset Formula $\to$ -\end_inset - -lo -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $H\raisebox{-2mm}{al}lo$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A= -\backslash -raisebox{-2mm -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\family sans -Ctrl+M -\family default - -\family sans -Ctrl+M -\family default - -\backslash -sqrt -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -The command -\series bold - -\backslash -mbox -\series default - is equivalent to -\series bold - -\backslash -fbox -\series default - and -\series bold - -\backslash -makebox -\series default - is equivalent to -\series bold - -\backslash -framebox -\series default -, with the difference that there is no frame. -\end_layout - -\begin_layout Subsection -Colored Boxes -\begin_inset CommandInset label -LatexCommand label -name "sub:Colored-Boxes" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Boxes ! colored -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To be able to use all commands explained in this section, the LaTeX-package - -\series bold -color -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -The LaTeX-package -\series bold -color -\series default - is part of every LaTeX standard installation. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! color -\end_layout - -\end_inset - - has to be loaded in the LaTeX-preamble with the line -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -When text is colored somewhere in the document with a predefined color, - LyX loads the LaTeX-package -\series bold -color -\series default - automatically. - Thus it is possible that the package is loaded twice, but this does not - cause problems. -\end_layout - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre -amble. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{color} -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -To color boxes, the command -\series bold - -\backslash -colorbox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -colorbox -\end_layout - -\end_inset - - is used in the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -colorbox{color}{box content} -\end_layout - -\begin_layout Standard -The box content can also be a box and a -\series bold - -\backslash -colorbox -\series default - can also be part of another box (see the 2nd and 3rd example). - When the box should contain a formula, an extra formula has to be created, - the same way as for -\series bold - -\backslash -raisebox -\series default -. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -This also applies for the command -\series bold - -\backslash -fcolorbox -\series default -. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -One of the following predefined colors can be chosen: -\end_layout - -\begin_layout Standard - -\series bold -black -\series default -, -\series bold -blue -\series default -, -\series bold -cyan -\series default -, -\series bold -green -\series default -, -\series bold -magenta -\series default -, -\series bold -red -\series default -, -\series bold -white -\series default - and -\series bold -yellow -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -colorbox{yellow -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -colorbox{green -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\backslash -fbox -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -fbox -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -colorbox{green -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\family sans -Ctrl+M -\family default - -\family sans -Ctrl+M -\family default - -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C=D -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -colorbox -\series default - only colors the box but not the characters in the box. - To color all characters, the whole formula is highlighted and the desired - color is chosen in the -\family sans -Text -\begin_inset space ~ -\end_inset - -Style -\family default - dialog. - The dialog can be called with the toolbar button -\begin_inset Graphics - filename ../images/dialog-show_character.png - scale 85 - -\end_inset - - or the menu -\family sans -Edit\SpecialChar \menuseparator -Text -\begin_inset space ~ -\end_inset - -Style\SpecialChar \menuseparator -Customized -\family default -. - The formula number then has the same color as the formula. - When the formula number should get another color than the formula characters, - the color must be changed within the formula. -\end_layout - -\begin_layout Standard -An example: -\end_layout - -\begin_layout Standard - -\color red -\begin_inset Formula -\begin{equation} -\int A=B\label{eq:red} -\end{equation} - -\end_inset - - -\color green - -\begin_inset Formula -\begin{equation} -\textcolor{red}{\int A=B}\label{eq:redgreen} -\end{equation} - -\end_inset - - -\end_layout - -\begin_layout Standard -Formula -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:red" - -\end_inset - - is completely colored red. -\begin_inset Newline newline -\end_inset - -Formula -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:redgreen" - -\end_inset - - was first completely colored green to set the color for the formula number. - Subsequently the formula characters were colored red. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -To color the frame different than the rest of the box, the command -\series bold - -\backslash -fcolorbox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! F ! -\backslash -fcolorbox -\end_layout - -\end_inset - - is used in the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -fcolorbox{frame color}{color}{box content} -\end_layout - -\begin_layout Standard -So -\series bold - -\backslash -fcolorbox -\series default - is an extension of the command -\series bold - -\backslash -colorbox -\series default -. - The frame width is set, like for -\series bold - -\backslash -framebox -\series default -, with -\series bold - -\backslash -fboxrule -\series default - and -\series bold - -\backslash -fboxsep -\series default -. - An example: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fboxrule 1mm -\backslash -fboxsep 1mm -\end_layout - -\end_inset - - -\begin_inset Formula -\[ -\fcolorbox{cyan}{magenta}{A=B} -\] - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fboxrule 0.4pt -\backslash -fboxsep 3pt -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -This formula was created with the command -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -fcolorbox{cyan -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{magenta -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{A=B -\series default -. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -To use other colors than the predefined ones, they have to be defined first. -\end_layout - -\begin_layout Standard -One can for example define the color -\begin_inset Quotes eld -\end_inset - - -\series bold -darkgreen -\series default - -\begin_inset Quotes erd -\end_inset - - with the LaTeX-preamble line: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -definecolor{darkgreen}{cmyk}{0.5, -\series default - -\series bold -0, -\series default - -\series bold -1, -\series default - -\series bold -0.5} -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -definecolor -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard - -\series bold -cmyk -\series default - is the color space that denotes the colors -\series bold -cyan -\series default -, -\series bold -magenta -\series default -, -\series bold -yellow -\series default - and -\series bold -black -\series default -. - The four comma separated numbers are the portion factor for the corresponding - colors of the color space. - The factors can be in the range of 0 -\begin_inset space \thinspace{} -\end_inset - -- -\begin_inset space \thinspace{} -\end_inset - -1. - Instead of -\series bold -cmyk -\series default - also the color space -\series bold -rgb -\series default - can be used for definitions. - -\series bold -rgb -\series default - denotes -\series bold -red -\series default -, -\series bold -green -\series default - and -\series bold -blue -\series default -, so that there are in this case three portion factors for the corresponding - colors. - Furthermore there is the color space -\series bold -gray -\series default - with one portion factor for the gray value. -\end_layout - -\begin_layout Standard -As example a framed box with the new defined color -\series bold -darkgreen -\series default - where the characters have been colored -\series bold -yellow -\series default -: -\begin_inset Formula -\begin{equation} -\colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}} -\end{equation} - -\end_inset - - -\end_layout - -\begin_layout Standard -Self-defined colors can also be used for text with the help of the command - -\series bold - -\backslash -textcolor -\series default -: -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Text ! colored -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -textcolor{darkgreen}{ -\end_layout - -\end_inset - -This sentence is -\begin_inset Quotes eld -\end_inset - -darkgreen -\begin_inset Quotes erd -\end_inset - -. -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -textcolor -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -textcolor -\end_layout - -\end_inset - - is used in the scheme -\series bold - -\backslash -textcolor{color}{characters to color} -\series default -. -\end_layout - -\begin_layout Subsection -Paragraph Boxes -\begin_inset CommandInset label -LatexCommand label -name "sub:Paragraph-Boxes" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Boxes ! as paragraph -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -A box that can contain several lines and paragraphs, a so-called paragraph - box (parbox), can be created with the menu -\family sans -Insert\SpecialChar \menuseparator -Box -\family default - or the toolbar button -\begin_inset Graphics - filename ../images/box-insert.png - scale 85 - -\end_inset - -. -\end_layout - -\begin_layout Standard -The following example shows a framed parbox in a line: -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -This is a line -\begin_inset Box Boxed -position "c" -hor_pos "c" -has_inner_box 1 -inner_pos "t" -use_parbox 1 -use_makebox 0 -width "5cm" -special "none" -height "1in" -height_special "totalheight" -status open - -\begin_layout Plain Layout -This is a paragraph box. - It is exactly 5 -\begin_inset space \thinspace{} -\end_inset - -cm long and can also contain formulas: -\begin_inset Formula $\int A\,\mathrm{d}s=C$ -\end_inset - - -\end_layout - -\end_inset - - with a parbox. -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - - -\end_layout - -\begin_layout Standard -Such a box is created by right-clicking on the gray box inset. - A dialog pops up showing the box properties. - In our case set: -\emph on -Decoration -\emph default -: Rectangular box, -\emph on -Inner Box -\emph default -: Parbox, -\emph on -Width -\emph default -: 5 -\begin_inset space \thinspace{} -\end_inset - -cm, -\emph on -Vertical Box Alignment -\emph default -: Middle -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -In LaTeX a parbox is created with the command -\series bold - -\backslash -parbox -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! P ! -\backslash -parbox -\end_layout - -\end_inset - - which has the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -parbox[position]{width}{box content} -\end_layout - -\begin_layout Standard -The positions -\emph on -b -\emph default - and -\emph on -t -\emph default - are possible. - -\emph on -b -\emph default - for -\begin_inset Quotes eld -\end_inset - -bottom -\begin_inset Quotes erd -\end_inset - - means that the box is aligned within the surrounding text with its last - line. - With -\emph on -t -\emph default - for -\begin_inset Quotes eld -\end_inset - -top -\begin_inset Quotes erd -\end_inset - - this is done with the first line. - When no position is given, the box will be vertically centered, see section - -\emph on -Boxes -\emph default - of the -\emph on -Embedded -\begin_inset space ~ -\end_inset - -Objects -\emph default - manual for examples. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -To frame formulas completely, including the formula number, the formula - must be set into a parbox. - To do this, the command -\series bold - -\backslash -fbox{ -\backslash -parbox{ -\backslash -linewidth-2 -\backslash -fboxsep-2 -\backslash -fboxrule}{ -\series default - is inserted in TeX-mode before the formula. - -\series bold - -\backslash -linewidth -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -linewidth -\end_layout - -\end_inset - - is hereby the line width set for the document. - Because the frame is outside the parbox, 2 -\begin_inset space \thinspace{} -\end_inset - -times the frame separation and the frame thickness must be subtracted from - the line width. - As this is not automatically done by LyX due to a bug -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #4483" -target "http://www.lyx.org/trac/ticket/4483" - -\end_inset - - -\end_layout - -\end_inset - -, TeX-mode has to be used. - To be able to multiply and subtract in arguments, the LaTeX-package -\series bold -calc -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout - -\series bold -calc -\series default - is part of every LaTeX standard installation. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! calc -\end_layout - -\end_inset - - must be loaded in the LaTeX-preamble with the line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{calc} -\end_layout - -\begin_layout Standard -Behind the formula both boxes are closed by entering -\series bold -}} -\series default - in TeX-mode. - Here is an example: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fboxsep 5mm -\backslash -fboxrule 5mm -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fbox{ -\backslash -parbox{ -\backslash -linewidth-2 -\backslash -fboxsep-2 -\backslash -fboxrule}{ -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{equation} -\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)} -\end{equation} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -}} -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fboxrule 0.4pt -\backslash -fboxsep 3pt -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -As a parbox is used as the argument of -\series bold - -\backslash -fbox -\series default -, there is in this case no difference between -\series bold - -\backslash -fbox -\series default - and -\series bold - -\backslash -boxed -\series default -. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -Paragraph boxes are very useful to comment formulas directly. - To do this, -\series bold - -\backslash -parbox -\series default - is used in combination with the command -\series bold - -\backslash -tag -\series default -. - (more about -\series bold - -\backslash -tag -\series default - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:User-defined-Numbering" - -\end_inset - -) -\end_layout - -\begin_layout Standard -An example of a formula commented with -\series bold - -\backslash -parbox -\series default -: -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -[5x-7b=3b -\backslash -tag*{ -\backslash -parbox{5cm}{ -\end_layout - -\end_inset - -This is a description. - It is distinctly separated from the formula and multiline. -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -}} -\backslash -] -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Such a formula must be inserted completely in TeX-mode because LyX does - not yet support the command -\series bold - -\backslash -parbox -\series default - in formulas. - The formula is created with the following command sequence: -\end_layout - -\begin_layout Standard -The command -\series bold - -\backslash -[5x-7b=3b -\backslash -tag* -\backslash -{ -\backslash -parbox{5cm}{ -\series default - is inserted in TeX-mode. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -When the formula style -\series bold -Indented -\series default - is used, -\series bold - -\backslash -tag* -\backslash -{ -\series default - can also be replaced by -\series bold - -\backslash -hfill -\series default -. - (formula styles see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - -) -\end_layout - -\end_inset - - Then the description follows as normal text and finally -\series bold -}} -\backslash -] -\series default - is inserted in TeX-mode. - The commands -\series bold - -\backslash -[ -\series default - and -\series bold - -\backslash -] -\series default - hereby create a displayed formula. -\end_layout - -\begin_layout Standard -The advantages of -\series bold - -\backslash -parbox -\series default - can be seen in this example that was -\begin_inset Quotes eld -\end_inset - -commented -\begin_inset Quotes erd -\end_inset - - using the mathematical textmode: -\begin_inset Formula -\[ -5x-7b=3b\textrm{This is a description. It is not separated from the formula ...} -\] - -\end_inset - - -\end_layout - -\begin_layout Section -Operators -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Operators -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Big Operators -\begin_inset CommandInset label -LatexCommand label -name "sub:Big-Operators" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Operators ! big -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Sums -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Integrals -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To be able to use all integral operators listed here, the option -\family sans -Use esint package automatically -\family default - must be set in the document settings under -\family sans -Math -\begin_inset space ~ -\end_inset - -Options -\family default -. -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -int -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! I ! -\backslash -int -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\int$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -oint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\oint$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ointctrclockwise -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ointctrclockwise$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ointclockwise -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ointclockwise$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sqint$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -fint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\begin_inset Formula $\fint$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -landupint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\begin_inset Formula $\landupint$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -landdownint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\begin_inset Formula $\landdownint$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigcap -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigcap$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigcup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigcup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sum -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -sum -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sum$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -prod -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! P ! -\backslash -prod -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\prod$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -coprod -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\coprod$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigodot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigodot$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigotimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigotimes$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigoplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigoplus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigwedge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigwedge$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigvee -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigvee$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigsqcup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigsqcup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -biguplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\biguplus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -All big operators can also be inserted via the math toolbar button -\begin_inset Graphics - filename ../images/math/intop.png - scale 85 - -\end_inset - -. -\end_layout - -\begin_layout Standard -The operators are called big because they are bigger than the sometimes - equal looking binary operators. - All big operators can have limits as described in the next subsection. -\end_layout - -\begin_layout Standard -For all integral operators there is a second version available, ending in - -\series bold -op -\series default -: -\series bold - -\backslash -intop -\series default -, -\series bold - -\backslash -ointop -\series default - etc.. - These operators are different from -\series bold - -\backslash -int -\series default - etc. -\begin_inset space \space{} -\end_inset - -in the style the operator limits are displayed, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Operator-Limits" - -\end_inset - -. - -\end_layout - -\begin_layout Subsubsection* -Advice for Integrals -\end_layout - -\begin_layout Standard -The letter -\emph on -d -\emph default - in an integral is an operator, that therefore has to be set upright. - This is done by highlighting the -\emph on -d -\emph default - and using the keyboard shortcut -\begin_inset Info -type "shortcut" -arg "font-roman" -\end_inset - - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -Font styles -\series bold - -\series default -see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Font-Styles" - -\end_inset - - -\end_layout - -\end_inset - -. - Finally the smallest space is inserted before the -\emph on -d -\emph default -, as this is usual for operators. - An example: -\end_layout - -\begin_layout Standard -incorrect: -\begin_inset Formula $\int A(x)dx$ -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout -in -\end_layout - -\end_inset - -correct: -\begin_inset Formula $\int A(x)\,\mathrm{d}x$ -\end_inset - - -\end_layout - -\begin_layout Standard -For multiple integrals there are the following commands: -\begin_inset VSpace medskip -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -iint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -oiint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqiint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -iiint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -iiiint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dotsint -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Subsection -Operator Limits -\begin_inset CommandInset label -LatexCommand label -name "sub:Operator-Limits" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Operators ! Limits -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Limits are created by super- and subscripts: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -prod^ -\backslash -infty -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset Formula $\to$ -\end_inset - -_0 -\begin_inset Formula $\to$ -\end_inset - -A(x) -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -Limits of inline formulas are set right beside the operator. - Limits in displayed formulas are set above or below the operator, except - for integral limits. -\end_layout - -\begin_layout Standard -To force that the limits are set beside the operator, the cursor is set - directly behind the operator and the limits type is changed with the menu - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Change Limits Type -\family default - to -\family sans -\series bold -Inline -\family default -\series default - (shortcut -\begin_inset Info -type "shortcut" -arg "math-limits" -\end_inset - -). - An example: -\end_layout - -\begin_layout Standard -The default limits type is this: -\begin_inset Formula -\[ -\sum_{x=0}^{\infty}\frac{1}{x^{2}} -\] - -\end_inset - -This is how it looks when the limits type was changed to -\family sans -\series bold -Inline -\family default -\series default -: -\begin_inset Formula -\[ -\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}} -\] - -\end_inset - -For integrals, except those ending with -\series bold -op -\series default - like -\series bold - -\backslash -intop -\series default -, -\series bold - -\backslash -ointop -\series default - etc., the limits are by default set beside the operator. - But for multiple integrals the limits are often set below the operator. - In the following example the limits type was therefore set to -\series bold -Display -\series default - and so set below the integrals: -\begin_inset Formula -\begin{equation} -\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt} -\end{equation} - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -To specify conditions for limits, the commands -\series bold - -\backslash -subarray -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -subarray -\end_layout - -\end_inset - - and -\series bold - -\backslash -substack -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -substack -\end_layout - -\end_inset - - are used. - To create for example this expression -\begin_inset Formula -\begin{equation} -\sum_{\begin{subarray}{c} -0 - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -+ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $+$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -- -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $-$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -pm -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\pm$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mp$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cdot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\cdot$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -times -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\times$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -div -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\div$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -raisebox{-1.2mm}{ -\end_layout - -\end_inset - -* -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $*$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -star -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\star$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -circ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\circ$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -diamond -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\diamond$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bullet -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bullet$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nabla -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nabla$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigtriangledown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigtriangledown$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigtriangleup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigtriangleup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Box -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Box$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cap -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\cap$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\cup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dagger -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\dagger$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddagger -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ddagger$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -wr -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\wr$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigcirc -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigcirc$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -wedge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\wedge$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vee -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\vee$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -oplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\oplus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ominus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ominus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -otimes -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\otimes$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -oslash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\oslash$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -odot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\odot$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -amalg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\amalg$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -uplus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\uplus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -setminus -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\setminus$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqcap -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sqcap$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqcup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sqcup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -triangleleft -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\triangleleft$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -triangleright -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\triangleright$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -All binary operators can also be inserted via the math toolbar button -\begin_inset Graphics - filename ../images/math/pm.png - scale 85 - -\end_inset - -. -\end_layout - -\begin_layout Standard -To typeset the Laplace operator also -\series bold - -\backslash -Delta -\series default - or -\series bold - -\backslash -nabla -\series default -^ -\series bold -2 -\series default - ( -\begin_inset Formula $\nabla^{2}$ -\end_inset - -) can be used instead of -\series bold - -\backslash -bigtriangleup -\series default - . -\end_layout - -\begin_layout Standard -The character -\family sans -Menu Separator -\family default - from the menu -\family sans -Insert\SpecialChar \menuseparator -Special Character -\family default - is the operator -\series bold - -\backslash -triangleright -\series default -. -\end_layout - -\begin_layout Subsection -Self-defined Operators -\begin_inset CommandInset label -LatexCommand label -name "sub:Self-defined-Operators" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Operators ! self-defined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -With the help of the command -\series bold - -\backslash -DeclareMathOperator -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dbinom@ -\backslash -DeclareMathOperator -\end_layout - -\end_inset - - custom operators can be defined in the LaTeX-preamble. - Its command scheme is: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -DeclareMathOperator{new command}{display} -\end_layout - -\begin_layout Standard -Display can be characters or symbols that define how the operator looks - in the output. - To define a big operator a * is set behind the command. - All self-defined big operators can have limits as described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Operator-Limits" - -\end_inset - -. -\end_layout - -\begin_layout Standard -For example the LaTeX-preamble line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -DeclareMathOperator*{ -\backslash -Lozenge}{ -\backslash -blacklozenge} -\end_layout - -\begin_layout Standard -defines the command -\series bold - -\backslash -Lozenge -\series default -, that inserts a big operator consisting of the lozenge symbol from -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Miscellaneous-Symbols" - -\end_inset - -: -\begin_inset Formula -\[ -\Lozenge_{n=1}^{\infty} -\] - -\end_inset - -The command for this formula is: -\series bold - -\backslash -Lozenge -\series default -^ -\series bold - -\backslash -infty -\begin_inset Formula $\to$ -\end_inset - -_n=1 -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -When self-defined operators are not used several times in the document, - they can also be defined with the commands -\series bold - -\backslash -mathop -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -mathop -\end_layout - -\end_inset - - and -\series bold - -\backslash -mathbin -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -mathbin -\end_layout - -\end_inset - -, which have the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -mathop{display} -\series default - and -\series bold - -\backslash -mathbin{display} -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -mathop -\series default - defines big operators, -\series bold - -\backslash -mathbin -\series default - binary operators. -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -mathop -\series default - can e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -be used to use one limit for several operators: -\end_layout - -\begin_layout Standard -\begin_inset Formula -\[ -\mathop{\sum\negmedspace\sum}_{i,j=1}^{N} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -The command for the formula above is: -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -mathop{ -\backslash -sum -\backslash -negmedspace -\backslash -sum -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold - -\begin_inset Formula $\to$ -\end_inset - -^N -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold -_i,j=1 -\end_layout - -\begin_layout Section -Fonts -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Fonts -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Font Styles -\begin_inset CommandInset label -LatexCommand label -name "sub:Font-Styles" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Font ! style -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Latin letters in formulas can be set in one of the following font styles: -\begin_inset VSpace -2mm -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -shortcut -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathbb -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -ABC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathbb{ABC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-noun" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathbf -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathbf{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-bold" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -boldsymbol -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\boldsymbol{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-boldsymbol" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathcal -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -ABC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathcal{ABC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-emph" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathfrak -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathfrak{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -- -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathscr -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathscr{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -- -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -shortcut -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathit -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathit{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -- -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathrm -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathrm{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-roman" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathsf -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathsf{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-sans" -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mathtt -\series bold - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series default -AbC -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathtt{AbC}$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Info -type "shortcuts" -arg "font-typewriter" -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - The styles -\series bold - -\backslash -mathbb -\series default - and -\series bold - -\backslash -mathcal -\series default - can only be used for big letters. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Predefined is the style -\series bold - -\backslash -mathnormal -\series default -. -\end_layout - -\begin_layout Standard -The style commands work also for letters in mathematical constructs: -\begin_inset Formula -\[ -\mathfrak{A=\frac{b}{C}} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -Characters in mathematical text don't appear in a math font style but in - the text font style -\series bold - -\backslash -textrm -\series default -. - That their style can't be set correctly via the text style dialog is a - bug in LyX. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #4629" -target "http://www.lyx.org/trac/ticket/4629" - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Instead of the style commands the dialog -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Text Style -\family default - or the toolbar button -\begin_inset Graphics - filename ../images/math/font.png - scale 85 - -\end_inset - - can be used. -\end_layout - -\begin_layout Subsection -Bold Formulas -\begin_inset CommandInset label -LatexCommand label -name "sub:Bold-Formulas" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! bold -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To make a complete formula bold, the command -\series bold - -\backslash -mathbf -\series default - from the previous subsection cannot be used, because it doesn't work for - small Greek letters. - Furthermore it prints Latin letters always upright, like in the following - equation: -\end_layout - -\begin_layout Standard -\begin_inset Formula -\[ -\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -To display the formula correctly, the command -\series bold - -\backslash -boldsymbol -\series default - is used: -\begin_inset Formula -\[ -\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}} -\] - -\end_inset - -It is also possible to set the formula in a -\series bold -boldmath environment -\series default -. - This environment is created by inserting the command -\series bold - -\backslash -boldmath -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -boldmath -\end_layout - -\end_inset - - in TeX-mode. - To end the environment, the command -\series bold - -\backslash -unboldmath -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! U ! -\backslash -unboldmath -\end_layout - -\end_inset - - is inserted in TeX-mode. -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -boldmath -\end_layout - -\end_inset - - -\begin_inset Formula -\[ -\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment} -\] - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -unboldmath -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Colored Formulas -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! colored -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Formulas can be colored like normal text: Highlight a formula or a formula - part and use the -\family sans -Text Style -\family default - dialog. - Here is a formula in magenta: -\begin_inset Formula -\[ -{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -You can also define your own colors as described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Colored-Boxes" - -\end_inset - -. - They can be used with the TeX code command -\series bold - -\backslash -textcolor -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -textcolor -\end_layout - -\end_inset - - in the scheme -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -textcolor{color}{characters or formula} -\end_layout - -\begin_layout Standard -The following example was colored completely dark green and partly red: -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -textcolor{darkgreen}{ -\end_layout - -\end_inset - - -\begin_inset Formula -\[ -\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)} -\] - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Due to a bug in LyX only complete formulas can be colored with self-defined - colors. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #5269" -target "http://www.lyx.org/trac/ticket/5269" - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Font Sizes -\begin_inset CommandInset label -LatexCommand label -name "sub:Font-Sizes" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Font ! size -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -For characters in formulas there are, analog to characters in text, the - following size commands: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -Huge -\series default -, -\series bold - -\backslash -huge -\series default -, -\series bold - -\backslash -LARGE -\series default -, -\series bold - -\backslash -Large -\series default -, -\series bold - -\backslash -large -\series default -, -\series bold - -\backslash -normalsize -\series default -, -\series bold - -\backslash -small -\series default -, -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -footnotesize -\series default -, -\series bold - -\backslash -scriptsize -\series default - and -\series bold - -\backslash -tiny -\end_layout - -\begin_layout Standard -The size produced by the commands depends on the document font size, which - corresponds to the command -\series bold - -\backslash -normalsize -\series default -. - The other commands produce smaller or larger sizes than -\series bold - -\backslash -normalsize -\series default -. - The font size can however not exceed a certain value. - Is for example the document font size 12 -\begin_inset space \thinspace{} -\end_inset - -pt, the command -\series bold - -\backslash -Huge -\series default - switches to the same size as -\series bold - -\backslash -huge -\series default -. - -\end_layout - -\begin_layout Standard -A size command is inserted in TeX-mode before the formula and sets the size - for all following formula and text characters. - To switch back to the initial size, the command -\series bold - -\backslash -normalsize -\series default - is inserted behind the formula in TeX-mode. -\end_layout - -\begin_layout Standard -Within a formula the size can be changed using the following size commands: -\end_layout - -\begin_layout Standard -\noindent -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -displaystyle -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -displaystyle -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -textstyle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -scriptstyle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -scriptscriptstyle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -After entering these commands, a blue box appears in which the formula parts - are inserted. -\end_layout - -\begin_layout Standard -There is a further method to change the font size, that though only works - for symbols or letters in mathematical text. - To use it, one of the above text size commands is inserted in mathematical - text. - All following characters until the end of the mathematical text or until - another size command will have the selected size. - Two examples: -\begin_inset VSpace -2mm -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -huge -\end_layout - -\end_inset - - -\begin_inset Formula -\[ -A=\frac{B}{c}\cdot\maltese -\] - -\end_inset - - -\begin_inset Formula -\[ -\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}} -\] - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -normalsize -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -Before both formulas the command -\series bold - -\backslash -huge -\series default - was inserted. - The command for the second formula is: -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -maltese -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A Alt+M M -\backslash -Large -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -maltese -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -textit -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset Formula $\to$ -\end_inset - - -\begin_inset Formula $\to$ -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset space \hspace*{} -\length 1cm -\end_inset - -Alt+M -\series default - -\series bold -M -\backslash -tiny -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -maltese -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -textit -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\end_layout - -\begin_layout Standard -If a symbol cannot be displayed in different sizes, it will always be displayed - in the default size. -\end_layout - -\begin_layout Section -Greek Letters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Greek letters -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Greek letters can also be inserted via the toolbar button -\begin_inset Graphics - filename ../images/math/alpha.png - scale 85 - -\end_inset - -. - All international typesetting norms purport that Greek letters in math - have to be typeset italic/slanted. - In some languages, like French or Russian, they are nevertheless sometimes - typeset upright. -\end_layout - -\begin_layout Subsection -Small Letters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Greek letters ! small -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -alpha -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\alpha$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -beta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\beta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -gamma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\gamma$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -delta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\delta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -epsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\epsilon$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varepsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varepsilon$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -zeta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\zeta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -eta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\eta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -theta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\theta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vartheta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\vartheta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -iota -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\iota$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -kappa -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\kappa$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varkappa -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varkappa$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lambda -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\lambda$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mu -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mu$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nu -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nu$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -xi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\xi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -o -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $o$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -pi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\pi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varpi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varpi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rho -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rho$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varrho -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varrho$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sigma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sigma$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varsigma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varsigma$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -tau -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\tau$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -upsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\upsilon$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -phi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\phi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varphi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varphi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -chi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\chi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -psi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\psi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -omega -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\omega$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - - -\end_layout - -\begin_layout Standard -How to create special upright Greek letters is explained in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Upright-small-Greek" - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Big Letters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Greek letters ! big -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Gamma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Gamma$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Delta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Delta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Theta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Theta$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Lambda -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Lambda$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Xi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Xi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Pi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Pi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Sigma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Sigma$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Upsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Upsilon$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Phi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Phi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Psi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Psi$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Omega -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Omega$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -That the big Greek letters appear upright is caused by a design bug when - TeX was developed. - To get correct italic big letters, begin every command with -\series bold -var -\series default -. - For example the command -\series bold - -\backslash -varGamma -\series default - produces -\begin_inset Formula $\varGamma$ -\end_inset - -. - Another way is to load the package -\series bold -fixmath -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout - -\series bold -fixmath -\series default - is part of the LaTeX-package -\series bold -was -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! was -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! fixmath -\end_layout - -\end_inset - - with the LaTeX-preamble line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{fixmath} -\end_layout - -\begin_layout Standard -Then all big Greek letters in a document will automatically be typeset italic. -\end_layout - -\begin_layout Subsection -Bold Letters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Greek letters ! bold -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Greek letters cannot be set with different font styles like Latin letters. - They can only be made bold with the command -\series bold - -\backslash -boldsymbol -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! B ! -\backslash -boldsymbol -\end_layout - -\end_inset - -. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Upsilon -\backslash -boldsymbol -\backslash -Upsilon -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -theta -\backslash -boldsymbol -\backslash -theta -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\theta\boldsymbol{\theta}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Section -Symbols -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -texorpdfstring{ -\end_layout - -\end_inset - - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -A list with all symbols of most of the LaTeX-packages can be found in -\begin_inset CommandInset citation -LatexCommand cite -key "Symbols" - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -}{} -\end_layout - -\end_inset - - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\backslash -texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. -\end_layout - -\begin_layout Plain Layout -More about -\backslash -texorpdfstring is in section -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Formulas-in-Section" - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Symbols -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Many of the symbols listed in this section can also be inserted via the - toolbar buttons -\begin_inset Graphics - filename ../images/math/nabla.png - scale 85 - -\end_inset - - and -\begin_inset Graphics - filename ../images/math/digamma.png - scale 85 - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Mathematical Symbols -\begin_inset CommandInset label -LatexCommand label -name "sub:Mathematical-Symbols" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Symbols ! mathematical -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -neg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\neg$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Im -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Im$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Re -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Re$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -aleph -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\aleph$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -partial -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\partial$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -infty -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\infty$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -wp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\wp$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -imath -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\imath$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -jmath -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\jmath$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -forall -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\forall$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -exists -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\exists$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nexists -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nexists$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -emptyset -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\emptyset$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varnothing -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varnothing$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dag -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\dag$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ddag -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ddag$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -complement -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -raisebox{-0.8mm}{ -\end_layout - -\end_inset - - -\begin_inset Formula $\complement$ -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Bbbk -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Bbbk$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -prime -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\prime$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -backprime -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\backprime$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mho -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mho$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -triangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\triangle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -angle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\angle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -measuredangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\measuredangle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sphericalangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sphericalangle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -top -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\top$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bot$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Subsection -Miscellaneous Symbols -\begin_inset CommandInset label -LatexCommand label -name "sub:Miscellaneous-Symbols" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Symbols ! miscellaneous -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\noindent -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -flat -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\flat$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -natural -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\natural$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sharp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sharp$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -surd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\surd$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -checkmark -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\checkmark$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -yen -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\yen$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -pounds -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\pounds$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -$ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\$$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -§ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $§$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hbar -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\hbar$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hslash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\hslash$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -clubsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\clubsuit$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -spadesuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\spadesuit$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bigstar -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bigstar$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -blacklozenge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\blacklozenge$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -blacktriangle -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\blacktriangle$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -blacktiangledown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\blacktriangledown$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bullet -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bullet$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -diamondsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\diamondsuit$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Diamond -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Diamond$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -heartsuit -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\heartsuit$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -P -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\P$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -copyright -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\copyright$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -circledR -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\circledR$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -maltese -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\maltese$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -diagup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\diagup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -diagdown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\diagdown$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -More symbols are listed in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Miscellaneous-special-Characters" - -\end_inset - -. -\end_layout - -\begin_layout Standard -Some symbols can be displayed in different sizes, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Font-Sizes" - -\end_inset - -. -\end_layout - -\begin_layout Subsection -The Euro-Symbol € -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Symbols ! Euro-symbol -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout - -\backslash -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -officialeuro -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To use the Euro symbol in formulas, the LaTeX-package -\series bold -eurosym -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! eurosym -\end_layout - -\end_inset - - must be installed and loaded with the LaTeX-preamble line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage[gennarrow]{eurosym} -\end_layout - -\begin_layout Standard -The Euro symbol can now be inserted with the command -\series bold - -\backslash -euro -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! E ! -\backslash -euro -\end_layout - -\end_inset - -. -\end_layout - -\begin_layout Standard -The Euro symbol can directly be inserted with the € key in mathematical - text, without having -\series bold -eurosym -\series default - installed. - When -\series bold -eurosym -\series default - is installed, -\series bold - -\backslash -euro -\series default - can also be inserted in TeX-mode. - The official currency symbol can then be inserted with the command -\series bold - -\backslash -officialeuro -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! O ! -\backslash -officialeuro -\end_layout - -\end_inset - -, that is only available in TeX-mode. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -ifeurosym -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following table will only be displayed when the LaTeX-package -\series bold -eurosym -\series default - is installed. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -An overview about the different Euro symbols: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -formula -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -euro -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\euro$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -mathematical text -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -€ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mbox{€}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -TeX-mode -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -officialeuro -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -officialeuro -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -else -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following will be displayed when the LaTeX-package -\series bold -eurosym -\series default - is not installed: -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -You need to install the LaTeX-package -\series bold -eurosym -\series default - to see the rest of this subsection in the output. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fi -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Section -Relations -\begin_inset CommandInset label -LatexCommand label -name "sec:Relations" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Relations -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Comparisons|see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Relations -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -All relations can also be inserted via the toolbar button -\begin_inset Graphics - filename ../images/math/leq.png - scale 85 - -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -< -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $<$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -le -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\le$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ll -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ll$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -prec -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\prec$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -preceq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\preceq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -subset -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\subset$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -subseteq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\subseteq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqsubseteq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sqsubseteq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -in -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\in$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vdash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\vdash$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -smile -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\smile$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lhd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\lhd$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -unlhd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\unlhd$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -gtrless -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\gtrless$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -mid -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mid$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nmid -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nmid$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -= -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $=$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not= -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\not=$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -equiv -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\equiv$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sim -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sim$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -simeq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\simeq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -approx -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\approx$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cong -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\cong$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bowtie -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\bowtie$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -notin -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\notin$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -perp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\perp$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -propto -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\propto$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -asymp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\asymp$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -doteq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\doteq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -circeq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\circeq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -models -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\models$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -widehat= -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\widehat{=}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -> -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $>$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ge -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ge$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -gg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\gg$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -succ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\succ$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -succeq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\succeq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -supset -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\supset$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -supseteq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\supseteq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sqsupseteq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\sqsupseteq$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ni -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\ni$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dashv -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\dashv$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -frown -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\frown$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rhd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\rhd$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -unrhd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\unrhd$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lessgtr -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\lessgtr$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -parallel -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\parallel$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -nparallel -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\nparallel$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -The characters -\series bold - -\backslash -lhd -\series default - and -\series bold - -\backslash -rhd -\series default - are bigger than the equal looking operators -\series bold - -\backslash -triangleleft -\series default - and -\series bold - -\backslash -triangleright -\series default -, respectively. -\end_layout - -\begin_layout Standard -Relations are, in contrary to symbols, always surrounded by space. -\end_layout - -\begin_layout Standard -Relations with labels can be created with the command -\series bold - -\backslash -stackrel -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -stackrel -\end_layout - -\end_inset - -: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A(r) -\backslash -stackrel -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -r -\backslash -to -\backslash -infty -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset Formula $\downarrow$ -\end_inset - - -\backslash -approx -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Section -Functions -\end_layout - -\begin_layout Subsection -Predefined Functions -\begin_inset CommandInset label -LatexCommand label -name "sub:Predefined-Functions" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Functions ! predefined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -In general, variables are set -\emph on -italic -\emph default - in mathematical expressions, but not function names, because -\begin_inset Formula $sin$ -\end_inset - - could be misunderstood as -\begin_inset Formula $s\cdot i\cdot n$ -\end_inset - -. - Therefore there are predefined functionswhich are additionally a bit separated - from prefactors. - They are inserted as commands starting with a backslash before their name. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -Asin(x)+B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $Asin(x)+B$ -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -A -\backslash -sin(x)+B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\sin(x)+B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -The following functions are predefined: -\end_layout - -\begin_layout Standard -\begin_inset VSpace -2mm -\end_inset - - -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sin -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sinh -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -arcsin -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sup -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cos -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cosh -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -arccos -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -inf -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -tan -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -tanh -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -arctan -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lim -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -coth -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -arg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -liminf -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -sec -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -min -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -deg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -limsup -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -csc -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -max -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -det -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Pr -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ln -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -exp -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dim -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -hom -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lg -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -log -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ker -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -gcd -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -They can also be inserted with the math toolbar button -\begin_inset Graphics - filename ../images/math/functions.png - scale 85 - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Self-defined Functions -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Functions ! self-defined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To use a function that is not predefined, like for example the sign function - sgn(x), there are two possibilities: -\end_layout - -\begin_layout Itemize -Define the function by inserting the following line to the LaTeX-preamble -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -For more about -\series bold - -\backslash -DeclareMathOperator -\series default - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Self-defined-Operators" - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset VSpace -3mm -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -DeclareMathOperator{ -\backslash -sgn}{sgn} -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! D ! -\backslash -dbinom@ -\backslash -DeclareMathOperator -\end_layout - -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset VSpace -2mm -\end_inset - - -\begin_inset Newline newline -\end_inset - -Now the new defined function can be called with the command -\series bold - -\backslash -sgn -\series default -. -\end_layout - -\begin_layout Itemize -Write the formula as usual, mark the formula name, in our example the letters - -\emph on -sgn -\emph default -, and change it to mathematical text. - Finally, a space is inserted between prefactor and function. -\end_layout - -\begin_layout Standard -The result is the same with both methods as with a predefined function -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -In LyX self-defined functions are displayed red, predefined ones black. -\end_layout - -\end_inset - -: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A -\backslash -sgn(x)+B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\sgn(x)+B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A -\backslash -, -\begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$ -\end_inset - -(x)+B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\,\textrm{sgn}(x)+B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -The first method is more suitable when the self-defined function should - be used several times. -\end_layout - -\begin_layout Subsection -Limits -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Limits -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -For limits, in addition to the commands -\series bold - -\backslash -lim -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -lim -\end_layout - -\end_inset - -, -\series bold - -\backslash -liminf -\series default - and -\series bold - -\backslash -limsup -\series default - the following functions are defined: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varliminf -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varliminf$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varlimsup -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varlimsup$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varprojlim -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varprojlim$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -varinjlim -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\varinjlim$ -\end_inset - - -\begin_inset Formula $\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -The limit is created by inserting a subscript. - It is set right beside the function in an inline formula: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset space \hspace{} -\length 1cm -\end_inset - -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -The space and -\series bold - -\backslash -raisebox -\series default - are used here as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lim_x -\backslash -to -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -x=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -In a displayed formula the limit is set below the formula, as usual: -\begin_inset Formula -\[ -\lim_{x\to A}x=B -\] - -\end_inset - - -\end_layout - -\begin_layout Subsection -Modulo-Functions -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Functions ! modulo- -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The modulo-function is special, because it exists in four variants. - The variants in a displayed formula are: -\begin_inset Formula -\begin{align*} -\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\ -\mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\ -\mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\ -\mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\ -\mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b -\end{align*} - -\end_inset - - -\end_layout - -\begin_layout Standard -In an inline formula less space is set before the function names for all - variants. - By default the modulo-functions take only the first following character - into account. - To use more than one character, one has to put them into TeX-braces: -\begin_inset Formula -\begin{align*} -\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\ -\mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\ -\mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d -\end{align*} - -\end_inset - - -\end_layout - -\begin_layout Section -Special Characters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Special characters -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Special Characters in Mathematical Text -\end_layout - -\begin_layout Standard -The following commands can only be used in mathematical text or in TeX-mode: -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -oe -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{œ}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -OE -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{Œ}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ae -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{æ}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -AE -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{Æ}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -aa -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{\aa}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -AA -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout - -\backslash -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -textrm{ -\backslash -AA} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{Å}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -i -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{ı}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -command -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -The space of 0 -\begin_inset space \thinspace{} -\end_inset - -mm is used for separation, because otherwise the output will be ¡ and ¿ - respectively. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -o -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{ø}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -O -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{Ø}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -l -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{ł}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -L -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{Ł}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -! -\begin_inset space \hspace{} -\length 0mm -\end_inset - -` -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{!`}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -? -\begin_inset space \hspace{} -\length 0mm -\end_inset - -` -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{?`}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -j -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\textrm{ȷ}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -The characters -\begin_inset Formula $\textrm{\textrm{Å}}$ -\end_inset - - and -\begin_inset Formula $\textrm{\textrm{Ø}}$ -\end_inset - - can also be inserted via the math toolbar button -\begin_inset Graphics - filename ../images/math/digamma.png - scale 85 - -\end_inset - -. -\end_layout - -\begin_layout Standard -An exception are the commands -\series bold -! -\begin_inset space \hspace{} -\length 0mm -\end_inset - -` -\series default - and -\series bold -? -\begin_inset space \hspace{} -\length 0mm -\end_inset - -` -\series default -, because they can be inserted in LyX directly to text. -\end_layout - -\begin_layout Subsection -Accents in Text -\begin_inset CommandInset label -LatexCommand label -name "sub:Accents-in-Text" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Accents ! in text -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -With the following commands all letters can be accented. - The commands must be inserted in TeX-mode. -\end_layout - -\begin_layout Standard -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash - -\begin_inset Quotes grd -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -"e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -`e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -`e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -^e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -=e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -=e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -u -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -u e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -b -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -b e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -t -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -ee -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -t ee -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -H -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -H e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -'e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -'e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -~e -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Tilde -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -~e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -.e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -.e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -v -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -v e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -d -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -d e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -c -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -e -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -c e -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -With the command -\series bold - -\backslash -t -\series default - also two different characters can be accented. - The command -\series bold - -\backslash -t -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -sz -\series default - creates: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -t sz -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The accents -\series bold -` -\series default - , -\series bold -' -\series default - and -\series bold -^ -\series default - can in combination with vowels directly be inserted with the keyboard without - using TeX-mode. - The same applies for the tilde -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -This only applies for keyboards where the tilde is defined as accent. -\end_layout - -\end_inset - - -\series bold -~ -\series default - in combination with -\emph on -a -\emph default - , -\emph on -n -\emph default - , or -\emph on -o -\emph default -. -\end_layout - -\begin_layout Standard -The commands -\series bold - -\backslash -b -\series default - , -\series bold - -\backslash -c -\series default - , -\series bold - -\backslash -d -\series default - , -\series bold - -\backslash -H -\series default - , -\series bold - -\backslash -t -\series default - , -\series bold - -\backslash -u -\series default - , -\series bold - -\backslash -v -\series default - and accents that are inserted directly with the keyboard are also available - in mathematical text. - For the other accents there are special math commands to be used in formulas, - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Accents-for-one" - -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -Furthermore, with the command -\series bold - -\backslash -textcircled -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -textcircled -\end_layout - -\end_inset - - all numbers and letters can be set into a circle, quasi accented with a - circle, similar to the copyright symbol. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -textcircled{w} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -textcircled{w} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Large -\backslash -textcircled{ -\backslash -normalsize -\backslash -protect -\backslash -raisebox{-1.5pt}{W}} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}$ -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -Large -\backslash -textcircled{ -\backslash -normalsize -\backslash -protect -\backslash -raisebox{-1.5pt}W} -\end_layout - -\end_inset - - -\begin_inset Formula $\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -One has to take care that the character fits in the circle. - -\series bold - -\backslash -Large -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Font-Sizes" - -\end_inset - - -\end_layout - -\end_inset - - specifies thereby the size of the circle. - With the help of -\series bold - -\backslash -raisebox -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Boxes-without-Frame" - -\end_inset - - -\end_layout - -\end_inset - - the character can be centered. -\end_layout - -\begin_layout Subsection -Old-style Figures -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Old-style Figures -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Old-style figures (also known as old-style numerals) are created with the - command -\series bold - -\backslash -oldstylenums -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! O ! -\backslash -oldstylenums -\end_layout - -\end_inset - -. - The command can be used in formulas and in TeX-mode. - The command scheme is: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -oldstylenums{number} -\end_layout - -\begin_layout Standard -The command -\series bold - -\backslash -oldstylenums{0123456789 -\series default - produces: -\begin_inset Formula $\oldstylenums{0123456789}$ -\end_inset - - -\end_layout - -\begin_layout Subsection -Miscellaneous special Characters -\begin_inset CommandInset label -LatexCommand label -name "sub:Miscellaneous-special-Characters" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Special characters ! miscellaneous -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The following characters can only be inserted to formulas by using commands: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\mathcircumflex$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -_ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\_$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\backslash -circ -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout - -\backslash -@° -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $^{\circ}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble - contains the following line -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -More about this is described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Text-Characters-in" - -\end_inset - -. -\end_layout - -\end_inset - -: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -DeclareInputtext{176}{ -\backslash -ifmmode^ -\backslash -circ -\backslash -else -\backslash -textdegree -\backslash -fi} -\end_layout - -\begin_layout Section -Formula Styles -\begin_inset CommandInset label -LatexCommand label -name "sec:Formula-Styles" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! styles -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Itemize -There are two different alignment styles: -\end_layout - -\begin_deeper -\begin_layout Description -Centered is the predefined standard -\end_layout - -\begin_layout Description -Indented for this the option -\series bold -fleqn -\series default - must be inserted in the menu -\family sans -Document\SpecialChar \menuseparator -Settings -\family default - under -\family sans -Document -\begin_inset space ~ -\end_inset - -Class -\end_layout - -\begin_layout Standard -When -\series bold -Indented -\series default - is used, the indentation can be adjusted with the length -\series bold - -\backslash -mathindent -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -mathindent -\end_layout - -\end_inset - -. - Should the distance be 15 -\begin_inset space \thinspace{} -\end_inset - -mm, the following command line is inserted in the LaTeX-preamble -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -setlength{ -\backslash -mathindent}{15mm} -\end_layout - -\begin_layout Standard -When no length is specified, the predefined value of 30 -\begin_inset space \thinspace{} -\end_inset - -pt will be used. -\end_layout - -\end_deeper -\begin_layout Itemize -And two different numbering styles: -\end_layout - -\begin_deeper -\begin_layout Description -Right is the predefined standard -\end_layout - -\begin_layout Description -Left for this the option -\series bold -leqno -\series default - must be inserted in the menu -\family sans -Document\SpecialChar \menuseparator -Settings -\family default - under -\family sans -Document -\begin_inset space ~ -\end_inset - -Class -\end_layout - -\end_deeper -\begin_layout Standard - -\series bold -fleqn -\series default - and -\series bold -leqno -\series default - can also be used together. - In this case both options are inserted, separated by a comma. -\end_layout - -\begin_layout Standard -The chosen styles are used for all displayed formulas of the document. - When both, centered and indented formulas should be created in a document, - the style -\series bold -Centered -\series default - is used. - The indented formulas are then set in a flalign environment, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Flalign-Environment" - -\end_inset - -. -\end_layout - -\begin_layout Section -Multiline Formulas -\begin_inset CommandInset label -LatexCommand label -name "sec:Multiline-Formulas" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -General -\end_layout - -\begin_layout Standard -In LyX multiline formulas are created by pressing -\series bold - -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - - -\series default - inside a formula. - This creates either an -\series bold -eqnarray environment -\series default - that is described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Eqnarray-Environment" - -\end_inset - - or, when the option -\family sans -Use AMS math package -\family default - in the document settings is selected, an -\series bold -align environment -\series default - that is described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Standard-align-Environment" - -\end_inset - -. - The align environment is recommended because it provides in any case a - typographically correct output. -\end_layout - -\begin_layout Standard -There are other multiline formula environments that can be created via the - menu -\family sans -Insert\SpecialChar \menuseparator -Math -\family default -. - These environments are described in the following sections. -\end_layout - -\begin_layout Standard -In all multiline formula environments a new line is created by pressing - -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - -. - To add or delete lines, the math toolbar buttons -\begin_inset Graphics - filename ../images/tabular-feature_append-row.png - scale 85 - -\end_inset - - or -\begin_inset Graphics - filename ../images/tabular-feature_delete-row.png - scale 85 - -\end_inset - -, respectively, or the menu -\family sans -Edit\SpecialChar \menuseparator -Rows & Columns -\family default - can be used. -\end_layout - -\begin_layout Subsubsection -Line Separation -\begin_inset CommandInset label -LatexCommand label -name "sub:Line-Separation" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! Line separation -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -There is sometimes not enough space in multiline formulas between the lines: -\begin_inset Formula -\begin{eqnarray*} -B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\ -4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0 -\end{eqnarray*} - -\end_inset - - -\end_layout - -\begin_layout Standard -In LaTeX additional line space is specified as optional argument of the - new line command. - This is not yet possible in LyX -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -see -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #1505" -target "http://www.lyx.org/trac/ticket/1505" - -\end_inset - - -\end_layout - -\end_inset - -, therefore the whole formula must be inserted in TeX-mode. - To add in our example space, the command -\series bold - -\backslash - -\backslash -[3mm] -\series default - is inserted at the end of the first line. - One gets: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -begin{eqnarray*} -\end_layout - -\begin_layout Plain Layout - -B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & - = & -\backslash -textrm{-}4x^{2}B^{2}+4x_{0}xB^{2} -\backslash - -\backslash -[3mm] -\end_layout - -\begin_layout Plain Layout - -4x^{2} -\backslash -left(B^{2}+x_{0}^{2} -\backslash -right)+4x_{0}x -\backslash -left(D-B^{2} -\backslash -right)+B^{2} -\backslash -left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2} -\backslash -right) & = & 0 -\end_layout - -\begin_layout Plain Layout - - -\backslash -end{eqnarray*} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -To set the line separation for all lines in a formula, the length -\series bold - -\backslash -jot -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! J ! -\backslash -jot -\end_layout - -\end_inset - - is changed. - The definition is: -\begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$ -\end_inset - -. - Predefined for -\series bold - -\backslash -jot -\series default - is the value 3 -\begin_inset space \thinspace{} -\end_inset - -pt. - To create 3 -\begin_inset space \thinspace{} -\end_inset - -mm additional line separation as in the previous example, the command -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -setlength{ -\backslash -jot}{3mm+3pt} -\end_layout - -\begin_layout Standard -is inserted in TeX-mode before the formula. - This requires that the LaTeX-package -\series bold -calc -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout - -\series bold -calc -\series default - is part of every LaTeX standard installation. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! calc -\end_layout - -\end_inset - - was loaded in LaTeX-preamble with the line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{calc} -\end_layout - -\begin_layout Standard -One gets: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -setlength{ -\backslash -jot}{3mm+3pt} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{eqnarray*} -B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\ -4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0 -\end{eqnarray*} - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -setlength{ -\backslash -jot}{3pt} -\end_layout - -\end_inset - - To get back to the predefined distance, -\series bold - -\backslash -jot -\series default - is set to the value 3 -\begin_inset space \thinspace{} -\end_inset - -pt. -\end_layout - -\begin_layout Subsubsection -Column Separation -\begin_inset CommandInset label -LatexCommand label -name "sub:Column-Separation" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! Column separation -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Multiline formulas form a matrix. - A formula in the eqnarray environment is for example a matrix with three - columns. - By changing the column separation in this environment, the space beside - the relation sign can be changed. -\end_layout - -\begin_layout Standard -The column separation is specified with the length -\series bold - -\backslash -arraycolsep -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -arraycolsep -\end_layout - -\end_inset - - according to: -\begin_inset Newline newline -\end_inset - -column separation = 2 -\begin_inset space \thinspace{} -\end_inset - - -\series bold - -\backslash -arraycolsep -\series default - -\begin_inset Newline newline -\end_inset - -Thus, the command -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -setlength{ -\backslash -arraycolsep}{1cm} -\end_layout - -\begin_layout Standard -inserted in TeX-mode, sets for all following formulas a column separation - of 2 -\begin_inset space \thinspace{} -\end_inset - -cm. - To get back to the predefined distance, -\series bold - -\backslash -arraycolsep -\series default - is set to 5 -\begin_inset space \thinspace{} -\end_inset - -pt. -\end_layout - -\begin_layout Standard -A formula with 2 -\begin_inset space \thinspace{} -\end_inset - -cm column separation: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -setlength{ -\backslash -arraycolsep}{1cm} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{eqnarray*} -A & = & B\\ -C & \ne & A -\end{eqnarray*} - -\end_inset - -A formula with the predefined column separation for matrices of 10 -\begin_inset space \thinspace{} -\end_inset - -pt: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -setlength{ -\backslash -arraycolsep}{5pt} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{eqnarray*} -A & = & B\\ -C & \ne & A -\end{eqnarray*} - -\end_inset - - -\end_layout - -\begin_layout Subsubsection -Long Formulas -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! long -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Long formulas can be typeset using these methods: -\end_layout - -\begin_layout Itemize -When one side of the equation is much shorter than the line width, this - one is chosen for the left side and the right side is typeset over two - lines: -\begin_inset Formula -\begin{eqnarray} -H & = & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\nonumber \\ - & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:shortlong} -\end{eqnarray} - -\end_inset - -The minus sign at the beginning of the second line does normally not appear - as an operator because it is the first character of the line. - Thus it would not be surrounded by space and could not be distinguished - from the fraction bar. - To avoid this, 3 -\begin_inset space \thinspace{} -\end_inset - -pt space was inserted behind the minus sign with the command -\series bold - -\backslash -hspace -\series default -. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -for more about -\series bold - -\backslash -hspace -\series default - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Variable-Space" - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! H ! -\backslash -hspace -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Itemize -When both sides of the equation are too long, the command -\series bold - -\backslash -lefteqn -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -lefteqn -\end_layout - -\end_inset - - is used. - It is inserted in the first column of the first line and causes all further - insertions to overwrite the following columns: -\begin_inset Formula -\begin{eqnarray} -\lefteqn{4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}}\nonumber \\ - & & -\hspace{3pt}B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\nonumber \\ - & & =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\label{eq:lefteqn} -\end{eqnarray} - -\end_inset - -After the insertion of -\series bold - -\backslash -lefteqn -\series default -, the cursor is in a purple box that is a bit shifted to the left from the - blue one. - In this the formula is inserted. -\begin_inset Newline newline -\end_inset - -The content of the further lines is inserted to the second or another formula - column. - The greater the column number where it was inserted, the larger the indentation. -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout -Note the following when using -\series bold - -\backslash -lefteqn -\series default -: -\end_layout - -\begin_layout Itemize -The formula doesn't use the full page width. - When e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -the term -\begin_inset Formula $-B^{2}$ -\end_inset - - is added to the first line in the above example, it would have been outside - the page margin. - To better use the width, negative space can be inserted at the beginning - of the first line. -\end_layout - -\begin_layout Itemize -Due to a bug in LyX the cursor cannot be set with the mouse into the first - line. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #1429" -target "http://www.lyx.org/trac/ticket/1429" - -\end_inset - - -\end_layout - -\end_inset - - One can only set the cursor at the beginning of the line and move it with - the arrow keys. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Itemize -Other methods to set long formulas are offered by the environments described - in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Multline-Environment" - -\end_inset - - and -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Multiline-Formula-Parts" - -\end_inset - -. -\end_layout - -\begin_layout Subsubsection -Multiline Brackets -\begin_inset CommandInset label -LatexCommand label -name "sub:Multiline-Brackets" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Brackets ! for multiline expressions -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -For brackets spanning multiple lines the following problem occurs: -\begin_inset Formula -\begin{eqnarray*} -A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\ - & & \left.\cdots+B-D\right] -\end{eqnarray*} - -\end_inset - - -\end_layout - -\begin_layout Standard -The closing bracket is smaller than the opening bracket because brackets - with variable size may not span multiple lines. -\end_layout - -\begin_layout Standard -To set the bracket size for the second line correctly, the first line is - ended with -\series bold - -\backslash -right. -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -right -\end_layout - -\end_inset - - and the second line with -\series bold - -\backslash -left. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -for more about -\series bold - -\backslash -left -\series default - and -\series bold - -\backslash -right -\series default - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Automatic-Bracket-Size" - -\end_inset - - -\end_layout - -\end_inset - - -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! L ! -\backslash -left -\end_layout - -\end_inset - -. - After -\series bold - -\backslash -left. - -\series default - the command -\series bold - -\backslash -vphantom -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold - -\backslash -prod -\series default -^ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold - -\backslash -infty -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\series bold - -\begin_inset Formula $\downarrow$ -\end_inset - -_R=1} -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! V ! -\backslash -vphantom -\end_layout - -\end_inset - - is inserted, because the multiplication operator with its limits is the - largest symbol in the first line and this should be the size for the bracket - in the second line. -\end_layout - -\begin_layout Standard -The result is this: -\begin_inset Formula -\begin{eqnarray*} -A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\ - & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right] -\end{eqnarray*} - -\end_inset - - -\end_layout - -\begin_layout Subsection -Align Environments -\end_layout - -\begin_layout Standard -Align environments can be used for every kind of multiline formulas. - They are especially useful to set several formulas side by side. -\end_layout - -\begin_layout Standard -Align environments consist of columns. - The odd columns are right aligned, the even ones left aligned. - Every line in an Align environment can be numbered. -\end_layout - -\begin_layout Standard -Align environments are created via the menu -\family sans -Insert\SpecialChar \menuseparator -Math -\family default -. - With the menu -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Change Formula Type -\family default - already existing formulas can be converted to Align environments. -\end_layout - -\begin_layout Standard -To add or delete columns, the math toolbar buttons -\begin_inset Graphics - filename ../images/tabular-feature_append-column.png - scale 85 - -\end_inset - - or -\begin_inset Graphics - filename ../images/tabular-feature_delete-column.png - scale 85 - -\end_inset - -, respectively, or the menu -\family sans -Edit\SpecialChar \menuseparator -Rows & Columns -\family default - can be used. -\end_layout - -\begin_layout Subsubsection -Standard align Environment -\begin_inset CommandInset label -LatexCommand label -name "sub:Standard-align-Environment" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! align environment -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -This Align environment is created by pressing -\begin_inset Info -type "shortcut" -arg "newline-insert newline" -\end_inset - - in a formula or by the menu -\family sans -Insert\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -AMS align Environment -\family default -. -\end_layout - -\begin_layout Standard -An example for two formulas set side by side, that are created with a four - column align environment: -\begin_inset Formula -\begin{align*} -A & =\sin(B) & C & =D\\ -C & \ne A & B & \ne D -\end{align*} - -\end_inset - -As it can be seen, the formulas in this environment are placed so as if - there would be a -\series bold - -\backslash -hfill -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -more about -\series bold - -\backslash -hfill -\series default - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Variable-Space" - -\end_inset - - -\end_layout - -\end_inset - - -\series default - before the first and after every even column. - When the formula style -\series bold -Indented -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -formula styles see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - - -\end_layout - -\end_inset - - -\series default - is used, the formula is set without the -\series bold - -\backslash -hfill -\series default - before the first column. -\end_layout - -\begin_layout Subsubsection -Alignat Environment -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! alignat environment -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The alignat environment has no predefined column separation. - It can be inserted manually with the spaces that are described -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Space" - -\end_inset - -. -\end_layout - -\begin_layout Standard -The above example in the alignat environment where 1 -\begin_inset space \thinspace{} -\end_inset - -cm space was inserted at the beginning of the second formula: -\begin_inset Formula -\begin{alignat*}{2} -A & =\sin(B) & \hspace{1cm}C & =D\\ -C & \ne A & B & \ne D -\end{alignat*} - -\end_inset - -Because the column separation can be set separately for every column, this - environment is especially suitable to set three and more formulas side - by side. -\end_layout - -\begin_layout Subsubsection -Flalign Environment -\begin_inset CommandInset label -LatexCommand label -name "sub:Flalign-Environment" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! flalign environment -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -In this environment the first two columns are always set as much as possible - to the left and the last two ones to the right. - An example: -\begin_inset Formula -\begin{flalign*} -A & =1 & B & =2 & C & =3\\ -X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4 -\end{flalign*} - -\end_inset - - -\end_layout - -\begin_layout Standard -By creating a flalign environment with an odd number of columns where an - empty TeX-brace is inserted to the last column, several formulas in a document - can be set to the left, although the formula style -\series bold -Centered -\series default - is used. - As example the indented formula -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:VolInt" - -\end_inset - -: -\begin_inset Formula -\begin{flalign} -\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {} -\end{flalign} - -\end_inset - -The first two columns contain the formula. - To indent it as with the formula style -\series bold -Indented -\series default -, 30 -\begin_inset space \thinspace{} -\end_inset - -pt space was inserted at the beginning of the first column. -\end_layout - -\begin_layout Subsection -Eqnarray Environment -\begin_inset CommandInset label -LatexCommand label -name "sub:Eqnarray-Environment" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! eqnarray environment -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -When this environment has been created, three blue boxes appear. - The content of the first box is right aligned, the content of the last - one left aligned. - The content of the middle box appears centered and a bit smaller, because - it is designed to insert there only relation characters. -\begin_inset Formula -\begin{eqnarray*} -\frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\ -AB & AB & AB\\ -A & = & A -\end{eqnarray*} - -\end_inset - - -\end_layout - -\begin_layout Subsection -Gather Environment -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! gather environment -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -This environment consists of only one centered column. - Every line can be numbered. -\begin_inset Formula -\begin{gather} -A=1\\ -X=\textrm{-}1 -\end{gather} - -\end_inset - - -\end_layout - -\begin_layout Subsection -Multline Environment -\begin_inset CommandInset label -LatexCommand label -name "sub:Multline-Environment" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! multline environment -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The multline environment consists, like the gather environment, of only - one column. - But the first line is left aligned, the last one right aligned. - All other lines are centered. - Therefore this environment is suitable for long formulas. - As example formula -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:lefteqn" - -\end_inset - - in the multline environment: -\begin_inset Formula -\begin{multline} -4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\ --B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\\ -=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}} -\end{multline} - -\end_inset - - -\end_layout - -\begin_layout Standard -In the output only the last (first) line of a multline environment appears - numbered when the document numbering is right (left). -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -numbering styles see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -With the commands -\series bold - -\backslash -shoveright -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -shoveright -\end_layout - -\end_inset - - and -\series bold - -\backslash -shoveleft -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -shoveleft -\end_layout - -\end_inset - - a centered line can be right or left aligned, respectively. - The commands are used as follows: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -shoveright{line content} -\series default - and -\series bold - -\backslash -shoveleft{line content} -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -The length -\series bold - -\backslash -multlinegap -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! M ! -\backslash -multlinegap -\end_layout - -\end_inset - - specifies the distance of the first line from the left page margin. - Predefined is the length 0 -\begin_inset space \thinspace{} -\end_inset - -pt. -\end_layout - -\begin_layout Standard -As example the above formula where the command -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -setlength{ -\backslash -multlinegap}{2cm} -\end_layout - -\begin_layout Standard -was inserted in TeX-mode before: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -setlength{ -\backslash -multlinegap}{2cm} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{multline} -4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\ -\shoveleft{-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}\\ -=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}} -\end{multline} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -setlength{ -\backslash -multlinegap}{0pt} -\end_layout - -\end_inset - -The second line was left aligned using -\series bold - -\backslash -shoveleft -\series default -. -\end_layout - -\begin_layout Subsection -Multiline Formula Parts -\begin_inset CommandInset label -LatexCommand label -name "sub:Multiline-Formula-Parts" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! formula parts -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To display only parts of a formula with multiple lines, one of the following - environments is used: -\series bold -aligned -\series default -, -\series bold -alignedat -\series default -, -\series bold -gathered -\series default - or -\series bold -split -\series default -. - They can be inserted via the menu -\family sans -Insert\SpecialChar \menuseparator -Math -\family default - or by using the commands described in this section. -\end_layout - -\begin_layout Standard -The first three have the same properties as the corresponding multiline - formula environments, but it is possible to set further formula parts beside - them. - An example: -\begin_inset Formula -\[ -\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\ -\Delta E\Delta t & \ge\frac{\hbar}{2} -\end{aligned} -\right\} \textrm{Uncertainty relations} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -To get this formula, a displayed formula is created where the command -\series bold - -\backslash -aligned -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -aligned -\end_layout - -\end_inset - - is inserted. - A purple box appears around the blue formula box where now columns and - lines can be added. - Outside the multiline environment other formula parts can be set, like - the brace. -\end_layout - -\begin_layout Standard -The aligned environment is also suitable for long formulas whose lines are - horizontally aligned. - Using aligned in a displayed formula has the advantage that the formula - number is vertically centered behind the lines. - As example formula -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:shortlong" - -\end_inset - - in the aligned environment: -\begin_inset Formula -\begin{equation} -\begin{aligned}H=\; & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\\ - & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|} -\end{aligned} -\end{equation} - -\end_inset - - -\end_layout - -\begin_layout Standard -To use the environments -\series bold -alignedat -\series default -, -\series bold -gathered -\series default -, or -\series bold -split -\series default -, the command -\series bold - -\backslash -alignedat -\series default -, -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -alignedat -\end_layout - -\end_inset - - -\series bold - -\backslash -gathered -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! G ! -\backslash -gathered -\end_layout - -\end_inset - -, or -\series bold - -\backslash -split -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! S ! -\backslash -split -\end_layout - -\end_inset - - are inserted, respectively. - The split environment has the same properties as the aligned environment - but it can only have two columns. -\end_layout - -\begin_layout Subsection -Text in multiline Formulas -\begin_inset CommandInset label -LatexCommand label -name "sub:Text-in-multiline" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Text ! in formulas -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! multiline ! text -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -In the Align environments, and the multline and gather environment, text - can be inserted that will appear in a separate line and doesn't affect - the column alignment. - To do this, the command -\series bold - -\backslash -intertext -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! I ! -\backslash -intertext -\end_layout - -\end_inset - - is used in the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -intertext{text} -\end_layout - -\begin_layout Standard -The text should not be longer than a line because it cannot be hyphenated. - As LyX doesn't yet support -\series bold - -\backslash -intertext -\series default - directly, the text is written as mathematical text. - -\series bold - -\backslash -intertext -\series default - must hereby be at the beginning of a line and appears in the output above - this line. - An example where the text was inserted at the beginning of the second line: -\begin_inset Formula -\begin{align} -I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\ -\intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi -\end{align} - -\end_inset - - -\end_layout - -\begin_layout Section -Formula Numbering -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! numbering|see -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -{ -\end_layout - -\end_inset - -Formula numbering -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -General -\end_layout - -\begin_layout Standard -Numbered formulas can be created with the menu -\family sans -Insert\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Numbered -\begin_inset space ~ -\end_inset - -Formula -\family default - (shortcut -\family sans -Ctrl+Alt -\begin_inset space ~ -\end_inset - -N -\family default -). - Existing formulas can be numbered with the menu -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Toggle -\begin_inset space ~ -\end_inset - -Numbering -\family default - (shortcut -\begin_inset Info -type "shortcut" -arg "math-number-toggle" -\end_inset - -). - The formula number is displayed in LyX behind the formula as a number sign - in parentheses. - The number sign is replaced in the output by the formula number. -\end_layout - -\begin_layout Standard -When numbering is turned on in multiline formulas, all lines will be numbered. - But the numbering can be controlled with the menu -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Toggle -\begin_inset space ~ -\end_inset - -Numbering -\begin_inset space ~ -\end_inset - -of -\begin_inset space ~ -\end_inset - -Line -\family default - (shortcut -\begin_inset Info -type "shortcut" -arg "math-number-line-toggle" -\end_inset - -) for every line. -\end_layout - -\begin_layout Standard -Except for inline formulas, all formulas can be numbered with two different - styles, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Cross-References -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Cross-references ! to formulas -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -All labeled formulas can be cross-referenced. - A label is added by the menu -\family sans -Insert\SpecialChar \menuseparator -Label -\family default - or the toolbar button -\begin_inset Graphics - filename ../images/label-insert.png - scale 85 - -\end_inset - -. - The cursor must hereby be inside a displayed formula. - Alternatively you can right-click on the formula and choose -\family sans -Equation Label -\family default -. - A dialog pops up displaying the prefix -\series bold -eq: -\series default - in a text field. - The label is inserted there behind the prefix. - The predefined prefix means -\begin_inset Quotes eld -\end_inset - -equation -\begin_inset Quotes erd -\end_inset - - and makes it easier to find labels in large documents because it marks - it as formula label to divide it from e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -section labels. - To change a label, the menu -\family sans -Insert\SpecialChar \menuseparator -Label -\family default - is used again or you right-click on a formula and then on -\family sans -Equation Label -\family default -. -\end_layout - -\begin_layout Standard -The name of the label is displayed in LyX within two parentheses behind - formula. - A formula with a label is always numbered. -\end_layout - -\begin_layout Standard -Cross-references are inserted via the menu -\family sans -Insert\SpecialChar \menuseparator -Cross-Reference -\family default - or with the toolbar button -\begin_inset Graphics - filename ../images/dialog-show-new-inset_ref.png - scale 85 - -\end_inset - -. - A formula cross-reference appears in the output as formula number. - When in the cross-reference dialog window the format -\series bold -() -\series default - is chosen, the cross-reference appears in the output as formula number - in parentheses. -\begin_inset Newline newline -\end_inset - -By right-clicking on a cross-reference in LyX, one jumps to the formula - that is referenced. -\end_layout - -\begin_layout Standard -Here are as examples cross-references to formulas of the following subsections: -\begin_inset Note Note -status open - -\begin_layout Plain Layout -Note the different cross-reference types. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The equations -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:tag" - -\end_inset - - and -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:c" - -\end_inset - - are equivalent. - In ( -\begin_inset CommandInset ref -LatexCommand ref -reference "eq:Lat" - -\end_inset - -) big Latin letters are used for the numbering in contrary to ( -\begin_inset CommandInset ref -LatexCommand ref -reference "eq:Rom" - -\end_inset - -). -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -When the argument of -\series bold - -\backslash -tag -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -tag -\series default - is described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:User-defined-Numbering" - -\end_inset - -. -\end_layout - -\end_inset - - -\series default - contains a box like in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Paragraph-Boxes" - -\end_inset - -, the formula cannot be referenced. -\end_layout - -\begin_layout Subsection -Subnumbering -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering ! subnumbering -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -With the help of the commands -\series bold - -\backslash -begin{subequations} -\series default - and -\series bold - -\backslash -end{subequations} -\series default - formulas can be subnumbered. - Both commands are inserted in TeX-mode. -\end_layout - -\begin_layout Standard -An example: -\begin_inset Formula -\begin{equation} -A=C-B\label{eq:a} -\end{equation} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -addtocounter{equation}{-1} -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -begin{subequations} -\end_layout - -\end_inset - - -\begin_inset VSpace -5mm -\end_inset - - -\begin_inset Formula -\begin{equation} -B=C-A\label{eq:b} -\end{equation} - -\end_inset - - -\begin_inset Formula -\begin{equation} -C=A+B\label{eq:c} -\end{equation} - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -end{subequations} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To create the example, the following is done: -\end_layout - -\begin_layout Enumerate -first formula is inserted -\end_layout - -\begin_layout Enumerate - -\series bold - -\backslash -addtocounter{equation}{-1} -\backslash -begin{subequations} -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -addtocounter -\end_layout - -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\series default -is inserted after the first formula -\end_layout - -\begin_layout Enumerate -second formula is inserted -\end_layout - -\begin_layout Enumerate -third formula is inserted -\end_layout - -\begin_layout Enumerate - -\series bold - -\backslash -end{subequations} -\series default - is inserted after the third formula -\end_layout - -\begin_layout Standard -Every formula between the commands -\series bold - -\backslash -begin -\series default - and -\series bold - -\backslash -end -\series default - is subnumbered as a, b, -\begin_inset Newline linebreak -\end_inset - -c, \SpecialChar \ldots{} - For multiline formulas every line will be subnumbered. - All subnumbered formulas are treated as -\emph on -one -\emph default - numbered formula. - But as every numbered formula increases the counter -\series bold -equation -\series default - by one, the command -\series bold - -\backslash -addtocounter -\series default - is needed to decrease it. - Otherwise the formulas -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:a" - -\end_inset - -, -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:b" - -\end_inset - -, -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:c" - -\end_inset - - would be numbered as -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:a" - -\end_inset - -, -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:d" - -\end_inset - -, -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:f" - -\end_inset - -. -\end_layout - -\begin_layout Standard -By inserting the commands in TeX-mode, a space is created between the first - two formulas. - To revert this -5 -\begin_inset space \thinspace{} -\end_inset - -mm vertical space is inserted after the command -\series bold - -\backslash -begin{subequations} -\series default -. - When the formula style -\series bold -Indented -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -formula styles see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - - -\end_layout - -\end_inset - - -\series default - is used, -7 -\begin_inset space \thinspace{} -\end_inset - -mm space is inserted instead. -\end_layout - -\begin_layout Standard -Here is an example for a multiline formula where the numbering was turned - off for the second line: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -begin{subequations} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{eqnarray} -A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\ - & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\ - & = & B^{2}-2BZ+Z^{2}\label{eq:f} -\end{eqnarray} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -end{subequations} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -User-defined Numbering -\begin_inset CommandInset label -LatexCommand label -name "sub:User-defined-Numbering" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering ! user-defined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering ! self-defined delimiters -\end_layout - -\end_inset - -With the standard numbering parentheses are set around the formula number. - To replace the parentheses for example by vertical bars, the following - line is added to the LaTeX-preamble: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -def -\backslash -tagform@#1{ -\backslash -maketag@@@{|#1|}} -\series default - -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -This macro is already declared in the LaTeX-preamble for testing. - To activate it, remove the percent sign at the beginning. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To use other characters, the vertical bars besides the -\series bold -#1 -\series default - are replaced by one ore more characters. - To get only the formula number the vertical bars are omitted. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -When there should be an expression of your choice instead of the consecutive - formula number in parentheses behind the formula, the command -\series bold - -\backslash -tag -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -tag -\end_layout - -\end_inset - - is used: -\begin_inset Formula -\begin{equation} -A+B=C\tag{something}\label{eq:tag} -\end{equation} - -\end_inset - -In this example the command -\series bold - -\backslash -tag -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -something -\series default - was inserted in the formula. -\end_layout - -\begin_layout Standard -When the command -\series bold - -\backslash -tag* -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -something -\series default - is inserted instead, the star prevents the parentheses around the expression: -\begin_inset Formula -\[ -A+B=C\tag*{something} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -To restart the formula numbering with new document parts or sections, the - following command is used: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -@addtoreset{equation}{part} -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - - ! -\backslash - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -addtoreset -\end_layout - -\end_inset - - -\begin_inset Newline newline -\end_inset - -resp. -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -@addtoreset{equation}{section} -\end_layout - -\begin_layout Standard -To be able to use these commands in TeX-mode, the -\begin_inset Quotes eld -\end_inset - -@ -\begin_inset Quotes erd -\end_inset - - character has to be made -\begin_inset Quotes eld -\end_inset - -active -\begin_inset Quotes erd -\end_inset - - for LaTeX using the command -\series bold - -\backslash -makeatletter. - -\series default - The command -\series bold - -\backslash -makeatother -\series default - reverts this. - So the command sequence in TeX-mode is: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -makeatletter -\begin_inset Newline newline -\end_inset - - -\backslash -@addtoreset{equation}{section} -\begin_inset Newline newline -\end_inset - - -\backslash -makeatother -\end_layout - -\begin_layout Standard -In the LaTeX-preamble -\series bold - -\backslash -makeatletter -\series default - and -\series bold - -\backslash -makeatother -\series default - can be omitted as they are automatically internally inserted by LyX. -\end_layout - -\begin_layout Standard -To revert -\series bold - -\backslash -@addtoreset -\series default -, the file -\series bold -remreset.sty -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout - -\series bold -remreset -\series default - is part of the LaTeX-package -\series bold -carlisle -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! carlisle -\end_layout - -\end_inset - - that is part of every LaTeX standard installation. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! remreset -\end_layout - -\end_inset - - has to be loaded in the LaTeX-preamble with the line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{remreset} -\end_layout - -\begin_layout Standard -Then the command -\series bold - -\backslash -@removefromreset -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - - ! -\backslash - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -@ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -" -\end_layout - -\end_inset - -removefromreset -\end_layout - -\end_inset - - can be used with the same scheme as -\series bold - -\backslash -@addtoreset -\series default -. -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - -Sometimes formulas should be numbered in the following form: -\end_layout - -\begin_layout Standard - -\family typewriter -(section number.formula number) -\end_layout - -\begin_layout Standard -The formula number should start with every section with -\begin_inset Quotes eld -\end_inset - -1 -\begin_inset Quotes erd -\end_inset - -. -\end_layout - -\begin_layout Standard -For this case there is the command -\series bold - -\backslash -numberwithin -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! N ! -\backslash -numberwithin -\end_layout - -\end_inset - -, which is used with the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -numberwithin{counter}{sectioning} -\end_layout - -\begin_layout Standard -Counter denotes what kind of numbering is affected, sectioning denotes what - number is before the dot. -\end_layout - -\begin_layout Standard -Thus in our case the following LaTeX-preamble or TeX code line is used: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -numberwithin{equation}{section} -\end_layout - -\begin_layout Standard -This is the result: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -numberwithin{equation}{section} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{equation} -A+B=C -\end{equation} - -\end_inset - - -\end_layout - -\begin_layout Standard -To number e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -tables so that the number of the part is the sectioning, -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -numberwithin{table}{part} -\series default - is used. -\end_layout - -\begin_layout Standard -To go back to the standard numbering or to prevent this kind of numbering - when it is defined by the document class, the following command is inserted - as TeX code or to the LaTeX-preamble: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -arabic{equation}} -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -arabic -\end_layout - -\end_inset - - -\series default - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -arabic{equation}} -\end_layout - -\end_inset - - -\series bold - -\begin_inset Newline newline -\end_inset - - -\series default -or -\series bold - -\begin_inset Newline newline -\end_inset - - -\backslash -renewcommand{ -\backslash -thetable}{ -\backslash -arabic{table}} -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -numberwithin -\series default - uses internally the command -\series bold - -\backslash -@addtoreset -\series default -, described above, that also needs to be reverted. -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -makeatletter -\end_layout - -\begin_layout Plain Layout - - -\backslash -@removefromreset{equation}{section} -\end_layout - -\begin_layout Plain Layout - - -\backslash -makeatother -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Numbering with Roman Numbers and Letters -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering ! with letters -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula numbering ! with Roman numbers -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Formulas can also be numbered with Roman numbers and Latin letters. - To number for example with small Roman numbers, the command -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -roman{equation}} -\end_layout - -\begin_layout Standard -is inserted before the formula in TeX-mode. - -\series bold - -\backslash -renewcommand -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -renewcommand -\end_layout - -\end_inset - - redefines the predefined command -\series bold - -\backslash -theequation -\series default - to the command -\series bold - -\backslash -roman{equation} -\series default -. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -The command -\series bold - -\backslash -renewcommand -\series default - has the same scheme like the command -\series bold - -\backslash -newcommand -\series default - that is described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:The-Command-newcommand" - -\end_inset - -. -\end_layout - -\end_inset - - -\series bold -equation -\series default - is the formula counter. - When the command -\series bold - -\backslash -the -\series default - is used as prefix for a counter, the value of the counter is output as - Arabic number. - When a formula is numbered, LaTeX sets internally the command -\series bold - -\backslash -theequation -\series default - behind the formula. - -\series bold - -\backslash -roman{equation} -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -roman -\end_layout - -\end_inset - - -\series default - outputs the counter as small Roman number. -\end_layout - -\begin_layout Standard -All formulas behind the command -\series bold - -\backslash -renew -\series default -c -\series bold -ommand -\series default - are now numbered Roman. - To switch to numbering with big Roman numbers, the command is inserted - again, but -\series bold - -\backslash -roman -\series default - is replaced by -\series bold - -\backslash -Roman -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! R ! -\backslash -roman@ -\backslash -Roman -\end_layout - -\end_inset - -. - To -\begin_inset Quotes eld -\end_inset - -number -\begin_inset Quotes erd -\end_inset - - with small Latin letters there is the command -\series bold - -\backslash -alph -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -alph -\end_layout - -\end_inset - -, for big ones there is the command -\series bold - -\backslash -Alph -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -alph@ -\backslash -Alph -\end_layout - -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -\color none -Note: -\series default - Only maximal 26 -\begin_inset space ~ -\end_inset - -formulas can be numbered with Latin letters in one document. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -roman{equation}} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Formula -\begin{equation} -A=\textrm{small roman} -\end{equation} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -Roman{equation}} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{equation} -B=\textrm{big Roman}\label{eq:Rom} -\end{equation} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -alph{equation}} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{equation} -C=\textrm{small Latin} -\end{equation} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -Alph{equation}} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{equation} -D=\textrm{big Latin}\label{eq:Lat} -\end{equation} - -\end_inset - - -\end_layout - -\begin_layout Standard -To switch back to the default numbering, insert the command: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -arabic{equation}} -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! A ! -\backslash -arabic -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -theequation}{ -\backslash -arabic{equation}} -\end_layout - -\end_inset - - -\begin_inset Formula -\begin{equation} -E=\textrm{Arabic} -\end{equation} - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -As you see, formulas are numbered serially independent from the numbering - style. - When then numbering should start with -\begin_inset Quotes eld -\end_inset - -1 -\begin_inset Quotes erd -\end_inset - - when the style is changed, new equation counters have to be defined. - A description about this can be found in the file -\begin_inset CommandInset href -LatexCommand href -name "Formula-numbering.lyx" -target "run:Formula-numbering.lyx" - -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -Chemical Symbols and Equations -\begin_inset CommandInset label -LatexCommand label -name "sub:Chemical-Symbols-and" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Chemical characters ! Symbols -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Chemical equations -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Symbols ! chemical -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -An example text from chemistry: -\end_layout - -\begin_layout Quote -The -\begin_inset Formula $\mathrm{SO_{4}^{2-}}$ -\end_inset - --ion reacts with two -\begin_inset Formula $\mathrm{Na^{+}}$ -\end_inset - --ions to sodium sulfate -\begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$ -\end_inset - -. - The chemical equation for this is: -\begin_inset Formula -\begin{equation} -\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction} -\end{equation} - -\end_inset - - -\end_layout - -\begin_layout Standard -This chemical equation can directly be created as formula. - To avoid that the symbols appear italic, everything is highlighted and - changed by the shortcut -\begin_inset Info -type "shortcut" -arg "font-roman" -\end_inset - - to the upright font style. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -font styles -\series bold - -\series default -see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Font-Styles" - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -A more convenient way to typeset chemical formulas is to use the command - -\series bold - -\backslash -ce -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -ce -\end_layout - -\end_inset - - that is available when the LaTeX-package -\series bold -mhchem -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! mhchem -\end_layout - -\end_inset - - is installed. - After inserting -\series bold - -\backslash -ce -\series default - to a formula a new blue box appears where chemical formulas can be inserted - in an intuitive way. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -H2CO3 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -SO4^2- -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -(NH4)2S -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -KCr(SO4)2.12H2O -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A-B -\backslash -dbond -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C -\backslash -tbond -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -D -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -^227 -\begin_inset Formula $\downarrow$ -\end_inset - -_90 -\begin_inset Formula $\to$ -\end_inset - -Th+ -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -CO2 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -<=> -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2CO -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -CO2 -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -C -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -->[ -\backslash -alpha][ -\backslash -beta] -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2CO} -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -\color none -Note: -\series default - Inserting a formula to a -\series bold - -\backslash -ce -\series default - box will lead to LaTeX errors due to a LyX bug. -\color inherit - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -\begin_inset CommandInset href -LatexCommand href -name "LyX-bug #8566" -target "http://www.lyx.org/trac/ticket/8566" - -\end_inset - - -\end_layout - -\end_inset - - -\color none - In this case TeX code has to be used like for -\series bold - -\backslash -ce{$ -\backslash -mu -\backslash -hyphen$Cl} -\series default -: -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -ce{$ -\backslash -mu -\backslash -hyphen$Cl} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -\color none -Note: -\series default - It is not possible in LyX to use the character ^ to get an up-arrow as - described in the -\series bold -mhchem -\series default - manual. - One instead uses a negative thin space followed by the command -\series bold - -\backslash -uparrow -\series default -: -\begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$ -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Using -\series bold - -\backslash -ce -\series default - the command for equation -\begin_inset space ~ -\end_inset - - -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:chem-reaction" - -\end_inset - - is: -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -ce -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -2Na+ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -+ -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -SO4^2- -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - --> -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -Na2SO4 -\end_layout - -\begin_layout Standard -To create multiline chemical equations first a multiline formula is created - as described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Multiline-Formulas" - -\end_inset - -. - Afterwards the command -\series bold - -\backslash -ce -\series default - is used in every small blue box of the formula. - -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:TEOS-reaction-1" - -\end_inset - - and -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:TEOS-reaction-2" - -\end_inset - - are an example of a multi-stage chemical reaction where every equation - has its own number. -\begin_inset Formula -\begin{eqnarray} -\ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\ -\ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2} -\end{eqnarray} - -\end_inset - - -\end_layout - -\begin_layout Standard -Besides -\series bold - -\backslash -ce -\series default - the -\series bold -mhchem -\series default - package provides the command -\series bold - -\backslash -cf -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! C ! -\backslash -cf -\end_layout - -\end_inset - - that has to be used for special cases. - For more information about -\series bold - -\backslash -cf -\series default - and more examples have a look at the documentation of -\series bold -mhchem -\series default -, -\begin_inset CommandInset citation -LatexCommand cite -key "mhchem" - -\end_inset - -. -\end_layout - -\begin_layout Section -Diagrams -\end_layout - -\begin_layout Standard -LyX supports two types of commutative diagrams: -\series bold -amscd -\series default - and -\series bold -xymatrix -\series default - that are explained in the following. -\end_layout - -\begin_layout Subsection -Amscd Diagrams -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Diagrams ! amscd -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Diagrams of this type visualize relations by vertical and horizontal lines - or arrows: -\begin_inset Formula -\[ -\begin{CD}A@>>>B@>>>C\\ -@AAA@.@VVV\\ -F@<<>> -\series default - a right arrow and -\series bold -@= -\series default - a long equal sign -\end_layout - -\begin_layout Itemize - -\series bold -@AAA -\series default - creates an up arrow, -\series bold -@VVV -\series default - a down arrow and -\series bold -@| -\series default - a vertical equal sign -\end_layout - -\begin_layout Itemize - -\series bold -@. - -\series default - is a placeholder for non-existent relations -\end_layout - -\begin_layout Standard -All arrows can be labeled as follows: -\end_layout - -\begin_layout Itemize -If text inserted between the first and second < or >, resp., it is placed - above the arrow. - When it is inserted between the second and third one, it appears under - the arrow. -\end_layout - -\begin_layout Itemize -When text for vertical arrows is inserted between the first and second A - or V, resp., it is placed left beside the arrow. - When it is inserted between the second and third one, it appears right - beside the arrow. - If the text contains an A or V, these letters must be set into a TeX-brace. -\end_layout - -\begin_layout Standard -As example a diagram with all possible relations: -\end_layout - -\begin_layout Standard -\begin_inset Formula -\[ -\begin{CD}A@>j>>B@>>k>C@=F\\ -@AmAA@.@VV{V}V@|\\ -D@<k>>F@=C -\end{CD} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -The command for this is: -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -CD -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A@>j>>B@>>k>C@=F Ctrl+Return -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\series bold - -\backslash -CD -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\end_layout - -\end_inset - -@AmAA@.@VV -\backslash -{V -\series default - -\begin_inset Formula $\to$ -\end_inset - - -\series bold -V@| Ctrl+Return -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\series bold - -\backslash -CD -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - - -\end_layout - -\end_inset - -D@<k>>F@=C -\end_layout - -\begin_layout Subsection -Xymatrix Diagrams -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Diagrams ! xymatrix -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To be able to use xymatrices, the LaTeX-package -\series bold -xypic -\series default - must be installed. - A xymatrix is created by inserting the command -\series bold - -\backslash -xymatrix -\series default - in a formula. - Then you are able to add new matrix columns and rows like for normal matrices, - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Matrices" - -\end_inset - -. -\end_layout - -\begin_layout Standard -In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows, - and much more. - All possibilities to create commutative diagrams and decorations are explained - in detail in the -\emph on -XY-pic manual -\emph default - that you find in the menu -\family sans -Help\SpecialChar \menuseparator -Specific -\begin_inset space ~ -\end_inset - -Manuals -\family default -. -\end_layout - -\begin_layout Subsection - -\noun on -Feynman -\noun default - Diagrams -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Diagrams ! Feynman -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To be able to use -\noun on -Feynman -\noun default --diagrams, the LaTeX-package -\series bold -feyn -\series default - must be installed. - A -\noun on -Feynman -\noun default --diagram is created by inserting the command -\series bold - -\backslash -Diagram -\series default - in a formula. - Then you are able to add new matrix columns and rows like for normal matrices, - see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Matrices" - -\end_inset - -. -\end_layout - -\begin_layout Standard -Examples how to create -\noun on -Feynman- -\noun default -diagrams in LyX is given in the -\emph on -Feynman-diagram manual -\emph default - that you find in the menu -\family sans -Help\SpecialChar \menuseparator -Specific -\begin_inset space ~ -\end_inset - -Manuals -\family default -. -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -User-defined Commands -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -User-defined commands -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - The names of user-defined commands and macros may only consist of Latin - letters. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -The Command -\backslash -newcommand -\begin_inset CommandInset label -LatexCommand label -name "sub:The-Command-newcommand" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -User-defined commands ! -\backslash -newcommand -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! N ! -\backslash -newcommand -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Many LaTeX-commands are too long to be used frequently. - But it is possible to define with the command -\series bold - -\backslash -newcommand -\series default - new shorter commands. -\end_layout - -\begin_layout Standard -The command scheme of -\series bold - -\backslash -newcommand -\series default - is: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -newcommand{new command name}[number of arguments][optional -\series default - -\series bold -value] -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\series bold - -\backslash -newcommand -\end_layout - -\end_inset - -{command definition} -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout - -\series bold -Note: -\series default - Assure that the name of the new command is not already used in your document - or by LaTeX-packages that you use. - When you for example define the command -\series bold - -\backslash -le -\series default - for -\series bold - -\backslash -Leftarrow -\series default -, you get an error message because -\series bold - -\backslash -le -\series default - is already defined as command for -\begin_inset Quotes eld -\end_inset - - -\begin_inset Formula $\le$ -\end_inset - - -\begin_inset Quotes erd -\end_inset - -. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The number of arguments is an integer in the range 0 -\begin_inset space \thinspace{} -\end_inset - -- -\begin_inset space \thinspace{} -\end_inset - -9 and specifies how many arguments the new command should have. - With the optional value a value for an optional argument can be predefined. - When this is done, the -\emph on -first -\emph default - -\emph on -a -\emph default -rgument of the new command is automatically an optional one. -\end_layout - -\begin_layout Standard -Here are some examples: -\end_layout - -\begin_layout Itemize -To define the command -\series bold - -\backslash -gr -\series default - for -\series bold - -\backslash -Longrightarrow -\series default -, the LaTeX-preamble line is: -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -newcommand{ -\backslash -gr}{ -\backslash -Longrightarrow} -\end_layout - -\begin_layout Itemize -To define the command -\series bold - -\backslash -us -\series default - for -\series bold - -\backslash -underline -\series default -, the argument (that should be underlined) must be taken into account. - For this the preamble line is: -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -newcommand{ -\backslash -us}[1]{ -\backslash -underline{#1}} -\series default - -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - -The character -\series bold -# -\series default - acts as argument placeholder, the -\series bold -1 -\series default - behind it denotes that it is the placeholder for the first argument. -\end_layout - -\begin_layout Itemize -For -\series bold - -\backslash -framebox -\series default - one can e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -define the command -\series bold - -\backslash -fb -\series default -: -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -newcommand{ -\backslash -fb}[3]{ -\backslash -framebox#1#2{$#3$}} -\series default - -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - -The two Dollar signs creates the extra formula needed for -\series bold - -\backslash -framebox -\series default -, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Boxes-with-Frame" - -\end_inset - -. -\end_layout - -\begin_layout Itemize -To create a new command for -\series bold - -\backslash -fcolorbox -\series default - where the color for the box need not be specified, the argument for the - color is defined optional: -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -newcommand{ -\backslash -cb}[3][white]{ -\backslash -fcolorbox{#2}{#1}{$#3$}} -\series default - -\begin_inset VSpace medskip -\end_inset - - -\begin_inset Newline newline -\end_inset - -When the color is not specified when using -\series bold - -\backslash -cb -\series default -, the predefined color -\series bold -white -\series default - will be used. -\end_layout - -\begin_layout Standard -A test of the new defined commands: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -A -\backslash -gr -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $A\gr B$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -us{ABcd -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -fb{[2cm] -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cb{red -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cb[green] -\backslash -{red -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Subsection -Math Macros -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -User-defined commands! Math macros -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Macros -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -User-defined commands are especially convenient for complex expressions. - When you are for example dealing with a document that has quadratic equations, - the same solution type occurs several times. - The general form of a quadratic equation is -\begin_inset Formula -\[ -0=\lambda^{2}+p\lambda+q -\] - -\end_inset - -The general form of the solution is -\begin_inset Formula -\[ -\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -To define a command for the solution formula where only the three parameters - -\begin_inset Formula $\lambda$ -\end_inset - -, -\begin_inset Formula $p$ -\end_inset - - and -\begin_inset Formula $q$ -\end_inset - - need to be specified and the index of -\begin_inset Formula $\lambda$ -\end_inset - - can be given optionally, the LaTeX-preamble line is -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -newcommand{ -\backslash -qG}[4][1, -\backslash -,2]{#2_{#1}=- -\backslash -frac{#3}{2} -\backslash -pm -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\series bold - -\backslash -newcommand -\end_layout - -\end_inset - - -\backslash -sqrt{ -\backslash -frac{#3^{2}}{4}-#4}} -\end_layout - -\begin_layout Standard -To create with this the solution formula, the command -\begin_inset Newline newline -\end_inset - - -\series bold - -\backslash -qG{ -\backslash -lambda -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{p -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{q -\series default - is inserted to a formula -\series bold -. -\end_layout - -\begin_layout Standard -The definition of the new command is unintuitive because one has to know - the schemes of all used LaTeX commands, e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -that a fraction is inserted in LaTeX as -\series bold - -\backslash -frac{numerator}{denominator} -\series default -. - Furthermore one can easily forget a brace in the definition and cannot - see in LyX what the new command is doing. - To avoid these problems LyX offers the possibility to use math macros instead - of the command -\series bold - -\backslash -newcommand -\series default -. -\end_layout - -\begin_layout Standard -A math macro is created by using the menu -\family sans -Insert\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\family default - or the toolbar button -\begin_inset Graphics - filename ../images/math-macro_newmacroname_newcommand.png - scale 85 - -\end_inset - -. - The math macro toolbar appears together with the following box where the - macro is defined: -\begin_inset Newline newline -\end_inset - - -\begin_inset space \hspace*{\fill} -\end_inset - - -\begin_inset Graphics - filename clipart/macrobox.png - -\end_inset - - -\begin_inset space \hspace*{\fill} -\end_inset - - -\begin_inset Newline newline -\end_inset - - -\begin_inset FormulaMacro -\newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}} -\end_inset - - -\backslash -newmacroname is the default name of the macro that should be changed to - something sensible. - The wanted formula is inserted in the first blue box. - An argument placeholder is inserted with the command -\series bold - -\backslash -#argumentnumber -\series default -, e. -\begin_inset space \thinspace{} -\end_inset - -g -\begin_inset space \space{} -\end_inset - - -\series bold - -\backslash -#1 -\series default - or by using the macro toolbar button -\begin_inset Graphics - filename ../images/math-macro-add-param.png - scale 85 - -\end_inset - -. - Argument placeholders are displayed red. - A maximum of 9 -\begin_inset space ~ -\end_inset - -arguments are possible. - Optional arguments are created with the toolbar button -\begin_inset Graphics - filename ../images/math-macro-add-optional-param.png - scale 85 - -\end_inset - -. - The first non-optional argument can be transformed to an optional one with - the toolbar button -\begin_inset Graphics - filename ../images/math-macro-make-optional.png - scale 85 - -\end_inset - -. - In the second blue box the appearance of the macro in LyX can be defined. - Normally you want to see it as it is defined, so the box is kept empty. - But when you have created a macro that needs lot of space on the screen, - you can insert in the box for example -\begin_inset Newline newline -\end_inset - - -\series bold -qG: -\backslash -#1 -\series default - -\series bold -, -\series default - -\series bold - -\backslash -#2 -\series default - -\series bold -, -\series default - -\series bold - -\backslash -#3, -\backslash -#4 -\begin_inset Newline newline -\end_inset - - -\series default -For the macro only the arguments with the macro name in front of them will - then be displayed in LyX, leading to a better overview. - The formula appears in the output as defined in the first box. -\begin_inset Newline newline -\end_inset - -The appearance of macros in formulas can furthermore be changed for single - macros by setting the cursor in the macro and using the menu -\family sans -View\SpecialChar \menuseparator -(Un)fold -\begin_inset space ~ -\end_inset - -Math -\begin_inset space ~ -\end_inset - -Macro -\family default -. -\end_layout - -\begin_layout Standard -To use a macro, the macro name is inserted as command to a formula, in our - case -\series bold - -\backslash -qG -\series default -. - Our macro looks in LyX like this: -\begin_inset Newline newline -\end_inset - - -\begin_inset space \hspace*{\fill} -\end_inset - - -\begin_inset Graphics - filename clipart/macrouse.png - -\end_inset - - -\begin_inset space \hspace*{\fill} -\end_inset - - -\begin_inset Newline newline -\end_inset - -Here is our macro example with the arguments -\begin_inset Formula $x$ -\end_inset - -, -\begin_inset Formula $\ln(x)$ -\end_inset - - and -\begin_inset Formula $B$ -\end_inset - -: -\end_layout - -\begin_layout Standard -\begin_inset Formula -\[ -\qG x{\ln(x)}B -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -LyX offers in the menu -\family sans -Tools\SpecialChar \menuseparator -Preferences\SpecialChar \menuseparator -Editing\SpecialChar \menuseparator -Control -\family default - different styles to edit macros. - To find the style that suits you the most, choose a style and set the cursor - in a macro formula to see the difference. -\end_layout - -\begin_layout Standard -A math macro is transformed internally to a -\series bold - -\backslash -newcommand -\series default - command when exporting the document. - The created -\series bold - -\backslash -newcommand -\series default - command is not placed in the LaTeX-preamble, therefore macros can only - be used in formulas that are in the document below the macro definition - box. -\end_layout - -\begin_layout Standard -Math macros can also be directly created from a -\series bold - -\backslash -newcommand -\series default - command. - When writing for example the command -\series bold - -\begin_inset Newline newline -\end_inset - - -\backslash -newcommand{ -\backslash -larrow}[2]{ -\backslash -xleftarrow[#2]{#1}} -\begin_inset Newline newline -\end_inset - - -\series default -in LyX as normal text, highlighting it completely and using then the shortcut - -\family sans -Ctrl+M -\family default -, the command will be transformed to a math macro. - Using this method you need to be careful that the -\series bold - -\backslash -newcommand -\series default - command is typed correctly, otherwise you get a faulty macro leading to - LaTeX errors. -\end_layout - -\begin_layout Standard -Math macros currently have the problem that further formulas in macro definition -s are handled wrongly. - Therefore the example -\series bold - -\backslash -fb -\series default - from -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:The-Command-newcommand" - -\end_inset - - cannot be created as macro. -\end_layout - -\begin_layout Standard -When the cursor is in a macro definition box, you will see the macro toolbar - in LyX: -\end_layout - -\begin_layout Standard -\begin_inset VSpace defskip -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Graphics - filename clipart/MacroToolbar.png - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Macros ! Toolbar -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset VSpace defskip -\end_inset - - -\end_layout - -\begin_layout Standard -The macro toolbar contains from left to right the following buttons: -\end_layout - -\begin_layout Standard -\begin_inset VSpace defskip -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-remove-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Remove Last Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-add-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Append Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-make-optional.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Make First Non-Optional into -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator - -\end_layout - -\end_inset - -Optional Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-make-nonoptional.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Make Last Optional into -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator - -\end_layout - -\end_inset - -Non-Optional Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-remove-optional-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Remove Optional Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-add-optional-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Insert Optional Argument -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-remove-greedy-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Remove Last Argument -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator - -\end_layout - -\end_inset - -Spitting Out To The Right -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-append-greedy-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Append Argument -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator - -\end_layout - -\end_inset - -Eating From The Right -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Graphics - filename ../images/math-macro-add-greedy-optional-param.png - rotateOrigin center - -\end_inset - - -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator -Append Optional Argument -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Macro -\begin_inset space ~ -\end_inset - -Definition\SpecialChar \menuseparator - -\end_layout - -\end_inset - -Eating From The Right -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Section -Computer Algebra Systems -\end_layout - -\begin_layout Standard -LyX offers the exchange between mathematical expressions written in LyX's - math editor and external applications or user defined scripts. - Currently supported applications are -\family sans -Maple -\family default -, -\family sans -Mathematica -\family default -, -\family sans -Maxima -\family default - and -\family sans -Octave -\family default -. - Note that the set of supported mathematical constructs is limited only - to very simple cases. -\end_layout - -\begin_layout Subsection -Usage -\end_layout - -\begin_layout Standard -Write some expression in a formula, go to the -\family sans -Edit\SpecialChar \menuseparator -Math\SpecialChar \menuseparator -Use Computer Algebra System -\family default - menu and choose the application you have installed on the computer. - After that the result of computation should show on the right side of the - expression together with the -\begin_inset Quotes eld -\end_inset - -= -\begin_inset Quotes erd -\end_inset - - operator. -\end_layout - -\begin_layout Standard -Here are few simple examples (with results from -\family typewriter -Maxima -\family default -) to show what kind of computations can be performed: -\end_layout - -\begin_layout Itemize -\begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$ -\end_inset - - -\end_layout - -\begin_layout Itemize -\begin_inset Formula $\frac{37.0}{3}=12.33333333333333$ -\end_inset - - -\end_layout - -\begin_layout Itemize -\begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$ -\end_inset - - -\end_layout - -\begin_layout Itemize -\begin_inset Formula $\det\left[\begin{array}{ccc} -1 & 6 & 7\\ -2 & 5 & 8\\ -3 & 4 & 17 -\end{array}\right]=-56$ -\end_inset - - -\end_layout - -\begin_layout Itemize -\begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$ -\end_inset - - -\end_layout - -\begin_layout Subsection -Keyboard shortcut -\end_layout - -\begin_layout Standard -Currently there is no keyboard shortcut for calling the algebra applications. - One can easily bind a shortcut to the -\family sans -math-extern -\family default - LyX function (see the -\family sans -\emph on -LyX Functions -\family default -\emph default - manual). - One could e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -bind the -\family sans -Return -\family default - key inside the math editor. - To bind it to -\family typewriter -Maxima -\family default - one would use this shortcut definition command: -\end_layout - -\begin_layout Standard - -\series bold -command-alternatives break-paragraph;math-extern maxima -\end_layout - -\begin_layout Section -Miscellaneous -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Miscellaneous -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Negative Numbers -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Numbers ! negative -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Negative numbers often look ugly in formulas because the minus sign before - the number is set with the same length as the minus operator sign. - When writing the negative number in normal text, the minus sign appears - correctly. -\end_layout - -\begin_layout Standard -Thus, the problem disappears when converting the minus sign to mathematical - text. -\end_layout - -\begin_layout Standard -An example to visualize the problem: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -normal text: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -x = -2 -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -formula: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $x=-2$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -solution: -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $x=\textrm{-}2$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Subsection -Comma as decimal Separator -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Comma -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -In LaTeX a comma inside a formula is used, according to the English convention, - as number group separator. - So there will be space added behind all commas in formulas. -\end_layout - -\begin_layout Standard -To avoid this, the comma is highlighted and changed to mathematical text - (shortcut -\begin_inset Info -type "shortcut" -arg "math-mode" -\end_inset - -). -\end_layout - -\begin_layout Standard -To use all formula commas in the document as decimal separator, the file - -\series bold -icomma.sty -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout - -\series bold -icomma -\series default - is part of the LaTeX-package -\series bold -was -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! was -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! icomma -\end_layout - -\end_inset - - is loaded with the LaTeX-preamble line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{icomma} -\end_layout - -\begin_layout Subsection -Physical Vectors -\begin_inset CommandInset label -LatexCommand label -name "sub:Physical-Vectors" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Vectors ! physical -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Predefined vectors are offered by the LaTeX-package -\series bold -braket -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! braket -\end_layout - -\end_inset - - that is loaded with the LaTeX-preamble line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{braket} -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -ifbraket -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following table will only be displayed when the LaTeX-package -\series bold -braket -\series default - is installed. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The following commands are defined: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Bra{ -\backslash -psi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Bra{\psi}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Ket{ -\backslash -psi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Ket{\psi}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Braket{ -\backslash -psi| -\backslash -phi -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\Braket{\psi|\phi}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -The command -\series bold - -\backslash -Braket -\series default - assures that all vertical bars are set in the size of the surrounding brackets: -\begin_inset Formula -\[ -\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}} -\] - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -else -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following will be displayed when the LaTeX-package -\series bold -braket -\series default - is not installed: -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -You need to install the LaTeX-package -\series bold -braket -\series default - to see the rest of this subsection in the output. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fi -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -The effect of -\series bold - -\backslash -Braket -\series default - can also be achieved using the command -\series bold - -\backslash -middle -\series default -, that is described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Automatic-Bracket-Size" - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Self-defined Fractions -\begin_inset CommandInset label -LatexCommand label -name "sub:Self-defined-Fractions" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Fractions ! self-defined -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To define custom commands for fractions, the command -\series bold - -\backslash -genfrac -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! G ! -\backslash -genfrac -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - is used in the following scheme: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -genfrac{left -\series default - -\series bold -bracket}{right -\series default - -\series bold -bracket}{fraction bar thickness}{style} -\begin_inset Newline newline -\end_inset - - -\begin_inset Phantom HPhantom -status open - -\begin_layout Plain Layout - -\series bold - -\backslash -genfrac -\end_layout - -\end_inset - -{numerator}{denominator} -\end_layout - -\begin_layout Standard -The style is a number in the range of 0 -\begin_inset space \thinspace{} -\end_inset - -- -\begin_inset space \thinspace{} -\end_inset - -3. -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Number -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Style (Size) -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -0 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -display style formula -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -1 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -inline formula -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -2 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -small -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -3 -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -tiny -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard -When no style is given, the size is adjusted to the surrounding environment - like for the command -\series bold - -\backslash -frac -\series default -. -\end_layout - -\begin_layout Standard -When no fraction bar thickness is given, the predefined value of 0.4 -\begin_inset space \thinspace{} -\end_inset - -pt will be used. -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -For example, the commands -\series bold - -\backslash -dfrac -\series default - and -\series bold - -\backslash -tbinom -\series default - from -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Fractions" - -\end_inset - - are defined with the commands -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -newcommand{ -\backslash -dfrac}[2]{ -\backslash -genfrac{}{}{}{0}{#1}{#2}} -\end_layout - -\begin_layout Standard -and -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -newcommand{ -\backslash -tbinom}[2]{ -\backslash -genfrac{(}{)}{0pt}{1}{#1}{#2}} -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -To define a fraction where the fraction bar thickness can be given as optional - argument, the following line is inserted to the LaTeX-preamble: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -newcommand{ -\backslash -fracS}[3][]{ -\backslash -genfrac{}{}{#1}{}{#2}{#3}} -\end_layout - -\begin_layout Standard -A test: -\begin_inset Formula -\begin{align*} -\text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\ -\text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B} -\end{align*} - -\end_inset - -As one can see, the distance of the numerator and the denominator to the - fraction bar is round about three times the bar thickness. -\end_layout - -\begin_layout Subsection -Canceled Formulas -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! canceled -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To cancel formulas or formula parts, the LaTeX-package -\series bold -cancel -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! cancel -\end_layout - -\end_inset - - has to be loaded with the LaTeX-preamble line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{cancel} -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -ifcancel -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following table will only be displayed when the LaTeX-package -\series bold -cancel -\series default - is installed. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -There are four ways to cancel formulas: -\end_layout - -\begin_layout Standard -\align center -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Result -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout -The space and -\series bold - -\backslash -raisebox -\series default - are used here as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cancel{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -bcancel{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -xcancel{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -cancelto{1 -\begin_inset Formula $\to$ -\end_inset - - -\backslash -{ -\backslash -int -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -A=B -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -cancelto -\series default - is especially suitable to visualize the reduction of fractions within formulas: -\begin_inset Formula -\[ -\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -To change the size of -\series bold - -\backslash -cancelto -\series default -'s -\begin_inset Quotes eld -\end_inset - -subscript -\begin_inset Quotes erd -\end_inset - - value one can load the package -\series bold -cancel -\series default - with either the option -\series bold -samesize -\series default - which leads to the same size as for the canceled value or with the option - -\series bold -Smaller -\series default - which makes is it a bit smaller than the size one gets without using a - package option. - In this document -\series bold -cancel -\series default - was loaded with this line: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage[samesize]{cancel} -\end_layout - -\begin_layout Standard -To color the cancellation bar one adds this command as TeX code: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -renewcommand{ -\backslash -CancelColor}{ -\backslash -color{red}} -\end_layout - -\begin_layout Standard - -\series bold -red -\series default - can be replaced by a color of your choice. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -CancelColor}{ -\backslash -color{red}} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Formula -\[ -\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -renewcommand{ -\backslash -CancelColor}{ -\backslash -color{black}} -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -reset the color -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -For further customizations, see the documentation of the package -\series bold -cancel -\series default -, -\begin_inset CommandInset citation -LatexCommand cite -key "cancel" - -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -else -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following will be displayed when the LaTeX-package -\series bold -cancel -\series default - is not installed: -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -You need to install the LaTeX-package -\series bold -cancel -\series default - to see the rest of this subsection in the output. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fi -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Subsection -Formulas in Section Headings -\begin_inset CommandInset label -LatexCommand label -name "sub:Formulas-in-Section" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! in section headings -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -When formulas are used in section headings, the following has to be taken - into account: -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout -When -\series bold -hyperref -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! hyperref -\end_layout - -\end_inset - - support is enabled in the document settings dialog under -\family sans -PDF -\begin_inset space ~ -\end_inset - -Properties -\family default -, PDF-bookmarks are created for every section heading in the table of contents. - If a section heading contains formulas, they are incorrectly displayed - in the bookmark text, because formulas in bookmarks infringe the PDF convention -s. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Both problems can be solved by inserting at the end of the section heading - a short title with the menu -\family sans -Insert\SpecialChar \menuseparator -Short -\begin_inset space ~ -\end_inset - -Title -\family default -. - Short titles are used as alternative for multiline section headings to - keep the table of contents clearly arranged. - Only the short title appears in the table of contents and therefore also - in the PDF-bookmark. -\end_layout - -\begin_layout Standard -When formulas should be used in the table of contents but -\series bold -hyperref -\series default - is used, one can use the following command in TeX-mode: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -texorpdfstring{part}{alternative} -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! T ! -\backslash -texorpdfstring -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Part is the part of the heading that shouldn't appear in the PDF-bookmark. - This can be characters, formulas, footnotes, but also cross-references. - The alternative is used instead of the part for the bookmark. -\end_layout - -\begin_layout Standard -Here are two example headings: -\begin_inset VSpace -3mm -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -boldmath -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsubsection -Heading without formula in table of contents -\begin_inset Formula $\sqrt{-1}=\mathrm{i}$ -\end_inset - - -\begin_inset Argument -status collapsed - -\begin_layout Plain Layout -Heading without formula in table of contents -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsubsection -Heading with formula in table of contents -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -texorpdfstring{ -\end_layout - -\end_inset - - -\begin_inset Formula $\sqrt{-1}=\mathrm{i}$ -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -}{} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -unboldmath -\end_layout - -\end_inset - -In the first heading a short title was used, in the second one -\series bold - -\backslash -texorpdfstring -\series default -. -\end_layout - -\begin_layout Standard -To get the same formatting as for the other headings, the complete heading - was set into a -\series bold -boldmath -\series default - environment -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Bold-Formulas" - -\end_inset - - -\end_layout - -\end_inset - -. -\end_layout - -\begin_layout Subsection -Formulas in multi-column Text -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! in multi-column text -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Formulas in multi-column text are often too wide to fit into a column and - thus need to be set over the whole page width. - This is done by using the LaTeX-package -\series bold -multicol -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout - -\series bold -multicol -\series default - is part of every LaTeX standard installation. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! multicol -\end_layout - -\end_inset - -, that is loaded with the LaTeX-preamble line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{multicol} -\end_layout - -\begin_layout Standard -\begin_inset Note Greyedout -status open - -\begin_layout Plain Layout -Note that in this case the setting -\family sans -Two-column -\begin_inset space ~ -\end_inset - -document -\family default - in the menu -\family sans -Document\SpecialChar \menuseparator -Settings -\family default - under -\family sans -Text -\begin_inset space ~ -\end_inset - -Layout -\family default -\emph on - -\emph default -must -\emph on -not -\emph default - be selected. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Before the multi-column text the command -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -begin{multicols}{column number} -\end_layout - -\begin_layout Standard -is written in TeX-mode. - The column number is a number in the range of 2 -\begin_inset space \thinspace{} -\end_inset - -- -\begin_inset space \thinspace{} -\end_inset - -10. - Before the formula the multi-column text is ended by inserting the command -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -end{multicols} -\end_layout - -\begin_layout Standard -in TeX-mode. -\end_layout - -\begin_layout Standard -Due to the command some space is automatically added before the formula. - To revert this, -6 -\begin_inset space \thinspace{} -\end_inset - -mm vertical space is inserted before the formula. - When the formula style -\series bold -Indented -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -formula styles see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - - -\end_layout - -\end_inset - - -\series default - is used, -9 -\begin_inset space \thinspace{} -\end_inset - -mm space is inserted instead. -\end_layout - -\begin_layout Standard -As example a multi-column text with a displayed formula: -\end_layout - -\begin_layout Standard - -\lang german -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -begin{multicols}{2} -\end_layout - -\end_inset - -Das Spektrum wird fouriertransformiert. - Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk -, Lösungsmittel) zu trennen. - Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns - nun das Aussehen des Ausgangssignals. - Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man - über alle Phasen integrieren muss. - Sei nun -\begin_inset Formula $S$ -\end_inset - - unser normiertes Ausgangssignal und -\begin_inset Formula $P$ -\end_inset - - die Phasenverteilungsfunktion, so ergibt sich die Beziehung -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -end{multicols} -\end_layout - -\end_inset - - -\begin_inset VSpace -6mm -\end_inset - - -\begin_inset Formula -\begin{equation} -S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi -\end{equation} - -\end_inset - - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -begin{multicols}{2} -\end_layout - -\end_inset - -wobei -\begin_inset Formula $S_{0}$ -\end_inset - - das Signal ohne Gradient ist und die Normierungsbedingung -\begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$ -\end_inset - - gilt. - Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen. - Direkt nach dem -\begin_inset Formula $\nicefrac{\pi}{2}$ -\end_inset - - -\begin_inset space \thinspace{} -\end_inset - --rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich - das Signal zusätzlich abschwächt. - Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten - -\begin_inset Formula $T_{2}$ -\end_inset - --Zeit. -\end_layout - -\begin_layout Standard - -\lang german -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -end{multicols} -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Formulas with Description of Variables -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Formula ! with description of variables -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -To describe variables within a formula, like in formula -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:within" - -\end_inset - -, a 2 -\series bold -× -\series default - -\begin_inset Formula $n$ -\end_inset - - -\begin_inset space ~ -\end_inset - -matrix is used with left aligned columns for the -\begin_inset Formula $n$ -\end_inset - - used variables. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -matrices see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Matrices" - -\end_inset - - -\end_layout - -\end_inset - - To set the description in a smaller size, before the matrix e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -the command -\series bold - -\backslash -footnotesize -\series default - is inserted. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -font sizes see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Font-Sizes" - -\end_inset - - -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -When the formula style -\series bold -Indented -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -formula styles see -\begin_inset CommandInset ref -LatexCommand ref -reference "sec:Formula-Styles" - -\end_inset - - -\end_layout - -\end_inset - - -\series default - is used, a -\series bold - -\backslash -hfill -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -hfill -\series default - only works in formulas with the style -\series bold -Indented -\series default -, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Variable-Space" - -\end_inset - -. -\end_layout - -\end_inset - - is inserted before and after the matrix to have the same separation of - the matrix from the equation and the side margin. -\end_layout - -\begin_layout Standard -When the formula style -\series bold -Centered -\series default - is used, the method described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Flalign-Environment" - -\end_inset - - is used to indent formulas. - Formula -\begin_inset CommandInset ref -LatexCommand eqref -reference "eq:within" - -\end_inset - - consists of five columns where in the first two columns contain the equation, - the third the matrix and the last one an empty TeX-brace. -\begin_inset Formula -\begin{flalign} -\hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll} -\rho & \textrm{density}\\ -V & \textrm{volume}\\ -g & \textrm{gravitational acceleration} -\end{array} & & {}\label{eq:within} -\end{flalign} - -\end_inset - - -\end_layout - -\begin_layout Subsection -Upright small Greek Letters -\begin_inset CommandInset label -LatexCommand label -name "sub:Upright-small-Greek" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Greek letters ! upright -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Most of the math fonts only provide italic small Greek letters. - But for symbols of elementary particles like pions and neutrinos, upright - Greek letters are needed. - The file -\series bold -upgreek.sty -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout - -\series bold -upgreek -\series default - is part of the LaTeX-package -\series bold -was -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! was -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -vspace{4mm} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - -. -\end_layout - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! upgreek -\end_layout - -\end_inset - - that is loaded with the LaTeX-preamble line -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -usepackage{upgreek} -\end_layout - -\begin_layout Standard -provides them. - -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -ifupgreek -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following table will only be displayed when the LaTeX-package -\series bold -upgreek -\series default - is installed: -\end_layout - -\end_inset - - They are created when the command for a small Greek letter is started with - -\series bold -up -\series default -. - For example the command -\series bold - -\backslash -uptau -\series default - creates this: -\begin_inset Formula $\uptau$ -\end_inset - - -\end_layout - -\begin_layout Standard -With these commands reactions of elementary particles can be typeset: -\begin_inset Formula -\[ -\uppi^{+}\to\upmu^{+}+\upnu_{\upmu} -\] - -\end_inset - - -\end_layout - -\begin_layout Standard -The upright letters are more bold and wider than the italic ones. - They should therefore not be used for units like -\begin_inset Quotes eld -\end_inset - -µm -\begin_inset Quotes erd -\end_inset - -. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -else -\end_layout - -\end_inset - - -\begin_inset Note Note -status open - -\begin_layout Plain Layout -The following will be displayed when the LaTeX-package -\series bold -upgreek -\series default - is not installed: -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -You need to install the LaTeX-package -\series bold -upgreek -\series default - to see the rest of this subsection in the output. -\end_layout - -\begin_layout Standard -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -fi -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Subsection -Text Characters in Formulas -\begin_inset CommandInset label -LatexCommand label -name "sub:Text-Characters-in" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Text ! in formulas -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -In some cases you might want to insert text characters directly into formulas. - When for example the centered dot · is often used in formulas like -\begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$ -\end_inset - -, one would have to insert the command -\series bold - -\backslash -cdot -\series default - -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Binary-Operators" - -\end_inset - - -\end_layout - -\end_inset - - all the time, because this character is defined in all encodings as text - character. - But the encoding can be changed by this LaTeX-preamble line: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -Declare Inputtext{183}{ -\backslash -ifmmode -\backslash -cdot -\backslash -else -\backslash -textperiodcentered -\backslash -f\SpecialChar \textcompwordmark{} -i} -\end_layout - -\begin_layout Standard -The character encoding (menu -\family sans -Document\SpecialChar \menuseparator -Settings\SpecialChar \menuseparator -Language -\family default -) specifies what character appears when a keyboard key is pressed. - When the key for the character '·' is pressed, internally the command -\series bold - -\backslash -textperiodcentered -\series default - is used. - But this command is not available in a formula so that you would get LaTeX-erro -rs. - With the changed encoding the right command is chosen automatically, depending - on if the character was inserted into a formula or not. -\end_layout - -\begin_layout Standard -The encoding of several characters is saved in definition files. - For example the encoding -\series bold -latin9 -\series default - is defined in the file -\series bold -latin9.def -\series default - which is in the installation folder of LaTeX. - Encodings should only be changed via the LaTeX-preamble and not in the - definition files. - Otherwise documents could not be edited by other LyX users working on other - computers. -\end_layout - -\begin_layout Standard -\begin_inset VSpace medskip -\end_inset - -Besides the centered dot, in this document the degree sign ° is defined - with the following LaTeX-preamble line so that it can be directly inserted - into a formula: -\end_layout - -\begin_layout Standard - -\series bold - -\backslash -DeclareInputtext{176}{ -\backslash -ifmmode^ -\backslash -circ -\backslash -else -\backslash -textdegree -\backslash -f\SpecialChar \textcompwordmark{} -i} -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -\start_of_appendix -Typographic Advice -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Typographic advice -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -This section is a summary of the most important typographic rules, listed - in ISO norms. -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -This collection was partly taken from the German semi-official dictionary - called -\begin_inset Quotes eld -\end_inset - -Duden -\begin_inset Quotes erd -\end_inset - - -\begin_inset CommandInset citation -LatexCommand cite -key "Duden" - -\end_inset - - that lists some of the ISO rules. - More rules are listed in -\begin_inset CommandInset citation -LatexCommand cite -key "Checklist" - -\end_inset - -. -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Itemize -Physical units are -\emph on -always -\emph default - set upright -\begin_inset Foot -status collapsed - -\begin_layout Plain Layout -done with font styles, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Font-Styles" - -\end_inset - - -\end_layout - -\end_inset - -, no matter if they appear in italic text: 30 -\begin_inset space \thinspace{} -\end_inset - -km/h -\begin_inset Newline newline -\end_inset - -Between the value and the unit is the smallest space, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Predefined-Space" - -\end_inset - -. -\begin_inset Newline newline -\end_inset - -This convention is automatically fulfilled when the command -\series bold - -\backslash -unittwo -\series default - is used. - When it is entered to a formula, two boxes appear. - In the first one the value is inserted, in the second one the unit, and - one gets as above: -\begin_inset Formula $\unit[30]{km/h}$ -\end_inset - - -\begin_inset space \thinspace{} -\end_inset - -. - Note that -\series bold - -\backslash -unittwo -\series default - is not a real LaTeX command but the command -\series bold - -\backslash -unit[value]{unit} -\series default -, therefore you cannot use it in TeX code. -\end_layout - -\begin_layout Itemize -Percent and perthousand signs are set like physical units: -\begin_inset Newline newline -\end_inset - -1,2 -\begin_inset space \thinspace{} -\end_inset - -‰ alcohol in blood -\end_layout - -\begin_layout Itemize -The degree sign follows directly on the value: 15°, but not when it is used - in units: 15 -\begin_inset space \thinspace{} -\end_inset - -°C -\end_layout - -\begin_layout Itemize -In numbers with more than four digits the smallest space is inserted before - every third digit to group them: -\family roman -\series medium -\shape up -\size normal -\emph off -\bar no -\noun off -\color none -18 -\begin_inset space \thinspace{} -\end_inset - -473 -\begin_inset space \thinspace{} -\end_inset - -588 -\end_layout - -\begin_layout Itemize -For dimensions like 120×90×40 -\begin_inset space \thinspace{} -\end_inset - -cm the multiplication sign -\begin_inset Quotes eld -\end_inset - -× -\begin_inset Quotes erd -\end_inset - - is used. - It is available either via the command -\series bold - -\backslash -times -\series default - or via the menu -\family sans -Insert\SpecialChar \menuseparator -Special Character\SpecialChar \menuseparator -Symbols -\family default -. -\end_layout - -\begin_layout Itemize -Functions with names consisting of several letters are set upright to avoid - confusions, see -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Predefined-Functions" - -\end_inset - -. -\end_layout - -\begin_layout Itemize -Indices consisting of several letters, are set upright: -\begin_inset Formula $E_{\mathrm{kin}}$ -\end_inset - - -\begin_inset Newline newline -\end_inset - -Components of matrices are set italic: -\begin_inset Formula $\hat{H}_{kl}$ -\end_inset - - -\end_layout - -\begin_layout Itemize -The differentiation/integration operator 'd', the Euler's number 'e' and - the imaginary unit 'i' should be set upright, to avoid mixing them up with - other variables. -\end_layout - -\begin_layout Itemize -The character that denotes a -\noun on -Fourier -\noun default - transformation is inserted either by the command -\series bold - -\backslash -mathscr -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -spce -\end_layout - -\end_inset - -F -\series default - or via the menu -\family sans -Insert\SpecialChar \menuseparator -Special Character\SpecialChar \menuseparator -Symbols\SpecialChar \menuseparator -Letterlike -\begin_inset space ~ -\end_inset - -Symbols -\family default -: -\begin_inset Formula $\mathscr{F}$ -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Section -Synonyms -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Synonyms -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Standard -Some characters and symbols can be created with several commands. - Here is a list of the synonym commands: -\end_layout - -\begin_layout Standard -\begin_inset VSpace bigskip -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -equivalent to -\begin_inset Note Note -status collapsed - -\begin_layout Plain Layout - -\series bold - -\backslash -raisebox -\series default - is only used as spacer. -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ast -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -raisebox{-1.2mm}{ -\end_layout - -\end_inset - -* -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - -} -\end_layout - -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -choose -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -binom -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -geq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ge -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lbrace -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -{ -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lbracket -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -[ -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leftarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -gets -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -leq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -le -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lor -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vee -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -neq -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not= -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -slash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -/ -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -vert -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -| -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Command -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -equivalent to -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -backslash -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash - -\backslash - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dasharrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -dashrightarrow -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -land -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -wedge -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rbrace -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -} -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rbracket -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -] -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -rightarrow -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -to -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -lnot -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -neg -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ne -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -not= -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -owns -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -ni -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -square -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Box -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -Vert -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout - -\backslash -| -\end_layout - -\end_inset - - - - -\end_inset - - -\begin_inset space \hfill{} -\end_inset - - -\end_layout - -\begin_layout Standard -\begin_inset Newpage newpage -\end_inset - - -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "TLC2" - -\end_inset - - -\shape smallcaps -Mittelbach, F. - ; Goossens, M. -\shape default -: -\shape italic -The LaTeX Companion -\shape default -. - Addison Wesley, 2004 -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "Mathmode" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Description" -target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf" - -\end_inset - - of LaTeX's math abilities -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "AMS" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Description" -target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf" - -\end_inset - - of -\begin_inset ERT -status collapsed - -\begin_layout Plain Layout - - -\backslash -AmS -\end_layout - -\end_inset - --LaTeX -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "Symbols" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "List" -target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf" - -\end_inset - - of all symbols available with LaTeX-packages -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "cancel" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Documentation" -target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf" - -\end_inset - - of the LaTeX-package -\series bold -cancel -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! cancel -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "hyperref" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Documentation" -target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf" - -\end_inset - - of the LaTeX-package -\series bold -hyperref -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! hyperref -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "mhchem" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Documentation" -target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf" - -\end_inset - - of the LaTeX-package -\series bold -mhchem -\series default - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Packages ! mhchem -\end_layout - -\end_inset - - -\end_layout - -\begin_layout Bibliography -\begin_inset CommandInset bibitem -LatexCommand bibitem -key "Mathclap" - -\end_inset - - -\begin_inset CommandInset href -LatexCommand href -name "Description" -target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf" - -\end_inset - - of the command -\series bold - -\backslash -mathclap -\series default -, described in -\begin_inset CommandInset ref -LatexCommand ref -reference "sub:Operator-Limits" - -\end_inset - - -\begin_inset Index idx -status collapsed - -\begin_layout Plain Layout -Commands ! 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For more info see http://www.lyx.org/ +\lyxformat 413 +\begin_document +\begin_header +\textclass scrartcl +\begin_preamble +% DO NOT ALTER THIS PREAMBLE!!! +% +% This preamble is designed to ensure that the file prints +% out as advertised. If you mess with this preamble, +% parts of this document may not print out as expected. If you +% have problems LaTeXing this file, please contact +% the documentation team +% email: lyx-docs@lists.lyx.org + +% if pdflatex is used +\usepackage{ifpdf} +\ifpdf + +% set fonts for nicer pdf view +\IfFileExists{lmodern.sty} + {\usepackage{lmodern}}{} + +\fi % end if pdflatex is used + +% solves the following problem: +% If the dection number consits of too many numerals the section heading +% will be printed in the TOC without a space between it and the section number. +% As solution more space between the number and the heading is inserted: +\renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}} +\renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}} + +% To be able to enter the character ° and · directly in LyX, +% see sec. 22.11 +\DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi} +\DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi} + +% increase link area for cross-references and autoname them, +\AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}} +\@ifundefined{extrasenglish}{\usepackage[english]{babel}}{} +\addto\extrasenglish{% + \renewcommand*{\equationautorefname}[1]{} + \renewcommand{\sectionautorefname}{sec.\negthinspace} + \renewcommand{\subsectionautorefname}{sec.\negthinspace} + \renewcommand{\subsubsectionautorefname}{sec.\negthinspace} +} + +% don't load packages twice +% see first footnote in sec. 9.3 +\@ifundefined{textcolor}{\usepackage{color}}{} + +% the pages of the TOC are numbered roman +% and a PDF-bookmark for the TOC is added +\pagenumbering{roman} +\let\myTOC\tableofcontents +\renewcommand{\tableofcontents}{% + \vspace{1cm} + \pdfbookmark[1]{\contentsname}{} + \myTOC + \cleardoublepage + \pagenumbering{arabic}} + +% insert additional vertical space of 1.5 mm between footnotes, +\let\myFoot\footnote +\renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}} + +% provides caption formatting +\setkomafont{captionlabel}{\bfseries} + +% used in sec. 24.5 +\usepackage[samesize]{cancel} + +% enables calculation of values +\usepackage{calc} + +% for multiple columns used in sec. 24.7 +\usepackage{multicol} + +% needed in sec. 19.4 +\usepackage{remreset} + +% for the Fourier transformation symbol +\usepackage{mathrsfs} + +% define a color, used in sec.9.3 +\definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5} + +% declare operators (see sec. 10.4 and sec. 15.2) +\DeclareMathOperator*{\Lozenge}{\blacklozenge} +\DeclareMathOperator{\sgn}{sgn} + +\newcommand{\spce}{\textvisiblespace} + +% example definitions for sec. 20.1 +\newcommand{\gr}{\Longrightarrow} +\newcommand{\us}[1]{\underline{#1}} +\newcommand{\fb}[3]{\framebox#1#2{$#3$}} +\newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}} +\newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}} + +% example macro from sec. 19.4 +%\def\tagform@#1{\maketag@@@{|#1|}} + +% macro from sec. 10.2 +\def\clap#1{\hbox to 0pt{\hss #1\hss}} +\def\mathclap {\mathpalette \mathclapinternal} +\def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}} + + +% ------------------------------------ +% used to check for needed LaTeX packages +\usepackage{ifthen} + +% check for package eurosym +% used for the Euro symbol +\newboolean{eurosym} +\IfFileExists{eurosym.sty} + {\usepackage[gennarrow]{eurosym} + \setboolean{eurosym}{true}} + {\setboolean{eurosym}{false}} + +% check for package braket +% used for physical vectors +\newboolean{braket} +\IfFileExists{braket.sty} + {\usepackage{braket} + \setboolean{braket}{true}} + {\setboolean{braket}{false}} + +% check for package cancel +\newboolean{cancel} +\IfFileExists{cancel.sty} + {\usepackage{cancel} + \setboolean{cancel}{true}} + {\setboolean{cancel}{false}} + +% check for package upgreek +\newboolean{upgreek} +\IfFileExists{upgreek.sty} + {\usepackage{upgreek} + \setboolean{upgreek}{true}} + {\setboolean{upgreek}{false}} +\end_preamble +\options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading +\use_default_options false +\maintain_unincluded_children false +\language english +\language_package default +\inputencoding auto +\fontencoding global +\font_roman default +\font_sans default +\font_typewriter default +\font_default_family default +\use_non_tex_fonts false +\font_sc false +\font_osf false +\font_sf_scale 100 +\font_tt_scale 100 + +\graphics default +\default_output_format default +\output_sync 0 +\bibtex_command default +\index_command default +\paperfontsize 12 +\spacing single +\use_hyperref true +\pdf_title "LyX's Math Manual" +\pdf_author "LyX Team, Uwe Stöhr" +\pdf_subject "LyX-documentation about math" +\pdf_keywords "LyX, Mathed" +\pdf_bookmarks true +\pdf_bookmarksnumbered true +\pdf_bookmarksopen true +\pdf_bookmarksopenlevel 1 +\pdf_breaklinks false +\pdf_pdfborder false +\pdf_colorlinks true +\pdf_backref false +\pdf_pdfusetitle false +\pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false" +\papersize a4paper +\use_geometry false +\use_amsmath 2 +\use_esint 1 +\use_mhchem 1 +\use_mathdots 1 +\cite_engine basic +\use_bibtopic false +\use_indices false +\paperorientation portrait +\suppress_date false +\use_refstyle 0 +\notefontcolor #0000ff +\index Index +\shortcut idx +\color #008000 +\end_index +\secnumdepth 4 +\tocdepth 3 +\paragraph_separation skip +\defskip medskip +\quotes_language english +\papercolumns 1 +\papersides 2 +\paperpagestyle plain +\bullet 1 0 6 -1 +\bullet 2 2 35 -1 +\bullet 3 2 7 -1 +\tracking_changes false +\output_changes false +\html_math_output 0 +\html_css_as_file 0 +\html_be_strict false +\end_header + +\begin_body + +\begin_layout Title +LyX's detailed Math manual +\end_layout + +\begin_layout Author +by the LyX Team +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +\noindent +If you have comments or error corrections, please send them to the LyX Documenta +tion mailing list: +\family typewriter + +\begin_inset CommandInset href +LatexCommand href +name "lyx-docs@lists.lyx.org" +target "lyx-docs@lists.lyx.org?subject=LyX's Math manual" +type "mailto:" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +author: Uwe Stöhr +\end_layout + +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\family sans +Version 2.0.x +\end_layout + +\begin_layout Standard +\begin_inset CommandInset toc +LatexCommand tableofcontents + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Note +status open + +\begin_layout Plain Layout +To export this document to PDF, PS or DVI the LaTeX-packages +\series bold +braket, cancel, eurosym, mathdots, mhchem +\series default + and +\series bold +was +\series default + should be installed. + If they are not installed the document can be exported anyway but the sections + where the packages are required will not appear in the output. + An exception is +\series bold +mhchem +\series default +; if it is not installed, this file cannot be exported. +\end_layout + +\begin_layout Plain Layout +The latest PDF-version of this document can be found here: +\begin_inset Newline newline +\end_inset + + +\series bold +http://wiki.lyx.org/LyX/DocumentationDevelopment#Math +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Section +Introduction +\end_layout + +\begin_layout Standard +This document explains LyX's math features and is furthermore a collection + of LaTeX-commands used for mathematical characters and constructs. + The explanations are designed for the usage of commands. + It is therefore required that you have read the section +\family typewriter +Mathematical +\begin_inset space ~ +\end_inset + +Formulas +\family default + of the User's Guide. +\end_layout + +\begin_layout Standard +Most of the characters and many constructs explained in this manual are + also accessible via the menu +\family sans +Insert +\series bold +\SpecialChar \menuseparator + +\series default +Math +\family default + or the +\family sans +math +\family default +\series bold + +\family sans +\series default +toolbar +\family default +. + But everybody who has to write lots of formulas will notice that it is + much faster to use commands instead of the math toolbar. + Therefore this manual is focused on commands but also mentions the correspondin +g toolbar buttons when available. +\end_layout + +\begin_layout Standard +If not specially mentioned the commands are only available within formulas. + To be able to use all commands explained in this document, the option +\family sans +Use AMS math package +\family default + must be checked in the document settings (menu +\family sans +Document\SpecialChar \menuseparator +Settings\SpecialChar \menuseparator +Math +\begin_inset space ~ +\end_inset + +Options +\family default +). +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +The option +\family sans +Use AMS math package automatically +\family default + only uses +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +AmS +\end_layout + +\end_inset + +-math when math constructs are found that are supported by LyX. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +This document doesn't list all +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +AmS +\end_layout + +\end_inset + +-math commands +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +A list with all +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +AmS +\end_layout + +\end_inset + +-math commands is in the file +\family sans + +\begin_inset CommandInset href +LatexCommand href +name "amsguide.ps" +target "ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps" + +\end_inset + + +\family default +, which is part of every LaTeX standard installation. +\end_layout + +\end_inset + + for lucidity reasons. +\end_layout + +\begin_layout Section +General Instructions +\end_layout + +\begin_layout Standard +To create an inline formula +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! inline +\end_layout + +\end_inset + + that is embedded into a text line, use one of the shortcuts +\begin_inset Info +type "shortcuts" +arg "math-mode" +\end_inset + + or the toolbar button +\begin_inset Graphics + filename ../images/math-mode.png + scale 85 + +\end_inset + +. +\begin_inset Newline newline +\end_inset + +To create a display style formula +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! display style +\end_layout + +\end_inset + + which will appear bigger, has a different format, and will be in a separate + paragraph, use one of these shortcuts: +\begin_inset Info +type "shortcuts" +arg "math-display" +\end_inset + +. +\end_layout + +\begin_layout Standard +To change a display style formula to an inline formula, set the cursor into + the formula and use one of the shortcuts +\begin_inset Info +type "shortcuts" +arg "math-mode" +\end_inset + + or the menu +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Change formula type +\family default +. + The same way is used to change an inline formula to a display style formula. +\end_layout + +\begin_layout Standard +To display parts of an inline formula in the size of a display style formula, + enter the command +\series bold + +\backslash +displaystyle +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +displaystyle +\end_layout + +\end_inset + + to a formula. + Then a new blue box appears in which the desired formula part is inserted. +\end_layout + +\begin_layout Standard +Only inline formulas are allowed inside tables. +\end_layout + +\begin_layout Standard +The +\family sans +math toolbar +\family default + can be turned on in the menu +\family sans +View\SpecialChar \menuseparator +Toolbars +\family default +. + When you click there on +\begin_inset Quotes eld +\end_inset + +Math +\begin_inset Quotes erd +\end_inset + + the toolbar will be shown permanently at the bottom; this state is visualized + in the +\family sans +Toolbars +\family default + menu with a checkmark. + When you click in this state again on +\begin_inset Quotes eld +\end_inset + +Math +\begin_inset Quotes erd +\end_inset + + in the +\family sans +Toolbars +\family default + menu, the +\family sans +math toolbar +\family default + is only shown when the cursor is within a formula; this state is visualized + by the renaming of the menu entry from +\begin_inset Quotes eld +\end_inset + +Math +\begin_inset Quotes erd +\end_inset + + to +\begin_inset Quotes eld +\end_inset + +Math +\begin_inset space ~ +\end_inset + +(auto) +\begin_inset Quotes erd +\end_inset + +. +\end_layout + +\begin_layout Standard +The TeX-mode +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +T@TeX-mode +\end_layout + +\end_inset + + is invoked by pressing the toolbar button +\begin_inset Graphics + filename ../images/ert-insert.png + scale 85 + +\end_inset + + or by using the menu +\family sans +Insert\SpecialChar \menuseparator +Te +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{} +\end_layout + +\end_inset + +X Code +\family default + (shortcut +\begin_inset Info +type "shortcut" +arg "ert-insert" +\end_inset + +). +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +In LyX there are three +\begin_inset Quotes eld +\end_inset + +proper names +\begin_inset Quotes erd +\end_inset + + that appear in the output with sub- and superscript letters: TeX, LaTeX + and LyX +\end_layout + +\begin_layout Plain Layout +To avoid that these names are recognized as proper names, a TeX-brace pair + is inserted. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To change the LaTeX-preamble +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +L@LaTeX-preamble +\end_layout + +\end_inset + +, use the menu +\family sans +Document\SpecialChar \menuseparator +Settings\SpecialChar \menuseparator +LaT +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{} +\end_layout + +\end_inset + +eX +\family default + +\family sans +Preamble +\family default +. +\end_layout + +\begin_layout Standard +To edit matrices, case differentiations and multiline formulas subsequently, + use the menus +\family sans +Edit\SpecialChar \menuseparator +Math +\family default + and +\family sans +Edit\SpecialChar \menuseparator +Rows +\begin_inset space \thinspace{} +\end_inset + +& +\begin_inset space \thinspace{} +\end_inset + +Columns, +\family default + or the +\family sans +table toolbar +\family default +. + When lines and columns are swapped via the menu, the column or line where + the cursor is in is exchanged with the column to the right or the line + below, respectively. + Is the cursor in the last column or row, the exchange is done with the + column to the left or the line above. +\end_layout + +\begin_layout Standard +To write text in formulas +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +For multiline formulas the command +\series bold + +\backslash +intertext +\series default + is used, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Text-in-multiline" + +\end_inset + +. +\end_layout + +\end_inset + + +\emph on +mathematical text +\emph default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Text ! in formulas +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Mathematical text +\end_layout + +\end_inset + + is used. + This mode is invoked with the shortcut +\begin_inset Info +type "shortcut" +arg "font-default" +\end_inset + + or by the insertion of the command +\series bold + +\backslash +text +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +text +\end_layout + +\end_inset + +. + The text appears black in LyX and can therefore be distinguished from the + other formula parts which appear blue. + In the output mathematical text is set upright, in contrary to other formula + parts. +\end_layout + +\begin_layout Subsection* +Command Scheme +\end_layout + +\begin_layout Standard +Most of the LaTeX-commands for math constructs have the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +commandname[optional +\series default + +\series bold +argument]{required +\series default + +\series bold +argument} +\end_layout + +\begin_layout Standard +A command always starts with a backslash +\begin_inset Quotes gld +\end_inset + + +\series bold + +\backslash + +\series default + +\begin_inset Quotes grd +\end_inset + +. + To omit optional arguments, also omit the associated brackets. + The braces around the required arguments are named in this document as + TeX-braces +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +T@TeX-braces +\end_layout + +\end_inset + +. + If you add in a formula a left brace to a command name, LyX automatically + creates a TeX-brace. + In all other cases TeX-braces are created in formulas with the command + +\series bold + +\backslash +{ +\series default +. + TeX-braces appear red in LyX, in contrary to normal braces which appear + blue. + In TeX-mode no command is needed to get TeX-braces. + TeX-braces don't appear in the output. +\end_layout + +\begin_layout Standard +When commands without arguments, like commands for symbols are entered in + TeX-mode, a space character must +\emph on +always +\emph default + be behind the command to end it. + This space doesn't appear in the output. + When the space should appear in the output, the space must be followed + by a protected space in normal text. +\end_layout + +\begin_layout Standard +A protected space is inserted with +\begin_inset Info +type "shortcuts" +arg "command-alternatives space-insert protected ; math-space" +\end_inset + +. +\end_layout + +\begin_layout Subsection* +\begin_inset Newpage newpage +\end_inset + +Syntax Explanation +\end_layout + +\begin_layout Itemize +The symbol +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +This visible space character can be created with the command +\series bold + +\backslash +textvisiblespace +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +textvisiblespace +\end_layout + +\end_inset + +, inserted in TeX-mode. +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\begin_inset space ~ +\end_inset + +denotes a space character to be input. +\end_layout + +\begin_layout Itemize +An arrow like +\begin_inset Formula $\to$ +\end_inset + + denotes the usage of the corresponding arrow key on the keyboard. + The +\family sans +Tab +\family default + key can often be used instead of +\begin_inset Formula $\to$ +\end_inset + + and +\begin_inset Formula $\downarrow$ +\end_inset + +, and +\family sans +Shift+Tab +\family default + instead of +\begin_inset Formula $\leftarrow$ +\end_inset + + and +\begin_inset Formula $\uparrow$ +\end_inset + +. +\end_layout + +\begin_layout Subsection* +Available units +\end_layout + +\begin_layout Standard +\align center +\begin_inset Float table +placement H +wide false +sideways false +status open + +\begin_layout Plain Layout +\align center +\begin_inset Caption + +\begin_layout Plain Layout +\begin_inset CommandInset label +LatexCommand label +name "tab:Available-units" + +\end_inset + +Available units +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Plain Layout +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Unit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Name / Description +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +mm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Millimeter +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +cm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Centimeter +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +in +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Inch (1 +\begin_inset space \thinspace{} +\end_inset + +in = 2,54 +\begin_inset space \thinspace{} +\end_inset + +cm) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +pt +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Point (72.27 +\begin_inset space \thinspace{} +\end_inset + +pt = 1 +\begin_inset space \thinspace{} +\end_inset + +in) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +pc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Pica (1 +\begin_inset space \thinspace{} +\end_inset + +pc = 12 +\begin_inset space \thinspace{} +\end_inset + +pt) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +sp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +scaled point (65536 +\begin_inset space \thinspace{} +\end_inset + +sp = 1 +\begin_inset space \thinspace{} +\end_inset + +pt) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +bp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +big point (72 +\begin_inset space \thinspace{} +\end_inset + +bp = 1 +\begin_inset space \thinspace{} +\end_inset + +in) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +dd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Didot (1 +\begin_inset space \thinspace{} +\end_inset + +dd +\begin_inset Formula $\approx$ +\end_inset + + 0.376 +\begin_inset space \thinspace{} +\end_inset + +mm) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +cc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Cicero (1 +\begin_inset space \thinspace{} +\end_inset + +cc = 12 +\begin_inset space \thinspace{} +\end_inset + +dd) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +ex +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Height of letter +\emph on + +\begin_inset Quotes eld +\end_inset + +x +\emph default + +\begin_inset Quotes erd +\end_inset + + in the current font +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +em +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +width of letter +\begin_inset Quotes eld +\end_inset + + +\emph on +M +\emph default + +\begin_inset Quotes erd +\end_inset + + in the current font +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +mu +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +math unit (1 +\begin_inset space \thinspace{} +\end_inset + +mu = +\begin_inset Formula $\nicefrac{1}{18}$ +\end_inset + + +\begin_inset space \thinspace{} +\end_inset + +em) +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Section +Basic Functions +\end_layout + +\begin_layout Subsection +Exponents +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Exponents +\end_layout + +\end_inset + + and Indices +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Indices +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Superscripts|see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Exponents +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Subscripts|see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Indices +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Indices are created with an underscore +\begin_inset Quotes eld +\end_inset + +_ +\begin_inset Quotes erd +\end_inset + + or via the math toolbar button +\begin_inset Graphics + filename ../images/math-subscript.png + scale 85 + +\end_inset + +, exponents with a caret +\begin_inset Quotes eld +\end_inset + +^ +\begin_inset Quotes erd +\end_inset + + or via the math toolbar button +\begin_inset Graphics + filename ../images/math-superscript.png + scale 85 + +\end_inset + +. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +B_V +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $B_{V}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +B^V +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}B^{V}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +B^ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}B^{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +As the caret is in some languages an accent, vowels will be accentuated + in this case and not set as exponents +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +Depending on the used keyboard settings this can also happen for characters + other than vowels. +\end_layout + +\end_inset + +. + To get exponents in this case, press +\family sans +Space +\family default + after the caret as in the last example. +\end_layout + +\begin_layout Subsection +Fractions +\begin_inset CommandInset label +LatexCommand label +name "sub:Fractions" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Fractions +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Fractions are generated with the command +\series bold + +\backslash +frac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! F ! +\backslash +frac +\end_layout + +\end_inset + + or via the math toolbar button +\begin_inset Graphics + filename ../images/math/frac.png + scale 50 + +\end_inset + +. + The font size is adjusted automatically, depending on whether the fraction + is in an inline or display style formula. + With the math toolbar button +\begin_inset Graphics + filename ../images/math/frac-square.png + scale 85 + +\end_inset + + you can select different fraction types. +\end_layout + +\begin_layout Standard +With the command +\series bold + +\backslash +dfrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dfrac +\end_layout + +\end_inset + + a fraction can be created that always has the size of a display style formula. + With +\series bold + +\backslash +tfrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +tfrac +\end_layout + +\end_inset + + the fraction appears always with the size of an inline formula. + An example: +\end_layout + +\begin_layout Standard +A line with the fraction +\begin_inset Formula $\frac{1}{2}$ +\end_inset + + that was created with the command +\series bold + +\backslash +frac +\series default +. +\end_layout + +\begin_layout Standard +A line with the fraction +\begin_inset Formula $\dfrac{1}{2}$ +\end_inset + + that was created with the command +\series bold + +\backslash +dfrac +\series default +. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +frac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dfrac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dfrac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +e^ +\backslash +frac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +1 +\begin_inset Formula $\downarrow$ +\end_inset + +2 +\begin_inset Formula $\downarrow\downarrow$ +\end_inset + +3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{8mm}{}\dfrac{e^{\frac{1}{2}}}{3}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + + +\begin_inset Newpage newpage +\end_inset + +For nested fractions the command +\series bold + +\backslash +cfrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +cfrac +\end_layout + +\end_inset + + can be used. + Here is an example: +\begin_inset VSpace -3mm +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Formula +\begin{align*} +\textrm{created with \textbf{\textbackslash frac}} & & \textrm{created with \textbf{\textbackslash cfrac}}\\ +\frac{A}{B+\frac{C+\frac{E}{F}}{D}} & & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}} +\end{align*} + +\end_inset + + +\end_layout + +\begin_layout Standard +The command for the example above is: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +cfrac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B+ +\backslash +cfrac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +C+ +\backslash +cfrac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +E +\begin_inset Formula $\downarrow$ +\end_inset + +F +\begin_inset Formula $\downarrow$ +\end_inset + +D +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + + +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +cfrac +\series default + sets the fraction always in the size of a displayed formula, also when + it is part of another fraction. +\end_layout + +\begin_layout Standard +It is possible to specify the alignment of the numerator. + The command +\series bold + +\backslash +cfracleft +\series default + is used to left align it, the command +\series bold + +\backslash +cfracright +\series default + to right-align it. + +\series bold + +\backslash +cfrac +\series default + centers the numerator. + These fractions demonstrate the different alignments: +\end_layout + +\begin_layout Standard + +\series bold +\begin_inset Formula +\[ +\cfrac[l]{A}{B+C}\,,\,\cfrac{A}{B+C}\,,\,\cfrac[r]{A}{B+C} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + +\series bold + +\backslash +cfracleft +\series default + and +\series bold + +\backslash +cfracright +\series default + are no real LaTeX commands but represent the command +\series bold + +\backslash +cfrac[alignment]{numerator}{denominator} +\series default + . + Therefore you cannot use them in TeX code. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +It is often advantageous to combine +\series bold + +\backslash +cfrac +\series default + and +\series bold + +\backslash +frac +\series default +: +\begin_inset Formula +\[ +\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +For inline fractions with a sloped fraction stroke you can use the command + +\series bold + +\backslash +nicefrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! N ! +\backslash +nicefrac +\end_layout + +\end_inset + +: +\begin_inset Formula $\nicefrac{5}{31}$ +\end_inset + + or +\series bold + +\backslash +unitfrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +unitfrac +\end_layout + +\end_inset + +: +\begin_inset Formula $\unitfrac{5}{31}$ +\end_inset + + There is furthermore the command +\series bold + +\backslash +unitfracthree +\series default + that offers to write a fraction in combination with a number: +\begin_inset Formula $\unitfrac[2]{1}{3}$ +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + +\series bold + +\backslash +unitfracthree +\series default + is not a real LaTeX command but the command +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +unitfrac[number]{numerator}{denominator} +\series default + . + Therefore you cannot use it in TeX code. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +How to define own fractions where the fraction stroke can be changed, is + explained in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Self-defined-Fractions" + +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Subsection +Roots +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Roots +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Square roots are created with +\series bold + +\backslash +sqrt +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +sqrt +\end_layout + +\end_inset + + or the math toolbar button +\begin_inset Graphics + filename ../images/math/sqrt.png + scale 85 + +\end_inset + +, all other roots with the command +\series bold + +\backslash +root +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +root +\end_layout + +\end_inset + + or with the math toolbar button +\begin_inset Graphics + filename ../images/math/root.png + scale 85 + +\end_inset + +. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqrt +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A-B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +root +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +3 +\begin_inset Formula $\downarrow$ +\end_inset + +A-B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +A square root can also be created with +\series bold + +\backslash +root +\series default + when the root index field is left empty. +\end_layout + +\begin_layout Standard +With certain indices the distance to the root is too small, like in this + formula: +\begin_inset Formula $\sqrt[\beta]{B}$ +\end_inset + + +\begin_inset Newline newline +\end_inset + +The +\begin_inset Formula $\beta$ +\end_inset + + touches the root. + To avoid this, the commands +\series bold + +\backslash +leftroot +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +leftroot +\end_layout + +\end_inset + + and +\series bold + +\backslash +uproot +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +uproot +\end_layout + +\end_inset + + are used with the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +leftroot{distance} +\series default + and +\series bold + +\backslash +uproot{distance} +\end_layout + +\begin_layout Standard +Distance is the number of Big Points (unit bp; +\begin_inset Formula $\mathrm{72\, bp=1\, inch}$ +\end_inset + +), that the index should be moved to the left or top, resp.. + The commands are written to the index. + This way the command +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +root +\backslash +leftroot{-1 +\begin_inset Formula $\to$ +\end_inset + + +\backslash +uproot{2 +\begin_inset Formula $\to$ +\end_inset + + +\backslash +beta +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\begin_inset Formula $\to$ +\end_inset + +B +\begin_inset Newline newline +\end_inset + + +\series default +produces a correct typeset formula: +\begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$ +\end_inset + + +\end_layout + +\begin_layout Subsection +Binomial Coefficients +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Binomial coefficients +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Binomial coefficients are inserted with the command +\series bold + +\backslash +binom +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +binom +\end_layout + +\end_inset + + or with the submenu of the math toolbar button +\begin_inset Graphics + filename ../images/math/frac-square.png + scale 85 + +\end_inset + +. + As with fractions ( +\series bold + +\backslash +frac +\series default +) in addition to +\series bold + +\backslash +binom +\series default + there are the commands +\series bold + +\backslash +dbinom +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dbinom +\end_layout + +\end_inset + + and +\series bold + +\backslash +tbinom +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +tbinom +\end_layout + +\end_inset + +. + For other brackets around binomial coeficients there are the commands +\series bold + +\backslash +brace +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +brace +\end_layout + +\end_inset + + and +\series bold + +\backslash +brack +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +brack +\end_layout + +\end_inset + +. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +binom +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dbinom +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +tbinom +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\tbinom{A}{B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +brack +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +brace +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Subsection +Case Differentiations +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Case differentiations +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cases +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\to$ +\end_inset + +B>0 +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +cases +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\begin{cases} +A & B>0\end{cases}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cases +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\begin{cases} +A & \textrm{for }x>0\\ +B & \textrm{for }x=0 +\end{cases}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +After inserting +\series bold + +\backslash +cases +\series default + or pressing the math toolbar button +\begin_inset Graphics + filename ../images/math/cases.png + scale 85 + +\end_inset + + you can create new lines with the shortcut +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + + or the table toolbar button +\begin_inset Graphics + filename ../images/tabular-feature_append-row.png + scale 85 + +\end_inset + +. +\end_layout + +\begin_layout Standard +The command +\series bold + +\backslash +cases +\series default + is also available via the menu +\family sans +Insert\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Cases-Environment +\family default +. +\end_layout + +\begin_layout Subsection +Negations +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Negations +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +By inserting +\series bold + +\backslash +not +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! N ! +\backslash +not +\end_layout + +\end_inset + + every character can be displayed canceled. + The characters are quasi accentuated by a slash. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not= +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\not=$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not +\backslash +le +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\not\le$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not +\backslash +parallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\not\parallel$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +The last example shows that not all negations look good. + Therefore there are special commands for some negations (see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Mathematical-Symbols" + +\end_inset + + and +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Relations" + +\end_inset + +). +\end_layout + +\begin_layout Subsection +Placeholders +\begin_inset CommandInset label +LatexCommand label +name "sub:Placeholders" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Placeholders +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Chemical characters ! Isotopes +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Isotopes|see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Chemical characters +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +When displaying e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +isotopes +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +Typesetting isotopes and chemical symbols is described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Chemical-Symbols-and" + +\end_inset + +. +\end_layout + +\end_inset + + the following problem occurs: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Indices created with sub- and superscripts: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +correct indices: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The shorter index is by default placed below or above the first character + of the longer index. + To avoid this there is the command +\series bold + +\backslash +phantom +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! P ! +\backslash +phantom +\end_layout + +\end_inset + + or the math toolbar button +\begin_inset space \thinspace{} +\end_inset + + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +can be found in the submenu of the toolbar button +\begin_inset Graphics + filename ../images/math/space.png + scale 85 + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Graphics + filename ../images/math/phantom.png + scale 85 + +\end_inset + + that creates one or more phantom characters. + When inserting +\series bold + +\backslash +phantom +\series default + a small blue box appears that is superposed with two red arrows. + The arrows indicate that the complete width and height of the box content + will be created as placeholder. + Phantom characters are accordingly placeholders with the size of the characters. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +^19 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +_ +\backslash +phantom +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +1 +\begin_inset Formula $\to$ +\end_inset + +9 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +F +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{1}9}^{19}\mathrm{F}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +^235 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +_ +\backslash +phantom +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +23 +\begin_inset Formula $\to$ +\end_inset + +9 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +F +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}{}_{\phantom{23}9}^{235}\mathrm{F}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Lambda^ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +phantom +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +ii +\begin_inset Formula $\to$ +\end_inset + +t +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +_MMt +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\Lambda_{MMt}^{\phantom{ii}t}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +Furthermore there are the commands +\series bold + +\backslash +vphantom +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! V ! +\backslash +vphantom +\end_layout + +\end_inset + + (toolbar button +\begin_inset space ~ +\end_inset + + +\begin_inset Graphics + filename ../images/math/vphantom.png + scale 85 + +\end_inset + +) and +\series bold + +\backslash +hphantom +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hphantom +\end_layout + +\end_inset + + (toolbar button +\begin_inset space ~ +\end_inset + + +\begin_inset Graphics + filename ../images/math/hphantom.png + scale 85 + +\end_inset + +). + +\series bold + +\backslash +hphantom +\series default + creates only space for the maximal height of the characters in the box + but not for its width. + +\series bold + +\backslash +vphantom +\series default + creates only space for the width of the box content. + Therefore the boxes of both commands have only one red arrow. +\end_layout + +\begin_layout Standard +For example the command +\series bold + +\backslash +vphantom +\series default + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series bold +a +\backslash +int +\series default + creates space for the height of the integral sign, +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +The command +\series bold + +\backslash +int +\series default + creates an integral sign, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Big-Operators" + +\end_inset + +. +\end_layout + +\end_inset + + because this is the larger character. + An example application is in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Multiline-Brackets" + +\end_inset + +. +\end_layout + +\begin_layout Standard +Placeholders can also be used for text when they are inserted via the menu + +\family sans +Insert\SpecialChar \menuseparator +Formatting\SpecialChar \menuseparator +Phantom +\family default +: +\end_layout + +\begin_layout Standard +This is a sentence. +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom Phantom +status open + +\begin_layout Plain Layout +This +\end_layout + +\end_inset + + is a sentence. +\end_layout + +\begin_layout Subsection +Lines +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Lines +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! underlined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overline +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A+B +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! O ! +\backslash +overline +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +underline +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A+B +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +underline +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overline +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +underline +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +In the last example it doesn't matter if first +\series bold + +\backslash +overline +\series default + or +\series bold + +\backslash +underline +\series default + is inserted. +\end_layout + +\begin_layout Standard +To double underline use +\series bold + +\backslash +underline +\series default + twice. +\end_layout + +\begin_layout Standard +It is possible to place up to 6 lines above or below characters. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +Custom lines can be created using the command +\series bold + +\backslash +rule +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +rule +\end_layout + +\end_inset + + which has the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +rule[vertical offset]{length}{thickness} +\end_layout + +\begin_layout Standard +The optional vertical offset shifts the line upwards (or downwards, when + the value is negative). + The units listed in +\begin_inset CommandInset ref +LatexCommand ref +reference "tab:Available-units" + +\end_inset + + can be used for the values. + Here are two example lines created with the commands +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +rule[-2ex]{3cm}{2pt} +\series default + and +\series bold + +\backslash +rule{2cm}{1pt} +\series default +: +\end_layout + +\begin_layout Standard +This is a sentence +\begin_inset Formula $\rule[-2ex]{3cm}{2pt}\rule{2cm}{1pt}$ +\end_inset + + with two lines. +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +rule +\series default + can also be used for text when a line is inserted via the menu +\family sans +Insert\SpecialChar \menuseparator +Formatting\SpecialChar \menuseparator +Horizontal +\begin_inset space ~ +\end_inset + +Line +\family default +: +\end_layout + +\begin_layout Standard +This is a sentence +\begin_inset CommandInset line +LatexCommand rule +offset "0.5ex" +width "3cm" +height "1pt" + +\end_inset + + with one line. +\end_layout + +\begin_layout Subsection +Ellipses +\begin_inset CommandInset label +LatexCommand label +name "sub:Ellipses" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Ellipses +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +There are different types of ellipses available. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +In the math toolbar in the submenu of the button +\begin_inset Graphics + filename ../images/math/ldots.png + scale 85 + +\end_inset + + +\end_layout + +\end_inset + + For listings dots at the baseline are used ( +\series bold + +\backslash +ldots +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +ldots +\end_layout + +\end_inset + +), while for operations dots are needed that are on the same height as the + operators ( +\series bold + +\backslash +cdots +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +cdots +\end_layout + +\end_inset + +). + When using the command +\series bold + +\backslash +dots +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dots +\end_layout + +\end_inset + +, LaTeX decides on the basis of the next character what type is used. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A_1 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +, +\backslash +dots +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +,A_n +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A_{1},\dots,A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A_1 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + ++ +\backslash +dots +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + ++A_n +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A_{1}+\dots+A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A_1 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +, +\backslash +ldots +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +,A_n +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A_{1},\ldots,A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A_1 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + ++ +\backslash +cdots +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + ++A_n +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A_{1}+\cdots+A_{n}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vdots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\vdots$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ddots$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +iddots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\iddots$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +3×3 +\begin_inset space \thinspace{} +\end_inset + +matrix with the different dots +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\begin{array}{ccc} +A_{11} & \cdots & A_{1m}\\ +\vdots & \ddots & \vdots\\ +A_{n1} & \cdots & A_{nm} +\end{array}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +The ellipses available in menu +\family sans +Insert\SpecialChar \menuseparator +Special +\begin_inset space ~ +\end_inset + +Character +\family default + are +\series bold + +\backslash +ldots +\series default +. +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +To use +\series bold + +\backslash +iddots +\series default +, one of the options +\family sans +Use mathdots package (automatically) +\family default + must be set in the document settings under +\family sans +Math +\begin_inset space ~ +\end_inset + +Options +\family default +. +\begin_inset Newline newline +\end_inset + +Using the option +\family sans +Use mathdots package +\family default + will improve the appearance of all dots in the documents if their font + style or size is not the default. +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +Specially for matrices there are ellipses that span over several columns. + They are created with the command +\series bold + +\backslash +hdotsfor +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hdotsfor +\end_layout + +\end_inset + +, that has the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +hdotsfor[distance]{number of columns} +\end_layout + +\begin_layout Standard +The number of columns specifies how many columns should be spanned. + Distance is a factor for the distance between the dots. +\end_layout + +\begin_layout Standard +In the following matrix the command +\series bold + +\backslash +hdotsfor[2]{4} +\series default + was inserted in the first box of the second line, to get an ellipsis with + a dot distance twice as long as with the command +\series bold + +\backslash +dots +\series default +: +\begin_inset Formula +\[ +\left(\begin{array}{cccc} +A & B & C & D\\ +\hdotsfor[2]{4}\\ +q & w & e & r +\end{array}\right) +\] + +\end_inset + +Note that the matrix fields that should be spanned must be empty, otherwise + you get LaTeX-errors. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +Furthermore you can fill with the command +\series bold + +\backslash +dotfill +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dotfill +\end_layout + +\end_inset + + the rest of a line with dots. + The effect of these commands is the same as with +\series bold + +\backslash +hfill +\series default +, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Variable-Space" + +\end_inset + +. +\end_layout + +\begin_layout Standard +For example the command +\series bold +A +\backslash +dotfill +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +B +\series default + produces +\end_layout + +\begin_layout Standard +\begin_inset Formula $A\dotfill B$ +\end_inset + + +\end_layout + +\begin_layout Standard +Similar to +\series bold + +\backslash +dotfill +\series default + there is for a line the command +\series bold + +\backslash +hrulefill +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hrulefill +\end_layout + +\end_inset + +: +\end_layout + +\begin_layout Standard +\begin_inset Formula $A\hrulefill B$ +\end_inset + + +\end_layout + +\begin_layout Standard +To use the commands for text, they have to be inserted in TeX-mode. +\end_layout + +\begin_layout Section +Matrices +\begin_inset CommandInset label +LatexCommand label +name "sec:Matrices" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Matrices +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Matrices can be inserted via the math toolbar button +\begin_inset Graphics + filename ../images/dialog-show_mathmatrix.png + scale 85 + +\end_inset + + or the menu +\family sans +Insert\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Matrix +\family default +. + In the matrix dialog you can specify the number of columns and rows, the + alignment and the decoration. + The vertical alignment is only of importance for matrices in inline formulas: +\end_layout + +\begin_layout Standard +The first matrix is top +\begin_inset Formula $\begin{array}[t]{cccc} +A & D & G & J\\ +B & E & H & K\\ +C & F & I & L +\end{array}$ +\end_inset + +, the second middle +\begin_inset Formula $\begin{array}{cccc} +A & D & G & J\\ +B & E & H & K\\ +C & F & I & L +\end{array}$ +\end_inset + + and the third bottom +\begin_inset Formula $\begin{array}[b]{cccc} +A & D & G & J\\ +B & E & H & K\\ +C & F & I & L +\end{array}$ +\end_inset + + aligned. +\end_layout + +\begin_layout Standard +The horizontal alignment specifies how the column entries should be aligned. + It is set by entering a letter for every column. + +\emph on +l +\emph default + denotes left aligned, +\emph on +c +\emph default + centered and +\emph on +r +\emph default + right aligned. + To create for example a 4 +\series bold +× +\series default +4 +\begin_inset space ~ +\end_inset + +matrix where the first column is left aligned, the second and third are + centered and the last one is right aligned, one enters for the horizontal + alignment +\series bold +lccr +\series default +. + Normally in a matrix all columns are centered, therefore the default for + every column is a +\series bold +c +\series default +. +\end_layout + +\begin_layout Standard +Horizontal alignment: +\end_layout + +\begin_layout Standard + +\series bold +lll +\series default + : +\begin_inset Formula $\begin{array}{lll} +10000 & D & G\\ +B & 10000 & H\\ +C & F & 10000 +\end{array}$ +\end_inset + + , +\series bold +ccc +\series default + : +\begin_inset Formula $\begin{array}{ccc} +10000 & D & G\\ +B & 10000 & H\\ +C & F & 10000 +\end{array}$ +\end_inset + + , +\series bold +rrr +\series default + : +\begin_inset Formula $\begin{array}{rrr} +10000 & D & G\\ +B & 10000 & H\\ +C & F & 10000 +\end{array}$ +\end_inset + + +\end_layout + +\begin_layout Standard +To add or delete rows and columns subsequently, the math toolbar buttons + +\begin_inset Graphics + filename ../images/tabular-feature_append-row.png + scale 85 + +\end_inset + +, +\begin_inset Graphics + filename ../images/tabular-feature_delete-row.png + scale 85 + +\end_inset + +, etc. +\begin_inset space \thinspace{} +\end_inset + +, or the menu +\family sans +Edit\SpecialChar \menuseparator +Rows & Columns +\family default + can be used. + New rows can also be created with +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +The +\family sans +Decoration +\family default + adds parentheses in the selected style around the matrix. + Alternatively, parentheses can can either be created with the commands + +\series bold + +\backslash +left +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +left +\end_layout + +\end_inset + + and +\series bold + +\backslash +right +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +right +\end_layout + +\end_inset + + (shortcut +\family sans +Alt+M +\begin_inset space ~ +\end_inset + +Parenthesis +\family default +), see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Automatic-Bracket-Size" + +\end_inset + +, or by using the following commands: +\begin_inset VSpace medskip +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bmatrix +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{7.5mm}{}\begin{bmatrix}\begin{array}{cc} +0 & \textrm{-}\mathrm{i}\\ +\mathrm{i} & 0 +\end{array}\end{bmatrix}\raisebox{-5.3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Bmatrix +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{7.5mm}{}\begin{Bmatrix}\begin{array}{cc} +0 & \textrm{-}\mathrm{i}\\ +\mathrm{i} & 0 +\end{array}\end{Bmatrix}\raisebox{-5.3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +pmatrix +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{7.5mm}{}\begin{pmatrix}\begin{array}{cc} +0 & \textrm{-}\mathrm{i}\\ +\mathrm{i} & 0 +\end{array}\end{pmatrix}\raisebox{-5.3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vmatrix +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{7.5mm}{}\begin{vmatrix}\begin{array}{cc} +0 & \textrm{-}\mathrm{i}\\ +\mathrm{i} & 0 +\end{array}\end{vmatrix}\raisebox{-5.3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Vmatrix +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{7.5mm}{}\begin{Vmatrix}\begin{array}{cc} +0 & \textrm{-}\mathrm{i}\\ +\mathrm{i} & 0 +\end{array}\end{Vmatrix}\raisebox{-5.3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +matrix +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +2 +\series bold +× +\series default +2 +\begin_inset space \thinspace{} +\end_inset + +matrix +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{7.5mm}{}\begin{matrix}\begin{array}{cc} +0 & \textrm{-}\mathrm{i}\\ +\mathrm{i} & 0 +\end{array}\end{matrix}\raisebox{-5.3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +When e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + + +\series bold + +\backslash +vmatrix +\series default + is inserted, a blue box appears between two vertical lines where the matrix + is inserted. +\begin_inset Newline newline +\end_inset + +Note that decorated matrices ignore the vertical alignment. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +As all multiline formulas are matrices, the length +\series bold + +\backslash +arraycolsep +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +arraycolsep +\end_layout + +\end_inset + + that is described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Column-Separation" + +\end_inset + + can also be used to change the column separation of matrices. +\end_layout + +\begin_layout Standard +To change the row separation, the command +\series bold + +\backslash +arraystretch +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +arraystretch +\end_layout + +\end_inset + + is used. + It is used as follows: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +renewcommand{ +\backslash +arraystretch}{stretch factor} +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +renewcommand +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The command +\series bold + +\backslash +renewcommand +\series default + assigns the stretch factor to the predefined command +\series bold + +\backslash +arraystretch +\series default +. + To double e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +the row separation, use the factor 2. + This is then used for all following matrices. + To go back to the original separation, assign the factor 1 to +\series bold + +\backslash +arraystretch +\series default +. +\end_layout + +\begin_layout Standard +To set matrices into a text line, the command +\series bold + +\backslash +smallmatrix +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +smallmatrix +\end_layout + +\end_inset + + is used. + When it is inserted a blue box with two dashed lines appears. + In this box the matrix is inserted. +\end_layout + +\begin_layout Standard +This is a matrix +\begin_inset Formula $\left(\begin{smallmatrix}A & B\\ +C & D +\end{smallmatrix}\right)$ +\end_inset + + in a text line. +\end_layout + +\begin_layout Section +Brackets and Delimiters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Brackets +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Delimiters +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Vertical Brackets and Delimiters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Brackets ! vertical +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +( +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $($ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +{ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\{$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +[ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $[$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +langle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\langle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lceil +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\lceil$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lfloor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\lfloor$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +/ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $/$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +| +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $|$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $)$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +] +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $]$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rceil +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rceil$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rfloor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rfloor$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\backslash + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\backslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +| +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\|$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard + +\series medium +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + In TeX-mode the command +\series bold + +\backslash +textbackslash +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +textbackslash +\end_layout + +\end_inset + + must be used for the backslash, because the command +\series bold + +\backslash + +\backslash + +\series default + produces a line break there. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +For all characters listed above the size can be adjusted with the commands + described in the following two subsections. + When using these commands, the characters < and > can directly be used + instead of the commands +\series bold + +\backslash +langle +\series default + and +\series bold + +\backslash +rangle +\series default +. +\end_layout + +\begin_layout Subsubsection +Manual Bracket Size +\begin_inset CommandInset label +LatexCommand label +name "sub:Manual-Bracket-Size" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Bracket size ! manual +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The bracket size can be specified manually by the LaTeX-commands +\series bold + +\backslash +big +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +big +\end_layout + +\end_inset + +, +\series bold + +\backslash +Big +\series default +, +\series bold + +\backslash +bigg +\series default + and +\series bold + +\backslash +Bigg +\series default +. + +\series bold + +\backslash +big +\series default + denotes the smallest and +\series bold + +\backslash +Bigg +\series default + the largest bracket size. +\end_layout + +\begin_layout Standard +These commands are used to emphasize levels of brackets: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +all brackets in the same size: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +this looks better: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +For the second formula the command +\series bold + +\backslash +Big((A+B)(A-B) +\backslash +Big)^ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +C +\series default + has been used. +\end_layout + +\begin_layout Standard +Here is an overview about all bracket sizes: +\end_layout + +\begin_layout Standard +\align center + +\backslash +Bigg( +\backslash +exp +\backslash +bigg< +\backslash +Big[ +\backslash +big{ +\backslash +ln(3x) +\backslash +big}^2 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +sin(x) +\backslash +Big]^ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +bigg> +\backslash +Bigg)^0,5 +\end_layout + +\begin_layout Standard +\align center +\begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$ +\end_inset + + +\end_layout + +\begin_layout Standard +Besides the +\series bold + +\backslash +big +\series default +-commands there is the variant +\series bold + +\backslash +bigm +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +bigm +\end_layout + +\end_inset + + that adds a bit more space between the bracket and its content, and the + variant +\series bold + +\backslash +bigl +\series default +- +\series bold + +\backslash +bigr +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +bigl - +\backslash +bigr +\end_layout + +\end_inset + +, that don't add additional space. + The +\emph on +l +\emph default + at the end of the command +\series bold + +\backslash +bigl +\series default + is for a left bracket; for a right bracket this will be replaced by an + +\emph on +r +\emph default +. + A left or right bracket can each be an opening or closing bracket. +\end_layout + +\begin_layout Standard +In the following table is a comparison of the variants: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Bigm( +\backslash +bigm( +\backslash +ln(3x) +\backslash +bigm)^2 +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default + +\backslash +Bigm) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5.5mm}{}\Bigm(\bigm(\ln(3x)\bigm)^{2}\Bigm)\raisebox{-3.25mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Big( +\backslash +big( +\backslash +ln(3x) +\backslash +big)^2 +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default + +\backslash +Big) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5.5mm}{}\Big(\big(\ln(3x)\big)^{2}\Big)\raisebox{-3.25mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Bigl( +\backslash +bigl( +\backslash +ln(3x) +\backslash +bigr)^2 +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default + +\backslash +Bigr) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5.5mm}{}\Bigl(\bigl(\ln(3x)\bigr)^{2}\Bigr)\raisebox{-3.25mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigl) +\backslash +ln(3x) +\backslash +bigr( +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Subsubsection +Automatic Bracket Size +\begin_inset CommandInset label +LatexCommand label +name "sub:Automatic-Bracket-Size" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Bracket size ! automatic +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Brackets with variable size can be inserted with the commands +\series bold + +\backslash +left +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +left +\end_layout + +\end_inset + + and +\series bold + +\backslash +right +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +right +\end_layout + +\end_inset + + or via the math toolbar button +\begin_inset Graphics + filename ../images/dialog-show_mathdelimiter.png + scale 85 + +\end_inset + +. + Directly behind +\series bold + +\backslash +left +\series default + and +\series bold + +\backslash +right +\series default + the wanted bracket must be inserted. + The bracket size will then automatically be calculated for the output. +\end_layout + +\begin_layout Standard +\align center +normal bracket: The command +\series bold + +\backslash +ln( +\backslash +frac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +C +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +) +\series default + creates +\begin_inset Formula +\[ +\ln(\frac{A}{C}) +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +multiline bracket: The command +\series bold + +\backslash +ln +\backslash +left( +\backslash +frac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +C +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +right) +\series default + creates +\begin_inset Formula +\[ +\ln\left(\frac{A}{C}\right) +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +Instead of +\series bold + +\backslash +left +\series default + and +\series bold + +\backslash +right +\series default + the shortcut +\family sans +Alt+M +\begin_inset space ~ +\end_inset + +Bracket +\family default + can be used. + This has the advantage that you can see in LyX immediately the real bracket + size and that the matching right bracket will be created too. +\begin_inset Newline newline +\end_inset + +The command for the last example would then be: +\series bold + +\backslash +ln Alt+M +\series default + +\series bold +( +\backslash +frac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +C +\end_layout + +\begin_layout Standard +To omit a left or right bracket, a dot is inserted for the omitted bracket. + For example the command +\series bold + +\backslash +left. +\backslash +frac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +right} +\series default + creates: +\series bold + +\begin_inset Formula +\[ +\left.\frac{A}{B}\right\} +\] + +\end_inset + + +\series default +The commands +\series bold + +\backslash +left +\series default + and +\series bold + +\backslash +right +\series default + will be converted by LyX to brackets in the right size when the document + is reloaded and an omitted bracket will appear as dashed line. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX, + the command +\series bold + +\backslash +middle +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +middle +\end_layout + +\end_inset + + is additionally available for all brackets and limits. + With this command the height of the following character is adapted to the + one of the surrounding brackets, what is e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +needed for physical vectors: +\begin_inset Formula +\[ +\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle +\] + +\end_inset + +For physical vectors there is a special LaTeX-package, described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Physical-Vectors" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Horizontal Brackets +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Brackets ! horizontal +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{2.3mm}{ +\end_layout + +\end_inset + + +\backslash +overbrace +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A+B +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +^ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +3 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! O ! +\backslash +overbrace +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\overbrace{A+B}^{3}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{-2.2mm}{ +\end_layout + +\end_inset + + +\backslash +underbrace +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A+B +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +_5 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +underbrace +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\underbrace{A+B}_{5}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overbrace +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +underbrace +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A+B_w +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +_7 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +^ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +C +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +In the last example it doesn't matter if +\series bold + +\backslash +overbrace +\series default + or +\series bold + +\backslash +underbrace +\series default + is inserted at first. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +When brackets are needed that overlap each other, multiline formulas, as + described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Multiline-Formulas" + +\end_inset + +, must be used: +\begin_inset Formula +\begin{eqnarray*} +A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\ + & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s} +\end{eqnarray*} + +\end_inset + +In the first row the formula is inserted together with the first brace. + It is hereby important that the space command +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +Space commands are explained in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Predefined-Space" + +\end_inset + +. +\end_layout + +\end_inset + + +\series bold + +\backslash +: +\series default + is inserted before the first +\begin_inset Formula $d$ +\end_inset + +, because the brace that ends behind the +\begin_inset Formula $q$ +\end_inset + + prevents that the following +\begin_inset Quotes eld +\end_inset + ++ +\begin_inset Quotes erd +\end_inset + + is surrounded by space. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +because a bracket is not handled as a character, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Binary-Operators" + +\end_inset + + +\end_layout + +\end_inset + + In the second row the second brace is inserted. + As it should begin before the +\begin_inset Formula $b$ +\end_inset + +, first the command +\series bold + +\backslash +hphantom{gggg+ +\backslash +:} +\series default + is inserted. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +more about +\series bold + +\backslash +hphantom +\series default + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Placeholders" + +\end_inset + + +\end_layout + +\end_inset + + This space is needed because the +\begin_inset Quotes eld +\end_inset + ++ +\begin_inset Quotes erd +\end_inset + + is also surrounded by space in the formula. + The brace is placed under the command +\series bold + +\backslash +hphantom{bbqq+dddd} +\series default +. +\end_layout + +\begin_layout Standard +It gets more complicated when brackets overlap each other, like in the following + example: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +setlength{ +\backslash +jot}{-6pt} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{eqnarray*} + & & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\ +A & = & \underbrace{gggg+bbqq}_{r}+\: dddd +\end{eqnarray*} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +setlength{ +\backslash +jot}{3pt} +\end_layout + +\end_inset + +The first formula row is the same as the second row of the previous example, + with the difference that the brace is above. + The second row contains the formula together with the second brace. + To avoid that there is space between the upper brace in the first row and + the formula, the row spacing needs to be reduced. + This is not easily possible due to a bug in LyX +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #1505" +target "http://www.lyx.org/trac/ticket/1505" + +\end_inset + + +\end_layout + +\end_inset + +. + As a solution for the problem, the global formula row separation +\series bold + +\backslash +jot +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! J ! +\backslash +jot +\end_layout + +\end_inset + + must be changed to -6 +\begin_inset space \thinspace{} +\end_inset + +pt before the formula with the command +\series bold + +\backslash +setlength{ +\backslash +jot}{-6pt} +\series default + in TeX-mode. + +\series bold + +\backslash +jot +\series default + is set back after the formula to the standard value of 3 +\begin_inset space \thinspace{} +\end_inset + +pt using the same command. + More about the row separation in formulas is explained in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Line-Separation" + +\end_inset + +. +\end_layout + +\begin_layout Section +Arrows +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Arrows +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Arrows can be inserted via the math toolbar button +\begin_inset Graphics + filename ../images/math/leftarrow.png + scale 85 + +\end_inset + + or the commands listed in the following subsections. +\end_layout + +\begin_layout Subsection +Horizontal Arrows +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Arrows ! horizontal +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +gets +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\gets$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Leftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Leftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +longleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\longleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Longleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Longleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leftharpoonup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\leftharpoonup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leftharpoondown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\leftharpoondown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hookleftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\hookleftarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +to +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\to$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Rightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Rightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +longrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\longrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Longrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Longrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rightharpoonup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rightharpoonup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rightharpoondown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rightharpoondown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hookrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\hookrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\leftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Leftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Leftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +longleftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\longleftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Longleftrightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Longleftrightarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rightleftharpoons +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rightleftharpoons$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hspace{} +\length 25pt +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mapsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mapsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +longmapsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\longmapsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leadsto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\leadsto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dasharrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\dasharrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +Arrows used as accents like e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +vector arrows are listed in +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Accents" + +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +Furthermore there are the labeled arrows +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Arrows ! labeled +\end_layout + +\end_inset + + +\series bold + +\backslash +xleftarrow +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! X ! +\backslash +xleftarrow +\end_layout + +\end_inset + + and +\series bold + +\backslash +xrightarrow +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! X ! +\backslash +xrightarrow +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + +. + When inserting one of these commands in a formula, an arrow with two blue + boxes appear where the label can be inserted. + The length of the arrow adapts to the label width. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +F(a) +\backslash +xleftarrow +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +x=a +\begin_inset Formula $\downarrow$ +\end_inset + +x>0 +\begin_inset Formula $\to$ +\end_inset + +F(x) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +F(x) +\backslash +xrightarrow +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +x=a +\begin_inset Formula $\downarrow$ +\end_inset + +x>0 +\begin_inset Formula $\to$ +\end_inset + +F(a) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Subsection +Vertical and diagonal Arrows +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Arrows ! diagonal +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Arrows ! vertical +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +uparrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\uparrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Uparrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Uparrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +updownarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\updownarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Updownarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Updownarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Downarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Downarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +downarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\downarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nearrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nearrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +searrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\searrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +swarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\swarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nwarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nwarrow$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +Vertical arrows can be used also as delimiters together with the commands + described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Manual-Bracket-Size" + +\end_inset + + and +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Automatic-Bracket-Size" + +\end_inset + +. +\end_layout + +\begin_layout Section +Accents +\begin_inset CommandInset label +LatexCommand label +name "sec:Accents" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Accents +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Accents can be inserted via the math toolbar button +\begin_inset Graphics + filename ../images/math/hat.png + scale 85 + +\end_inset + + or the commands listed in the following subsections. +\end_layout + +\begin_layout Subsection +Accents for one Character +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +texorpdfstring{ +\end_layout + +\end_inset + + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +accents in text see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Accents-in-Text" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +}{} +\end_layout + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +texorpdfstring +\series default + is used to avoid that the footnote appears in the PDF-bookmark. +\end_layout + +\begin_layout Plain Layout +More about +\series bold + +\backslash +texorpdfstring +\series default + is in section +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Formulas-in-Section" + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset CommandInset label +LatexCommand label +name "sub:Accents-for-one" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Accents ! for one character +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dot +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\dot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddot +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\ddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dddot +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\dddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddddot +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vec +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Vectors +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\vec{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bar +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\bar{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathring +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\mathring{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +tilde +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\tilde{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hat +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\hat{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +check +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\check{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +acute +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\acute{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +grave +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\grave{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +breve +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\breve{A}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + + +\end_layout + +\begin_layout Standard +You can directly insert accents like é to formulas. + LyX will transform them to the corresponding accent command. + For umlauts +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Umlauts +\end_layout + +\end_inset + + it is better to insert a quotation mark before the vowel. + These two characters are then treated by LaTeX as +\emph on +one +\emph default + character when the formula part with the umlaut is marked as German. + In contrary to +\series bold + +\backslash +ddot +\series default +, with this method +\begin_inset Quotes eld +\end_inset + +real +\begin_inset Quotes erd +\end_inset + + umlauts are created as demonstrated in the following example: +\end_layout + +\begin_layout Standard +\begin_inset VSpace -2mm +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + and the 0 +\begin_inset space \thinspace{} +\end_inset + +pt space are only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\lang ngerman +\begin_inset Quotes grd +\end_inset + +i +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset space \hspace{} +\length 0pt +\end_inset + + +\lang ngerman + +\begin_inset Formula $"i$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddot +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +i +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\ddot{i}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +Another advantage to +\series bold + +\backslash +ddot +\series default + is that umlauts can directly be converted to mathematical text because + the accent commands above are +\emph on +not allowed +\emph default + +\emph on +in mathematical text +\emph default +. + To convert an accented character to mathematical text, only the character + under the accent may be converted. + This applies also for all other conversions, e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +to italic or bold. +\end_layout + +\begin_layout Standard +In mathematical text, umlauts and other accented characters can directly + be inserted. +\end_layout + +\begin_layout Subsection +Accents for several Characters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Accents ! for several characters +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overleftarrow +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +underleftarrow +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overleftrightarrow +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +underleftrightarrow +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +overrightarrow +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +underrightarrow +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +widetilde +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +widehat +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +With these commands as many characters as you like can be accented. + But the accents +\series bold + +\backslash +widetilde +\series default + and +\series bold + +\backslash +widehat +\series default + will only be set in the output with a length of three characters, as shown + in the following example: +\begin_inset Formula +\[ +\widetilde{A+B=C-D} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +With the commands +\series bold + +\backslash +overset +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! O ! +\backslash +overset +\end_layout + +\end_inset + + and +\series bold + +\backslash +underset +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +underset +\end_layout + +\end_inset + + described in the previous subsection it is also possible to accent several + characters. + The command +\series bold + +\backslash +underset +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\begin_inset Formula $\downarrow$ +\end_inset + +*** +\series default + creates: +\begin_inset Formula +\[ +\underset{***}{A=B} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Section +Space +\begin_inset CommandInset label +LatexCommand label +name "sub:Space" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Space ! horizontal +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Predefined Space +\begin_inset CommandInset label +LatexCommand label +name "sub:Predefined-Space" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Space ! horizontal ! predefined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Sometimes it is necessary to insert horizontal space into a formula. + This is done by inserting a protected space (shortcut +\begin_inset Info +type "shortcut" +arg "command-alternatives space-insert protected ; math-space" +\end_inset + +). + A +\begin_inset Quotes eld +\end_inset + + +\color blue + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\color inherit + +\begin_inset Quotes erd +\end_inset + + appears and by pressing +\family sans +Space +\family default + several times one can select one of eight different space sizes. + The spaces can also be inserted using the math toolbar button +\begin_inset Graphics + filename ../images/math/space.png + scale 85 + +\end_inset + + or special commands. + Independent from the inserted command, one can select the size again by + pressing +\family sans +Space +\family default + afterwards. +\end_layout + +\begin_layout Standard +\noindent +\align center +\begin_inset VSpace -5mm +\end_inset + + +\begin_inset Tabular + + + + + + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +, +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +; +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +quad +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +qquad +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +! +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +Number of +\family sans +Space +\family default + keystrokes after inserting the protected space +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +1 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +2 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +4 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +5 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\, B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\: B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\; B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\quad B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\qquad B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\! B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +The last size seem to produce no space. + It is displayed red in LyX contrary to the other sizes, because it is a + negative space. + There are two more negative spaces: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +negmedspace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +negthickspace +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +Number of +\family sans +Space +\family default + keystrokes after inserting the protected space +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +6 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +7 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\negmedspace B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\negthickspace B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +Negative spaces can lead to characters overlapping each other. + Thus they can be used to enforce ligatures, which are e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +useful for summation operators: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sum +\backslash +sum +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +f_kl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sum +\backslash +negmedspace +\backslash +sum +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +f_kl +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\sum\negmedspace\sum f_{kl}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +Relations like for example equal signs, are always surrounded by space. + To suppress this, the equal sign is placed into a TeX-brace. + The following example demonstrates this: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +normal equation +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A=B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\begin_inset Formula $\raisebox{5mm}{}$ +\end_inset + +equation without space +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A{=}B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\noindent +The command for the last formula is: +\series bold +A +\backslash +{= +\begin_inset Formula $\to$ +\end_inset + +B +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +Spaces are needed for physical units, because the space between the value + and the unit is the smallest one and not a normal space. + For units in text, the smallest space is inserted via the menu +\family sans +Insert\SpecialChar \menuseparator +Formatting\SpecialChar \menuseparator +Thin +\begin_inset space ~ +\end_inset + +Space +\family default + (shortcut +\begin_inset Info +type "shortcut" +arg "space-insert thin" +\end_inset + +). +\end_layout + +\begin_layout Standard +An example to visualize the difference: +\end_layout + +\begin_layout Standard +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +24 kW +\begin_inset Formula $\cdot$ +\end_inset + +h +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +space between value and unit +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +24 +\begin_inset space \thinspace{} +\end_inset + +kW +\begin_inset Formula $\cdot$ +\end_inset + +h +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +smallest space between value and unit +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Subsection +Variable Space +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +texorpdfstring{ +\end_layout + +\end_inset + + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +for vertical space in formulas see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Line-Separation" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +}{} +\end_layout + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\backslash +texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. +\end_layout + +\begin_layout Plain Layout +More about +\backslash +texorpdfstring is in section +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Formulas-in-Section" + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset CommandInset label +LatexCommand label +name "sub:Variable-Space" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Space ! horizontal ! variable +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Space with a defined length can be inserted with the command +\series bold + +\backslash +hspace +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hspace +\end_layout + +\end_inset + +. + Then a long +\begin_inset Quotes eld +\end_inset + + +\color blue + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\color inherit + +\begin_inset Quotes erd +\end_inset + + appears. + The length can be specified by left-clicking on the +\begin_inset Quotes eld +\end_inset + + +\color blue + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\color inherit + +\begin_inset Quotes erd +\end_inset + +. + The length may also be negative. + To insert as much space as is available, the command +\series bold + +\backslash +hfill +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hfill +\end_layout + +\end_inset + + is used. +\end_layout + +\begin_layout Standard +\begin_inset VSpace -1mm +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command ( +\backslash +hspace length) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A=B +\backslash +hspace +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\begin_inset Formula $\to$ +\end_inset + +A +\backslash +not=C (3 +\begin_inset space \thinspace{} +\end_inset + +cm) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A=B\hspace{3cm}A\not=C$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A +\backslash +hspace +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\begin_inset Formula $\to$ +\end_inset + +A +\backslash +not=A (-1 +\begin_inset space \thinspace{} +\end_inset + +mm) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\hspace{-1mm}A\not=A$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A=A +\backslash +hfill +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +B=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A=A\hfill B=B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +In the last example the available space is given by the longest column entry + of the table. + In an inline formula the space depends on the length of the line in which + +\series bold + +\backslash +hfill +\series default + is inserted. + Thus, when the line uses the full width, no space will be created. + +\series bold + +\backslash +hfill +\series default + only has an effect on displayed formulas when the formula style +\series bold +Indented +\series default + is used. + (Formula styles are explained in +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + +.) +\end_layout + +\begin_layout Standard +Besides +\series bold + +\backslash +hfill +\series default +, there are the commands +\series bold + +\backslash +dotfill +\series default + and +\series bold + +\backslash +hrulefill +\series default + that fill the space with a pattern, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Ellipses" + +\end_inset + + for an example. +\end_layout + +\begin_layout Standard +For text, variable space can be inserted via the menu +\family sans +Insert\SpecialChar \menuseparator +Formatting\SpecialChar \menuseparator +Horizontal +\begin_inset space ~ +\end_inset + +Space +\family default +: +\end_layout + +\begin_layout Standard +This is a line with +\begin_inset space \hspace{} +\length 2cm +\end_inset + +2 +\begin_inset space \thinspace{} +\end_inset + +cm space. +\end_layout + +\begin_layout Standard +This is a line with +\begin_inset space \hfill{} +\end_inset + +maximum space. +\end_layout + +\begin_layout Subsection +Space besides inline Formulas +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Space ! besides inline formulas +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The space that surrounds inline formulas can be adjusted with the length + +\series bold + +\backslash +mathsurround +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +mathsurround +\end_layout + +\end_inset + +. + The value of a length is set with the command +\series bold + +\backslash +setlength +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +setlength +\end_layout + +\end_inset + + which has the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +setlength{length name}{value} +\end_layout + +\begin_layout Standard +To set +\series bold + +\backslash +mathsurround +\series default + to the value 5 +\begin_inset space \thinspace{} +\end_inset + +mm, the command +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +setlength{ +\backslash +mathsurround}{5mm} +\end_layout + +\begin_layout Standard +is inserted in TeX-mode. + 5 +\begin_inset space \thinspace{} +\end_inset + +mm space will now be set around all inline formulas: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +setlength{ +\backslash +mathsurround}{5mm} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +This is a line with an inline formula +\begin_inset Formula $A=B$ +\end_inset + + with 5 +\begin_inset space \thinspace{} +\end_inset + +mm surrounding space. +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +setlength{ +\backslash +mathsurround}{0pt} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To return to the predefined value, +\series bold + +\backslash +mathsurround +\series default + is set to the value 0 +\begin_inset space \thinspace{} +\end_inset + +pt. +\end_layout + +\begin_layout Section +Boxes and Frames +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Boxes +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Frames | see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Boxes +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Boxes for text are described in chapter +\family typewriter +Boxes +\family default + in the +\family typewriter +Embedded +\begin_inset space ~ +\end_inset + +Objects +\family default + manual. +\end_layout + +\begin_layout Subsection +Boxes with Frame +\begin_inset CommandInset label +LatexCommand label +name "sub:Boxes-with-Frame" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Boxes ! with frame +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +It is possible to frame a formula or part of one with the commands +\series bold + +\backslash +fbox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! F ! +\backslash +fbox +\end_layout + +\end_inset + + and +\series bold + +\backslash +boxed +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +boxed +\end_layout + +\end_inset + +. +\end_layout + +\begin_layout Standard +When one of these commands is inserted in a formula, a blue box appears + within a frame to enter formula parts. + For +\series bold + +\backslash +fbox +\series default + an additional formula has to be created by +\family sans +Ctrl+M +\family default + within this box, because the box content will otherwise be treated as mathemati +cal text. + When +\series bold + +\backslash +boxed +\series default + is used, a new formula is automatically created inside the frame. +\end_layout + +\begin_layout Standard +The command +\series bold + +\backslash +fbox +\series default + is not suitable to frame displayed formulas because the formula will always + be set in the size of the text. + +\series bold + +\backslash +boxed +\series default + is in contrary not suitable to frame inline formulas, because the formula + will always be set in the size of a displayed formula. +\end_layout + +\begin_layout Standard +An extension to +\series bold + +\backslash +fbox +\series default + is the command +\series bold + +\backslash +framebox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! F ! +\backslash +framebox +\end_layout + +\end_inset + + where additionally the frame width and the alignment can be specified. + +\series bold + +\backslash +framebox +\series default + is used in the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +framebox[frame width][position]{box content} +\end_layout + +\begin_layout Standard +The position can either be +\emph on +l +\emph default + or +\emph on +r +\emph default +. + +\emph on +l +\emph default + left aligns, +\emph on +r +\emph default + right aligns the formula in the box. + When no position is given, the formula will be centered. +\begin_inset Newline newline +\end_inset + +If no width is given, also no position can be given. + In this case the frame width is adjusted to the box content like for +\series bold + +\backslash +fbox +\series default +. +\end_layout + +\begin_layout Standard +When the command +\series bold + +\backslash +framebox +\series default + is inserted, a box appears containing three blue boxes. + The first two boxes are surrounded by brackets and denote the two optional + arguments. + The third box is for formula parts like for +\series bold + +\backslash +fbox +\series default +. +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +fbox +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\family sans +Ctrl+M +\family default + +\backslash +int +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\fbox{\ensuremath{\int A=B}}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +boxed +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +int +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A+ +\backslash +fbox +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +framebox +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +20mm +\begin_inset Formula $\to$ +\end_inset + + +\begin_inset Formula $\to$ +\end_inset + + +\family sans +Ctrl+M +\family default + +\backslash +frac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\downarrow$ +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}$ +\end_inset + + +\begin_inset Formula $\framebox[20mm][]{\ensuremath{\frac{A}{B}}}$ +\end_inset + + +\begin_inset Formula $\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +The frame thickness can also be adjusted. + To do this the following commands have to be inserted in TeX-mode before + the formula +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +fboxrule +\series default + +\series bold + +\begin_inset Quotes eld +\end_inset + +thickness +\begin_inset Quotes erd +\end_inset + + +\series default + +\series bold + +\backslash +fboxsep +\series default + +\series bold + +\begin_inset Quotes eld +\end_inset + +distance +\begin_inset Quotes erd +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Quotes eld +\end_inset + +distance +\begin_inset Quotes erd +\end_inset + + specifies the minimal distance between the frame and the first character + in the box. + An example for this is the following framed formula: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fboxrule 2mm +\backslash +fboxsep 3mm +\end_layout + +\end_inset + + +\begin_inset Formula +\[ +\boxed{A+B=C} +\] + +\end_inset + +Before this formula the commands +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +fboxrule +\series default + +\series bold +2mm +\series default + +\series bold + +\backslash +fboxsep +\series default + +\series bold +3mm +\end_layout + +\begin_layout Standard +were inserted in TeX-mode. + The given values are used for all following boxes. +\end_layout + +\begin_layout Standard +To return to the standard frame size, the command +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +fboxrule +\series default + +\series bold +0.4pt +\series default + +\series bold + +\backslash +fboxsep +\series default + +\series bold +3pt +\series default + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fboxrule 0.4pt +\backslash +fboxsep 3pt +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +is inserted in TeX-mode before the next formula. +\end_layout + +\begin_layout Subsection +Boxes without Frame +\begin_inset CommandInset label +LatexCommand label +name "sub:Boxes-without-Frame" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Boxes ! without frame +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +For boxes without a frame there are the following box commands: +\series bold + +\backslash +mbox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +mbox +\end_layout + +\end_inset + +, +\series bold + +\backslash +makebox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +makebox +\end_layout + +\end_inset + + and +\series bold + +\backslash +raisebox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +raisebox +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +With +\series bold + +\backslash +raisebox +\series default + a box can be super- or subscripted. + But in contrary to normal super- and subscripting, the characters in the + box keep their font size. + +\series bold + +\backslash +raisebox +\series default + is used in the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +raisebox{height}{box content} +\end_layout + +\begin_layout Standard +When the box should contain a formula, an extra formula is needed like for + +\series bold + +\backslash +fbox +\series default +. + +\series medium + +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + For +\series bold + +\backslash +raisebox +\series default + this extra formula is created by pressing +\family sans +Ctrl+M +\family default + twice instead of once because LyX doesn't yet support +\series bold + +\backslash +raisebox +\series default + directly. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +H +\backslash +raisebox{2mm +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{al +\begin_inset Formula $\to$ +\end_inset + + lo +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $H\raisebox{2mm}{al}lo$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +H +\backslash +raisebox{-2mm +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{al +\begin_inset Formula $\to$ +\end_inset + +lo +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $H\raisebox{-2mm}{al}lo$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A= +\backslash +raisebox{-2mm +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\family sans +Ctrl+M +\family default + +\family sans +Ctrl+M +\family default + +\backslash +sqrt +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A=\raisebox{-2mm}{\mbox{\ensuremath{\sqrt{B}}}}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +The command +\series bold + +\backslash +mbox +\series default + is equivalent to +\series bold + +\backslash +fbox +\series default + and +\series bold + +\backslash +makebox +\series default + is equivalent to +\series bold + +\backslash +framebox +\series default +, with the difference that there is no frame. +\end_layout + +\begin_layout Subsection +Colored Boxes +\begin_inset CommandInset label +LatexCommand label +name "sub:Colored-Boxes" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Boxes ! colored +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To be able to use all commands explained in this section, the LaTeX-package + +\series bold +color +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +The LaTeX-package +\series bold +color +\series default + is part of every LaTeX standard installation. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! color +\end_layout + +\end_inset + + has to be loaded in the LaTeX-preamble with the line +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +When text is colored somewhere in the document with a predefined color, + LyX loads the LaTeX-package +\series bold +color +\series default + automatically. + Thus it is possible that the package is loaded twice, but this does not + cause problems. +\end_layout + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre +amble. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage{color} +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +To color boxes, the command +\series bold + +\backslash +colorbox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +colorbox +\end_layout + +\end_inset + + is used in the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +colorbox{color}{box content} +\end_layout + +\begin_layout Standard +The box content can also be a box and a +\series bold + +\backslash +colorbox +\series default + can also be part of another box (see the 2nd and 3rd example). + When the box should contain a formula, an extra formula has to be created, + the same way as for +\series bold + +\backslash +raisebox +\series default +. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +This also applies for the command +\series bold + +\backslash +fcolorbox +\series default +. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +One of the following predefined colors can be chosen: +\end_layout + +\begin_layout Standard + +\series bold +black +\series default +, +\series bold +blue +\series default +, +\series bold +cyan +\series default +, +\series bold +green +\series default +, +\series bold +magenta +\series default +, +\series bold +red +\series default +, +\series bold +white +\series default + and +\series bold +yellow +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +colorbox{yellow +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +colorbox{green +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\backslash +fbox +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +fbox +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +colorbox{green +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\family sans +Ctrl+M +\family default + +\family sans +Ctrl+M +\family default + +\backslash +int +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +C=D +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{7mm}{}\fbox{\colorbox{green}{\mbox{\ensuremath{\int C=D}}}}\raisebox{-5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +colorbox +\series default + only colors the box but not the characters in the box. + To color all characters, the whole formula is highlighted and the desired + color is chosen in the +\family sans +Text +\begin_inset space ~ +\end_inset + +Style +\family default + dialog. + The dialog can be called with the toolbar button +\begin_inset Graphics + filename ../images/dialog-show_character.png + scale 85 + +\end_inset + + or the menu +\family sans +Edit\SpecialChar \menuseparator +Text +\begin_inset space ~ +\end_inset + +Style\SpecialChar \menuseparator +Customized +\family default +. + The formula number then has the same color as the formula. + When the formula number should get another color than the formula characters, + the color must be changed within the formula. +\end_layout + +\begin_layout Standard +An example: +\end_layout + +\begin_layout Standard + +\color red +\begin_inset Formula +\begin{equation} +\int A=B\label{eq:red} +\end{equation} + +\end_inset + + +\color green + +\begin_inset Formula +\begin{equation} +\textcolor{red}{\int A=B}\label{eq:redgreen} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Standard +Formula +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:red" + +\end_inset + + is completely colored red. +\begin_inset Newline newline +\end_inset + +Formula +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:redgreen" + +\end_inset + + was first completely colored green to set the color for the formula number. + Subsequently the formula characters were colored red. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +To color the frame different than the rest of the box, the command +\series bold + +\backslash +fcolorbox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! F ! +\backslash +fcolorbox +\end_layout + +\end_inset + + is used in the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +fcolorbox{frame color}{color}{box content} +\end_layout + +\begin_layout Standard +So +\series bold + +\backslash +fcolorbox +\series default + is an extension of the command +\series bold + +\backslash +colorbox +\series default +. + The frame width is set, like for +\series bold + +\backslash +framebox +\series default +, with +\series bold + +\backslash +fboxrule +\series default + and +\series bold + +\backslash +fboxsep +\series default +. + An example: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fboxrule 1mm +\backslash +fboxsep 1mm +\end_layout + +\end_inset + + +\begin_inset Formula +\[ +\fcolorbox{cyan}{magenta}{A=B} +\] + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fboxrule 0.4pt +\backslash +fboxsep 3pt +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +This formula was created with the command +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +fcolorbox{cyan +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{magenta +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{A=B +\series default +. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +To use other colors than the predefined ones, they have to be defined first. +\end_layout + +\begin_layout Standard +One can for example define the color +\begin_inset Quotes eld +\end_inset + + +\series bold +darkgreen +\series default + +\begin_inset Quotes erd +\end_inset + + with the LaTeX-preamble line: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +definecolor{darkgreen}{cmyk}{0.5, +\series default + +\series bold +0, +\series default + +\series bold +1, +\series default + +\series bold +0.5} +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +definecolor +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard + +\series bold +cmyk +\series default + is the color space that denotes the colors +\series bold +cyan +\series default +, +\series bold +magenta +\series default +, +\series bold +yellow +\series default + and +\series bold +black +\series default +. + The four comma separated numbers are the portion factor for the corresponding + colors of the color space. + The factors can be in the range of 0 +\begin_inset space \thinspace{} +\end_inset + +- +\begin_inset space \thinspace{} +\end_inset + +1. + Instead of +\series bold +cmyk +\series default + also the color space +\series bold +rgb +\series default + can be used for definitions. + +\series bold +rgb +\series default + denotes +\series bold +red +\series default +, +\series bold +green +\series default + and +\series bold +blue +\series default +, so that there are in this case three portion factors for the corresponding + colors. + Furthermore there is the color space +\series bold +gray +\series default + with one portion factor for the gray value. +\end_layout + +\begin_layout Standard +As example a framed box with the new defined color +\series bold +darkgreen +\series default + where the characters have been colored +\series bold +yellow +\series default +: +\begin_inset Formula +\begin{equation} +\colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Standard +Self-defined colors can also be used for text with the help of the command + +\series bold + +\backslash +textcolor +\series default +: +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Text ! colored +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +textcolor{darkgreen}{ +\end_layout + +\end_inset + +This sentence is +\begin_inset Quotes eld +\end_inset + +darkgreen +\begin_inset Quotes erd +\end_inset + +. +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +textcolor +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +textcolor +\end_layout + +\end_inset + + is used in the scheme +\series bold + +\backslash +textcolor{color}{characters to color} +\series default +. +\end_layout + +\begin_layout Subsection +Paragraph Boxes +\begin_inset CommandInset label +LatexCommand label +name "sub:Paragraph-Boxes" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Boxes ! as paragraph +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +A box that can contain several lines and paragraphs, a so-called paragraph + box (parbox), can be created with the menu +\family sans +Insert\SpecialChar \menuseparator +Box +\family default + or the toolbar button +\begin_inset Graphics + filename ../images/box-insert.png + scale 85 + +\end_inset + +. +\end_layout + +\begin_layout Standard +The following example shows a framed parbox in a line: +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +This is a line +\begin_inset Box Boxed +position "c" +hor_pos "c" +has_inner_box 1 +inner_pos "t" +use_parbox 1 +use_makebox 0 +width "5cm" +special "none" +height "1in" +height_special "totalheight" +status open + +\begin_layout Plain Layout +This is a paragraph box. + It is exactly 5 +\begin_inset space \thinspace{} +\end_inset + +cm long and can also contain formulas: +\begin_inset Formula $\int A\,\mathrm{d}s=C$ +\end_inset + + +\end_layout + +\end_inset + + with a parbox. +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + + +\end_layout + +\begin_layout Standard +Such a box is created by right-clicking on the gray box inset. + A dialog pops up showing the box properties. + In our case set: +\emph on +Decoration +\emph default +: Rectangular box, +\emph on +Inner Box +\emph default +: Parbox, +\emph on +Width +\emph default +: 5 +\begin_inset space \thinspace{} +\end_inset + +cm, +\emph on +Vertical Box Alignment +\emph default +: Middle +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +In LaTeX a parbox is created with the command +\series bold + +\backslash +parbox +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! P ! +\backslash +parbox +\end_layout + +\end_inset + + which has the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +parbox[position]{width}{box content} +\end_layout + +\begin_layout Standard +The positions +\emph on +b +\emph default + and +\emph on +t +\emph default + are possible. + +\emph on +b +\emph default + for +\begin_inset Quotes eld +\end_inset + +bottom +\begin_inset Quotes erd +\end_inset + + means that the box is aligned within the surrounding text with its last + line. + With +\emph on +t +\emph default + for +\begin_inset Quotes eld +\end_inset + +top +\begin_inset Quotes erd +\end_inset + + this is done with the first line. + When no position is given, the box will be vertically centered, see section + +\emph on +Boxes +\emph default + of the +\emph on +Embedded +\begin_inset space ~ +\end_inset + +Objects +\emph default + manual for examples. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +To frame formulas completely, including the formula number, the formula + must be set into a parbox. + To do this, the command +\series bold + +\backslash +fbox{ +\backslash +parbox{ +\backslash +linewidth-2 +\backslash +fboxsep-2 +\backslash +fboxrule}{ +\series default + is inserted in TeX-mode before the formula. + +\series bold + +\backslash +linewidth +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +linewidth +\end_layout + +\end_inset + + is hereby the line width set for the document. + Because the frame is outside the parbox, 2 +\begin_inset space \thinspace{} +\end_inset + +times the frame separation and the frame thickness must be subtracted from + the line width. + As this is not automatically done by LyX due to a bug +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #4483" +target "http://www.lyx.org/trac/ticket/4483" + +\end_inset + + +\end_layout + +\end_inset + +, TeX-mode has to be used. + To be able to multiply and subtract in arguments, the LaTeX-package +\series bold +calc +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout + +\series bold +calc +\series default + is part of every LaTeX standard installation. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! calc +\end_layout + +\end_inset + + must be loaded in the LaTeX-preamble with the line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage{calc} +\end_layout + +\begin_layout Standard +Behind the formula both boxes are closed by entering +\series bold +}} +\series default + in TeX-mode. + Here is an example: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fboxsep 5mm +\backslash +fboxrule 5mm +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fbox{ +\backslash +parbox{ +\backslash +linewidth-2 +\backslash +fboxsep-2 +\backslash +fboxrule}{ +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{equation} +\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)} +\end{equation} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +}} +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fboxrule 0.4pt +\backslash +fboxsep 3pt +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +As a parbox is used as the argument of +\series bold + +\backslash +fbox +\series default +, there is in this case no difference between +\series bold + +\backslash +fbox +\series default + and +\series bold + +\backslash +boxed +\series default +. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +Paragraph boxes are very useful to comment formulas directly. + To do this, +\series bold + +\backslash +parbox +\series default + is used in combination with the command +\series bold + +\backslash +tag +\series default +. + (more about +\series bold + +\backslash +tag +\series default + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:User-defined-Numbering" + +\end_inset + +) +\end_layout + +\begin_layout Standard +An example of a formula commented with +\series bold + +\backslash +parbox +\series default +: +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +[5x-7b=3b +\backslash +tag*{ +\backslash +parbox{5cm}{ +\end_layout + +\end_inset + +This is a description. + It is distinctly separated from the formula and multiline. +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +}} +\backslash +] +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Such a formula must be inserted completely in TeX-mode because LyX does + not yet support the command +\series bold + +\backslash +parbox +\series default + in formulas. + The formula is created with the following command sequence: +\end_layout + +\begin_layout Standard +The command +\series bold + +\backslash +[5x-7b=3b +\backslash +tag* +\backslash +{ +\backslash +parbox{5cm}{ +\series default + is inserted in TeX-mode. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +When the formula style +\series bold +Indented +\series default + is used, +\series bold + +\backslash +tag* +\backslash +{ +\series default + can also be replaced by +\series bold + +\backslash +hfill +\series default +. + (formula styles see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + +) +\end_layout + +\end_inset + + Then the description follows as normal text and finally +\series bold +}} +\backslash +] +\series default + is inserted in TeX-mode. + The commands +\series bold + +\backslash +[ +\series default + and +\series bold + +\backslash +] +\series default + hereby create a displayed formula. +\end_layout + +\begin_layout Standard +The advantages of +\series bold + +\backslash +parbox +\series default + can be seen in this example that was +\begin_inset Quotes eld +\end_inset + +commented +\begin_inset Quotes erd +\end_inset + + using the mathematical textmode: +\begin_inset Formula +\[ +5x-7b=3b\textrm{This is a description. It is not separated from the formula ...} +\] + +\end_inset + + +\end_layout + +\begin_layout Section +Operators +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Operators +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Big Operators +\begin_inset CommandInset label +LatexCommand label +name "sub:Big-Operators" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Operators ! big +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Sums +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Integrals +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To be able to use all integral operators listed here, the option +\family sans +Use esint package automatically +\family default + must be set in the document settings under +\family sans +Math +\begin_inset space ~ +\end_inset + +Options +\family default +. +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +int +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! I ! +\backslash +int +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\int$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +oint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\oint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ointctrclockwise +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ointctrclockwise$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ointclockwise +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ointclockwise$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sqint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +fint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\begin_inset Formula $\fint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +landupint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\begin_inset Formula $\landupint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +landdownint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\begin_inset Formula $\landdownint$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigcap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigcap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sum +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +sum +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sum$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +prod +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! P ! +\backslash +prod +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\prod$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +coprod +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\coprod$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigodot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigodot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigotimes +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigotimes$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigoplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigoplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigwedge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigwedge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigvee +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigvee$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigsqcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigsqcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +biguplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\biguplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +All big operators can also be inserted via the math toolbar button +\begin_inset Graphics + filename ../images/math/intop.png + scale 85 + +\end_inset + +. +\end_layout + +\begin_layout Standard +The operators are called big because they are bigger than the sometimes + equal looking binary operators. + All big operators can have limits as described in the next subsection. +\end_layout + +\begin_layout Standard +For all integral operators there is a second version available, ending in + +\series bold +op +\series default +: +\series bold + +\backslash +intop +\series default +, +\series bold + +\backslash +ointop +\series default + etc.. + These operators are different from +\series bold + +\backslash +int +\series default + etc. +\begin_inset space \space{} +\end_inset + +in the style the operator limits are displayed, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Operator-Limits" + +\end_inset + +. + +\end_layout + +\begin_layout Subsubsection* +Advice for Integrals +\end_layout + +\begin_layout Standard +The letter +\emph on +d +\emph default + in an integral is an operator, that therefore has to be set upright. + This is done by highlighting the +\emph on +d +\emph default + and using the keyboard shortcut +\begin_inset Info +type "shortcut" +arg "font-roman" +\end_inset + + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +Font styles +\series bold + +\series default +see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Font-Styles" + +\end_inset + + +\end_layout + +\end_inset + +. + Finally the smallest space is inserted before the +\emph on +d +\emph default +, as this is usual for operators. + An example: +\end_layout + +\begin_layout Standard +incorrect: +\begin_inset Formula $\int A(x)dx$ +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout +in +\end_layout + +\end_inset + +correct: +\begin_inset Formula $\int A(x)\,\mathrm{d}x$ +\end_inset + + +\end_layout + +\begin_layout Standard +For multiple integrals there are the following commands: +\begin_inset VSpace medskip +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +iint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +oiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +iiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +iiiint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dotsint +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Subsection +Operator Limits +\begin_inset CommandInset label +LatexCommand label +name "sub:Operator-Limits" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Operators ! Limits +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Limits are created by super- and subscripts: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +prod^ +\backslash +infty +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\begin_inset Formula $\to$ +\end_inset + +_0 +\begin_inset Formula $\to$ +\end_inset + +A(x) +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\prod_{0}^{\infty}A(x)\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +Limits of inline formulas are set right beside the operator. + Limits in displayed formulas are set above or below the operator, except + for integral limits. +\end_layout + +\begin_layout Standard +To force that the limits are set beside the operator, the cursor is set + directly behind the operator and the limits type is changed with the menu + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Change Limits Type +\family default + to +\family sans +\series bold +Inline +\family default +\series default + (shortcut +\begin_inset Info +type "shortcut" +arg "math-limits" +\end_inset + +). + An example: +\end_layout + +\begin_layout Standard +The default limits type is this: +\begin_inset Formula +\[ +\sum_{x=0}^{\infty}\frac{1}{x^{2}} +\] + +\end_inset + +This is how it looks when the limits type was changed to +\family sans +\series bold +Inline +\family default +\series default +: +\begin_inset Formula +\[ +\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}} +\] + +\end_inset + +For integrals, except those ending with +\series bold +op +\series default + like +\series bold + +\backslash +intop +\series default +, +\series bold + +\backslash +ointop +\series default + etc., the limits are by default set beside the operator. + But for multiple integrals the limits are often set below the operator. + In the following example the limits type was therefore set to +\series bold +Display +\series default + and so set below the integrals: +\begin_inset Formula +\begin{equation} +\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +To specify conditions for limits, the commands +\series bold + +\backslash +subarray +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +subarray +\end_layout + +\end_inset + + and +\series bold + +\backslash +substack +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +substack +\end_layout + +\end_inset + + are used. + To create for example this expression +\begin_inset Formula +\begin{equation} +\sum_{\begin{subarray}{c} +0 + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout ++ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $+$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +- +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $-$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +pm +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\pm$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cdot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\cdot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +times +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\times$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +div +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\div$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{-1.2mm}{ +\end_layout + +\end_inset + +* +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $*$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +star +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\star$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +circ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\circ$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +diamond +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\diamond$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bullet +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bullet$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nabla +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nabla$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigtriangledown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigtriangledown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigtriangleup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigtriangleup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Box +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Box$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\cap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\cup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dagger +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\dagger$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddagger +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ddagger$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +wr +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\wr$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigcirc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigcirc$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +wedge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\wedge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vee +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\vee$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +oplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\oplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ominus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ominus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +otimes +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\otimes$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +oslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\oslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +odot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\odot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +amalg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\amalg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +uplus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\uplus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +setminus +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\setminus$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqcap +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sqcap$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqcup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sqcup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +triangleleft +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\triangleleft$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +triangleright +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\triangleright$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +All binary operators can also be inserted via the math toolbar button +\begin_inset Graphics + filename ../images/math/pm.png + scale 85 + +\end_inset + +. +\end_layout + +\begin_layout Standard +To typeset the Laplace operator also +\series bold + +\backslash +Delta +\series default + or +\series bold + +\backslash +nabla +\series default +^ +\series bold +2 +\series default + ( +\begin_inset Formula $\nabla^{2}$ +\end_inset + +) can be used instead of +\series bold + +\backslash +bigtriangleup +\series default + . +\end_layout + +\begin_layout Standard +The character +\family sans +Menu Separator +\family default + from the menu +\family sans +Insert\SpecialChar \menuseparator +Special Character +\family default + is the operator +\series bold + +\backslash +triangleright +\series default +. +\end_layout + +\begin_layout Subsection +Self-defined Operators +\begin_inset CommandInset label +LatexCommand label +name "sub:Self-defined-Operators" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Operators ! self-defined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +With the help of the command +\series bold + +\backslash +DeclareMathOperator +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dbinom@ +\backslash +DeclareMathOperator +\end_layout + +\end_inset + + custom operators can be defined in the LaTeX-preamble. + Its command scheme is: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +DeclareMathOperator{new command}{display} +\end_layout + +\begin_layout Standard +Display can be characters or symbols that define how the operator looks + in the output. + To define a big operator a * is set behind the command. + All self-defined big operators can have limits as described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Operator-Limits" + +\end_inset + +. +\end_layout + +\begin_layout Standard +For example the LaTeX-preamble line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +DeclareMathOperator*{ +\backslash +Lozenge}{ +\backslash +blacklozenge} +\end_layout + +\begin_layout Standard +defines the command +\series bold + +\backslash +Lozenge +\series default +, that inserts a big operator consisting of the lozenge symbol from +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Miscellaneous-Symbols" + +\end_inset + +: +\begin_inset Formula +\[ +\Lozenge_{n=1}^{\infty} +\] + +\end_inset + +The command for this formula is: +\series bold + +\backslash +Lozenge +\series default +^ +\series bold + +\backslash +infty +\begin_inset Formula $\to$ +\end_inset + +_n=1 +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +When self-defined operators are not used several times in the document, + they can also be defined with the commands +\series bold + +\backslash +mathop +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +mathop +\end_layout + +\end_inset + + and +\series bold + +\backslash +mathbin +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +mathbin +\end_layout + +\end_inset + +, which have the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +mathop{display} +\series default + and +\series bold + +\backslash +mathbin{display} +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +mathop +\series default + defines big operators, +\series bold + +\backslash +mathbin +\series default + binary operators. +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +mathop +\series default + can e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +be used to use one limit for several operators: +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +\mathop{\sum\negmedspace\sum}_{i,j=1}^{N} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +The command for the formula above is: +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +mathop{ +\backslash +sum +\backslash +negmedspace +\backslash +sum +\series default + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series bold + +\begin_inset Formula $\to$ +\end_inset + +^N +\series default + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series bold +_i,j=1 +\end_layout + +\begin_layout Section +Fonts +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Fonts +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Font Styles +\begin_inset CommandInset label +LatexCommand label +name "sub:Font-Styles" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Font ! style +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Latin letters in formulas can be set in one of the following font styles: +\begin_inset VSpace -2mm +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +shortcut +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathbb +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default +ABC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathbb{ABC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-noun" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathbf +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathbf{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-bold" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +boldsymbol +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\boldsymbol{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-boldsymbol" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathcal +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default +ABC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathcal{ABC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-emph" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathfrak +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathfrak{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +- +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathscr +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathscr{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +- +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +shortcut +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathit +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathit{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +- +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathrm +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathrm{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-roman" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathsf +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathsf{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-sans" +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mathtt +\series bold + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series default +AbC +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathtt{AbC}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Info +type "shortcuts" +arg "font-typewriter" +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + The styles +\series bold + +\backslash +mathbb +\series default + and +\series bold + +\backslash +mathcal +\series default + can only be used for big letters. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Predefined is the style +\series bold + +\backslash +mathnormal +\series default +. +\end_layout + +\begin_layout Standard +The style commands work also for letters in mathematical constructs: +\begin_inset Formula +\[ +\mathfrak{A=\frac{b}{C}} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +Characters in mathematical text don't appear in a math font style but in + the text font style +\series bold + +\backslash +textrm +\series default +. + That their style can't be set correctly via the text style dialog is a + bug in LyX. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #4629" +target "http://www.lyx.org/trac/ticket/4629" + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Instead of the style commands the dialog +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Text Style +\family default + or the toolbar button +\begin_inset Graphics + filename ../images/math/font.png + scale 85 + +\end_inset + + can be used. +\end_layout + +\begin_layout Subsection +Bold Formulas +\begin_inset CommandInset label +LatexCommand label +name "sub:Bold-Formulas" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! bold +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To make a complete formula bold, the command +\series bold + +\backslash +mathbf +\series default + from the previous subsection cannot be used, because it doesn't work for + small Greek letters. + Furthermore it prints Latin letters always upright, like in the following + equation: +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +To display the formula correctly, the command +\series bold + +\backslash +boldsymbol +\series default + is used: +\begin_inset Formula +\[ +\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}} +\] + +\end_inset + +It is also possible to set the formula in a +\series bold +boldmath environment +\series default +. + This environment is created by inserting the command +\series bold + +\backslash +boldmath +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +boldmath +\end_layout + +\end_inset + + in TeX-mode. + To end the environment, the command +\series bold + +\backslash +unboldmath +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! U ! +\backslash +unboldmath +\end_layout + +\end_inset + + is inserted in TeX-mode. +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +boldmath +\end_layout + +\end_inset + + +\begin_inset Formula +\[ +\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment} +\] + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +unboldmath +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Colored Formulas +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! colored +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Formulas can be colored like normal text: Highlight a formula or a formula + part and use the +\family sans +Text Style +\family default + dialog. + Here is a formula in magenta: +\begin_inset Formula +\[ +{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +You can also define your own colors as described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Colored-Boxes" + +\end_inset + +. + They can be used with the TeX code command +\series bold + +\backslash +textcolor +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +textcolor +\end_layout + +\end_inset + + in the scheme +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +textcolor{color}{characters or formula} +\end_layout + +\begin_layout Standard +The following example was colored completely dark green and partly red: +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +textcolor{darkgreen}{ +\end_layout + +\end_inset + + +\begin_inset Formula +\[ +\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)} +\] + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Due to a bug in LyX only complete formulas can be colored with self-defined + colors. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #5269" +target "http://www.lyx.org/trac/ticket/5269" + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Font Sizes +\begin_inset CommandInset label +LatexCommand label +name "sub:Font-Sizes" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Font ! size +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +For characters in formulas there are, analog to characters in text, the + following size commands: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +Huge +\series default +, +\series bold + +\backslash +huge +\series default +, +\series bold + +\backslash +LARGE +\series default +, +\series bold + +\backslash +Large +\series default +, +\series bold + +\backslash +large +\series default +, +\series bold + +\backslash +normalsize +\series default +, +\series bold + +\backslash +small +\series default +, +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +footnotesize +\series default +, +\series bold + +\backslash +scriptsize +\series default + and +\series bold + +\backslash +tiny +\end_layout + +\begin_layout Standard +The size produced by the commands depends on the document font size, which + corresponds to the command +\series bold + +\backslash +normalsize +\series default +. + The other commands produce smaller or larger sizes than +\series bold + +\backslash +normalsize +\series default +. + The font size can however not exceed a certain value. + Is for example the document font size 12 +\begin_inset space \thinspace{} +\end_inset + +pt, the command +\series bold + +\backslash +Huge +\series default + switches to the same size as +\series bold + +\backslash +huge +\series default +. + +\end_layout + +\begin_layout Standard +A size command is inserted in TeX-mode before the formula and sets the size + for all following formula and text characters. + To switch back to the initial size, the command +\series bold + +\backslash +normalsize +\series default + is inserted behind the formula in TeX-mode. +\end_layout + +\begin_layout Standard +Within a formula the size can be changed using the following size commands: +\end_layout + +\begin_layout Standard +\noindent +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +displaystyle +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +displaystyle +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6.5mm}{}{\displaystyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-5.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +textstyle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}{\textstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +scriptstyle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}{\scriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +scriptscriptstyle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}{\scriptscriptstyle E_{\mathrm{pot_{1}}}=\frac{K}{l+\frac{m}{n_{2}}}}\raisebox{-3.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +After entering these commands, a blue box appears in which the formula parts + are inserted. +\end_layout + +\begin_layout Standard +There is a further method to change the font size, that though only works + for symbols or letters in mathematical text. + To use it, one of the above text size commands is inserted in mathematical + text. + All following characters until the end of the mathematical text or until + another size command will have the selected size. + Two examples: +\begin_inset VSpace -2mm +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +huge +\end_layout + +\end_inset + + +\begin_inset Formula +\[ +A=\frac{B}{c}\cdot\maltese +\] + +\end_inset + + +\begin_inset Formula +\[ +\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}} +\] + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +normalsize +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +Before both formulas the command +\series bold + +\backslash +huge +\series default + was inserted. + The command for the second formula is: +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +maltese +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A Alt+M M +\backslash +Large +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +maltese +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +textit +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset Formula $\to$ +\end_inset + + +\begin_inset Formula $\to$ +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset space \hspace*{} +\length 1cm +\end_inset + +Alt+M +\series default + +\series bold +M +\backslash +tiny +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +maltese +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +textit +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\end_layout + +\begin_layout Standard +If a symbol cannot be displayed in different sizes, it will always be displayed + in the default size. +\end_layout + +\begin_layout Section +Greek Letters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Greek letters +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Greek letters can also be inserted via the toolbar button +\begin_inset Graphics + filename ../images/math/alpha.png + scale 85 + +\end_inset + +. + All international typesetting norms purport that Greek letters in math + have to be typeset italic/slanted. + In some languages, like French or Russian, they are nevertheless sometimes + typeset upright. +\end_layout + +\begin_layout Subsection +Small Letters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Greek letters ! small +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +alpha +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\alpha$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +beta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\beta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +gamma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\gamma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +delta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\delta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +epsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\epsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varepsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varepsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +zeta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\zeta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +eta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\eta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\theta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vartheta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\vartheta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +iota +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\iota$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +kappa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\kappa$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varkappa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varkappa$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lambda +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\lambda$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mu +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mu$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nu +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nu$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +xi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\xi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +o +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $o$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +pi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\pi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varpi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varpi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rho +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rho$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varrho +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varrho$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varsigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varsigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +tau +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\tau$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\upsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\phi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varphi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varphi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +chi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\chi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\psi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +omega +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\omega$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + + +\end_layout + +\begin_layout Standard +How to create special upright Greek letters is explained in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Upright-small-Greek" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Big Letters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Greek letters ! big +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Gamma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Gamma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Delta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Delta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Theta$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Lambda +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Lambda$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Xi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Xi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Pi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Pi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Sigma +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Sigma$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Upsilon$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Phi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Psi$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Omega +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Omega$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +That the big Greek letters appear upright is caused by a design bug when + TeX was developed. + To get correct italic big letters, begin every command with +\series bold +var +\series default +. + For example the command +\series bold + +\backslash +varGamma +\series default + produces +\begin_inset Formula $\varGamma$ +\end_inset + +. + Another way is to load the package +\series bold +fixmath +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout + +\series bold +fixmath +\series default + is part of the LaTeX-package +\series bold +was +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! was +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! fixmath +\end_layout + +\end_inset + + with the LaTeX-preamble line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage{fixmath} +\end_layout + +\begin_layout Standard +Then all big Greek letters in a document will automatically be typeset italic. +\end_layout + +\begin_layout Subsection +Bold Letters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Greek letters ! bold +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Greek letters cannot be set with different font styles like Latin letters. + They can only be made bold with the command +\series bold + +\backslash +boldsymbol +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! B ! +\backslash +boldsymbol +\end_layout + +\end_inset + +. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Upsilon +\backslash +boldsymbol +\backslash +Upsilon +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +theta +\backslash +boldsymbol +\backslash +theta +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\theta\boldsymbol{\theta}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Section +Symbols +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +texorpdfstring{ +\end_layout + +\end_inset + + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +A list with all symbols of most of the LaTeX-packages can be found in +\begin_inset CommandInset citation +LatexCommand cite +key "Symbols" + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +}{} +\end_layout + +\end_inset + + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\backslash +texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. +\end_layout + +\begin_layout Plain Layout +More about +\backslash +texorpdfstring is in section +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Formulas-in-Section" + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Symbols +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Many of the symbols listed in this section can also be inserted via the + toolbar buttons +\begin_inset Graphics + filename ../images/math/nabla.png + scale 85 + +\end_inset + + and +\begin_inset Graphics + filename ../images/math/digamma.png + scale 85 + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Mathematical Symbols +\begin_inset CommandInset label +LatexCommand label +name "sub:Mathematical-Symbols" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Symbols ! mathematical +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +neg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\neg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Im +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Im$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Re +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Re$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +aleph +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\aleph$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +partial +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\partial$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +infty +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\infty$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +wp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\wp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +imath +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\imath$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +jmath +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\jmath$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +forall +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\forall$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +exists +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\exists$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nexists +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nexists$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +emptyset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\emptyset$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varnothing +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varnothing$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dag +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\dag$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ddag +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ddag$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +complement +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{-0.8mm}{ +\end_layout + +\end_inset + + +\begin_inset Formula $\complement$ +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Bbbk +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Bbbk$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +prime +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\prime$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +backprime +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\backprime$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mho +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mho$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +triangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\triangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +angle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\angle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +measuredangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\measuredangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sphericalangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sphericalangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +top +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\top$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bot$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Subsection +Miscellaneous Symbols +\begin_inset CommandInset label +LatexCommand label +name "sub:Miscellaneous-Symbols" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Symbols ! miscellaneous +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\noindent +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +flat +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\flat$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +natural +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\natural$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sharp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sharp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +surd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\surd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +checkmark +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\checkmark$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +yen +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\yen$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +pounds +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\pounds$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +$ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\$$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +§ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $§$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hbar +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\hbar$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\hslash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +clubsuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\clubsuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +spadesuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\spadesuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bigstar +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bigstar$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +blacklozenge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\blacklozenge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +blacktriangle +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\blacktriangle$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +blacktiangledown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\blacktriangledown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bullet +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bullet$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +diamondsuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\diamondsuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Diamond +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Diamond$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +heartsuit +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\heartsuit$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +P +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\P$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +copyright +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\copyright$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +circledR +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\circledR$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +maltese +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\maltese$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +diagup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\diagup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +diagdown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\diagdown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +More symbols are listed in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Miscellaneous-special-Characters" + +\end_inset + +. +\end_layout + +\begin_layout Standard +Some symbols can be displayed in different sizes, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Font-Sizes" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +The Euro-Symbol € +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Symbols ! Euro-symbol +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout + +\backslash +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +officialeuro +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To use the Euro symbol in formulas, the LaTeX-package +\series bold +eurosym +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! eurosym +\end_layout + +\end_inset + + must be installed and loaded with the LaTeX-preamble line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage[gennarrow]{eurosym} +\end_layout + +\begin_layout Standard +The Euro symbol can now be inserted with the command +\series bold + +\backslash +euro +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! E ! +\backslash +euro +\end_layout + +\end_inset + +. +\end_layout + +\begin_layout Standard +The Euro symbol can directly be inserted with the € key in mathematical + text, without having +\series bold +eurosym +\series default + installed. + When +\series bold +eurosym +\series default + is installed, +\series bold + +\backslash +euro +\series default + can also be inserted in TeX-mode. + The official currency symbol can then be inserted with the command +\series bold + +\backslash +officialeuro +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! O ! +\backslash +officialeuro +\end_layout + +\end_inset + +, that is only available in TeX-mode. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +ifeurosym +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following table will only be displayed when the LaTeX-package +\series bold +eurosym +\series default + is installed. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +An overview about the different Euro symbols: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +formula +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +euro +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\euro$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +mathematical text +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +€ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mbox{€}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +TeX-mode +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +officialeuro +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +officialeuro +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +else +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following will be displayed when the LaTeX-package +\series bold +eurosym +\series default + is not installed: +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +You need to install the LaTeX-package +\series bold +eurosym +\series default + to see the rest of this subsection in the output. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fi +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Section +Relations +\begin_inset CommandInset label +LatexCommand label +name "sec:Relations" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Relations +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Comparisons|see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Relations +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +All relations can also be inserted via the toolbar button +\begin_inset Graphics + filename ../images/math/leq.png + scale 85 + +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +< +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $<$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +le +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\le$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ll +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ll$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +prec +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\prec$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +preceq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\preceq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +subset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\subset$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +subseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\subseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqsubseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sqsubseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +in +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\in$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vdash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\vdash$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +smile +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\smile$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\lhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +unlhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\unlhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +gtrless +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\gtrless$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +mid +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mid$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nmid +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nmid$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout += +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $=$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not= +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\not=$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +equiv +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\equiv$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sim$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +simeq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\simeq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +approx +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\approx$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cong +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\cong$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bowtie +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\bowtie$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +notin +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\notin$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +perp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\perp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +propto +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\propto$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +asymp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\asymp$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +doteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\doteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +circeq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\circeq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +models +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\models$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +widehat= +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\widehat{=}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +> +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $>$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ge +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ge$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +gg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\gg$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +succ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\succ$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +succeq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\succeq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +supset +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\supset$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +supseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\supseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sqsupseteq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\sqsupseteq$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ni +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\ni$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dashv +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\dashv$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +frown +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\frown$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\rhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +unrhd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\unrhd$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lessgtr +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\lessgtr$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +parallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\parallel$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +nparallel +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\nparallel$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +The characters +\series bold + +\backslash +lhd +\series default + and +\series bold + +\backslash +rhd +\series default + are bigger than the equal looking operators +\series bold + +\backslash +triangleleft +\series default + and +\series bold + +\backslash +triangleright +\series default +, respectively. +\end_layout + +\begin_layout Standard +Relations are, in contrary to symbols, always surrounded by space. +\end_layout + +\begin_layout Standard +Relations with labels can be created with the command +\series bold + +\backslash +stackrel +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +stackrel +\end_layout + +\end_inset + +: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A(r) +\backslash +stackrel +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +r +\backslash +to +\backslash +infty +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\begin_inset Formula $\downarrow$ +\end_inset + + +\backslash +approx +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}A(r)\stackrel{r\to\infty}{\approx}B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Section +Functions +\end_layout + +\begin_layout Subsection +Predefined Functions +\begin_inset CommandInset label +LatexCommand label +name "sub:Predefined-Functions" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Functions ! predefined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +In general, variables are set +\emph on +italic +\emph default + in mathematical expressions, but not function names, because +\begin_inset Formula $sin$ +\end_inset + + could be misunderstood as +\begin_inset Formula $s\cdot i\cdot n$ +\end_inset + +. + Therefore there are predefined functionswhich are additionally a bit separated + from prefactors. + They are inserted as commands starting with a backslash before their name. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +Asin(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $Asin(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +A +\backslash +sin(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\sin(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +The following functions are predefined: +\end_layout + +\begin_layout Standard +\begin_inset VSpace -2mm +\end_inset + + +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sin +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sinh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +arcsin +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sup +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cos +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cosh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +arccos +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +inf +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +tan +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +tanh +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +arctan +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lim +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +coth +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +arg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +liminf +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +sec +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +min +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +deg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +limsup +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +csc +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +max +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +det +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Pr +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ln +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +exp +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +hom +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lg +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +log +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ker +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +gcd +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +They can also be inserted with the math toolbar button +\begin_inset Graphics + filename ../images/math/functions.png + scale 85 + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Self-defined Functions +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Functions ! self-defined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To use a function that is not predefined, like for example the sign function + sgn(x), there are two possibilities: +\end_layout + +\begin_layout Itemize +Define the function by inserting the following line to the LaTeX-preamble +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +For more about +\series bold + +\backslash +DeclareMathOperator +\series default + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Self-defined-Operators" + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset VSpace -3mm +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +DeclareMathOperator{ +\backslash +sgn}{sgn} +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! D ! +\backslash +dbinom@ +\backslash +DeclareMathOperator +\end_layout + +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset VSpace -2mm +\end_inset + + +\begin_inset Newline newline +\end_inset + +Now the new defined function can be called with the command +\series bold + +\backslash +sgn +\series default +. +\end_layout + +\begin_layout Itemize +Write the formula as usual, mark the formula name, in our example the letters + +\emph on +sgn +\emph default +, and change it to mathematical text. + Finally, a space is inserted between prefactor and function. +\end_layout + +\begin_layout Standard +The result is the same with both methods as with a predefined function +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +In LyX self-defined functions are displayed red, predefined ones black. +\end_layout + +\end_inset + +: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A +\backslash +sgn(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\sgn(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A +\backslash +, +\begin_inset Formula $\underbrace{\textrm{sgn}}_{\textrm{Alt+M}\,\textrm{M}}$ +\end_inset + +(x)+B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\,\textrm{sgn}(x)+B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +The first method is more suitable when the self-defined function should + be used several times. +\end_layout + +\begin_layout Subsection +Limits +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Limits +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +For limits, in addition to the commands +\series bold + +\backslash +lim +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +lim +\end_layout + +\end_inset + +, +\series bold + +\backslash +liminf +\series default + and +\series bold + +\backslash +limsup +\series default + the following functions are defined: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varliminf +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varliminf$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varlimsup +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varlimsup$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varprojlim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varprojlim$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +varinjlim +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\varinjlim$ +\end_inset + + +\begin_inset Formula $\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +The limit is created by inserting a subscript. + It is set right beside the function in an inline formula: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset space \hspace{} +\length 1cm +\end_inset + +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +The space and +\series bold + +\backslash +raisebox +\series default + are used here as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lim_x +\backslash +to +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +x=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\hspace{1cm}\raisebox{5mm}{}\lim_{x\to A}x=B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +In a displayed formula the limit is set below the formula, as usual: +\begin_inset Formula +\[ +\lim_{x\to A}x=B +\] + +\end_inset + + +\end_layout + +\begin_layout Subsection +Modulo-Functions +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Functions ! modulo- +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The modulo-function is special, because it exists in four variants. + The variants in a displayed formula are: +\begin_inset Formula +\begin{align*} +\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\ +\mathrm{a\backslash mod\textrm{\spce}b} & & a\mod b\\ +\mathrm{a\backslash pmod\textrm{\spce}b} & & a\pmod b\\ +\mathrm{a\backslash bmod\textrm{\spce}b} & & a\bmod b\\ +\mathrm{a\backslash pod\textrm{\spce}b} & & a\pod b +\end{align*} + +\end_inset + + +\end_layout + +\begin_layout Standard +In an inline formula less space is set before the function names for all + variants. + By default the modulo-functions take only the first following character + into account. + To use more than one character, one has to put them into TeX-braces: +\begin_inset Formula +\begin{align*} +\underline{\textrm{Command}\raisebox{-0.9mm}{}} & & \underline{\textrm{Result}}\\ +\mathrm{a\backslash pod\textrm{\spce}bcd} & & a\pod bcd\\ +\mathrm{a\backslash pod\backslash\{bc\to d} & & a\pod{bc}d +\end{align*} + +\end_inset + + +\end_layout + +\begin_layout Section +Special Characters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Special characters +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Special Characters in Mathematical Text +\end_layout + +\begin_layout Standard +The following commands can only be used in mathematical text or in TeX-mode: +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +oe +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{œ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +OE +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{Œ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ae +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{æ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +AE +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{Æ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +aa +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{\aa}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +AA +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout + +\backslash +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +textrm{ +\backslash +AA} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{Å}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +i +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{ı}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +command +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +The space of 0 +\begin_inset space \thinspace{} +\end_inset + +mm is used for separation, because otherwise the output will be ¡ and ¿ + respectively. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +o +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{ø}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +O +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{Ø}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +l +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{ł}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +L +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{Ł}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +! +\begin_inset space \hspace{} +\length 0mm +\end_inset + +` +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{!`}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +? +\begin_inset space \hspace{} +\length 0mm +\end_inset + +` +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{?`}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +j +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\textrm{ȷ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +The characters +\begin_inset Formula $\textrm{\textrm{Å}}$ +\end_inset + + and +\begin_inset Formula $\textrm{\textrm{Ø}}$ +\end_inset + + can also be inserted via the math toolbar button +\begin_inset Graphics + filename ../images/math/digamma.png + scale 85 + +\end_inset + +. +\end_layout + +\begin_layout Standard +An exception are the commands +\series bold +! +\begin_inset space \hspace{} +\length 0mm +\end_inset + +` +\series default + and +\series bold +? +\begin_inset space \hspace{} +\length 0mm +\end_inset + +` +\series default +, because they can be inserted in LyX directly to text. +\end_layout + +\begin_layout Subsection +Accents in Text +\begin_inset CommandInset label +LatexCommand label +name "sub:Accents-in-Text" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Accents ! in text +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +With the following commands all letters can be accented. + The commands must be inserted in TeX-mode. +\end_layout + +\begin_layout Standard +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\begin_inset Quotes grd +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +"e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +`e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +`e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +^ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +^e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +=e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +=e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +u +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +u e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +b +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +b e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +t +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +ee +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +t ee +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +H +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +H e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +'e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +'e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +~e +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Tilde +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +~e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +.e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +.e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +v +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +v e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +d +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +d e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +c +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +e +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +c e +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +With the command +\series bold + +\backslash +t +\series default + also two different characters can be accented. + The command +\series bold + +\backslash +t +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +sz +\series default + creates: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +t sz +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The accents +\series bold +` +\series default + , +\series bold +' +\series default + and +\series bold +^ +\series default + can in combination with vowels directly be inserted with the keyboard without + using TeX-mode. + The same applies for the tilde +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +This only applies for keyboards where the tilde is defined as accent. +\end_layout + +\end_inset + + +\series bold +~ +\series default + in combination with +\emph on +a +\emph default + , +\emph on +n +\emph default + , or +\emph on +o +\emph default +. +\end_layout + +\begin_layout Standard +The commands +\series bold + +\backslash +b +\series default + , +\series bold + +\backslash +c +\series default + , +\series bold + +\backslash +d +\series default + , +\series bold + +\backslash +H +\series default + , +\series bold + +\backslash +t +\series default + , +\series bold + +\backslash +u +\series default + , +\series bold + +\backslash +v +\series default + and accents that are inserted directly with the keyboard are also available + in mathematical text. + For the other accents there are special math commands to be used in formulas, + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Accents-for-one" + +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +Furthermore, with the command +\series bold + +\backslash +textcircled +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +textcircled +\end_layout + +\end_inset + + all numbers and letters can be set into a circle, quasi accented with a + circle, similar to the copyright symbol. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +textcircled{w} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +textcircled{w} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Large +\backslash +textcircled{ +\backslash +normalsize +\backslash +protect +\backslash +raisebox{-1.5pt}{W}} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}$ +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +Large +\backslash +textcircled{ +\backslash +normalsize +\backslash +protect +\backslash +raisebox{-1.5pt}W} +\end_layout + +\end_inset + + +\begin_inset Formula $\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +One has to take care that the character fits in the circle. + +\series bold + +\backslash +Large +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Font-Sizes" + +\end_inset + + +\end_layout + +\end_inset + + specifies thereby the size of the circle. + With the help of +\series bold + +\backslash +raisebox +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Boxes-without-Frame" + +\end_inset + + +\end_layout + +\end_inset + + the character can be centered. +\end_layout + +\begin_layout Subsection +Old-style Figures +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Old-style Figures +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Old-style figures (also known as old-style numerals) are created with the + command +\series bold + +\backslash +oldstylenums +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! O ! +\backslash +oldstylenums +\end_layout + +\end_inset + +. + The command can be used in formulas and in TeX-mode. + The command scheme is: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +oldstylenums{number} +\end_layout + +\begin_layout Standard +The command +\series bold + +\backslash +oldstylenums{0123456789 +\series default + produces: +\begin_inset Formula $\oldstylenums{0123456789}$ +\end_inset + + +\end_layout + +\begin_layout Subsection +Miscellaneous special Characters +\begin_inset CommandInset label +LatexCommand label +name "sub:Miscellaneous-special-Characters" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Special characters ! miscellaneous +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The following characters can only be inserted to formulas by using commands: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +^ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\mathcircumflex$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +_ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\_$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +^ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\backslash +circ +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout + +\backslash +@° +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $^{\circ}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble + contains the following line +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +More about this is described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Text-Characters-in" + +\end_inset + +. +\end_layout + +\end_inset + +: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +DeclareInputtext{176}{ +\backslash +ifmmode^ +\backslash +circ +\backslash +else +\backslash +textdegree +\backslash +fi} +\end_layout + +\begin_layout Section +Formula Styles +\begin_inset CommandInset label +LatexCommand label +name "sec:Formula-Styles" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! styles +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Itemize +There are two different alignment styles: +\end_layout + +\begin_deeper +\begin_layout Description +Centered is the predefined standard +\end_layout + +\begin_layout Description +Indented for this the option +\series bold +fleqn +\series default + must be inserted in the menu +\family sans +Document\SpecialChar \menuseparator +Settings +\family default + under +\family sans +Document +\begin_inset space ~ +\end_inset + +Class +\end_layout + +\begin_layout Standard +When +\series bold +Indented +\series default + is used, the indentation can be adjusted with the length +\series bold + +\backslash +mathindent +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +mathindent +\end_layout + +\end_inset + +. + Should the distance be 15 +\begin_inset space \thinspace{} +\end_inset + +mm, the following command line is inserted in the LaTeX-preamble +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +setlength{ +\backslash +mathindent}{15mm} +\end_layout + +\begin_layout Standard +When no length is specified, the predefined value of 30 +\begin_inset space \thinspace{} +\end_inset + +pt will be used. +\end_layout + +\end_deeper +\begin_layout Itemize +And two different numbering styles: +\end_layout + +\begin_deeper +\begin_layout Description +Right is the predefined standard +\end_layout + +\begin_layout Description +Left for this the option +\series bold +leqno +\series default + must be inserted in the menu +\family sans +Document\SpecialChar \menuseparator +Settings +\family default + under +\family sans +Document +\begin_inset space ~ +\end_inset + +Class +\end_layout + +\end_deeper +\begin_layout Standard + +\series bold +fleqn +\series default + and +\series bold +leqno +\series default + can also be used together. + In this case both options are inserted, separated by a comma. +\end_layout + +\begin_layout Standard +The chosen styles are used for all displayed formulas of the document. + When both, centered and indented formulas should be created in a document, + the style +\series bold +Centered +\series default + is used. + The indented formulas are then set in a flalign environment, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Flalign-Environment" + +\end_inset + +. +\end_layout + +\begin_layout Section +Multiline Formulas +\begin_inset CommandInset label +LatexCommand label +name "sec:Multiline-Formulas" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +General +\end_layout + +\begin_layout Standard +In LyX multiline formulas are created by pressing +\series bold + +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + + +\series default + inside a formula. + This creates either an +\series bold +eqnarray environment +\series default + that is described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Eqnarray-Environment" + +\end_inset + + or, when the option +\family sans +Use AMS math package +\family default + in the document settings is selected, an +\series bold +align environment +\series default + that is described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Standard-align-Environment" + +\end_inset + +. + The align environment is recommended because it provides in any case a + typographically correct output. +\end_layout + +\begin_layout Standard +There are other multiline formula environments that can be created via the + menu +\family sans +Insert\SpecialChar \menuseparator +Math +\family default +. + These environments are described in the following sections. +\end_layout + +\begin_layout Standard +In all multiline formula environments a new line is created by pressing + +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + +. + To add or delete lines, the math toolbar buttons +\begin_inset Graphics + filename ../images/tabular-feature_append-row.png + scale 85 + +\end_inset + + or +\begin_inset Graphics + filename ../images/tabular-feature_delete-row.png + scale 85 + +\end_inset + +, respectively, or the menu +\family sans +Edit\SpecialChar \menuseparator +Rows & Columns +\family default + can be used. +\end_layout + +\begin_layout Subsubsection +Line Separation +\begin_inset CommandInset label +LatexCommand label +name "sub:Line-Separation" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! Line separation +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +There is sometimes not enough space in multiline formulas between the lines: +\begin_inset Formula +\begin{eqnarray*} +B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\ +4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0 +\end{eqnarray*} + +\end_inset + + +\end_layout + +\begin_layout Standard +In LaTeX additional line space is specified as optional argument of the + new line command. + This is not yet possible in LyX +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +see +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #1505" +target "http://www.lyx.org/trac/ticket/1505" + +\end_inset + + +\end_layout + +\end_inset + +, therefore the whole formula must be inserted in TeX-mode. + To add in our example space, the command +\series bold + +\backslash + +\backslash +[3mm] +\series default + is inserted at the end of the first line. + One gets: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +begin{eqnarray*} +\end_layout + +\begin_layout Plain Layout + +B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & + = & +\backslash +textrm{-}4x^{2}B^{2}+4x_{0}xB^{2} +\backslash + +\backslash +[3mm] +\end_layout + +\begin_layout Plain Layout + +4x^{2} +\backslash +left(B^{2}+x_{0}^{2} +\backslash +right)+4x_{0}x +\backslash +left(D-B^{2} +\backslash +right)+B^{2} +\backslash +left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2} +\backslash +right) & = & 0 +\end_layout + +\begin_layout Plain Layout + + +\backslash +end{eqnarray*} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +To set the line separation for all lines in a formula, the length +\series bold + +\backslash +jot +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! J ! +\backslash +jot +\end_layout + +\end_inset + + is changed. + The definition is: +\begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$ +\end_inset + +. + Predefined for +\series bold + +\backslash +jot +\series default + is the value 3 +\begin_inset space \thinspace{} +\end_inset + +pt. + To create 3 +\begin_inset space \thinspace{} +\end_inset + +mm additional line separation as in the previous example, the command +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +setlength{ +\backslash +jot}{3mm+3pt} +\end_layout + +\begin_layout Standard +is inserted in TeX-mode before the formula. + This requires that the LaTeX-package +\series bold +calc +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout + +\series bold +calc +\series default + is part of every LaTeX standard installation. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! calc +\end_layout + +\end_inset + + was loaded in LaTeX-preamble with the line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage{calc} +\end_layout + +\begin_layout Standard +One gets: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +setlength{ +\backslash +jot}{3mm+3pt} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{eqnarray*} +B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\ +4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0 +\end{eqnarray*} + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +setlength{ +\backslash +jot}{3pt} +\end_layout + +\end_inset + + To get back to the predefined distance, +\series bold + +\backslash +jot +\series default + is set to the value 3 +\begin_inset space \thinspace{} +\end_inset + +pt. +\end_layout + +\begin_layout Subsubsection +Column Separation +\begin_inset CommandInset label +LatexCommand label +name "sub:Column-Separation" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! Column separation +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Multiline formulas form a matrix. + A formula in the eqnarray environment is for example a matrix with three + columns. + By changing the column separation in this environment, the space beside + the relation sign can be changed. +\end_layout + +\begin_layout Standard +The column separation is specified with the length +\series bold + +\backslash +arraycolsep +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +arraycolsep +\end_layout + +\end_inset + + according to: +\begin_inset Newline newline +\end_inset + +column separation = 2 +\begin_inset space \thinspace{} +\end_inset + + +\series bold + +\backslash +arraycolsep +\series default + +\begin_inset Newline newline +\end_inset + +Thus, the command +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +setlength{ +\backslash +arraycolsep}{1cm} +\end_layout + +\begin_layout Standard +inserted in TeX-mode, sets for all following formulas a column separation + of 2 +\begin_inset space \thinspace{} +\end_inset + +cm. + To get back to the predefined distance, +\series bold + +\backslash +arraycolsep +\series default + is set to 5 +\begin_inset space \thinspace{} +\end_inset + +pt. +\end_layout + +\begin_layout Standard +A formula with 2 +\begin_inset space \thinspace{} +\end_inset + +cm column separation: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +setlength{ +\backslash +arraycolsep}{1cm} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{eqnarray*} +A & = & B\\ +C & \ne & A +\end{eqnarray*} + +\end_inset + +A formula with the predefined column separation for matrices of 10 +\begin_inset space \thinspace{} +\end_inset + +pt: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +setlength{ +\backslash +arraycolsep}{5pt} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{eqnarray*} +A & = & B\\ +C & \ne & A +\end{eqnarray*} + +\end_inset + + +\end_layout + +\begin_layout Subsubsection +Long Formulas +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! long +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Long formulas can be typeset using these methods: +\end_layout + +\begin_layout Itemize +When one side of the equation is much shorter than the line width, this + one is chosen for the left side and the right side is typeset over two + lines: +\begin_inset Formula +\begin{eqnarray} +H & = & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\nonumber \\ + & & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:shortlong} +\end{eqnarray} + +\end_inset + +The minus sign at the beginning of the second line does normally not appear + as an operator because it is the first character of the line. + Thus it would not be surrounded by space and could not be distinguished + from the fraction bar. + To avoid this, 3 +\begin_inset space \thinspace{} +\end_inset + +pt space was inserted behind the minus sign with the command +\series bold + +\backslash +hspace +\series default +. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +for more about +\series bold + +\backslash +hspace +\series default + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Variable-Space" + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! H ! +\backslash +hspace +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Itemize +When both sides of the equation are too long, the command +\series bold + +\backslash +lefteqn +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +lefteqn +\end_layout + +\end_inset + + is used. + It is inserted in the first column of the first line and causes all further + insertions to overwrite the following columns: +\begin_inset Formula +\begin{eqnarray} +\lefteqn{4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}}\nonumber \\ + & & -\hspace{3pt}B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\nonumber \\ + & & =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\label{eq:lefteqn} +\end{eqnarray} + +\end_inset + +After the insertion of +\series bold + +\backslash +lefteqn +\series default +, the cursor is in a purple box that is a bit shifted to the left from the + blue one. + In this the formula is inserted. +\begin_inset Newline newline +\end_inset + +The content of the further lines is inserted to the second or another formula + column. + The greater the column number where it was inserted, the larger the indentation. +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout +Note the following when using +\series bold + +\backslash +lefteqn +\series default +: +\end_layout + +\begin_layout Itemize +The formula doesn't use the full page width. + When e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +the term +\begin_inset Formula $-B^{2}$ +\end_inset + + is added to the first line in the above example, it would have been outside + the page margin. + To better use the width, negative space can be inserted at the beginning + of the first line. +\end_layout + +\begin_layout Itemize +Due to a bug in LyX the cursor cannot be set with the mouse into the first + line. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #1429" +target "http://www.lyx.org/trac/ticket/1429" + +\end_inset + + +\end_layout + +\end_inset + + One can only set the cursor at the beginning of the line and move it with + the arrow keys. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Itemize +Other methods to set long formulas are offered by the environments described + in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Multline-Environment" + +\end_inset + + and +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Multiline-Formula-Parts" + +\end_inset + +. +\end_layout + +\begin_layout Subsubsection +Multiline Brackets +\begin_inset CommandInset label +LatexCommand label +name "sub:Multiline-Brackets" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Brackets ! for multiline expressions +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +For brackets spanning multiple lines the following problem occurs: +\begin_inset Formula +\begin{eqnarray*} +A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\ + & & \left.\cdots+B-D\right] +\end{eqnarray*} + +\end_inset + + +\end_layout + +\begin_layout Standard +The closing bracket is smaller than the opening bracket because brackets + with variable size may not span multiple lines. +\end_layout + +\begin_layout Standard +To set the bracket size for the second line correctly, the first line is + ended with +\series bold + +\backslash +right. +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +right +\end_layout + +\end_inset + + and the second line with +\series bold + +\backslash +left. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +for more about +\series bold + +\backslash +left +\series default + and +\series bold + +\backslash +right +\series default + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Automatic-Bracket-Size" + +\end_inset + + +\end_layout + +\end_inset + + +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! L ! +\backslash +left +\end_layout + +\end_inset + +. + After +\series bold + +\backslash +left. + +\series default + the command +\series bold + +\backslash +vphantom +\series default + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series bold + +\backslash +prod +\series default +^ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series bold + +\backslash +infty +\series default + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\series bold + +\begin_inset Formula $\downarrow$ +\end_inset + +_R=1} +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! V ! +\backslash +vphantom +\end_layout + +\end_inset + + is inserted, because the multiplication operator with its limits is the + largest symbol in the first line and this should be the size for the bracket + in the second line. +\end_layout + +\begin_layout Standard +The result is this: +\begin_inset Formula +\begin{eqnarray*} +A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\ + & & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right] +\end{eqnarray*} + +\end_inset + + +\end_layout + +\begin_layout Subsection +Align Environments +\end_layout + +\begin_layout Standard +Align environments can be used for every kind of multiline formulas. + They are especially useful to set several formulas side by side. +\end_layout + +\begin_layout Standard +Align environments consist of columns. + The odd columns are right aligned, the even ones left aligned. + Every line in an Align environment can be numbered. +\end_layout + +\begin_layout Standard +Align environments are created via the menu +\family sans +Insert\SpecialChar \menuseparator +Math +\family default +. + With the menu +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Change Formula Type +\family default + already existing formulas can be converted to Align environments. +\end_layout + +\begin_layout Standard +To add or delete columns, the math toolbar buttons +\begin_inset Graphics + filename ../images/tabular-feature_append-column.png + scale 85 + +\end_inset + + or +\begin_inset Graphics + filename ../images/tabular-feature_delete-column.png + scale 85 + +\end_inset + +, respectively, or the menu +\family sans +Edit\SpecialChar \menuseparator +Rows & Columns +\family default + can be used. +\end_layout + +\begin_layout Subsubsection +Standard align Environment +\begin_inset CommandInset label +LatexCommand label +name "sub:Standard-align-Environment" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! align environment +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +This Align environment is created by pressing +\begin_inset Info +type "shortcut" +arg "newline-insert newline" +\end_inset + + in a formula or by the menu +\family sans +Insert\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +AMS align Environment +\family default +. +\end_layout + +\begin_layout Standard +An example for two formulas set side by side, that are created with a four + column align environment: +\begin_inset Formula +\begin{align*} +A & =\sin(B) & C & =D\\ +C & \ne A & B & \ne D +\end{align*} + +\end_inset + +As it can be seen, the formulas in this environment are placed so as if + there would be a +\series bold + +\backslash +hfill +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +more about +\series bold + +\backslash +hfill +\series default + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Variable-Space" + +\end_inset + + +\end_layout + +\end_inset + + +\series default + before the first and after every even column. + When the formula style +\series bold +Indented +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +formula styles see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + + +\end_layout + +\end_inset + + +\series default + is used, the formula is set without the +\series bold + +\backslash +hfill +\series default + before the first column. +\end_layout + +\begin_layout Subsubsection +Alignat Environment +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! alignat environment +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The alignat environment has no predefined column separation. + It can be inserted manually with the spaces that are described +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Space" + +\end_inset + +. +\end_layout + +\begin_layout Standard +The above example in the alignat environment where 1 +\begin_inset space \thinspace{} +\end_inset + +cm space was inserted at the beginning of the second formula: +\begin_inset Formula +\begin{alignat*}{2} +A & =\sin(B) & \hspace{1cm}C & =D\\ +C & \ne A & B & \ne D +\end{alignat*} + +\end_inset + +Because the column separation can be set separately for every column, this + environment is especially suitable to set three and more formulas side + by side. +\end_layout + +\begin_layout Subsubsection +Flalign Environment +\begin_inset CommandInset label +LatexCommand label +name "sub:Flalign-Environment" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! flalign environment +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +In this environment the first two columns are always set as much as possible + to the left and the last two ones to the right. + An example: +\begin_inset Formula +\begin{flalign*} +A & =1 & B & =2 & C & =3\\ +X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4 +\end{flalign*} + +\end_inset + + +\end_layout + +\begin_layout Standard +By creating a flalign environment with an odd number of columns where an + empty TeX-brace is inserted to the last column, several formulas in a document + can be set to the left, although the formula style +\series bold +Centered +\series default + is used. + As example the indented formula +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:VolInt" + +\end_inset + +: +\begin_inset Formula +\begin{flalign} +\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {} +\end{flalign} + +\end_inset + +The first two columns contain the formula. + To indent it as with the formula style +\series bold +Indented +\series default +, 30 +\begin_inset space \thinspace{} +\end_inset + +pt space was inserted at the beginning of the first column. +\end_layout + +\begin_layout Subsection +Eqnarray Environment +\begin_inset CommandInset label +LatexCommand label +name "sub:Eqnarray-Environment" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! eqnarray environment +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +When this environment has been created, three blue boxes appear. + The content of the first box is right aligned, the content of the last + one left aligned. + The content of the middle box appears centered and a bit smaller, because + it is designed to insert there only relation characters. +\begin_inset Formula +\begin{eqnarray*} +\frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\ +AB & AB & AB\\ +A & = & A +\end{eqnarray*} + +\end_inset + + +\end_layout + +\begin_layout Subsection +Gather Environment +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! gather environment +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +This environment consists of only one centered column. + Every line can be numbered. +\begin_inset Formula +\begin{gather} +A=1\\ +X=\textrm{-}1 +\end{gather} + +\end_inset + + +\end_layout + +\begin_layout Subsection +Multline Environment +\begin_inset CommandInset label +LatexCommand label +name "sub:Multline-Environment" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! multline environment +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The multline environment consists, like the gather environment, of only + one column. + But the first line is left aligned, the last one right aligned. + All other lines are centered. + Therefore this environment is suitable for long formulas. + As example formula +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:lefteqn" + +\end_inset + + in the multline environment: +\begin_inset Formula +\begin{multline} +4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\ +-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\\ +=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}} +\end{multline} + +\end_inset + + +\end_layout + +\begin_layout Standard +In the output only the last (first) line of a multline environment appears + numbered when the document numbering is right (left). +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +numbering styles see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +With the commands +\series bold + +\backslash +shoveright +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +shoveright +\end_layout + +\end_inset + + and +\series bold + +\backslash +shoveleft +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +shoveleft +\end_layout + +\end_inset + + a centered line can be right or left aligned, respectively. + The commands are used as follows: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +shoveright{line content} +\series default + and +\series bold + +\backslash +shoveleft{line content} +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +The length +\series bold + +\backslash +multlinegap +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +multlinegap +\end_layout + +\end_inset + + specifies the distance of the first line from the left page margin. + Predefined is the length 0 +\begin_inset space \thinspace{} +\end_inset + +pt. +\end_layout + +\begin_layout Standard +As example the above formula where the command +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +setlength{ +\backslash +multlinegap}{2cm} +\end_layout + +\begin_layout Standard +was inserted in TeX-mode before: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +setlength{ +\backslash +multlinegap}{2cm} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{multline} +4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\ +\shoveleft{-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}\\ +=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}} +\end{multline} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +setlength{ +\backslash +multlinegap}{0pt} +\end_layout + +\end_inset + +The second line was left aligned using +\series bold + +\backslash +shoveleft +\series default +. +\end_layout + +\begin_layout Subsection +Multiline Formula Parts +\begin_inset CommandInset label +LatexCommand label +name "sub:Multiline-Formula-Parts" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! formula parts +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To display only parts of a formula with multiple lines, one of the following + environments is used: +\series bold +aligned +\series default +, +\series bold +alignedat +\series default +, +\series bold +gathered +\series default + or +\series bold +split +\series default +. + They can be inserted via the menu +\family sans +Insert\SpecialChar \menuseparator +Math +\family default + or by using the commands described in this section. +\end_layout + +\begin_layout Standard +The first three have the same properties as the corresponding multiline + formula environments, but it is possible to set further formula parts beside + them. + An example: +\begin_inset Formula +\[ +\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\ +\Delta E\Delta t & \ge\frac{\hbar}{2} +\end{aligned} +\right\} \textrm{Uncertainty relations} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +To get this formula, a displayed formula is created where the command +\series bold + +\backslash +aligned +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +aligned +\end_layout + +\end_inset + + is inserted. + A purple box appears around the blue formula box where now columns and + lines can be added. + Outside the multiline environment other formula parts can be set, like + the brace. +\end_layout + +\begin_layout Standard +The aligned environment is also suitable for long formulas whose lines are + horizontally aligned. + Using aligned in a displayed formula has the advantage that the formula + number is vertically centered behind the lines. + As example formula +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:shortlong" + +\end_inset + + in the aligned environment: +\begin_inset Formula +\begin{equation} +\begin{aligned}H=\; & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\\ + & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|} +\end{aligned} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Standard +To use the environments +\series bold +alignedat +\series default +, +\series bold +gathered +\series default +, or +\series bold +split +\series default +, the command +\series bold + +\backslash +alignedat +\series default +, +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +alignedat +\end_layout + +\end_inset + + +\series bold + +\backslash +gathered +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! G ! +\backslash +gathered +\end_layout + +\end_inset + +, or +\series bold + +\backslash +split +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! S ! +\backslash +split +\end_layout + +\end_inset + + are inserted, respectively. + The split environment has the same properties as the aligned environment + but it can only have two columns. +\end_layout + +\begin_layout Subsection +Text in multiline Formulas +\begin_inset CommandInset label +LatexCommand label +name "sub:Text-in-multiline" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Text ! in formulas +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! multiline ! text +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +In the Align environments, and the multline and gather environment, text + can be inserted that will appear in a separate line and doesn't affect + the column alignment. + To do this, the command +\series bold + +\backslash +intertext +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! I ! +\backslash +intertext +\end_layout + +\end_inset + + is used in the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +intertext{text} +\end_layout + +\begin_layout Standard +The text should not be longer than a line because it cannot be hyphenated. + As LyX doesn't yet support +\series bold + +\backslash +intertext +\series default + directly, the text is written as mathematical text. + +\series bold + +\backslash +intertext +\series default + must hereby be at the beginning of a line and appears in the output above + this line. + An example where the text was inserted at the beginning of the second line: +\begin_inset Formula +\begin{align} +I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\ +\intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi +\end{align} + +\end_inset + + +\end_layout + +\begin_layout Section +Formula Numbering +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! numbering|see +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{ +\end_layout + +\end_inset + +Formula numbering +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +General +\end_layout + +\begin_layout Standard +Numbered formulas can be created with the menu +\family sans +Insert\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Numbered +\begin_inset space ~ +\end_inset + +Formula +\family default + (shortcut +\family sans +Ctrl+Alt +\begin_inset space ~ +\end_inset + +N +\family default +). + Existing formulas can be numbered with the menu +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Toggle +\begin_inset space ~ +\end_inset + +Numbering +\family default + (shortcut +\begin_inset Info +type "shortcut" +arg "math-number-toggle" +\end_inset + +). + The formula number is displayed in LyX behind the formula as a number sign + in parentheses. + The number sign is replaced in the output by the formula number. +\end_layout + +\begin_layout Standard +When numbering is turned on in multiline formulas, all lines will be numbered. + But the numbering can be controlled with the menu +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Toggle +\begin_inset space ~ +\end_inset + +Numbering +\begin_inset space ~ +\end_inset + +of +\begin_inset space ~ +\end_inset + +Line +\family default + (shortcut +\begin_inset Info +type "shortcut" +arg "math-number-line-toggle" +\end_inset + +) for every line. +\end_layout + +\begin_layout Standard +Except for inline formulas, all formulas can be numbered with two different + styles, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Cross-References +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Cross-references ! to formulas +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +All labeled formulas can be cross-referenced. + A label is added by the menu +\family sans +Insert\SpecialChar \menuseparator +Label +\family default + or the toolbar button +\begin_inset Graphics + filename ../images/label-insert.png + scale 85 + +\end_inset + +. + The cursor must hereby be inside a displayed formula. + Alternatively you can right-click on the formula and choose +\family sans +Equation Label +\family default +. + A dialog pops up displaying the prefix +\series bold +eq: +\series default + in a text field. + The label is inserted there behind the prefix. + The predefined prefix means +\begin_inset Quotes eld +\end_inset + +equation +\begin_inset Quotes erd +\end_inset + + and makes it easier to find labels in large documents because it marks + it as formula label to divide it from e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +section labels. + To change a label, the menu +\family sans +Insert\SpecialChar \menuseparator +Label +\family default + is used again or you right-click on a formula and then on +\family sans +Equation Label +\family default +. +\end_layout + +\begin_layout Standard +The name of the label is displayed in LyX within two parentheses behind + formula. + A formula with a label is always numbered. +\end_layout + +\begin_layout Standard +Cross-references are inserted via the menu +\family sans +Insert\SpecialChar \menuseparator +Cross-Reference +\family default + or with the toolbar button +\begin_inset Graphics + filename ../images/dialog-show-new-inset_ref.png + scale 85 + +\end_inset + +. + A formula cross-reference appears in the output as formula number. + When in the cross-reference dialog window the format +\series bold +() +\series default + is chosen, the cross-reference appears in the output as formula number + in parentheses. +\begin_inset Newline newline +\end_inset + +By right-clicking on a cross-reference in LyX, one jumps to the formula + that is referenced. +\end_layout + +\begin_layout Standard +Here are as examples cross-references to formulas of the following subsections: +\begin_inset Note Note +status open + +\begin_layout Plain Layout +Note the different cross-reference types. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The equations +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:tag" + +\end_inset + + and +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:c" + +\end_inset + + are equivalent. + In ( +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:Lat" + +\end_inset + +) big Latin letters are used for the numbering in contrary to ( +\begin_inset CommandInset ref +LatexCommand ref +reference "eq:Rom" + +\end_inset + +). +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +When the argument of +\series bold + +\backslash +tag +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +tag +\series default + is described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:User-defined-Numbering" + +\end_inset + +. +\end_layout + +\end_inset + + +\series default + contains a box like in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Paragraph-Boxes" + +\end_inset + +, the formula cannot be referenced. +\end_layout + +\begin_layout Subsection +Subnumbering +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering ! subnumbering +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +With the help of the commands +\series bold + +\backslash +begin{subequations} +\series default + and +\series bold + +\backslash +end{subequations} +\series default + formulas can be subnumbered. + Both commands are inserted in TeX-mode. +\end_layout + +\begin_layout Standard +An example: +\begin_inset Formula +\begin{equation} +A=C-B\label{eq:a} +\end{equation} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +addtocounter{equation}{-1} +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +begin{subequations} +\end_layout + +\end_inset + + +\begin_inset VSpace -5mm +\end_inset + + +\begin_inset Formula +\begin{equation} +B=C-A\label{eq:b} +\end{equation} + +\end_inset + + +\begin_inset Formula +\begin{equation} +C=A+B\label{eq:c} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +end{subequations} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To create the example, the following is done: +\end_layout + +\begin_layout Enumerate +first formula is inserted +\end_layout + +\begin_layout Enumerate + +\series bold + +\backslash +addtocounter{equation}{-1} +\backslash +begin{subequations} +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +addtocounter +\end_layout + +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\series default +is inserted after the first formula +\end_layout + +\begin_layout Enumerate +second formula is inserted +\end_layout + +\begin_layout Enumerate +third formula is inserted +\end_layout + +\begin_layout Enumerate + +\series bold + +\backslash +end{subequations} +\series default + is inserted after the third formula +\end_layout + +\begin_layout Standard +Every formula between the commands +\series bold + +\backslash +begin +\series default + and +\series bold + +\backslash +end +\series default + is subnumbered as a, b, +\begin_inset Newline linebreak +\end_inset + +c, \SpecialChar \ldots{} + For multiline formulas every line will be subnumbered. + All subnumbered formulas are treated as +\emph on +one +\emph default + numbered formula. + But as every numbered formula increases the counter +\series bold +equation +\series default + by one, the command +\series bold + +\backslash +addtocounter +\series default + is needed to decrease it. + Otherwise the formulas +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:a" + +\end_inset + +, +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:b" + +\end_inset + +, +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:c" + +\end_inset + + would be numbered as +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:a" + +\end_inset + +, +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:d" + +\end_inset + +, +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:f" + +\end_inset + +. +\end_layout + +\begin_layout Standard +By inserting the commands in TeX-mode, a space is created between the first + two formulas. + To revert this -5 +\begin_inset space \thinspace{} +\end_inset + +mm vertical space is inserted after the command +\series bold + +\backslash +begin{subequations} +\series default +. + When the formula style +\series bold +Indented +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +formula styles see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + + +\end_layout + +\end_inset + + +\series default + is used, -7 +\begin_inset space \thinspace{} +\end_inset + +mm space is inserted instead. +\end_layout + +\begin_layout Standard +Here is an example for a multiline formula where the numbering was turned + off for the second line: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +begin{subequations} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{eqnarray} +A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\ + & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\ + & = & B^{2}-2BZ+Z^{2}\label{eq:f} +\end{eqnarray} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +end{subequations} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +User-defined Numbering +\begin_inset CommandInset label +LatexCommand label +name "sub:User-defined-Numbering" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering ! user-defined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering ! self-defined delimiters +\end_layout + +\end_inset + +With the standard numbering parentheses are set around the formula number. + To replace the parentheses for example by vertical bars, the following + line is added to the LaTeX-preamble: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +def +\backslash +tagform@#1{ +\backslash +maketag@@@{|#1|}} +\series default + +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +This macro is already declared in the LaTeX-preamble for testing. + To activate it, remove the percent sign at the beginning. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To use other characters, the vertical bars besides the +\series bold +#1 +\series default + are replaced by one ore more characters. + To get only the formula number the vertical bars are omitted. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +When there should be an expression of your choice instead of the consecutive + formula number in parentheses behind the formula, the command +\series bold + +\backslash +tag +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +tag +\end_layout + +\end_inset + + is used: +\begin_inset Formula +\begin{equation} +A+B=C\tag{something}\label{eq:tag} +\end{equation} + +\end_inset + +In this example the command +\series bold + +\backslash +tag +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +something +\series default + was inserted in the formula. +\end_layout + +\begin_layout Standard +When the command +\series bold + +\backslash +tag* +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +something +\series default + is inserted instead, the star prevents the parentheses around the expression: +\begin_inset Formula +\[ +A+B=C\tag*{something} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +To restart the formula numbering with new document parts or sections, the + following command is used: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +@addtoreset{equation}{part} +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + + ! +\backslash + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +addtoreset +\end_layout + +\end_inset + + +\begin_inset Newline newline +\end_inset + +resp. +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +@addtoreset{equation}{section} +\end_layout + +\begin_layout Standard +To be able to use these commands in TeX-mode, the +\begin_inset Quotes eld +\end_inset + +@ +\begin_inset Quotes erd +\end_inset + + character has to be made +\begin_inset Quotes eld +\end_inset + +active +\begin_inset Quotes erd +\end_inset + + for LaTeX using the command +\series bold + +\backslash +makeatletter. + +\series default + The command +\series bold + +\backslash +makeatother +\series default + reverts this. + So the command sequence in TeX-mode is: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +makeatletter +\begin_inset Newline newline +\end_inset + + +\backslash +@addtoreset{equation}{section} +\begin_inset Newline newline +\end_inset + + +\backslash +makeatother +\end_layout + +\begin_layout Standard +In the LaTeX-preamble +\series bold + +\backslash +makeatletter +\series default + and +\series bold + +\backslash +makeatother +\series default + can be omitted as they are automatically internally inserted by LyX. +\end_layout + +\begin_layout Standard +To revert +\series bold + +\backslash +@addtoreset +\series default +, the file +\series bold +remreset.sty +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout + +\series bold +remreset +\series default + is part of the LaTeX-package +\series bold +carlisle +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! carlisle +\end_layout + +\end_inset + + that is part of every LaTeX standard installation. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! remreset +\end_layout + +\end_inset + + has to be loaded in the LaTeX-preamble with the line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage{remreset} +\end_layout + +\begin_layout Standard +Then the command +\series bold + +\backslash +@removefromreset +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + + ! +\backslash + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +@ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +" +\end_layout + +\end_inset + +removefromreset +\end_layout + +\end_inset + + can be used with the same scheme as +\series bold + +\backslash +@addtoreset +\series default +. +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + +Sometimes formulas should be numbered in the following form: +\end_layout + +\begin_layout Standard + +\family typewriter +(section number.formula number) +\end_layout + +\begin_layout Standard +The formula number should start with every section with +\begin_inset Quotes eld +\end_inset + +1 +\begin_inset Quotes erd +\end_inset + +. +\end_layout + +\begin_layout Standard +For this case there is the command +\series bold + +\backslash +numberwithin +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! N ! +\backslash +numberwithin +\end_layout + +\end_inset + +, which is used with the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +numberwithin{counter}{sectioning} +\end_layout + +\begin_layout Standard +Counter denotes what kind of numbering is affected, sectioning denotes what + number is before the dot. +\end_layout + +\begin_layout Standard +Thus in our case the following LaTeX-preamble or TeX code line is used: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +numberwithin{equation}{section} +\end_layout + +\begin_layout Standard +This is the result: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +numberwithin{equation}{section} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{equation} +A+B=C +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Standard +To number e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +tables so that the number of the part is the sectioning, +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +numberwithin{table}{part} +\series default + is used. +\end_layout + +\begin_layout Standard +To go back to the standard numbering or to prevent this kind of numbering + when it is defined by the document class, the following command is inserted + as TeX code or to the LaTeX-preamble: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +arabic{equation}} +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +arabic +\end_layout + +\end_inset + + +\series default + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +arabic{equation}} +\end_layout + +\end_inset + + +\series bold + +\begin_inset Newline newline +\end_inset + + +\series default +or +\series bold + +\begin_inset Newline newline +\end_inset + + +\backslash +renewcommand{ +\backslash +thetable}{ +\backslash +arabic{table}} +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +numberwithin +\series default + uses internally the command +\series bold + +\backslash +@addtoreset +\series default +, described above, that also needs to be reverted. +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +makeatletter +\end_layout + +\begin_layout Plain Layout + + +\backslash +@removefromreset{equation}{section} +\end_layout + +\begin_layout Plain Layout + + +\backslash +makeatother +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Numbering with Roman Numbers and Letters +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering ! with letters +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula numbering ! with Roman numbers +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Formulas can also be numbered with Roman numbers and Latin letters. + To number for example with small Roman numbers, the command +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +roman{equation}} +\end_layout + +\begin_layout Standard +is inserted before the formula in TeX-mode. + +\series bold + +\backslash +renewcommand +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +renewcommand +\end_layout + +\end_inset + + redefines the predefined command +\series bold + +\backslash +theequation +\series default + to the command +\series bold + +\backslash +roman{equation} +\series default +. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +The command +\series bold + +\backslash +renewcommand +\series default + has the same scheme like the command +\series bold + +\backslash +newcommand +\series default + that is described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:The-Command-newcommand" + +\end_inset + +. +\end_layout + +\end_inset + + +\series bold +equation +\series default + is the formula counter. + When the command +\series bold + +\backslash +the +\series default + is used as prefix for a counter, the value of the counter is output as + Arabic number. + When a formula is numbered, LaTeX sets internally the command +\series bold + +\backslash +theequation +\series default + behind the formula. + +\series bold + +\backslash +roman{equation} +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +roman +\end_layout + +\end_inset + + +\series default + outputs the counter as small Roman number. +\end_layout + +\begin_layout Standard +All formulas behind the command +\series bold + +\backslash +renew +\series default +c +\series bold +ommand +\series default + are now numbered Roman. + To switch to numbering with big Roman numbers, the command is inserted + again, but +\series bold + +\backslash +roman +\series default + is replaced by +\series bold + +\backslash +Roman +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! R ! +\backslash +roman@ +\backslash +Roman +\end_layout + +\end_inset + +. + To +\begin_inset Quotes eld +\end_inset + +number +\begin_inset Quotes erd +\end_inset + + with small Latin letters there is the command +\series bold + +\backslash +alph +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +alph +\end_layout + +\end_inset + +, for big ones there is the command +\series bold + +\backslash +Alph +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +alph@ +\backslash +Alph +\end_layout + +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +\color none +Note: +\series default + Only maximal 26 +\begin_inset space ~ +\end_inset + +formulas can be numbered with Latin letters in one document. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +roman{equation}} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Formula +\begin{equation} +A=\textrm{small roman} +\end{equation} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +Roman{equation}} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{equation} +B=\textrm{big Roman}\label{eq:Rom} +\end{equation} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +alph{equation}} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{equation} +C=\textrm{small Latin} +\end{equation} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +Alph{equation}} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{equation} +D=\textrm{big Latin}\label{eq:Lat} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Standard +To switch back to the default numbering, insert the command: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +arabic{equation}} +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! A ! +\backslash +arabic +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +theequation}{ +\backslash +arabic{equation}} +\end_layout + +\end_inset + + +\begin_inset Formula +\begin{equation} +E=\textrm{Arabic} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +As you see, formulas are numbered serially independent from the numbering + style. + When then numbering should start with +\begin_inset Quotes eld +\end_inset + +1 +\begin_inset Quotes erd +\end_inset + + when the style is changed, new equation counters have to be defined. + A description about this can be found in the file +\begin_inset CommandInset href +LatexCommand href +name "Formula-numbering.lyx" +target "run:Formula-numbering.lyx" + +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Section +Chemical Symbols and Equations +\begin_inset CommandInset label +LatexCommand label +name "sub:Chemical-Symbols-and" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Chemical characters ! Symbols +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Chemical equations +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Symbols ! chemical +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +An example text from chemistry: +\end_layout + +\begin_layout Quote +The +\begin_inset Formula $\mathrm{SO_{4}^{2-}}$ +\end_inset + +-ion reacts with two +\begin_inset Formula $\mathrm{Na^{+}}$ +\end_inset + +-ions to sodium sulfate +\begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$ +\end_inset + +. + The chemical equation for this is: +\begin_inset Formula +\begin{equation} +\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Standard +This chemical equation can directly be created as formula. + To avoid that the symbols appear italic, everything is highlighted and + changed by the shortcut +\begin_inset Info +type "shortcut" +arg "font-roman" +\end_inset + + to the upright font style. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +font styles +\series bold + +\series default +see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Font-Styles" + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +A more convenient way to typeset chemical formulas is to use the command + +\series bold + +\backslash +ce +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +ce +\end_layout + +\end_inset + + that is available when the LaTeX-package +\series bold +mhchem +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! mhchem +\end_layout + +\end_inset + + is installed. + After inserting +\series bold + +\backslash +ce +\series default + to a formula a new blue box appears where chemical formulas can be inserted + in an intuitive way. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +H2CO3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\ce{H2CO3}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +SO4^2- +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\ce{SO4^{2-}}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +(NH4)2S +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\ce{(NH4)2S}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +KCr(SO4)2.12H2O +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\ce{KCr(SO4)2.12H2O}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A-B +\backslash +dbond +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +C +\backslash +tbond +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +D +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\ce{A-B\dbond C\tbond D}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +^227 +\begin_inset Formula $\downarrow$ +\end_inset + +_90 +\begin_inset Formula $\to$ +\end_inset + +Th+ +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\ce{_{90}^{227}Th+}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +CO2 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + ++ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +C +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +<=> +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +2CO +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\ce{CO2 + C <=> 2CO}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ce +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +CO2 +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + ++ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +C +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +->[ +\backslash +alpha][ +\backslash +beta] +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +2CO} +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{5mm}{}\ce{CO2 + C ->[\alpha][\beta] 2CO}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +\color none +Note: +\series default + Inserting a formula to a +\series bold + +\backslash +ce +\series default + box will lead to LaTeX errors due to a LyX bug. +\color inherit + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +\begin_inset CommandInset href +LatexCommand href +name "LyX-bug #8566" +target "http://www.lyx.org/trac/ticket/8566" + +\end_inset + + +\end_layout + +\end_inset + + +\color none + In this case TeX code has to be used like for +\series bold + +\backslash +ce{$ +\backslash +mu +\backslash +hyphen$Cl} +\series default +: +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +ce{$ +\backslash +mu +\backslash +hyphen$Cl} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +\color none +Note: +\series default + It is not possible in LyX to use the character ^ to get an up-arrow as + described in the +\series bold +mhchem +\series default + manual. + One instead uses a negative thin space followed by the command +\series bold + +\backslash +uparrow +\series default +: +\begin_inset Formula $\ce{Fe + 2H+ -> Fe^{2+} + H2\negthinspace\uparrow}$ +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Using +\series bold + +\backslash +ce +\series default + the command for equation +\begin_inset space ~ +\end_inset + + +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:chem-reaction" + +\end_inset + + is: +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +ce +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +2Na+ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + ++ +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +SO4^2- +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +-> +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +Na2SO4 +\end_layout + +\begin_layout Standard +To create multiline chemical equations first a multiline formula is created + as described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Multiline-Formulas" + +\end_inset + +. + Afterwards the command +\series bold + +\backslash +ce +\series default + is used in every small blue box of the formula. + +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:TEOS-reaction-1" + +\end_inset + + and +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:TEOS-reaction-2" + +\end_inset + + are an example of a multi-stage chemical reaction where every equation + has its own number. +\begin_inset Formula +\begin{eqnarray} +\ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\ +\ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2} +\end{eqnarray} + +\end_inset + + +\end_layout + +\begin_layout Standard +Besides +\series bold + +\backslash +ce +\series default + the +\series bold +mhchem +\series default + package provides the command +\series bold + +\backslash +cf +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! C ! +\backslash +cf +\end_layout + +\end_inset + + that has to be used for special cases. + For more information about +\series bold + +\backslash +cf +\series default + and more examples have a look at the documentation of +\series bold +mhchem +\series default +, +\begin_inset CommandInset citation +LatexCommand cite +key "mhchem" + +\end_inset + +. +\end_layout + +\begin_layout Section +Diagrams +\end_layout + +\begin_layout Standard +LyX supports two types of commutative diagrams: +\series bold +amscd +\series default + and +\series bold +xymatrix +\series default + that are explained in the following. +\end_layout + +\begin_layout Subsection +Amscd Diagrams +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Diagrams ! amscd +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Diagrams of this type visualize relations by vertical and horizontal lines + or arrows: +\begin_inset Formula +\[ +\begin{CD}A@>>>B@>>>C\\ +@AAA@.@VVV\\ +F@<<>> +\series default + a right arrow and +\series bold +@= +\series default + a long equal sign +\end_layout + +\begin_layout Itemize + +\series bold +@AAA +\series default + creates an up arrow, +\series bold +@VVV +\series default + a down arrow and +\series bold +@| +\series default + a vertical equal sign +\end_layout + +\begin_layout Itemize + +\series bold +@. + +\series default + is a placeholder for non-existent relations +\end_layout + +\begin_layout Standard +All arrows can be labeled as follows: +\end_layout + +\begin_layout Itemize +If text inserted between the first and second < or >, resp., it is placed + above the arrow. + When it is inserted between the second and third one, it appears under + the arrow. +\end_layout + +\begin_layout Itemize +When text for vertical arrows is inserted between the first and second A + or V, resp., it is placed left beside the arrow. + When it is inserted between the second and third one, it appears right + beside the arrow. + If the text contains an A or V, these letters must be set into a TeX-brace. +\end_layout + +\begin_layout Standard +As example a diagram with all possible relations: +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +\begin{CD}A@>j>>B@>>k>C@=F\\ +@AmAA@.@VV{V}V@|\\ +D@<k>>F@=C +\end{CD} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +The command for this is: +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +CD +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A@>j>>B@>>k>C@=F Ctrl+Return +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\series bold + +\backslash +CD +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\end_layout + +\end_inset + +@AmAA@.@VV +\backslash +{V +\series default + +\begin_inset Formula $\to$ +\end_inset + + +\series bold +V@| Ctrl+Return +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\series bold + +\backslash +CD +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + + +\end_layout + +\end_inset + +D@<k>>F@=C +\end_layout + +\begin_layout Subsection +Xymatrix Diagrams +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Diagrams ! xymatrix +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To be able to use xymatrices, the LaTeX-package +\series bold +xypic +\series default + must be installed. + A xymatrix is created by inserting the command +\series bold + +\backslash +xymatrix +\series default + in a formula. + Then you are able to add new matrix columns and rows like for normal matrices, + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Matrices" + +\end_inset + +. +\end_layout + +\begin_layout Standard +In contrary to amscd diagrams, xymatrices supports diagonal and curved arrows, + and much more. + All possibilities to create commutative diagrams and decorations are explained + in detail in the +\emph on +XY-pic manual +\emph default + that you find in the menu +\family sans +Help\SpecialChar \menuseparator +Specific +\begin_inset space ~ +\end_inset + +Manuals +\family default +. +\end_layout + +\begin_layout Subsection + +\noun on +Feynman +\noun default + Diagrams +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Diagrams ! Feynman +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To be able to use +\noun on +Feynman +\noun default +-diagrams, the LaTeX-package +\series bold +feyn +\series default + must be installed. + A +\noun on +Feynman +\noun default +-diagram is created by inserting the command +\series bold + +\backslash +Diagram +\series default + in a formula. + Then you are able to add new matrix columns and rows like for normal matrices, + see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Matrices" + +\end_inset + +. +\end_layout + +\begin_layout Standard +Examples how to create +\noun on +Feynman- +\noun default +diagrams in LyX is given in the +\emph on +Feynman-diagram manual +\emph default + that you find in the menu +\family sans +Help\SpecialChar \menuseparator +Specific +\begin_inset space ~ +\end_inset + +Manuals +\family default +. +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Section +User-defined Commands +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +User-defined commands +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + The names of user-defined commands and macros may only consist of Latin + letters. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +The Command +\backslash +newcommand +\begin_inset CommandInset label +LatexCommand label +name "sub:The-Command-newcommand" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +User-defined commands ! +\backslash +newcommand +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! N ! +\backslash +newcommand +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Many LaTeX-commands are too long to be used frequently. + But it is possible to define with the command +\series bold + +\backslash +newcommand +\series default + new shorter commands. +\end_layout + +\begin_layout Standard +The command scheme of +\series bold + +\backslash +newcommand +\series default + is: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +newcommand{new command name}[number of arguments][optional +\series default + +\series bold +value] +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\series bold + +\backslash +newcommand +\end_layout + +\end_inset + +{command definition} +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note: +\series default + Assure that the name of the new command is not already used in your document + or by LaTeX-packages that you use. + When you for example define the command +\series bold + +\backslash +le +\series default + for +\series bold + +\backslash +Leftarrow +\series default +, you get an error message because +\series bold + +\backslash +le +\series default + is already defined as command for +\begin_inset Quotes eld +\end_inset + + +\begin_inset Formula $\le$ +\end_inset + + +\begin_inset Quotes erd +\end_inset + +. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The number of arguments is an integer in the range 0 +\begin_inset space \thinspace{} +\end_inset + +- +\begin_inset space \thinspace{} +\end_inset + +9 and specifies how many arguments the new command should have. + With the optional value a value for an optional argument can be predefined. + When this is done, the +\emph on +first +\emph default + +\emph on +a +\emph default +rgument of the new command is automatically an optional one. +\end_layout + +\begin_layout Standard +Here are some examples: +\end_layout + +\begin_layout Itemize +To define the command +\series bold + +\backslash +gr +\series default + for +\series bold + +\backslash +Longrightarrow +\series default +, the LaTeX-preamble line is: +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +newcommand{ +\backslash +gr}{ +\backslash +Longrightarrow} +\end_layout + +\begin_layout Itemize +To define the command +\series bold + +\backslash +us +\series default + for +\series bold + +\backslash +underline +\series default +, the argument (that should be underlined) must be taken into account. + For this the preamble line is: +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +newcommand{ +\backslash +us}[1]{ +\backslash +underline{#1}} +\series default + +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + +The character +\series bold +# +\series default + acts as argument placeholder, the +\series bold +1 +\series default + behind it denotes that it is the placeholder for the first argument. +\end_layout + +\begin_layout Itemize +For +\series bold + +\backslash +framebox +\series default + one can e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +define the command +\series bold + +\backslash +fb +\series default +: +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +newcommand{ +\backslash +fb}[3]{ +\backslash +framebox#1#2{$#3$}} +\series default + +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + +The two Dollar signs creates the extra formula needed for +\series bold + +\backslash +framebox +\series default +, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Boxes-with-Frame" + +\end_inset + +. +\end_layout + +\begin_layout Itemize +To create a new command for +\series bold + +\backslash +fcolorbox +\series default + where the color for the box need not be specified, the argument for the + color is defined optional: +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +newcommand{ +\backslash +cb}[3][white]{ +\backslash +fcolorbox{#2}{#1}{$#3$}} +\series default + +\begin_inset VSpace medskip +\end_inset + + +\begin_inset Newline newline +\end_inset + +When the color is not specified when using +\series bold + +\backslash +cb +\series default +, the predefined color +\series bold +white +\series default + will be used. +\end_layout + +\begin_layout Standard +A test of the new defined commands: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +A +\backslash +gr +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $A\gr B$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +us{ABcd +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +fb{[2cm] +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\backslash +int +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cb{red +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\backslash +int +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cb[green] +\backslash +{red +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\backslash +int +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{6mm}{}\cb[green]{red}{\int A=B}\raisebox{-4mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Subsection +Math Macros +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +User-defined commands! Math macros +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Macros +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +User-defined commands are especially convenient for complex expressions. + When you are for example dealing with a document that has quadratic equations, + the same solution type occurs several times. + The general form of a quadratic equation is +\begin_inset Formula +\[ +0=\lambda^{2}+p\lambda+q +\] + +\end_inset + +The general form of the solution is +\begin_inset Formula +\[ +\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +To define a command for the solution formula where only the three parameters + +\begin_inset Formula $\lambda$ +\end_inset + +, +\begin_inset Formula $p$ +\end_inset + + and +\begin_inset Formula $q$ +\end_inset + + need to be specified and the index of +\begin_inset Formula $\lambda$ +\end_inset + + can be given optionally, the LaTeX-preamble line is +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +newcommand{ +\backslash +qG}[4][1, +\backslash +,2]{#2_{#1}=- +\backslash +frac{#3}{2} +\backslash +pm +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\series bold + +\backslash +newcommand +\end_layout + +\end_inset + + +\backslash +sqrt{ +\backslash +frac{#3^{2}}{4}-#4}} +\end_layout + +\begin_layout Standard +To create with this the solution formula, the command +\begin_inset Newline newline +\end_inset + + +\series bold + +\backslash +qG{ +\backslash +lambda +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{p +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{q +\series default + is inserted to a formula +\series bold +. +\end_layout + +\begin_layout Standard +The definition of the new command is unintuitive because one has to know + the schemes of all used LaTeX commands, e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +that a fraction is inserted in LaTeX as +\series bold + +\backslash +frac{numerator}{denominator} +\series default +. + Furthermore one can easily forget a brace in the definition and cannot + see in LyX what the new command is doing. + To avoid these problems LyX offers the possibility to use math macros instead + of the command +\series bold + +\backslash +newcommand +\series default +. +\end_layout + +\begin_layout Standard +A math macro is created by using the menu +\family sans +Insert\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\family default + or the toolbar button +\begin_inset Graphics + filename ../images/math-macro_newmacroname_newcommand.png + scale 85 + +\end_inset + +. + The math macro toolbar appears together with the following box where the + macro is defined: +\begin_inset Newline newline +\end_inset + + +\begin_inset space \hspace*{\fill} +\end_inset + + +\begin_inset Graphics + filename clipart/macrobox.png + +\end_inset + + +\begin_inset space \hspace*{\fill} +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset FormulaMacro +\newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}} +\end_inset + + +\backslash +newmacroname is the default name of the macro that should be changed to + something sensible. + The wanted formula is inserted in the first blue box. + An argument placeholder is inserted with the command +\series bold + +\backslash +#argumentnumber +\series default +, e. +\begin_inset space \thinspace{} +\end_inset + +g +\begin_inset space \space{} +\end_inset + + +\series bold + +\backslash +#1 +\series default + or by using the macro toolbar button +\begin_inset Graphics + filename ../images/math-macro-add-param.png + scale 85 + +\end_inset + +. + Argument placeholders are displayed red. + A maximum of 9 +\begin_inset space ~ +\end_inset + +arguments are possible. + Optional arguments are created with the toolbar button +\begin_inset Graphics + filename ../images/math-macro-add-optional-param.png + scale 85 + +\end_inset + +. + The first non-optional argument can be transformed to an optional one with + the toolbar button +\begin_inset Graphics + filename ../images/math-macro-make-optional.png + scale 85 + +\end_inset + +. + In the second blue box the appearance of the macro in LyX can be defined. + Normally you want to see it as it is defined, so the box is kept empty. + But when you have created a macro that needs lot of space on the screen, + you can insert in the box for example +\begin_inset Newline newline +\end_inset + + +\series bold +qG: +\backslash +#1 +\series default + +\series bold +, +\series default + +\series bold + +\backslash +#2 +\series default + +\series bold +, +\series default + +\series bold + +\backslash +#3, +\backslash +#4 +\begin_inset Newline newline +\end_inset + + +\series default +For the macro only the arguments with the macro name in front of them will + then be displayed in LyX, leading to a better overview. + The formula appears in the output as defined in the first box. +\begin_inset Newline newline +\end_inset + +The appearance of macros in formulas can furthermore be changed for single + macros by setting the cursor in the macro and using the menu +\family sans +View\SpecialChar \menuseparator +(Un)fold +\begin_inset space ~ +\end_inset + +Math +\begin_inset space ~ +\end_inset + +Macro +\family default +. +\end_layout + +\begin_layout Standard +To use a macro, the macro name is inserted as command to a formula, in our + case +\series bold + +\backslash +qG +\series default +. + Our macro looks in LyX like this: +\begin_inset Newline newline +\end_inset + + +\begin_inset space \hspace*{\fill} +\end_inset + + +\begin_inset Graphics + filename clipart/macrouse.png + +\end_inset + + +\begin_inset space \hspace*{\fill} +\end_inset + + +\begin_inset Newline newline +\end_inset + +Here is our macro example with the arguments +\begin_inset Formula $x$ +\end_inset + +, +\begin_inset Formula $\ln(x)$ +\end_inset + + and +\begin_inset Formula $B$ +\end_inset + +: +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +\qG x{\ln(x)}B +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +LyX offers in the menu +\family sans +Tools\SpecialChar \menuseparator +Preferences\SpecialChar \menuseparator +Editing\SpecialChar \menuseparator +Control +\family default + different styles to edit macros. + To find the style that suits you the most, choose a style and set the cursor + in a macro formula to see the difference. +\end_layout + +\begin_layout Standard +A math macro is transformed internally to a +\series bold + +\backslash +newcommand +\series default + command when exporting the document. + The created +\series bold + +\backslash +newcommand +\series default + command is not placed in the LaTeX-preamble, therefore macros can only + be used in formulas that are in the document below the macro definition + box. +\end_layout + +\begin_layout Standard +Math macros can also be directly created from a +\series bold + +\backslash +newcommand +\series default + command. + When writing for example the command +\series bold + +\begin_inset Newline newline +\end_inset + + +\backslash +newcommand{ +\backslash +larrow}[2]{ +\backslash +xleftarrow[#2]{#1}} +\begin_inset Newline newline +\end_inset + + +\series default +in LyX as normal text, highlighting it completely and using then the shortcut + +\family sans +Ctrl+M +\family default +, the command will be transformed to a math macro. + Using this method you need to be careful that the +\series bold + +\backslash +newcommand +\series default + command is typed correctly, otherwise you get a faulty macro leading to + LaTeX errors. +\end_layout + +\begin_layout Standard +Math macros currently have the problem that further formulas in macro definition +s are handled wrongly. + Therefore the example +\series bold + +\backslash +fb +\series default + from +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:The-Command-newcommand" + +\end_inset + + cannot be created as macro. +\end_layout + +\begin_layout Standard +When the cursor is in a macro definition box, you will see the macro toolbar + in LyX: +\end_layout + +\begin_layout Standard +\begin_inset VSpace defskip +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Graphics + filename clipart/MacroToolbar.png + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Macros ! Toolbar +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset VSpace defskip +\end_inset + + +\end_layout + +\begin_layout Standard +The macro toolbar contains from left to right the following buttons: +\end_layout + +\begin_layout Standard +\begin_inset VSpace defskip +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Graphics + filename ../images/math-macro-remove-param.png + rotateOrigin center + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Remove Last Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Graphics + filename ../images/math-macro-add-param.png + rotateOrigin center + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Append Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Graphics + filename ../images/math-macro-make-optional.png + rotateOrigin center + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Make First Non-Optional into +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator + +\end_layout + +\end_inset + +Optional Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Graphics + filename ../images/math-macro-make-nonoptional.png + rotateOrigin center + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Make Last Optional into +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator + +\end_layout + +\end_inset + +Non-Optional Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Graphics + filename ../images/math-macro-remove-optional-param.png + rotateOrigin center + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Remove Optional Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Graphics + filename ../images/math-macro-add-optional-param.png + rotateOrigin center + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Insert Optional Argument +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Graphics + filename ../images/math-macro-remove-greedy-param.png + rotateOrigin center + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Remove Last Argument +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator + +\end_layout + +\end_inset + +Spitting Out To The Right +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Graphics + filename ../images/math-macro-append-greedy-param.png + rotateOrigin center + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Append Argument +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator + +\end_layout + +\end_inset + +Eating From The Right +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Graphics + filename ../images/math-macro-add-greedy-optional-param.png + rotateOrigin center + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator +Append Optional Argument +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Macro +\begin_inset space ~ +\end_inset + +Definition\SpecialChar \menuseparator + +\end_layout + +\end_inset + +Eating From The Right +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Section +Computer Algebra Systems +\end_layout + +\begin_layout Standard +LyX offers the exchange between mathematical expressions written in LyX's + math editor and external applications or user defined scripts. + Currently supported applications are +\family sans +Maple +\family default +, +\family sans +Mathematica +\family default +, +\family sans +Maxima +\family default + and +\family sans +Octave +\family default +. + Note that the set of supported mathematical constructs is limited only + to very simple cases. +\end_layout + +\begin_layout Subsection +Usage +\end_layout + +\begin_layout Standard +Write some expression in a formula, go to the +\family sans +Edit\SpecialChar \menuseparator +Math\SpecialChar \menuseparator +Use Computer Algebra System +\family default + menu and choose the application you have installed on the computer. + After that the result of computation should show on the right side of the + expression together with the +\begin_inset Quotes eld +\end_inset + += +\begin_inset Quotes erd +\end_inset + + operator. +\end_layout + +\begin_layout Standard +Here are few simple examples (with results from +\family typewriter +Maxima +\family default +) to show what kind of computations can be performed: +\end_layout + +\begin_layout Itemize +\begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$ +\end_inset + + +\end_layout + +\begin_layout Itemize +\begin_inset Formula $\frac{37.0}{3}=12.33333333333333$ +\end_inset + + +\end_layout + +\begin_layout Itemize +\begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$ +\end_inset + + +\end_layout + +\begin_layout Itemize +\begin_inset Formula $\det\left[\begin{array}{ccc} +1 & 6 & 7\\ +2 & 5 & 8\\ +3 & 4 & 17 +\end{array}\right]=-56$ +\end_inset + + +\end_layout + +\begin_layout Itemize +\begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$ +\end_inset + + +\end_layout + +\begin_layout Subsection +Keyboard shortcut +\end_layout + +\begin_layout Standard +Currently there is no keyboard shortcut for calling the algebra applications. + One can easily bind a shortcut to the +\family sans +math-extern +\family default + LyX function (see the +\family sans +\emph on +LyX Functions +\family default +\emph default + manual). + One could e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +bind the +\family sans +Return +\family default + key inside the math editor. + To bind it to +\family typewriter +Maxima +\family default + one would use this shortcut definition command: +\end_layout + +\begin_layout Standard + +\series bold +command-alternatives break-paragraph;math-extern maxima +\end_layout + +\begin_layout Section +Miscellaneous +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Miscellaneous +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Negative Numbers +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Numbers ! negative +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Negative numbers often look ugly in formulas because the minus sign before + the number is set with the same length as the minus operator sign. + When writing the negative number in normal text, the minus sign appears + correctly. +\end_layout + +\begin_layout Standard +Thus, the problem disappears when converting the minus sign to mathematical + text. +\end_layout + +\begin_layout Standard +An example to visualize the problem: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +normal text: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +x = -2 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +formula: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $x=-2$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +solution: +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $x=\textrm{-}2$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Subsection +Comma as decimal Separator +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Comma +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +In LaTeX a comma inside a formula is used, according to the English convention, + as number group separator. + So there will be space added behind all commas in formulas. +\end_layout + +\begin_layout Standard +To avoid this, the comma is highlighted and changed to mathematical text + (shortcut +\begin_inset Info +type "shortcut" +arg "math-mode" +\end_inset + +). +\end_layout + +\begin_layout Standard +To use all formula commas in the document as decimal separator, the file + +\series bold +icomma.sty +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout + +\series bold +icomma +\series default + is part of the LaTeX-package +\series bold +was +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! was +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! icomma +\end_layout + +\end_inset + + is loaded with the LaTeX-preamble line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage{icomma} +\end_layout + +\begin_layout Subsection +Physical Vectors +\begin_inset CommandInset label +LatexCommand label +name "sub:Physical-Vectors" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Vectors ! physical +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Predefined vectors are offered by the LaTeX-package +\series bold +braket +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! braket +\end_layout + +\end_inset + + that is loaded with the LaTeX-preamble line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage{braket} +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +ifbraket +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following table will only be displayed when the LaTeX-package +\series bold +braket +\series default + is installed. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The following commands are defined: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Bra{ +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Bra{\psi}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Ket{ +\backslash +psi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Ket{\psi}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Braket{ +\backslash +psi| +\backslash +phi +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\Braket{\psi|\phi}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +The command +\series bold + +\backslash +Braket +\series default + assures that all vertical bars are set in the size of the surrounding brackets: +\begin_inset Formula +\[ +\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}} +\] + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +else +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following will be displayed when the LaTeX-package +\series bold +braket +\series default + is not installed: +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +You need to install the LaTeX-package +\series bold +braket +\series default + to see the rest of this subsection in the output. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fi +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +The effect of +\series bold + +\backslash +Braket +\series default + can also be achieved using the command +\series bold + +\backslash +middle +\series default +, that is described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Automatic-Bracket-Size" + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Self-defined Fractions +\begin_inset CommandInset label +LatexCommand label +name "sub:Self-defined-Fractions" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Fractions ! self-defined +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To define custom commands for fractions, the command +\series bold + +\backslash +genfrac +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! G ! +\backslash +genfrac +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + is used in the following scheme: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +genfrac{left +\series default + +\series bold +bracket}{right +\series default + +\series bold +bracket}{fraction bar thickness}{style} +\begin_inset Newline newline +\end_inset + + +\begin_inset Phantom HPhantom +status open + +\begin_layout Plain Layout + +\series bold + +\backslash +genfrac +\end_layout + +\end_inset + +{numerator}{denominator} +\end_layout + +\begin_layout Standard +The style is a number in the range of 0 +\begin_inset space \thinspace{} +\end_inset + +- +\begin_inset space \thinspace{} +\end_inset + +3. +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Number +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Style (Size) +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +0 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +display style formula +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +1 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +inline formula +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +2 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +small +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +tiny +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard +When no style is given, the size is adjusted to the surrounding environment + like for the command +\series bold + +\backslash +frac +\series default +. +\end_layout + +\begin_layout Standard +When no fraction bar thickness is given, the predefined value of 0.4 +\begin_inset space \thinspace{} +\end_inset + +pt will be used. +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +For example, the commands +\series bold + +\backslash +dfrac +\series default + and +\series bold + +\backslash +tbinom +\series default + from +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Fractions" + +\end_inset + + are defined with the commands +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +newcommand{ +\backslash +dfrac}[2]{ +\backslash +genfrac{}{}{}{0}{#1}{#2}} +\end_layout + +\begin_layout Standard +and +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +newcommand{ +\backslash +tbinom}[2]{ +\backslash +genfrac{(}{)}{0pt}{1}{#1}{#2}} +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +To define a fraction where the fraction bar thickness can be given as optional + argument, the following line is inserted to the LaTeX-preamble: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +newcommand{ +\backslash +fracS}[3][]{ +\backslash +genfrac{}{}{#1}{}{#2}{#3}} +\end_layout + +\begin_layout Standard +A test: +\begin_inset Formula +\begin{align*} +\text{Command} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\ +\text{Result} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B} +\end{align*} + +\end_inset + +As one can see, the distance of the numerator and the denominator to the + fraction bar is round about three times the bar thickness. +\end_layout + +\begin_layout Subsection +Canceled Formulas +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! canceled +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To cancel formulas or formula parts, the LaTeX-package +\series bold +cancel +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! cancel +\end_layout + +\end_inset + + has to be loaded with the LaTeX-preamble line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage{cancel} +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +ifcancel +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following table will only be displayed when the LaTeX-package +\series bold +cancel +\series default + is installed. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +There are four ways to cancel formulas: +\end_layout + +\begin_layout Standard +\align center +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +Result +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout +The space and +\series bold + +\backslash +raisebox +\series default + are used here as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cancel{ +\backslash +int +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +bcancel{ +\backslash +int +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +xcancel{ +\backslash +int +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +cancelto{1 +\begin_inset Formula $\to$ +\end_inset + + +\backslash +{ +\backslash +int +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +A=B +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $\raisebox{7mm}{}\cancelto{1}{\int A=B}\raisebox{-2.5mm}{}\hspace{3mm}$ +\end_inset + + +\end_layout + +\end_inset + + + + +\end_inset + + +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +cancelto +\series default + is especially suitable to visualize the reduction of fractions within formulas: +\begin_inset Formula +\[ +\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +To change the size of +\series bold + +\backslash +cancelto +\series default +'s +\begin_inset Quotes eld +\end_inset + +subscript +\begin_inset Quotes erd +\end_inset + + value one can load the package +\series bold +cancel +\series default + with either the option +\series bold +samesize +\series default + which leads to the same size as for the canceled value or with the option + +\series bold +Smaller +\series default + which makes is it a bit smaller than the size one gets without using a + package option. + In this document +\series bold +cancel +\series default + was loaded with this line: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage[samesize]{cancel} +\end_layout + +\begin_layout Standard +To color the cancellation bar one adds this command as TeX code: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +renewcommand{ +\backslash +CancelColor}{ +\backslash +color{red}} +\end_layout + +\begin_layout Standard + +\series bold +red +\series default + can be replaced by a color of your choice. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +CancelColor}{ +\backslash +color{red}} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +renewcommand{ +\backslash +CancelColor}{ +\backslash +color{black}} +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +reset the color +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +For further customizations, see the documentation of the package +\series bold +cancel +\series default +, +\begin_inset CommandInset citation +LatexCommand cite +key "cancel" + +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +else +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following will be displayed when the LaTeX-package +\series bold +cancel +\series default + is not installed: +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +You need to install the LaTeX-package +\series bold +cancel +\series default + to see the rest of this subsection in the output. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fi +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Subsection +Formulas in Section Headings +\begin_inset CommandInset label +LatexCommand label +name "sub:Formulas-in-Section" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! in section headings +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +When formulas are used in section headings, the following has to be taken + into account: +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout +When +\series bold +hyperref +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! hyperref +\end_layout + +\end_inset + + support is enabled in the document settings dialog under +\family sans +PDF +\begin_inset space ~ +\end_inset + +Properties +\family default +, PDF-bookmarks are created for every section heading in the table of contents. + If a section heading contains formulas, they are incorrectly displayed + in the bookmark text, because formulas in bookmarks infringe the PDF convention +s. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Both problems can be solved by inserting at the end of the section heading + a short title with the menu +\family sans +Insert\SpecialChar \menuseparator +Short +\begin_inset space ~ +\end_inset + +Title +\family default +. + Short titles are used as alternative for multiline section headings to + keep the table of contents clearly arranged. + Only the short title appears in the table of contents and therefore also + in the PDF-bookmark. +\end_layout + +\begin_layout Standard +When formulas should be used in the table of contents but +\series bold +hyperref +\series default + is used, one can use the following command in TeX-mode: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +texorpdfstring{part}{alternative} +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! T ! +\backslash +texorpdfstring +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Part is the part of the heading that shouldn't appear in the PDF-bookmark. + This can be characters, formulas, footnotes, but also cross-references. + The alternative is used instead of the part for the bookmark. +\end_layout + +\begin_layout Standard +Here are two example headings: +\begin_inset VSpace -3mm +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +boldmath +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsubsection +Heading without formula in table of contents +\begin_inset Formula $\sqrt{-1}=\mathrm{i}$ +\end_inset + + +\begin_inset Argument +status collapsed + +\begin_layout Plain Layout +Heading without formula in table of contents +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsubsection +Heading with formula in table of contents +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +texorpdfstring{ +\end_layout + +\end_inset + + +\begin_inset Formula $\sqrt{-1}=\mathrm{i}$ +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +}{} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +unboldmath +\end_layout + +\end_inset + +In the first heading a short title was used, in the second one +\series bold + +\backslash +texorpdfstring +\series default +. +\end_layout + +\begin_layout Standard +To get the same formatting as for the other headings, the complete heading + was set into a +\series bold +boldmath +\series default + environment +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Bold-Formulas" + +\end_inset + + +\end_layout + +\end_inset + +. +\end_layout + +\begin_layout Subsection +Formulas in multi-column Text +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! in multi-column text +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Formulas in multi-column text are often too wide to fit into a column and + thus need to be set over the whole page width. + This is done by using the LaTeX-package +\series bold +multicol +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout + +\series bold +multicol +\series default + is part of every LaTeX standard installation. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! multicol +\end_layout + +\end_inset + +, that is loaded with the LaTeX-preamble line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage{multicol} +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout +Note that in this case the setting +\family sans +Two-column +\begin_inset space ~ +\end_inset + +document +\family default + in the menu +\family sans +Document\SpecialChar \menuseparator +Settings +\family default + under +\family sans +Text +\begin_inset space ~ +\end_inset + +Layout +\family default +\emph on + +\emph default +must +\emph on +not +\emph default + be selected. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Before the multi-column text the command +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +begin{multicols}{column number} +\end_layout + +\begin_layout Standard +is written in TeX-mode. + The column number is a number in the range of 2 +\begin_inset space \thinspace{} +\end_inset + +- +\begin_inset space \thinspace{} +\end_inset + +10. + Before the formula the multi-column text is ended by inserting the command +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +end{multicols} +\end_layout + +\begin_layout Standard +in TeX-mode. +\end_layout + +\begin_layout Standard +Due to the command some space is automatically added before the formula. + To revert this, -6 +\begin_inset space \thinspace{} +\end_inset + +mm vertical space is inserted before the formula. + When the formula style +\series bold +Indented +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +formula styles see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + + +\end_layout + +\end_inset + + +\series default + is used, -9 +\begin_inset space \thinspace{} +\end_inset + +mm space is inserted instead. +\end_layout + +\begin_layout Standard +As example a multi-column text with a displayed formula: +\end_layout + +\begin_layout Standard + +\lang german +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +begin{multicols}{2} +\end_layout + +\end_inset + +Das Spektrum wird fouriertransformiert. + Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk +, Lösungsmittel) zu trennen. + Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns + nun das Aussehen des Ausgangssignals. + Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man + über alle Phasen integrieren muss. + Sei nun +\begin_inset Formula $S$ +\end_inset + + unser normiertes Ausgangssignal und +\begin_inset Formula $P$ +\end_inset + + die Phasenverteilungsfunktion, so ergibt sich die Beziehung +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +end{multicols} +\end_layout + +\end_inset + + +\begin_inset VSpace -6mm +\end_inset + + +\begin_inset Formula +\begin{equation} +S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi +\end{equation} + +\end_inset + + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +begin{multicols}{2} +\end_layout + +\end_inset + +wobei +\begin_inset Formula $S_{0}$ +\end_inset + + das Signal ohne Gradient ist und die Normierungsbedingung +\begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$ +\end_inset + + gilt. + Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen. + Direkt nach dem +\begin_inset Formula $\nicefrac{\pi}{2}$ +\end_inset + + +\begin_inset space \thinspace{} +\end_inset + +-rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich + das Signal zusätzlich abschwächt. + Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten + +\begin_inset Formula $T_{2}$ +\end_inset + +-Zeit. +\end_layout + +\begin_layout Standard + +\lang german +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +end{multicols} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Formulas with Description of Variables +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Formula ! with description of variables +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +To describe variables within a formula, like in formula +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:within" + +\end_inset + +, a 2 +\series bold +× +\series default + +\begin_inset Formula $n$ +\end_inset + + +\begin_inset space ~ +\end_inset + +matrix is used with left aligned columns for the +\begin_inset Formula $n$ +\end_inset + + used variables. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +matrices see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Matrices" + +\end_inset + + +\end_layout + +\end_inset + + To set the description in a smaller size, before the matrix e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +the command +\series bold + +\backslash +footnotesize +\series default + is inserted. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +font sizes see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Font-Sizes" + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +When the formula style +\series bold +Indented +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +formula styles see +\begin_inset CommandInset ref +LatexCommand ref +reference "sec:Formula-Styles" + +\end_inset + + +\end_layout + +\end_inset + + +\series default + is used, a +\series bold + +\backslash +hfill +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +hfill +\series default + only works in formulas with the style +\series bold +Indented +\series default +, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Variable-Space" + +\end_inset + +. +\end_layout + +\end_inset + + is inserted before and after the matrix to have the same separation of + the matrix from the equation and the side margin. +\end_layout + +\begin_layout Standard +When the formula style +\series bold +Centered +\series default + is used, the method described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Flalign-Environment" + +\end_inset + + is used to indent formulas. + Formula +\begin_inset CommandInset ref +LatexCommand eqref +reference "eq:within" + +\end_inset + + consists of five columns where in the first two columns contain the equation, + the third the matrix and the last one an empty TeX-brace. +\begin_inset Formula +\begin{flalign} +\hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll} +\rho & \textrm{density}\\ +V & \textrm{volume}\\ +g & \textrm{gravitational acceleration} +\end{array} & & {}\label{eq:within} +\end{flalign} + +\end_inset + + +\end_layout + +\begin_layout Subsection +Upright small Greek Letters +\begin_inset CommandInset label +LatexCommand label +name "sub:Upright-small-Greek" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Greek letters ! upright +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Most of the math fonts only provide italic small Greek letters. + But for symbols of elementary particles like pions and neutrinos, upright + Greek letters are needed. + The file +\series bold +upgreek.sty +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout + +\series bold +upgreek +\series default + is part of the LaTeX-package +\series bold +was +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! was +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +vspace{4mm} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + +. +\end_layout + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! upgreek +\end_layout + +\end_inset + + that is loaded with the LaTeX-preamble line +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +usepackage{upgreek} +\end_layout + +\begin_layout Standard +provides them. + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +ifupgreek +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following table will only be displayed when the LaTeX-package +\series bold +upgreek +\series default + is installed: +\end_layout + +\end_inset + + They are created when the command for a small Greek letter is started with + +\series bold +up +\series default +. + For example the command +\series bold + +\backslash +uptau +\series default + creates this: +\begin_inset Formula $\uptau$ +\end_inset + + +\end_layout + +\begin_layout Standard +With these commands reactions of elementary particles can be typeset: +\begin_inset Formula +\[ +\uppi^{+}\to\upmu^{+}+\upnu_{\upmu} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +The upright letters are more bold and wider than the italic ones. + They should therefore not be used for units like +\begin_inset Quotes eld +\end_inset + +µm +\begin_inset Quotes erd +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +else +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +The following will be displayed when the LaTeX-package +\series bold +upgreek +\series default + is not installed: +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +You need to install the LaTeX-package +\series bold +upgreek +\series default + to see the rest of this subsection in the output. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +fi +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Subsection +Text Characters in Formulas +\begin_inset CommandInset label +LatexCommand label +name "sub:Text-Characters-in" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Text ! in formulas +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +In some cases you might want to insert text characters directly into formulas. + When for example the centered dot · is often used in formulas like +\begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$ +\end_inset + +, one would have to insert the command +\series bold + +\backslash +cdot +\series default + +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Binary-Operators" + +\end_inset + + +\end_layout + +\end_inset + + all the time, because this character is defined in all encodings as text + character. + But the encoding can be changed by this LaTeX-preamble line: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +Declare Inputtext{183}{ +\backslash +ifmmode +\backslash +cdot +\backslash +else +\backslash +textperiodcentered +\backslash +f\SpecialChar \textcompwordmark{} +i} +\end_layout + +\begin_layout Standard +The character encoding (menu +\family sans +Document\SpecialChar \menuseparator +Settings\SpecialChar \menuseparator +Language +\family default +) specifies what character appears when a keyboard key is pressed. + When the key for the character '·' is pressed, internally the command +\series bold + +\backslash +textperiodcentered +\series default + is used. + But this command is not available in a formula so that you would get LaTeX-erro +rs. + With the changed encoding the right command is chosen automatically, depending + on if the character was inserted into a formula or not. +\end_layout + +\begin_layout Standard +The encoding of several characters is saved in definition files. + For example the encoding +\series bold +latin9 +\series default + is defined in the file +\series bold +latin9.def +\series default + which is in the installation folder of LaTeX. + Encodings should only be changed via the LaTeX-preamble and not in the + definition files. + Otherwise documents could not be edited by other LyX users working on other + computers. +\end_layout + +\begin_layout Standard +\begin_inset VSpace medskip +\end_inset + +Besides the centered dot, in this document the degree sign ° is defined + with the following LaTeX-preamble line so that it can be directly inserted + into a formula: +\end_layout + +\begin_layout Standard + +\series bold + +\backslash +DeclareInputtext{176}{ +\backslash +ifmmode^ +\backslash +circ +\backslash +else +\backslash +textdegree +\backslash +f\SpecialChar \textcompwordmark{} +i} +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Section +\start_of_appendix +Typographic Advice +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Typographic advice +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +This section is a summary of the most important typographic rules, listed + in ISO norms. +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +This collection was partly taken from the German semi-official dictionary + called +\begin_inset Quotes eld +\end_inset + +Duden +\begin_inset Quotes erd +\end_inset + + +\begin_inset CommandInset citation +LatexCommand cite +key "Duden" + +\end_inset + + that lists some of the ISO rules. + More rules are listed in +\begin_inset CommandInset citation +LatexCommand cite +key "Checklist" + +\end_inset + +. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Itemize +Physical units are +\emph on +always +\emph default + set upright +\begin_inset Foot +status collapsed + +\begin_layout Plain Layout +done with font styles, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Font-Styles" + +\end_inset + + +\end_layout + +\end_inset + +, no matter if they appear in italic text: 30 +\begin_inset space \thinspace{} +\end_inset + +km/h +\begin_inset Newline newline +\end_inset + +Between the value and the unit is the smallest space, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Predefined-Space" + +\end_inset + +. +\begin_inset Newline newline +\end_inset + +This convention is automatically fulfilled when the command +\series bold + +\backslash +unittwo +\series default + is used. + When it is entered to a formula, two boxes appear. + In the first one the value is inserted, in the second one the unit, and + one gets as above: +\begin_inset Formula $\unit[30]{km/h}$ +\end_inset + + +\begin_inset space \thinspace{} +\end_inset + +. + Note that +\series bold + +\backslash +unittwo +\series default + is not a real LaTeX command but the command +\series bold + +\backslash +unit[value]{unit} +\series default +, therefore you cannot use it in TeX code. +\end_layout + +\begin_layout Itemize +Percent and perthousand signs are set like physical units: +\begin_inset Newline newline +\end_inset + +1.2 +\begin_inset space \thinspace{} +\end_inset + +‰ alcohol in blood +\end_layout + +\begin_layout Itemize +The degree sign follows directly on the value: 15°, but not when it is used + in units: 15 +\begin_inset space \thinspace{} +\end_inset + +°C +\end_layout + +\begin_layout Itemize +In numbers with more than four digits the smallest space is inserted before + every third digit to group them: +\family roman +\series medium +\shape up +\size normal +\emph off +\bar no +\noun off +\color none +18 +\begin_inset space \thinspace{} +\end_inset + +473 +\begin_inset space \thinspace{} +\end_inset + +588 +\end_layout + +\begin_layout Itemize +For dimensions like 120×90×40 +\begin_inset space \thinspace{} +\end_inset + +cm the multiplication sign +\begin_inset Quotes eld +\end_inset + +× +\begin_inset Quotes erd +\end_inset + + is used. + It is available either via the command +\series bold + +\backslash +times +\series default + or via the menu +\family sans +Insert\SpecialChar \menuseparator +Special Character\SpecialChar \menuseparator +Symbols +\family default +. +\end_layout + +\begin_layout Itemize +Functions with names consisting of several letters are set upright to avoid + confusions, see +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Predefined-Functions" + +\end_inset + +. +\end_layout + +\begin_layout Itemize +Indices consisting of several letters, are set upright: +\begin_inset Formula $E_{\mathrm{kin}}$ +\end_inset + + +\begin_inset Newline newline +\end_inset + +Components of matrices are set italic: +\begin_inset Formula $\hat{H}_{kl}$ +\end_inset + + +\end_layout + +\begin_layout Itemize +The differentiation/integration operator 'd', the Euler's number 'e' and + the imaginary unit 'i' should be set upright, to avoid mixing them up with + other variables. +\end_layout + +\begin_layout Itemize +The character that denotes a +\noun on +Fourier +\noun default + transformation is inserted either by the command +\series bold + +\backslash +mathscr +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +spce +\end_layout + +\end_inset + +F +\series default + or via the menu +\family sans +Insert\SpecialChar \menuseparator +Special Character\SpecialChar \menuseparator +Symbols\SpecialChar \menuseparator +Letterlike +\begin_inset space ~ +\end_inset + +Symbols +\family default +: +\begin_inset Formula $\mathscr{F}$ +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Section +Synonyms +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Synonyms +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Some characters and symbols can be created with several commands. + Here is a list of the synonym commands: +\end_layout + +\begin_layout Standard +\begin_inset VSpace bigskip +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +equivalent to +\begin_inset Note Note +status collapsed + +\begin_layout Plain Layout + +\series bold + +\backslash +raisebox +\series default + is only used as spacer. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ast +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +raisebox{-1.2mm}{ +\end_layout + +\end_inset + +* +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +} +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +choose +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +binom +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +geq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ge +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lbrace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +{ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lbracket +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +[ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leftarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +gets +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +leq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +le +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lor +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vee +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +neq +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not= +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +slash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +/ +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +vert +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +| +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\begin_inset Tabular + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +Command +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +equivalent to +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +backslash +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash + +\backslash + +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dasharrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +dashrightarrow +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +land +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +wedge +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rbrace +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +} +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rbracket +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +] +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +rightarrow +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +to +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +lnot +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +neg +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ne +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +not= +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +owns +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +ni +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +square +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Box +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +Vert +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout + +\backslash +| +\end_layout + +\end_inset + + + + +\end_inset + + +\begin_inset space \hfill{} +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Newpage newpage +\end_inset + + +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "TLC2" + +\end_inset + + +\shape smallcaps +Mittelbach, F. + ; Goossens, M. +\shape default +: +\shape italic +The LaTeX Companion +\shape default +. + Addison Wesley, 2004 +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "Mathmode" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Description" +target "ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf" + +\end_inset + + of LaTeX's math abilities +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "AMS" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Description" +target "ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf" + +\end_inset + + of +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + + +\backslash +AmS +\end_layout + +\end_inset + +-LaTeX +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "Symbols" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "List" +target "ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf" + +\end_inset + + of all symbols available with LaTeX-packages +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "cancel" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Documentation" +target "http://mirrors.ctan.org/macros/latex/contrib/cancel/cancel.pdf" + +\end_inset + + of the LaTeX-package +\series bold +cancel +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! cancel +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "hyperref" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Documentation" +target "http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf" + +\end_inset + + of the LaTeX-package +\series bold +hyperref +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! hyperref +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "mhchem" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Documentation" +target "http://www.ctan.org/tex-archive/macros/latex/contrib/mhchem/mhchem.pdf" + +\end_inset + + of the LaTeX-package +\series bold +mhchem +\series default + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Packages ! mhchem +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "Mathclap" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Description" +target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf" + +\end_inset + + of the command +\series bold + +\backslash +mathclap +\series default +, described in +\begin_inset CommandInset ref +LatexCommand ref +reference "sub:Operator-Limits" + +\end_inset + + +\begin_inset Index idx +status collapsed + +\begin_layout Plain Layout +Commands ! M ! +\backslash +mathclap +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "Duden" + +\end_inset + + +\emph on +Duden Band 1 +\emph default +. + 22. + Auflage, Duden 2001 +\end_layout + +\begin_layout Bibliography +\begin_inset CommandInset bibitem +LatexCommand bibitem +key "Checklist" + +\end_inset + + +\begin_inset CommandInset href +LatexCommand href +name "Check list" +target "http://physics.nist.gov/Document/checklist.pdf" + +\end_inset + + for reviewing manuscripts +\end_layout + +\begin_layout Standard +\begin_inset CommandInset index_print +LatexCommand printindex +type "idx" + +\end_inset + + +\end_layout + +\end_body +\end_document diff --git a/lib/doc/UserGuide.lyx b/lib/doc/UserGuide.lyx index 736b175fc3..bcee3b4300 100644 --- a/lib/doc/UserGuide.lyx +++ b/lib/doc/UserGuide.lyx @@ -28029,7 +28029,7 @@ Subindex. \end_layout \begin_layout Section -Nomenclature / Glossary +Nomenclature/Glossary \begin_inset Index idx status collapsed @@ -28082,13 +28082,14 @@ name "sec:Nomenclature" \end_layout \begin_layout Standard -Sometimes you need to compile a list of symbols that are mentioned in your - document with a brief explanation of them – a so called nomenclature or - glossary. +Sometimes you need to provide a list of technical terms or symbols that + are mentioned in your document with a brief explanation of them – a so + called nomenclature or glossary. \end_layout \begin_layout Standard -To be able to create nomenclatures, you need the LaTeX package +To be able to create nomenclatures or glossaries, you need the LaTeX package + \series bold nomencl \series default @@ -28152,8 +28153,16 @@ Nom \begin_layout Standard A nomenclature entry consists of two main entries. - The first is the symbol that you want to refer to. - The second is the description of the symbol. + The first is the term or +\family sans +Symbol +\family default + that you wish to define. + The second is the +\family sans +Description +\family default + of the term or symbol. \end_layout \begin_layout Standard @@ -28375,7 +28384,7 @@ should appear in nomenclature entries they need to be escaped by adding \begin_inset CommandInset nomenclature LatexCommand nomenclature symbol "\"@, \"|, \"!, \"\"" -description "The quote sign is output by writing ' \"\"\"\" '" +description "The quote sign is output by writing ‘ \"\"\"\" '" \end_inset @@ -28399,7 +28408,8 @@ Nomenclature ! Sort order \begin_layout Standard The nomenclature entries are sorted alphabetically by the LaTeX-code of the symbol definition. - This leads to undesired results when you for example have symbols in formulas. + This leads to undesired results when you, for example, have symbols in + formulas. Suppose you have nomenclature entries for the symbols \emph on a @@ -28537,7 +28547,7 @@ The nomencl \series default package offers some options to adjust the appearance of the nomenclature. - Here are some of its options, for more have a look at its documentation: + Here are some of its options; for more have a look at its documentation: \end_layout \begin_layout Description @@ -28754,15 +28764,7 @@ Nomenclature ! Printing To print the nomenclature, use the menu \family sans Insert\SpecialChar \menuseparator -Lists -\begin_inset space ~ -\end_inset - -/ -\begin_inset space ~ -\end_inset - -TOC\SpecialChar \menuseparator +Lists/TOC\SpecialChar \menuseparator Nomenclature \family default . @@ -28998,7 +29000,7 @@ Here is an example, where only the question text appears, the answer branch \begin_layout Standard \begin_inset Branch Question -status collapsed +status open \begin_layout Standard Question: Who was the first physics Nobel prize winner? @@ -29116,8 +29118,7 @@ Exam-Question-Answer.pdf \end_inset if both branches were active. - This helps you to easily export different versions of your document without - much hassle. + This helps you to export different versions of your document easily. \end_layout \begin_layout Standard @@ -29201,7 +29202,7 @@ answer}[1]{#1} \begin_layout Standard \begin_inset Branch Question -status collapsed +status open \begin_layout Standard \begin_inset ERT @@ -29272,7 +29273,7 @@ answer}[1]{#1} \end_layout \begin_layout Standard -Now it is possible to use the commands +Now it is possible to use the \series bold \backslash @@ -29286,7 +29287,7 @@ question{\SpecialChar \ldots{} answer{\SpecialChar \ldots{} } \series default - to obtain conditional output. + commands to obtain conditional output. Here is an example formula where only the \series bold @@ -29313,6 +29314,32 @@ Math manual. \end_layout +\begin_layout Standard +Each type of branch is allowed to have its specific style defined in layout + files (e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +any branch inset can be automatically wrapped by your own LaTeX commands.). + For this advanced usage, see the +\emph on +Customization +\emph default + manual, section +\begin_inset Quotes eld +\end_inset + +Flex insets and InsetLayout +\begin_inset Quotes erd +\end_inset + +). +\end_layout + \begin_layout Section PDF Properties \begin_inset CommandInset label @@ -29337,14 +29364,13 @@ PDF properties \begin_layout Standard The \family sans -Document Settings -\family default - dialog allows you in the -\family sans +Document\SpecialChar \menuseparator +Settings\SpecialChar \menuseparator PDF Properties \family default - to set up special options for the PDF output of your document. - All options there are provided by the LaTeX-package + dialog allows you to set up special options for the PDF output of your + document. + All these options are provided by the LaTeX-package \series bold hyperref \series default @@ -29358,27 +29384,164 @@ LaTeX-packages ! hyperref \end_inset -. + which will link all cross-references in the DVI- and PDF-output. + This means that the reader of your document will be able to click on a + table of contents entry or on a reference to move to the cross-referenced + part of the document. + \end_layout \begin_layout Standard -Using -\series bold -hyperref -\series default - will link all cross-references in the DVI- and PDF-output. - This means that the reader of your document will be able to click on a - table of contents entry or on a reference and he is shown the referenced - document part. - You can specify in the dialog tab +The header information in the dialog tab +\family sans +General +\family default + is saved together with the PDF as file properties. + Many programs are able to extract this information, for example, automatically + to recognize who the author is and what the PDF is about. + This is very useful to sort, classify or use PDFs for bibliography issues. + When the option +\family sans +Automatically +\begin_inset space ~ +\end_inset + +fill +\begin_inset space ~ +\end_inset + +header +\family default + is set, LyX tries to extract the header information from your document + title and author entries. + The option +\family sans +Load +\begin_inset space ~ +\end_inset + +in +\begin_inset space ~ +\end_inset + +fullscreen +\begin_inset space ~ +\end_inset + +mode +\family default + will open the PDF in fullscreen mode, which is useful for presentations. +\end_layout + +\begin_layout Standard +You can specify in the dialog tab \family sans Hyperlinks \family default how the links will look and if links for bibliographical backreferences are created. - The backreferences will appear in the bibliography behind the different - entries, showing the number of the section, slide, or page where the entry - is referenced. + The +\family sans +Break +\begin_inset space ~ +\end_inset + +links +\begin_inset space ~ +\end_inset + +over +\begin_inset space ~ +\end_inset + +lines +\family default + option allows long links to be split; +\family sans +No +\begin_inset space ~ +\end_inset + +frames +\begin_inset space ~ +\end_inset + +around +\begin_inset space ~ +\end_inset + +links +\family default + and +\family sans +Color +\begin_inset space ~ +\end_inset + +links +\family default + both turn off the default behavior of enclosing all links in frames; +\family sans +Color +\begin_inset space ~ +\end_inset + +links +\family default + colors the different links. + The default colors are: +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color magenta +magenta +\color inherit + for hyperlinks and URLs +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color red +red +\color inherit + for links +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color green +green +\color inherit + for citations +\end_layout + +\begin_layout Standard +but you can change these in the field +\family sans +Additional options +\family default +. + For example, in this document they were changed with the additional options: +\end_layout + +\begin_layout Standard + +\series bold +linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue +\end_layout + +\begin_layout Standard +If the option +\family sans +Backreferences +\family default + is set, the hyperlinks will appear in the bibliography after the different + entries, showing, depending on the option selected, the number of the section, + slide or page where the entry is referenced. \end_layout \begin_layout Standard @@ -29386,12 +29549,20 @@ In the dialog tab \family sans Bookmarks \family default - you can set if PDF-bookmarks should be created for every section of your - document to make it easier for readers to navigate through the document. + you can specify if PDF-bookmarks should be created for every section of + your document to make it easier for readers to navigate through the document. You can decide if the bookmarks should be numbered like your document sections or not. - With the open bookmarks level you can specify what sectioning level should - be displayed in the bookmarks when opening the PDF. + With the +\family sans +Open bookmarks +\family default + +\family sans +Level +\family default + you can specify what sectioning level should be displayed in the bookmarks + when opening the PDF. For example level \begin_inset space ~ \end_inset @@ -29403,38 +29574,6 @@ Bookmarks 1 will only display the sections. \end_layout -\begin_layout Standard -The header information in the dialog tab -\family sans -General -\family default - are saved together with the PDF as file properties. - Many programs are able to extract this information to e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -automatically recognize who the author is and what the PDF is about. - This is very useful to sort, classify, or use PDFs for bibliography issues. - When the option -\family sans -Automatic fill header -\family default - is set, LyX tries to extract the header information from your document - title and author settings. -\end_layout - -\begin_layout Standard -The option -\family sans -Load in fullscreen mode -\family default - will open the PDF in fullscreen mode, which is useful for presentations. -\end_layout - \begin_layout Standard PDF properties are also used in this document. When you look in its document settings, you can see that some additional @@ -29443,7 +29582,7 @@ PDF properties are also used in this document. hyperref \series default options are used. - For an explanation of them we refer you to the hyperref manual + For an explanation of all them we refer you to the hyperref manual \begin_inset CommandInset citation LatexCommand cite key "hyperref" @@ -29491,9 +29630,8 @@ As LyX uses LaTeX in the background, it supports many LaTeX commands and LaTeX contains hundreds of packages that provide different commands. All the time packages are being updated and new ones added. This has the advantage that you can typeset nearly everything as there - is for every problem a LaTeX-package. - But LyX can of course not be up to date and support all packages and their - commands. + is a LaTeX-package for every problem, though LyX cannot support all packages + and their commands. \end_layout \begin_layout Standard @@ -29502,7 +29640,18 @@ But don't worry, you can use any LaTeX-command directly in LyX inside the A TeX Code box is created by the menu \family sans Insert\SpecialChar \menuseparator -TeX +Te +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{} +\end_layout + +\end_inset + +X \begin_inset space ~ \end_inset @@ -29615,7 +29764,7 @@ Note: \end_layout \begin_layout Subsection -Short Introduction to the LaTeX Syntax +A Short Introduction to the LaTeX Syntax \begin_inset Argument status collapsed @@ -29659,16 +29808,8 @@ program your text. This has the advantage that the layout of the document can be changed at any time if you know the right commands. - E. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space \space{} -\end_inset - -imagine you have to write a manual for a product and the deadline is the - end of the day. + For example, imagine you have to write a manual for a product and the deadline + is the end of the day. Your boss has just complimented you for your good work but wants to have all caption labels bold. But you have over a hundred figure and table captions with non-bold labels @@ -29680,7 +29821,7 @@ imagine you have to write a manual for a product and the deadline is the \begin_layout Standard Now LaTeX comes into play. As mentioned above, for every problem there exists a LaTeX-package. - First you have to find out which and therefore look into the LaTeX package + First you have to find out which and therefore look in the LaTeX package database, \begin_inset CommandInset citation LatexCommand cite @@ -29712,6 +29853,26 @@ LaTeX-packages ! caption Document\SpecialChar \menuseparator Settings \family default +\SpecialChar \menuseparator + +\family sans +LaT +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{} +\end_layout + +\end_inset + +eX +\begin_inset space ~ +\end_inset + +Preamble +\family default ) with the command \end_layout @@ -30050,7 +30211,15 @@ Header/Footer line \begin_layout Standard To define a custom page header and footer line for your document, you need - to set the headings style to + to set the +\family sans +Page +\begin_inset space ~ +\end_inset + +style +\family default + to \family sans Fancy \family default @@ -30143,7 +30312,7 @@ for the different positions in the header/footer. \end_layout \begin_layout Standard -Normally, headers and footers are set up in the beginning of the document. +Normally, headers and footers are set up at the beginning of the document. But you can change them anywhere you want to. Figure \begin_inset space ~ @@ -30164,7 +30333,7 @@ reference "fig:Page-layout" placement h wide false sideways false -status collapsed +status open \begin_layout Plain Layout \noindent @@ -30352,6 +30521,34 @@ Page layout with custom header and footer line. \end_inset +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Note +\series default +: some document classes implement their own customized page headers and + footers if +\family sans +Page +\begin_inset space ~ +\end_inset + +style +\family default + is set to “Default”. + Check what these are before you specify your own customized page headers + and footers. +\end_layout + +\end_inset + + \end_layout \begin_layout Subsection @@ -30359,17 +30556,13 @@ Definition \end_layout \begin_layout Standard -To define your header line, add all 3 -\begin_inset space ~ -\end_inset - -header styles. - The things you add to the styles appear on uneven pages, the things in - the optional arguments on even pages. +To define your header line, add all three header styles. + The things you add to the styles appear on odd numbered pages, the things + in the optional arguments on even numbered pages. For single-sided documents, the optional arguments will not be used and can be omitted. If you leave a style or its argument empty, nothing appears in the output. - Defining the footer line works similar. + Defining the footer line works similarly. \end_layout \begin_layout Standard @@ -30498,7 +30691,7 @@ headrulewidth \backslash footrulewidth \series default - in the following scheme: + in the following way: \end_layout \begin_layout Standard @@ -30512,7 +30705,7 @@ headrulewidth}{thickness} \end_layout \begin_layout Standard -Where thickness is a size in standard units like +where thickness is a size in standard units like \family sans pt \family default @@ -30565,7 +30758,28 @@ headheight \backslash footheight \series default - in this scheme in your document preamble: + in this entry in +\family sans +Document\SpecialChar \menuseparator +Settings\SpecialChar \menuseparator +Lat +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{} +\end_layout + +\end_inset + +eX +\begin_inset space ~ +\end_inset + +Preamble +\family default +: \end_layout \begin_layout Standard @@ -30579,10 +30793,10 @@ headheight}{height} \end_layout \begin_layout Standard -Where height is a size in standard units. +where height is a size in standard units. If you don't know which amount of space is needed for the height, define - your header/footer and preview your document as PDF. - Then open the LaTeX logfile via the menu + your header/footer and preview your document as a PDF. + Then open the LaTeX logfile with the menu \family sans Document\SpecialChar \menuseparator La @@ -30598,7 +30812,7 @@ status collapsed TeX Log \family default - and look via the button + and use the button \family sans Next \begin_inset space ~ @@ -30606,7 +30820,7 @@ Next Warning \family default - if you find a warning of the package + to see if you can find a warning about the package \series bold fancyhdr \series default @@ -30743,15 +30957,8 @@ pt \begin_layout Standard In principle you can use almost everything in headers/footers, except floats. - For more special things like e. -\begin_inset space \thinspace{} -\end_inset - -g. -\begin_inset space ~ -\end_inset - -thumb-indexes, see the manual of the + For more specialized features, for example, thumb-indexes, see the manual + of the \series bold fancyhdr \series default @@ -30937,6 +31144,27 @@ Size is the multiplication factor for the size. \end_layout +\begin_layout Standard +If you would like to see everything but your math formulas typeset by LaTeX, + set +\family sans +Instant +\begin_inset space ~ +\end_inset + +Preview +\family default + to +\family sans +No +\begin_inset space ~ +\end_inset + +math +\family default +. +\end_layout + \begin_layout Standard Previews are generated when you load a document into LyX and when you finish editing an inset. @@ -30961,7 +31189,7 @@ Display Graphics \family default . - Reopening the documents will fix such problems. + Reopening the document will fix such problems. \end_layout \end_inset @@ -31240,12 +31468,19 @@ View Source \family default and a window will be shown where you can see the LaTeX-source code. - The window shows the source of the whole paragraph where the cursor is - currently in. + The window shows the source of the whole paragraph in which the cursor + currently sits. You can also select document parts in LyX's main window, then only this selection (when it is more than one paragraph) is shown as source code. To view the whole document as source, enable the corresponding option in the source view window. + If you check +\family sans +Automatic update +\family default +, you can see the changes as you make them in LyX; but note that if you + have several documents open, this will slow things down as LyX updates + them all, not just the one which is open at the time. \end_layout \begin_layout Section diff --git a/lib/doc/de/UserGuide.lyx b/lib/doc/de/UserGuide.lyx index da2c0e6752..5c7028356b 100644 --- a/lib/doc/de/UserGuide.lyx +++ b/lib/doc/de/UserGuide.lyx @@ -29972,6 +29972,24 @@ Mathe Handbuchs. \end_layout +\begin_layout Standard +Jeder Branchtyp kann einen speziellen Stil haben, der in Layout-Dateien + definiert werden kann. + Für diese fortgeschrittene Anwendung siehe das +\emph on +Anpassung +\emph default + Handbuch, Abschnitt +\begin_inset Quotes gld +\end_inset + +Flexible Einfügungen und InsetLayout +\begin_inset Quotes grd +\end_inset + +). +\end_layout + \begin_layout Section PDF-Eigenschaften \begin_inset Index idx @@ -30029,28 +30047,6 @@ hyperref ein Leser, der die DVI- oder PDF-Ausgabe auf seinem PC liest, einen Querverweis anklicken kann und so zur entsprechenden Stelle gelangt, wie es auch im Internet passiert. - Auf der Karteikarte -\family sans -Hyperlinks -\family default - können Sie festlegen, wie die Querverweise aussehen sollen, und ob bibliografis -che Rückverweise angelegt werden sollen. -\end_layout - -\begin_layout Standard -Auf der Karteikarte -\family sans -Lesezeichen -\family default - können Sie festlegen, ob welche erzeugt und auch nummeriert werden sollen. - Das erleichtert es Lesern, durch die PDF-Ausgabe des Dokuments zu navigieren. - Mit -\family sans -Ebene -\family default - legen Sie fest, welche Lesezeichen angezeigt werden sollen. - 2 zum Beispiel zeigt die Lesezeichen aller Abschnitte und Unterabschnitte, - während 1 nur Abschnitte berücksichtigt. \end_layout \begin_layout Standard @@ -30079,10 +30075,7 @@ eintragen \family default angekreuzt, versucht LyX, diese Informationen aus dem Titel und dem Autor des Dokuments zu gewinnen. -\end_layout - -\begin_layout Standard -Die Option + Die Option \family sans Im \begin_inset space \space{} @@ -30098,6 +30091,134 @@ Vollbildmodus ionen hilfreich ist. \end_layout +\begin_layout Standard +Auf der Karteikarte +\family sans +Hyperlinks +\family default + können Sie festlegen, wie die Querverweise aussehen sollen, und ob bibliografis +che Rückverweise angelegt werden sollen. +\end_layout + +\begin_layout Standard +Mit die Option +\family sans +Links am Zeilenende umbrechen +\family default + können lange Links umgebrochen werden; +\family sans +Keine +\begin_inset space ~ +\end_inset + +Rahmen +\begin_inset space ~ +\end_inset + +um +\begin_inset space ~ +\end_inset + +Links +\family default + und +\family sans +Links +\begin_inset space ~ +\end_inset + +einfärben +\family default + schalten beide die Eingenschaft aus, dass standardmäßig Rahmen um Links + gezeichnet werden; +\family sans +Links +\begin_inset space ~ +\end_inset + +einfärben +\family default + färbt die verschiedenen Links. + Die verschiedenen Farben sind: +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color magenta +magenta +\color inherit + für Hyperlinks und URLs +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color red +rot +\color inherit + für links +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color green +grün +\color inherit + für Zitate +\end_layout + +\begin_layout Standard +die aber im Feld +\family sans +Zusätzliche Optionen +\family default + geändert werden können. + Dies wurde z. +\begin_inset space \thinspace{} +\end_inset + +B. + in diesem Dokument mit den Optionen +\end_layout + +\begin_layout Standard + +\series bold +linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue +\end_layout + +\begin_layout Standard +getan. +\end_layout + +\begin_layout Standard +Wenn die Option +\family sans +Rückverweise +\family default + ausgewählt ist, erscheinen die Hyperlinks im Literaturverzeichnis hinter + den Einträgen, je nach Einstellung, als Nummer des Abschnitts, der Folie + oder Seite in/auf der sie referenziert sind. +\end_layout + +\begin_layout Standard +In der Karteikarte +\family sans +Lesezeichen +\family default + können Sie festlegen, ob welche erzeugt und auch nummeriert werden sollen. + Das erleichtert es Lesern, durch die PDF-Ausgabe des Dokuments zu navigieren. + Mit +\family sans +Ebene +\family default + legen Sie fest, welche Lesezeichen angezeigt werden sollen. + 2 zum Beispiel zeigt die Lesezeichen aller Abschnitte und Unterabschnitte, + während 1 nur Abschnitte berücksichtigt. +\end_layout + \begin_layout Standard Auch in diesem Handbuch werden PDF-Eigenschaften benutzt, wie Sie im Dialogfenst er @@ -30472,6 +30593,22 @@ LaTeX-Paket ! caption Dokument\SpecialChar \menuseparator Einstellungen \family default +\SpecialChar \menuseparator + +\family sans +LaT +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{} +\end_layout + +\end_inset + +eX-Vorspann +\family default ) mit dem Befehl \end_layout @@ -30785,7 +30922,7 @@ Roman{page} \end_layout \begin_layout Section -Benutzerdefinierte Kopf/Fußzeilen +Benutzerdefinierte Kopf-/Fußzeilen \begin_inset CommandInset label LatexCommand label name "sec:Benutzerdefinierte-Kopf/Fußzeile" @@ -30817,7 +30954,7 @@ Kopf/Fußzeile \begin_layout Standard Um eigene Kopf- und Fußzeilen für ein Dokument zu definieren, muss man den - Stil + Seitenstil \family sans ausgefallen \family default @@ -31115,6 +31252,37 @@ Seitenlayout mit benutzerdefinierter Kopf/Fußzeile. \end_inset +\end_layout + +\begin_layout Standard +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +Achtung +\series default +: Einige Dokumentklassen definieren ihre eigenen Kopf-/Fußzeilen wenn +\family sans +Seiten-Stil +\family default + auf +\begin_inset Quotes gld +\end_inset + +Standard +\begin_inset Quotes grd +\end_inset + + gesetzt ist. + Daher sollten Sie deren Stil ausprobieren bevor Sie eigenen Kopf-/Fußzeilen + definieren. +\end_layout + +\end_inset + + \end_layout \begin_layout Subsection @@ -31707,6 +31875,26 @@ Vorschaugröße ist der Multiplikationsfaktor für die Größe. \end_layout +\begin_layout Standard +Wenn Sie alles außer Mathe vorschauen wollen, setzen Sie +\family sans +Sofortige +\begin_inset space \space{} +\end_inset + +Vorschau +\family default + auf +\family sans +Kein +\begin_inset space ~ +\end_inset + +Mathe +\family default +. +\end_layout + \begin_layout Standard Vorschauen werden erzeugt, wenn Sie ein Dokument öffnen oder eine Einfügung verlassen. @@ -32024,6 +32212,13 @@ ansehen der Code der Auswahl angezeigt (wenn es mehr als ein Absatz ist). Um das gesamte Dokument als Quellcode anzusehen, verwendet man die entsprechend e Option im Quellcode-Fenster. + Verwendet man die Option +\family sans +Automatische Aktualisierung +\family default +, werden die Änderungen, die man am Dokument vornimmt, sofort angezeigt; + aber beachten Sie, dass das LyX langsamer machen kann, wenn mehrere Dateien + geöffnet sind, da LyX alle geöffneten Dateien aktualisiert. \end_layout \begin_layout Section @@ -32139,11 +32334,9 @@ ersetzen Umschalt \family default +F oder den Werkzeugleistenknopf -\begin_inset Graphics - filename ../../images/dialog-toggle_findreplaceadv.png - scale 85 - groupId Icon - +\begin_inset Info +type "icon" +arg "dialog-toggle findreplaceadv" \end_inset aktiviert. @@ -32295,7 +32488,11 @@ Suchen \family default Feld eingegeben wurden, können mit Segmenten ersetzt werden, die im \family sans -Ersetzen durch +Ersetzen +\begin_inset space ~ +\end_inset + +durch \family default \noun on @@ -32316,7 +32513,11 @@ Umschalt+Enter \family default während der Cursor sich im Feld \family sans -Ersetzen durch +Ersetzen +\begin_inset space ~ +\end_inset + +durch \family default \noun on diff --git a/lib/doc/es/UserGuide.lyx b/lib/doc/es/UserGuide.lyx index 28110f623b..15e0573a67 100644 --- a/lib/doc/es/UserGuide.lyx +++ b/lib/doc/es/UserGuide.lyx @@ -29917,6 +29917,36 @@ Ecuaciones . \end_layout +\begin_layout Standard + +\lang english +Each type of branch is allowed to have its specific style defined in layout + files (e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +any branch inset can be automatically wrapped by your own LaTeX commands.). + For this advanced usage, see the +\emph on +Customization +\emph default + manual, section +\lang spanish + +\begin_inset Quotes fld +\end_inset + +Flex insets and InsetLayout +\begin_inset Quotes frd +\end_inset + +). +\end_layout + \begin_layout Section Propiedades PDF \begin_inset CommandInset label @@ -29963,49 +29993,14 @@ LaTeX, paquetes ! hyperref \end_inset -. -\end_layout - -\begin_layout Standard -Utilizando -\series bold -hyperref -\series default - se enlazan todas las referencias cruzadas en las salidas DVI y PDF. + +\lang english +which will link +\lang spanish +todas las referencias cruzadas en las salidas DVI y PDF. Esto significa que el lector puede desplazarse por las partes del documento referenciadas haciendo clic sobre una entrada del índice general o una referencia. - En la pestaña -\family sans -Hiperenlaces -\family default - del diálogo puedes especificar el aspecto de los enlaces y si se crean - enlaces para las referencias bibliográficas. - Estas aparecerán en la bibliografía detrás de las diferentes entradas, - mostrando el número de la sección, transparencia o página donde la entrada - está referenciada. -\end_layout - -\begin_layout Standard -En la pestaña -\family sans -Marcadores -\family default - puedes determinar si se crean marcadores para cada sección del documento - para facilitar al lector la navegación por el mismo. - Puedes decidir si los marcadores se numeran o no como las secciones del - documento. - Con el nivel de marcadores abiertos puedes determinar qué niveles de sección - deben mostrarse al abrir el PDF. - Por ejemplo, un nivel -\begin_inset space ~ -\end_inset - -2 mostrará las secciones y subsecciones, un nivel -\begin_inset space ~ -\end_inset - -1 mostrará sólo las secciones. \end_layout \begin_layout Standard @@ -30029,16 +30024,160 @@ Llenar automáticamente la información de cabecera \family default , LyX intenta extraer la información de cabecera a partir de la configuración del título y del autor del documento. -\end_layout - -\begin_layout Standard -La opción + La opción \family sans Modo pantalla completa \family default abre el PDF en pantalla completa, útil para presentaciones. \end_layout +\begin_layout Standard +En la pestaña +\family sans +Hiperenlaces +\family default + del diálogo puedes especificar el aspecto de los enlaces y si se crean + enlaces para las referencias bibliográficas. +\end_layout + +\begin_layout Standard + +\lang english +The +\family sans +Break +\begin_inset space ~ +\end_inset + +links +\begin_inset space ~ +\end_inset + +over +\begin_inset space ~ +\end_inset + +lines +\family default + option allows long links to be split; +\family sans +No +\begin_inset space ~ +\end_inset + +frames +\begin_inset space ~ +\end_inset + +around +\begin_inset space ~ +\end_inset + +links +\family default + and +\family sans +Color +\begin_inset space ~ +\end_inset + +links +\family default + both turn off the default behavior of enclosing all links in frames; +\family sans +Color +\begin_inset space ~ +\end_inset + +links +\family default + colors the different links. + The default colors are: +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color magenta +\lang english +magenta +\color inherit + for hyperlinks and URLs +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color red +\lang english +red +\color inherit + for links +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color green +\lang english +green +\color inherit + for citations +\end_layout + +\begin_layout Standard + +\lang english +but you can change these in the field +\family sans +Additional options +\family default +. + For example, in this document they were changed with the additional options: +\end_layout + +\begin_layout Standard + +\series bold +linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue +\end_layout + +\begin_layout Standard + +\lang english +If the option +\family sans +Backreferences +\family default + is set, the hyperlinks will appear in the bibliography after the different + entries +\lang spanish +, mostrando el número de la sección, transparencia o página donde la entrada + está referenciada. +\end_layout + +\begin_layout Standard +En la pestaña +\family sans +Marcadores +\family default + puedes determinar si se crean marcadores para cada sección del documento + para facilitar al lector la navegación por el mismo. + Puedes decidir si los marcadores se numeran o no como las secciones del + documento. + Con el nivel de marcadores abiertos puedes determinar qué niveles de sección + deben mostrarse al abrir el PDF. + Por ejemplo, un nivel +\begin_inset space ~ +\end_inset + +2 mostrará las secciones y subsecciones, un nivel +\begin_inset space ~ +\end_inset + +1 mostrará sólo las secciones. +\end_layout + \begin_layout Standard En este documento se han utilizado las propiedades PDF. Si miras la configuración del documento puedes ver algunas opciones adicionales @@ -30318,6 +30457,32 @@ LaTeX, paquetes ! caption Documento\SpecialChar \menuseparator Configuración \family default +\SpecialChar \menuseparator + +\family sans +\lang english +LaT +\lang spanish + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{} +\end_layout + +\end_inset + + +\lang english +eX +\begin_inset space ~ +\end_inset + +Preamble +\family default +\lang spanish ) con el comando \end_layout @@ -30685,7 +30850,11 @@ Configuración\SpecialChar \menuseparator Módulos \family default . - Este módulo ofrece 6 estilos: + Este módulo ofrece 6 +\begin_inset space ~ +\end_inset + +Sestilos: \end_layout \begin_layout Description @@ -30979,6 +31148,45 @@ Diseño de página con encabezado y pie personalizados \end_inset +\end_layout + +\begin_layout Standard + +\lang english +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +\lang english +Note +\series default +: some document classes implement their own customized page headers and + footers if +\family sans +Page +\begin_inset space ~ +\end_inset + +style +\family default + is set to +\begin_inset Quotes fld +\end_inset + +Default +\begin_inset Quotes frd +\end_inset + +. + Check what these are before you specify your own customized page headers + and footers. +\end_layout + +\end_inset + + \end_layout \begin_layout Subsection @@ -31513,6 +31721,29 @@ Tamaño de la vista es el factor de multiplicación para el tamaño. \end_layout +\begin_layout Standard + +\lang english +If you would like to see everything but your math formulas typeset by LaTeX, + set +\family sans +Instant +\begin_inset space ~ +\end_inset + +Preview +\family default + to +\family sans +No +\begin_inset space ~ +\end_inset + +math +\family default +. +\end_layout + \begin_layout Standard Las vistas se generan cuando cargas un documento en Lyx y cuando terminas de editar el objeto insertado. @@ -31808,6 +32039,15 @@ e al párrafo en el que se encuentre el cursor. También puedes seleccionar varios párrafos para ver su código. Para ver el código de todo el documento, marca la opción correspondiente en la ventana de código. + +\lang english +If you check +\family sans +Automatic update +\family default +, you can see the changes as you make them in LyX; but note that if you + have several documents open, this will slow things down as LyX updates + them all, not just the one which is open at the time. \end_layout \begin_layout Section diff --git a/lib/doc/fr/UserGuide.lyx b/lib/doc/fr/UserGuide.lyx index c25e87baee..a8e26781ee 100644 --- a/lib/doc/fr/UserGuide.lyx +++ b/lib/doc/fr/UserGuide.lyx @@ -30800,6 +30800,36 @@ Math s. \end_layout +\begin_layout Standard + +\lang english +Each type of branch is allowed to have its specific style defined in layout + files (e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +any branch inset can be automatically wrapped by your own LaTeX commands.). + For this advanced usage, see the +\emph on +Customization +\emph default + manual, section +\lang french + +\begin_inset Quotes fld +\end_inset + +Flex insets and InsetLayout +\begin_inset Quotes frd +\end_inset + +). +\end_layout + \begin_layout Section Propriétés du PDF \begin_inset CommandInset label @@ -30845,28 +30875,165 @@ Paquetages LaTeX ! hyperref \end_inset -. -\end_layout - -\begin_layout Standard -En utilisant -\series bold -hyperref -\series default -, toutes les références croisées seront transformées en liens dans les sorties + +\lang english +which will link +\lang french + toutes les références croisées seront transformées en liens dans les sorties DVI et PDF. Cela signifie que le lecteur de votre document pourra cliquer sur un élément de la table de matières ou sur une référence pour voir la partie du document référencée. - Dans l'onglet +\end_layout + +\begin_layout Standard +Les informations d'en-tête que vous pouvez entrer dans l'onglet +\family sans +Général +\family default + sont enregistrées dans le fichier PDF comme propriétés du fichier. + De nombreux programmes sont capables d'extraire ces informations pour par + exemple reconnaître automatiquement qui est l'auteur ou quel est le sujet + d'un PDF donné. + C'est très utilisé pour trier, classer ou utiliser les PDF pour des recherches + bibliographiques. + Quand l'option +\family sans +Compléter automatiquement l'en-tête +\family default + est activée, LyX essaie d'extraire les informations de l'en-tête à partir + du titre de votre document et des données sur l'auteur. + L'option +\family sans +Charger en mode plein écran +\family default + ouvrira le PDF en mode plein écran, ce qui est particulièrement utile pour + les présentations. +\end_layout + +\begin_layout Standard +Dans l'onglet \family sans hyperlien \family default vous pouvez préciser l'aspect que devront avoir les liens et si des renvois bibliographiques doivent être créés. - Ces renvois apparaîtront dans la bibliographie à la fin des différentes - entrées, indiquant le numéro de la section, de la diapositive ou de la - page du document où cette entrée est citée. +\end_layout + +\begin_layout Standard + +\lang english +The +\family sans +Break +\begin_inset space ~ +\end_inset + +links +\begin_inset space ~ +\end_inset + +over +\begin_inset space ~ +\end_inset + +lines +\family default + option allows long links to be split; +\family sans +No +\begin_inset space ~ +\end_inset + +frames +\begin_inset space ~ +\end_inset + +around +\begin_inset space ~ +\end_inset + +links +\family default + and +\family sans +Color +\begin_inset space ~ +\end_inset + +links +\family default + both turn off the default behavior of enclosing all links in frames; +\family sans +Color +\begin_inset space ~ +\end_inset + +links +\family default + colors the different links. + The default colors are: +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color magenta +\lang english +magenta +\color inherit + for hyperlinks and URLs +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color red +\lang english +red +\color inherit + for links +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color green +\lang english +green +\color inherit + for citations +\end_layout + +\begin_layout Standard + +\lang english +but you can change these in the field +\family sans +Additional options +\family default +. + For example, in this document they were changed with the additional options: +\end_layout + +\begin_layout Standard + +\series bold +linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue +\end_layout + +\begin_layout Standard + +\lang english +If the option +\family sans +Backreferences +\family default + is set, the hyperlinks will appear in the bibliography after the different + entries +\lang french +, indiquant le numéro de la section, de la diapositive ou de la page du + document où cette entrée est citée. \end_layout \begin_layout Standard @@ -30896,35 +31063,6 @@ Ouverture des signets \end_layout -\begin_layout Standard -Les informations d'en-tête que vous pouvez entrer dans l'onglet -\family sans -Général -\family default - sont enregistrées dans le fichier PDF comme propriétés du fichier. - De nombreux programmes sont capables d'extraire ces informations pour par - exemple reconnaître automatiquement qui est l'auteur ou quel est le sujet - d'un PDF donné. - C'est très utilisé pour trier, classer ou utiliser les PDF pour des recherches - bibliographiques. - Quand l'option -\family sans -Compléter automatiquement l'en-tête -\family default - est activée, LyX essaie d'extraire les informations de l'en-tête à partir - du titre de votre document et des données sur l'auteur. - -\end_layout - -\begin_layout Standard -L'option -\family sans -Charger en mode plein écran -\family default - ouvrira le PDF en mode plein écran, ce qui est particulièrement utile pour - les présentations. -\end_layout - \begin_layout Standard Les propriétés du PDF sont aussi utilisées dans ce document. Si vous regardez dans les paramètres du présent document, vous verrez que @@ -31211,6 +31349,32 @@ Paquetages LaTeX ! caption Document\SpecialChar \menuseparator Paramètres \family default +\SpecialChar \menuseparator + +\family sans +\lang english +LaT +\lang french + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{} +\end_layout + +\end_inset + + +\lang english +eX +\begin_inset space ~ +\end_inset + +Preamble +\family default +\lang french ) avec la commande \end_layout @@ -31586,7 +31750,11 @@ Personnalisation en-têtes/pieds de page \end_inset . - Ce module propose les 6 styles suivants: + Ce module propose les 6 +\begin_inset space ~ +\end_inset + +styles suivants: \end_layout \begin_layout Description @@ -31852,6 +32020,37 @@ Mise en page avec en-tête et pied de page \end_inset +\end_layout + +\begin_layout Standard + +\lang english +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +\lang english +Note +\series default +: some document classes implement their own customized page headers and + footers if +\family sans +Page +\begin_inset space ~ +\end_inset + +style +\family default + is set to “Default”. + Check what these are before you specify your own customized page headers + and footers. +\end_layout + +\end_inset + + \end_layout \begin_layout Subsection @@ -32446,10 +32645,9 @@ Préférences \family sans Apparence\SpecialChar \menuseparator Affichage écran. -\end_layout -\begin_layout Standard -Activez ensuit +\family default + Activez ensuit \family sans Aperçu \begin_inset space ~ @@ -32481,6 +32679,29 @@ l'aperçu est le facteur multiplicatif pour la taille. \end_layout +\begin_layout Standard + +\lang english +If you would like to see everything but your math formulas typeset by LaTeX, + set +\family sans +Instant +\begin_inset space ~ +\end_inset + +Preview +\family default + to +\family sans +No +\begin_inset space ~ +\end_inset + +math +\family default +. +\end_layout + \begin_layout Standard Les aperçus sont générés quand vous chargez un document et quand vous avez fini d'éditer un insert. @@ -32808,6 +33029,15 @@ source complet \family default . + +\lang english +If you check +\family sans +Automatic update +\family default +, you can see the changes as you make them in LyX; but note that if you + have several documents open, this will slow things down as LyX updates + them all, not just the one which is open at the time. \end_layout \begin_layout Section diff --git a/lib/doc/ja/UserGuide.lyx b/lib/doc/ja/UserGuide.lyx index 7bd585ba7e..d37ac8f570 100644 --- a/lib/doc/ja/UserGuide.lyx +++ b/lib/doc/ja/UserGuide.lyx @@ -23910,6 +23910,34 @@ x^{2}-2x-2\Rightarrow\question{x_{1}}\answer{x_{2}}=1\question{+\sqrt{3}}\answer 』をご覧ください。 \end_layout +\begin_layout Standard + +\lang english +Each type of branch is allowed to have its specific style defined in layout + files (e. +\begin_inset space \thinspace{} +\end_inset + +g. +\begin_inset space \space{} +\end_inset + +any branch inset can be automatically wrapped by your own LaTeX commands.). + For this advanced usage, see the +\emph on +Customization +\emph default + manual, section +\begin_inset Quotes eld +\end_inset + +Flex insets and InsetLayout +\begin_inset Quotes erd +\end_inset + +). +\end_layout + \begin_layout Section PDF特性 \begin_inset CommandInset label @@ -23947,31 +23975,14 @@ Latexぱっけーじ@LaTeXパッケージ ! hyperref \end_inset -を利用します。 -\end_layout - -\begin_layout Standard - -\series bold -hyperref -\series default -を使うと、DVI出力とPDF出力中で、すべての相互参照がリンクとして現れます。つまり、あなたの文書の読者は、目次や参照をクリックして、文書の参照されている部分へ -と移動することができるのです。ダイアログタブにある -\family sans -ハイパーリンク -\family default -では、リンクの外観や書誌情報の逆参照リンクを生成するかどうかを指定することができます。逆参照は、書誌情報の各項目のうしろに、項目が引用された節やスライド、ページ -を表示するものです。 -\end_layout - -\begin_layout Standard - -\family sans -しおり -\family default -ダイアログタブでは、読者が文書内を動き回るのに便利なように、文書の各節のPDFしおりを設定するかどうかを指定することができます。しおりが、文書の節見出しと同様に -番号を振るかどうかを指定することもできます。開くしおりの階層では、PDFを開いたときにどの節階層まで表示するかを指定することができます。例えば、階層を2にしたと -きには、すべての節と小節が表示され、階層を１にすると節のみが表示されます。 +を利用します +\lang english +which will link all cross-references in the DVI- and PDF-output. + This means that the reader of your document will be able to click on a + table of contents entry or on a reference to move to the cross-referenced + part of the document +\lang japanese +。 \end_layout \begin_layout Standard @@ -23985,14 +23996,140 @@ hyperref 自動的にヘッダを補完 \family default オプションを有効にすると、LyXはヘッダ情報を、文書のタイトルと著者の設定から自動的に抽出しようと試みます。 +\family sans +全画面モードで読み込む +\family default +オプションは、PDFを全画面モードで開きますので、プレゼンテーションに便利です。 +\end_layout + +\begin_layout Standard + +\lang english +You can specify in the dialog tab +\family sans +Hyperlinks +\family default + how the links will look and if links for bibliographical backreferences + are created. + The +\family sans +Break +\begin_inset space ~ +\end_inset + +links +\begin_inset space ~ +\end_inset + +over +\begin_inset space ~ +\end_inset + +lines +\family default + option allows long links to be split; +\family sans +No +\begin_inset space ~ +\end_inset + +frames +\begin_inset space ~ +\end_inset + +around +\begin_inset space ~ +\end_inset + +links +\family default + and +\family sans +Color +\begin_inset space ~ +\end_inset + +links +\family default + both turn off the default behavior of enclosing all links in frames; +\family sans +Color +\begin_inset space ~ +\end_inset + +links +\family default + colors the different links. + The default colors are: +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color magenta +\lang english +magenta +\color inherit + for hyperlinks and URLs +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color red +\lang english +red +\color inherit + for links +\end_layout + +\begin_layout Labeling +\labelwidthstring 00.00.0000 + +\color green +\lang english +green +\color inherit + for citations +\end_layout + +\begin_layout Standard + +\lang english +but you can change these in the field +\family sans +Additional options +\family default +. + For example, in this document they were changed with the additional options: +\end_layout + +\begin_layout Standard + +\series bold +linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue +\end_layout + +\begin_layout Standard + +\lang english +If the option +\family sans +Backreferences +\family default + is set, the hyperlinks will appear in the bibliography after the different + entries, showing, depending on the option selected, the number of the section, + slide or page where the entry is referenced. \end_layout \begin_layout Standard \family sans -全画面モードで読み込む +しおり \family default -オプションは、PDFを全画面モードで開きますので、プレゼンテーションに便利です。 +ダイアログタブでは、読者が文書内を動き回るのに便利なように、文書の各節のPDFしおりを設定するかどうかを指定することができます。しおりが、文書の節見出しと同様に +番号を振るかどうかを指定することもできます。開くしおりの階層では、PDFを開いたときにどの節階層まで表示するかを指定することができます。例えば、階層を2にしたと +きには、すべての節と小節が表示され、階層を１にすると節のみが表示されます。 \end_layout \begin_layout Standard @@ -24244,7 +24381,33 @@ Latexぱっけーじ@LaTeXパッケージ ! caption 文書\SpecialChar \menuseparator 設定 \family default -メニュー）で +メニュー\SpecialChar \menuseparator + +\family sans +\lang english +LaT +\lang japanese + +\begin_inset ERT +status collapsed + +\begin_layout Plain Layout + +{} +\end_layout + +\end_inset + + +\lang english +eX +\begin_inset space ~ +\end_inset + +Preamble +\family default +\lang japanese +）で \end_layout \begin_layout Standard @@ -24799,6 +24962,37 @@ name "fig:ページレイアウト" \end_inset +\end_layout + +\begin_layout Standard + +\lang english +\begin_inset Note Greyedout +status open + +\begin_layout Plain Layout + +\series bold +\lang english +Note +\series default +: some document classes implement their own customized page headers and + footers if +\family sans +Page +\begin_inset space ~ +\end_inset + +style +\family default + is set to “Default”. + Check what these are before you specify your own customized page headers + and footers. +\end_layout + +\end_inset + + \end_layout \begin_layout Subsection @@ -25251,6 +25445,29 @@ pnmcrop とあるのは、大きさの倍率因子のことです。 \end_layout +\begin_layout Standard + +\lang english +If you would like to see everything but your math formulas typeset by LaTeX, + set +\family sans +Instant +\begin_inset space ~ +\end_inset + +Preview +\family default + to +\family sans +No +\begin_inset space ~ +\end_inset + +math +\family default +. +\end_layout + \begin_layout Standard すると、LyXに文書を読み込んだり挿入枠を編集し終わったりすると、プレビューが生成されるようになります。すでに読み込まれた文書のプレビューは、 \family sans @@ -25530,6 +25747,14 @@ LaTeXソースコード メニューを使用すると、ウィンドウが開いてLaTeXコードを見ることができるようになります。このウィンドウには、現在カーソルがある段落全体のソースを表示します。L yXのメインウィンドウで文書の一部を選択すれば、（1段落以上を選択しているときには）選択部分のみがソースコードとして表示されます。文書全体をソースとして閲覧した いときには、ソース閲覧ウィンドウにある、そのオプションを有効にしてください。 +\lang english +If you check +\family sans +Automatic update +\family default +, you can see the changes as you make them in LyX; but note that if you + have several documents open, this will slow things down as LyX updates + them all, not just the one which is open at the time. \end_layout \begin_layout Section