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"" \author "" \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 Standard \noindent If you have comments or error corrections, please send them to the LyX Documenta tion mailing list: \family typewriter \begin_inset ERT status collapsed \begin_layout Standard \backslash href{mailto:lyx-docs@lists.lyx.org?subject=LyX's Math manual}{ \end_layout \end_inset lyx-docs@lists.lyx.org \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset \begin_inset Note Note status collapsed \begin_layout Standard author: Uwe Stöhr \end_layout \end_inset \newline \newline \family sans Version 1.5.7 \end_layout \begin_layout Standard \begin_inset LatexCommand tableofcontents \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Standard To export this document to PDF, PS, or DVI the LaTeX-packages \series bold eurosym, \series default \series bold multirow, \series default and \series bold was \series default must be installed. If they are not installed you can export the document anyway but the sections where the packages are required won't appear in the output. \end_layout \begin_layout Standard The latest PDF-version of this document can be found here: \newline \series bold http://wiki.lyx.org/LyX/DocumentationDevelopment#Math \end_layout \end_inset \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Section Introduction \begin_inset LatexCommand label name "sec:Introduction" \end_inset \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\InsetSpace ~ 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 used in the document settings (menu \family sans Document\SpecialChar \menuseparator Settings\SpecialChar \menuseparator Math\InsetSpace ~ Options \family default ). \begin_inset Foot status collapsed \begin_layout Standard The option \family sans Use AMS math package automatically \family default only uses \begin_inset ERT status collapsed \begin_layout Standard \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 Standard \backslash AmS \end_layout \end_inset -math commands \begin_inset Foot status collapsed \begin_layout Standard A list with all \begin_inset ERT status collapsed \begin_layout Standard \backslash AmS \end_layout \end_inset -math commands is in the file \begin_inset ERT status collapsed \begin_layout Standard \backslash href{ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps}{ \end_layout \end_inset \family sans amsguide.ps \family default \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset , which is part of every LaTeX standard installation. \end_layout \end_inset for lucidity reasons. \end_layout \begin_layout Section General Instructions \begin_inset LatexCommand label name "sec:General-Instructions" \end_inset \end_layout \begin_layout Standard To create an inline formula \begin_inset LatexCommand index name "Formula ! inline" \end_inset that is embedded into a text line, press \family sans Ctrl-m \family default or the toolbar button \begin_inset Graphics filename ../images/math-mode.xpm scale 85 \end_inset \newline To create a display style formula \begin_inset LatexCommand index name "Formula ! display style" \end_inset that will appear bigger and in an own paragraph, press \family sans Ctrl-M \family default . \end_layout \begin_layout Standard To change a display style formula to an inline formula, set the cursor into the formula and press \family sans Ctrl-M \family default or use 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 \begin_inset LatexCommand index name "Commands ! D ! \\textbackslash displaystyle" \end_inset \series default 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\InsetSpace ~ (auto) \begin_inset Quotes erd \end_inset . \end_layout \begin_layout Standard The TeX-mode \begin_inset LatexCommand index name "T@\\TeX-mode" \end_inset is invoked by pressing the toolbar button \begin_inset Graphics filename ../images/ert-insert.xpm scale 85 \end_inset or by using the menu \family sans Insert\SpecialChar \menuseparator T \begin_inset ERT status collapsed \begin_layout Standard { \end_layout \end_inset e \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset X Code \family default (shortcut \family sans Ctrl-l \family default ). \begin_inset Note Note status collapsed \begin_layout Standard 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 Standard To avoid that these names are recognized as proper names, TeX-braces are set around one of the letters of the name. \end_layout \end_inset \end_layout \begin_layout Standard To change the LaTeX-preamble \begin_inset LatexCommand index name "L@\\LaTeX-preamble" \end_inset , use the menu \family sans Document\SpecialChar \menuseparator Settings\SpecialChar \menuseparator La \begin_inset ERT status collapsed \begin_layout Standard { \end_layout \end_inset T \begin_inset ERT status collapsed \begin_layout Standard } \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, the menus \family sans Edit\SpecialChar \menuseparator Math \family default and \family sans Edit\SpecialChar \menuseparator Rows\InsetSpace \thinspace{} &\InsetSpace \thinspace{} Columns, \family default or the \family sans table toolbar \family default can be used. 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 Standard For multiline formulas the command \series bold \backslash intertext \series default is used, see \begin_inset LatexCommand ref reference "sub:Text-in-multiline" \end_inset . \end_layout \end_inset \emph on mathematical text \emph default \begin_inset LatexCommand index name "Text ! in formulas" \end_inset \begin_inset LatexCommand index name "Mathematical text" \end_inset is used. This mode is invoked with the the shortcut \family sans Alt-m\InsetSpace ~ m \family default or by the insertion of the command \series bold \backslash text \begin_inset LatexCommand index name "Commands ! T ! \\textbackslash text" \end_inset \series default . The text appears black in LyX and can therefore be distinguished from the other formula parts that 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 starts always 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 LatexCommand index name "T@\\TeX-braces" \end_inset . If you add in a formula a left brace to a command name, LyX creates automatical ly 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 that 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 \family sans Ctrl-Space \family default . \end_layout \begin_layout Subsection* \newpage Syntax Explanation \end_layout \begin_layout Itemize The symbol \begin_inset Foot status collapsed \begin_layout Standard This visible space character can be created with the command \series bold \backslash textvisiblespace \series default \begin_inset LatexCommand index name "Commands ! T ! \\textbackslash textvisiblespace" \end_inset , inserted in TeX-mode. \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \InsetSpace ~ 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. \end_layout \begin_layout Subsection* Used units \end_layout \begin_layout Standard \align center \begin_inset Float table placement H wide false sideways false status open \begin_layout Standard \align center \begin_inset Caption \begin_layout Standard \begin_inset LatexCommand label name "tab:Used-units" \end_inset Used units \end_layout \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Unit \end_layout \end_inset \begin_inset Text \begin_layout Standard Name / Description \end_layout \end_inset \begin_inset Text \begin_layout Standard mm \end_layout \end_inset \begin_inset Text \begin_layout Standard Millimeter \end_layout \end_inset \begin_inset Text \begin_layout Standard cm \end_layout \end_inset \begin_inset Text \begin_layout Standard Centimeter \end_layout \end_inset \begin_inset Text \begin_layout Standard in \end_layout \end_inset \begin_inset Text \begin_layout Standard Inch (1\InsetSpace \thinspace{} in = 2,54\InsetSpace \thinspace{} cm) \end_layout \end_inset \begin_inset Text \begin_layout Standard pt \end_layout \end_inset \begin_inset Text \begin_layout Standard Point (72.27\InsetSpace \thinspace{} pt = 1\InsetSpace \thinspace{} in) \end_layout \end_inset \begin_inset Text \begin_layout Standard pc \end_layout \end_inset \begin_inset Text \begin_layout Standard Pica (1\InsetSpace \thinspace{} pc = 12\InsetSpace \thinspace{} pt) \end_layout \end_inset \begin_inset Text \begin_layout Standard sp \end_layout \end_inset \begin_inset Text \begin_layout Standard scaled point (65536\InsetSpace \thinspace{} sp = 1\InsetSpace \thinspace{} pt) \end_layout \end_inset \begin_inset Text \begin_layout Standard bp \end_layout \end_inset \begin_inset Text \begin_layout Standard big point (72\InsetSpace \thinspace{} bp = 1\InsetSpace \thinspace{} in) \end_layout \end_inset \begin_inset Text \begin_layout Standard dd \end_layout \end_inset \begin_inset Text \begin_layout Standard Didot (1\InsetSpace \thinspace{} dd \begin_inset Formula $\approx$ \end_inset 0.376\InsetSpace \thinspace{} mm) \end_layout \end_inset \begin_inset Text \begin_layout Standard cc \end_layout \end_inset \begin_inset Text \begin_layout Standard Cicero (1\InsetSpace \thinspace{} cc = 12\InsetSpace \thinspace{} dd) \end_layout \end_inset \begin_inset Text \begin_layout Standard ex \end_layout \end_inset \begin_inset Text \begin_layout Standard 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 Standard em \end_layout \end_inset \begin_inset Text \begin_layout Standard 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 Standard mu \end_layout \end_inset \begin_inset Text \begin_layout Standard math unit (1\InsetSpace \thinspace{} mu = \begin_inset Formula $\nicefrac{1}{18}$ \end_inset \InsetSpace \thinspace{} em) \end_layout \end_inset \end_inset \end_layout \end_inset \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Section Basic Functions \end_layout \begin_layout Subsection Exponents \begin_inset LatexCommand index name "Exponents" \end_inset and Indices \begin_inset LatexCommand index name "Indices" \end_inset \begin_inset LatexCommand index name "Superscripts|see{Exponents}" \end_inset \begin_inset LatexCommand index name "Subscripts|see{Indices}" \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.xpm 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.xpm scale 85 \end_inset . \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard B_V \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $B_{V}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard B^V \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}B^{V}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard B^ \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard Depending on the used keyboard settings this can also happen for other character s than vowels. \end_layout \end_inset . To get in this case exponents, press \family sans Space \family default after the caret as in the last example. \end_layout \begin_layout Subsection Fractions \begin_inset LatexCommand label name "sub:Fractions" \end_inset \begin_inset LatexCommand index name "Fractions" \end_inset \end_layout \begin_layout Standard Fractions are generated with the command \series bold \backslash frac \series default \begin_inset LatexCommand index name "Commands ! F ! \\textbackslash frac" \end_inset or via the math toolbar button \begin_inset Graphics filename ../images/math/frac.xpm 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.xpm scale 85 \end_inset you can select different fraction types. \end_layout \begin_layout Standard With the command \series bold \backslash dfrac \begin_inset LatexCommand index name "Commands ! D ! \\textbackslash dfrac" \end_inset \series default a fraction can be created that has in any case the size of a display style formula. With \series bold \backslash tfrac \begin_inset LatexCommand index name "Commands ! T ! \\textbackslash tfrac" \end_inset \series default 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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash frac \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dfrac \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dfrac \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset e^ \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash frac \begin_inset ERT status collapsed \begin_layout Standard \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 Standard \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 \newpage For nested fractions the command \series bold \backslash cfrac \series default \begin_inset LatexCommand index name "Commands ! C ! \\textbackslash cfrac" \end_inset can be used. Here 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{A \begin_inset Formula $\to$ \end_inset \backslash {B+ \backslash cfrac{C+ \backslash cfrac{E \begin_inset Formula $\to$ \end_inset \backslash {F \begin_inset Formula $\to\to$ \end_inset \backslash {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. \series bold \backslash cfrac \series default has the following command scheme: \end_layout \begin_layout Standard \series bold \backslash cfrac[numerator position]{numerator}{denominator} \end_layout \begin_layout Standard The numerator position can be \emph on l \emph default , \emph on c \emph default , or \emph on r \emph default . l or r aligns the numerator to the left or right, resp.\InsetSpace ~ with the fraction stroke. When \emph on c \emph default or no position is given, the numerator appears centered. These fractions demonstrate the different alignments: \newline \series bold \begin_inset Formula $\cfrac[l]{A}{B+C}$ \end_inset , \begin_inset Formula $\cfrac{A}{B+C}$ \end_inset , \begin_inset Formula $\cfrac[r]{A}{B+C}$ \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 \begin_inset LatexCommand index name "Commands ! N ! \\textbackslash nicefrac" \end_inset \series default : \begin_inset Formula $\nicefrac{5}{31}$ \end_inset \end_layout \begin_layout Standard How to define own fractions where the fraction stroke can be changed, is explained in \begin_inset LatexCommand ref reference "sub:Self-defined-Fractions" \end_inset . \end_layout \begin_layout Subsection Roots \begin_inset LatexCommand index name "Roots" \end_inset \end_layout \begin_layout Standard Square roots are created with \series bold \backslash sqrt \series default \begin_inset LatexCommand index name "Commands ! S ! \\textbackslash sqrt" \end_inset or the math toolbar button \begin_inset Graphics filename ../images/math/sqrt.xpm scale 85 \end_inset , all other roots with the command \series bold \backslash root \series default \begin_inset LatexCommand index name "Commands ! R ! \\textbackslash root" \end_inset or with the math toolbar button \begin_inset Graphics filename ../images/math/root.xpm scale 85 \end_inset . \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sqrt \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A-B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash root \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset 3 \begin_inset Formula $\downarrow$ \end_inset A-B \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 \newline The \begin_inset Formula $\beta$ \end_inset touches the root. To avoid this, the commands \series bold \backslash leftroot \series default \begin_inset LatexCommand index name "Commands ! L ! \\textbackslash leftroot" \end_inset and \series bold \backslash uproot \series default \begin_inset LatexCommand index name "Commands ! U ! \\textbackslash uproot" \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 \newline \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 Standard \backslash spce \end_layout \end_inset \begin_inset Formula $\to$ \end_inset B \newline \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 LatexCommand index name "Binomial coefficient s" \end_inset \end_layout \begin_layout Standard Binomial coefficients are inserted with the command \series bold \backslash binom \series default \begin_inset LatexCommand index name "Commands ! B ! \\textbackslash binom" \end_inset or with the submenu of the math toolbar button \begin_inset Graphics filename ../images/math/frac-square.xpm scale 85 \end_inset . \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash binom \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dbinom{A \begin_inset Formula $\to$ \end_inset \backslash {B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash brack \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \series bold \begin_inset LatexCommand index name "Commands ! B ! \\textbackslash brack" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}{A \brack B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash brace \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \series bold \begin_inset LatexCommand index name "Commands ! B ! \\textbackslash brace" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}{A \brace B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \end_inset \end_layout \begin_layout Standard Analog to fractions ( \series bold \backslash frac \series default ) there are besides \series bold \backslash binom \series default the commands \series bold \backslash dbinom \begin_inset LatexCommand index name "Commands ! D ! \\textbackslash dbinom" \end_inset \series default and \series bold \backslash tbinom \series default \begin_inset LatexCommand index name "Commands ! T ! \\textbackslash tbinom" \end_inset with the following command scheme: \end_layout \begin_layout Standard \series bold \backslash dbinom{numerator}{denominator} \series default and \newline \series bold \backslash tbinom{numerator}{denominator} \end_layout \begin_layout Subsection Case differentiations \begin_inset LatexCommand index name "Case differentiations " \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cases \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \begin_inset Formula $\to$ \end_inset B>0 \begin_inset LatexCommand index name "Commands ! C ! \\textbackslash cases" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\begin{cases} A & B>0\end{cases}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cases \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset Ctrl-Enter \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 the usage of the math toolbar button \begin_inset Graphics filename ../images/math/cases.xpm scale 85 \end_inset you can create new lines with the shortcut \family sans Ctrl-Return \family default or the table toolbar button \begin_inset Graphics filename ../images/tabular-feature_append-row.xpm 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 LatexCommand index name "Negations" \end_inset \end_layout \begin_layout Standard By inserting of \series bold \backslash not \series default \begin_inset LatexCommand index name "Commands ! N ! \\textbackslash not" \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash not= \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\not=$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash not \backslash le \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\not\le$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash not \backslash parallel \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 for some negations special commands (see \begin_inset LatexCommand ref reference "sub:Mathematical-Symbols" \end_inset and \begin_inset LatexCommand ref reference "sec:Relations" \end_inset ). \end_layout \begin_layout Subsection Placeholders \begin_inset LatexCommand label name "sub:Placeholders" \end_inset \begin_inset LatexCommand index name "Placeholders" \end_inset \begin_inset LatexCommand index name "Chemical characters ! Isotopes" \end_inset \begin_inset LatexCommand index name "Isotopes|see{Chemical characters}" \end_inset \end_layout \begin_layout Standard When displaying e.\InsetSpace \thinspace{} g.\InsetSpace ~ isotopes \begin_inset Foot status collapsed \begin_layout Standard More about chemical symbols is written in \begin_inset 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 Standard Indices created with sub- and superscripts: \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard correct indices: \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \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 LatexCommand index name "Commands ! P ! \\textbackslash phantom" \end_inset or the math toolbar button\InsetSpace \thinspace{} \begin_inset Foot status collapsed \begin_layout Standard can be found in the submenu of the toolbar button \begin_inset Graphics filename ../images/math/space.xpm scale 85 \end_inset \end_layout \end_inset \begin_inset Graphics filename ../images/math/phantom.xpm 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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard ^19 \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset _ \backslash phantom \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset 1 \begin_inset Formula $\to$ \end_inset 9 \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset F \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard ^235 \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset _ \backslash phantom \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset 23 \begin_inset Formula $\to$ \end_inset 9 \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset F \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \backslash Lambda^ \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash phantom \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset ii \begin_inset Formula $\to$ \end_inset t \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset _MMt \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 LatexCommand index name "Commands ! V ! \\textbackslash vphantom" \end_inset (toolbar button \InsetSpace ~ \begin_inset Graphics filename ../images/math/vphantom.xpm scale 85 \end_inset ) and \series bold \backslash hphantom \series default \begin_inset LatexCommand index name "Commands ! H ! \\textbackslash hphantom" \end_inset (toolbar button \InsetSpace ~ \begin_inset Graphics filename ../images/math/hphantom.xpm 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 creates \series bold \backslash vphantom \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series bold a \backslash int \series default space for the height of the integral sign, \begin_inset Foot status collapsed \begin_layout Standard The command \series bold \backslash int \series default creates an integral sign, see \begin_inset 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 LatexCommand ref reference "sub:Multiline-Brackets" \end_inset . \end_layout \begin_layout Subsection Lines \begin_inset LatexCommand index name "Lines" \end_inset \begin_inset LatexCommand index name "Formula ! underlined" \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash overline \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A+B \begin_inset LatexCommand index name "Commands ! O ! \\textbackslash overline" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash underline \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A+B \begin_inset LatexCommand index name "Commands ! U ! \\textbackslash underline" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash overline \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash underline \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A+B \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 e.\InsetSpace \thinspace{} g. results, one uses \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 Subsection Ellipses \begin_inset LatexCommand index name "Ellipses" \end_inset \end_layout \begin_layout Standard There are different types of ellipses available. \begin_inset Foot status collapsed \begin_layout Standard In the math toolbar in the submenu of the button \begin_inset Graphics filename ../images/math/ldots.xpm scale 85 \end_inset \end_layout \end_inset For listings dots at the baseline are used ( \series bold \backslash ldots \series default \begin_inset LatexCommand index name "Commands ! L ! \\textbackslash ldots" \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 LatexCommand index name "Commands ! C ! \\textbackslash cdots" \end_inset ). When using the command \series bold \backslash dots \series default \begin_inset LatexCommand index name "Commands ! D ! \\textbackslash dots" \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard A_1 \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset , \backslash dots \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset ,A_n \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A_{1},\dots,A_{n}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard A_1 \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset + \backslash dots \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset +A_n \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A_{1}+\dots+A_{n}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard A_1 \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset , \backslash ldots \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset ,A_n \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A_{1},\ldots,A_{n}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard A_1 \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset + \backslash cdots \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset +A_n \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A_{1}+\cdots+A_{n}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash vdots \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\vdots$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ddots \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\ddots$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard 3×3\InsetSpace \thinspace{} matrix with the different dots \end_layout \end_inset \begin_inset Text \begin_layout Standard \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\InsetSpace ~ Character \family default are \series bold \backslash ldots \series 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 LatexCommand index name "Commands ! H ! \\textbackslash hdotsfor" \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 LatexCommand index name "Commands ! D ! \\textbackslash dotfill" \end_inset the rest of a line with dots. The effect of these commands is the same like with \series bold \backslash hfill \series default , see \begin_inset 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 Standard \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 Analog to \series bold \backslash dotfill \series default there is for a line the command \series bold \backslash hrulefill \series default \begin_inset LatexCommand index name "Commands ! H ! \\textbackslash hrulefill" \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 LatexCommand label name "sec:Matrices" \end_inset \begin_inset LatexCommand index name "Matrices" \end_inset \end_layout \begin_layout Standard Matrices can be inserted via the math toolbar button \begin_inset Graphics filename ../images/dialog-show_mathmatrix.xpm scale 85 \end_inset or the menu \family sans Insert\SpecialChar \menuseparator Math\SpecialChar \menuseparator Matrix \family default . You will be asked for the number of matrix columns and rows, and the alignment. The vertical alignment is hereby 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\InsetSpace ~ 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 are in a matrix all columns centered, therefore the default is 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.xpm scale 85 \end_inset , \begin_inset Graphics filename ../images/tabular-feature_delete-row.xpm scale 85 \end_inset , etc.\InsetSpace \thinspace{} , or the menu \family sans Edit\SpecialChar \menuseparator Rows & Columns \family default can be used. New rows can also be created with \family sans Ctrl-Return \family default . \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Parentheses around a matrix can can either be created with the commands \series bold \backslash left \series default \begin_inset LatexCommand index name "Commands ! L ! \\textbackslash left" \end_inset and \series bold \backslash right \series default \begin_inset LatexCommand index name "Commands ! R ! \\textbackslash right" \end_inset (shortcut \family sans Alt-m\InsetSpace ~ parenthesis \family default ), see \begin_inset 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 \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bmatrix \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} matrix \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \backslash Bmatrix \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} matrix \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \backslash pmatrix \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} matrix \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash vmatrix \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} matrix \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \backslash Vmatrix \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} matrix \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \backslash matrix \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} matrix \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset When e.\InsetSpace \thinspace{} g.\InsetSpace ~ \series bold \backslash vmatrix \series default is inserted, a blue box appears between two vertical lines where the matrix is inserted. \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 LatexCommand index name "Commands ! A ! \\textbackslash arraycolsep" \end_inset that is described in \begin_inset 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 LatexCommand index name "Commands ! A ! \\textbackslash arraystretch" \end_inset is used. It is used as follows: \end_layout \begin_layout Standard \series bold \backslash renewcommand{ \backslash arraystretch}{stretch factor} \begin_inset LatexCommand index name "Commands ! R ! \\textbackslash renewcommand" \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.\InsetSpace \thinspace{} g.\InsetSpace ~ 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 LatexCommand index name "Commands ! S ! \\textbackslash smallmatrix" \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 LatexCommand index name "Brackets" \end_inset \begin_inset LatexCommand index name "Delimiters" \end_inset \end_layout \begin_layout Subsection Vertical Brackets and Delimiters \begin_inset LatexCommand index name "Brackets ! vertical" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard ( \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $($ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard { \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\{$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard [ \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $[$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash langle \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\langle$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash lceil \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\lceil$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash lfloor \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\lfloor$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard / \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $/$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard | \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $|$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard ) \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $)$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard } \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard ] \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $]$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash rangle \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\rangle$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash rceil \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\rceil$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash rfloor \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\rfloor$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash \backslash \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\backslash$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash | \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\|$ \end_inset \end_layout \end_inset \end_inset \hfill \end_layout \begin_layout Standard \series medium \begin_inset Note Greyedout status open \begin_layout Standard \series bold Note: \series default In TeX-mode the command \series bold \backslash textbackslash \series default \begin_inset LatexCommand index name "Commands ! T ! \\textbackslash textbackslash" \end_inset must be used for the backslash, because the command \series bold \backslash \backslash \series default produces there a line break. \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 LatexCommand label name "sub:Manual-Bracket-Size" \end_inset \begin_inset LatexCommand index name "Bracket size ! manual" \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 LatexCommand index name "Commands ! B ! \\textbackslash big" \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 Standard all brackets in the same size: \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard this looks better: \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \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 Standard \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 Standard \backslash spce \end_layout \end_inset \backslash sin(x) \backslash Big]^ \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \begin_inset ERT status collapsed \begin_layout Standard \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 \newpage Besides the \series bold \backslash big \series default -commands there is the variant \series bold \backslash bigm \series default \begin_inset LatexCommand index name "Commands ! B ! \\textbackslash bigm" \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 LatexCommand index name "Commands ! B ! \\textbackslash bigl - \\textbackslash bigr" \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Bigm( \backslash bigm( \backslash ln(3x) \backslash bigm)^2 \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default \backslash Bigm) \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \backslash Big( \backslash big( \backslash ln(3x) \backslash big)^2 \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default \backslash Big) \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \backslash Bigl( \backslash bigl( \backslash ln(3x) \backslash bigr)^2 \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default \backslash Bigr) \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \backslash bigl) \backslash ln(3x) \backslash bigr( \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 LatexCommand label name "sub:Automatic-Bracket-Size" \end_inset \begin_inset LatexCommand index name "Bracket size ! automatic" \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 LatexCommand index name "Commands ! L ! \\textbackslash left" \end_inset and \series bold \backslash right \series default \begin_inset LatexCommand index name "Commands ! R ! \\textbackslash right" \end_inset or via the math toolbar button \begin_inset Graphics filename ../images/dialog-show_mathdelimiter.xpm 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 Standard \backslash spce \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset C \begin_inset ERT status collapsed \begin_layout Standard \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 Standard \backslash spce \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset C \begin_inset ERT status collapsed \begin_layout Standard \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\InsetSpace ~ 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. \newline 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 Standard \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 Standard \backslash spce \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \begin_inset ERT status collapsed \begin_layout Standard \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 LatexCommand index name "Commands ! M ! \\textbackslash middle" \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.\InsetSpace \thinspace{} g.\InsetSpace ~ 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 LatexCommand ref reference "sub:Physical-Vectors" \end_inset . \end_layout \begin_layout Subsection Horizontal Brackets \begin_inset LatexCommand index name "Brackets ! horizontal" \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash raisebox{2.3mm}{ \end_layout \end_inset \backslash overbrace \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A+B \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset ^ \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset 3 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \begin_inset LatexCommand index name "Commands ! O ! \\textbackslash overbrace" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\overbrace{A+B}^{3}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash raisebox{-2.2mm}{ \end_layout \end_inset \backslash underbrace \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A+B \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset _5 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \begin_inset LatexCommand index name "Commands ! U ! \\textbackslash underbrace" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\underbrace{A+B}_{5}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash overbrace \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash underbrace \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A+B_w \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset _7 \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset ^ \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset C \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 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 Standard Space commands are explained in \begin_inset 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 Standard because a bracket is not handled as character, see \begin_inset 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 Standard more about \series bold \backslash hphantom \series default see \begin_inset 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 Standard \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 Standard \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 need to be reduced. This is not easily possible due to a bug in LyX \begin_inset Foot status collapsed \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{ \end_layout \end_inset LyX-bug #1505 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset . As solution for the problem, the global formula row separation \series bold \backslash jot \series default \begin_inset LatexCommand index name "Commands ! J ! \\textbackslash jot" \end_inset must be changed to -6\InsetSpace \thinspace{} 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\InsetSpace \thinspace{} pt using the same command. More about the row separation in formulas is explained in \begin_inset LatexCommand ref reference "sub:Line-Separation" \end_inset . \end_layout \begin_layout Section Arrows \begin_inset LatexCommand index name "Arrows" \end_inset \end_layout \begin_layout Standard Arrows can be inserted via the math toolbar button \begin_inset Graphics filename ../images/math/leftarrow.xpm scale 85 \end_inset or the commands listed in the following subsections. \end_layout \begin_layout Subsection Horizontal Arrows \begin_inset LatexCommand index name "Arrows ! horizontal" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash gets \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\gets$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Leftarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Leftarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash longleftarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\longleftarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Longleftarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Longleftarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash leftharpoonup \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\leftharpoonup$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash leftharpoondown \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\leftharpoondown$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash hookleftarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\hookleftarrow$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash to \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\to$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Rightarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Rightarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash longrightarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\longrightarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Longrightarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Longrightarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash rightharpoonup \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\rightharpoonup$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash rightharpoondown \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\rightharpoondown$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash hookrightarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\hookrightarrow$ \end_inset \end_layout \end_inset \end_inset \hfill \end_layout \begin_layout Standard \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash leftrightarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\leftrightarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Leftrightarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Leftrightarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash longleftrightarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\longleftrightarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Longleftrightarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Longleftrightarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash rightleftharpoons \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\rightleftharpoons$ \end_inset \end_layout \end_inset \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{25pt} \end_layout \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mapsto \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mapsto$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash longmapsto \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\longmapsto$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash leadsto \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\leadsto$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dasharrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\dasharrow$ \end_inset \end_layout \end_inset \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Arrows used as accent like e.\InsetSpace \thinspace{} g.\InsetSpace ~ vector arrows are listed in \begin_inset 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 LatexCommand index name "Arrows ! labeled" \end_inset \series bold \backslash xleftarrow \series default \begin_inset LatexCommand index name "Commands ! X ! \\textbackslash xleftarrow" \end_inset and \series bold \backslash xrightarrow \series default \begin_inset LatexCommand index name "Commands ! X ! \\textbackslash xrightarrow\\vspace{4mm}" \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard F(a) \backslash xleftarrow \begin_inset ERT status collapsed \begin_layout Standard \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 Standard \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 Standard F(x) \backslash xrightarrow \begin_inset ERT status collapsed \begin_layout Standard \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 Standard \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 LatexCommand index name "Arrows ! diagonal" \end_inset \begin_inset LatexCommand index name "Arrows ! vertical" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash uparrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\uparrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Uparrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Uparrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash updownarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\updownarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Updownarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Updownarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Downarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Downarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash downarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\downarrow$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash nearrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\nearrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash searrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\searrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash swarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\swarrow$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash nwarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\nwarrow$ \end_inset \end_layout \end_inset \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Vertical arrows can be used also as delimiter together with the commands described in \begin_inset LatexCommand ref reference "sub:Manual-Bracket-Size" \end_inset and \begin_inset LatexCommand ref reference "sub:Automatic-Bracket-Size" \end_inset . \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Section Accents \begin_inset LatexCommand label name "sec:Accents" \end_inset \begin_inset LatexCommand index name "Accents" \end_inset \end_layout \begin_layout Standard Accents can be inserted via the math toolbar button \begin_inset Graphics filename ../images/math/hat.xpm 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 Standard \backslash texorpdfstring{ \end_layout \end_inset \begin_inset Foot status collapsed \begin_layout Standard accents in text see \begin_inset LatexCommand ref reference "sub:Accents-in-Text" \end_inset \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard }{} \end_layout \end_inset \begin_inset Note Note status collapsed \begin_layout Standard \backslash texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. \end_layout \begin_layout Standard More about \backslash texorpdfstring is in section \begin_inset LatexCommand ref reference "sub:Formulas-in-Section" \end_inset . \end_layout \end_inset \begin_inset LatexCommand label name "sub:Accents-for-one" \end_inset \begin_inset LatexCommand index name "Accents ! for one character" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dot \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\dot{A}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ddot \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dddot \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ddddot{A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash vec \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \begin_inset LatexCommand index name "Vectors" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\vec{A}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bar \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\bar{A}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mathring \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash tilde \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash hat \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\hat{A}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash check \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\check{A}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash acute \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\acute{A}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash grave \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\grave{A}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash breve \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\breve{A}$ \end_inset \end_layout \end_inset \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset To create umlauts \begin_inset LatexCommand index name "Umlauts" \end_inset in formulas, a quotation mark is inserted 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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \lang ngerman \begin_inset Quotes grd \end_inset i \end_layout \end_inset \begin_inset Text \begin_layout Standard \lang ngerman \begin_inset Formula $"i$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ddot \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset i \end_layout \end_inset \begin_inset Text \begin_layout Standard \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.\InsetSpace \thinspace{} g.\InsetSpace ~ 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 Operators \begin_inset LatexCommand index name "Accents ! for operators" \end_inset \end_layout \begin_layout Standard With the commands \series bold \backslash overset \series default \begin_inset LatexCommand index name "Commands ! O ! \\textbackslash overset" \end_inset and \series bold \backslash underset \series default \begin_inset LatexCommand index name "Commands ! U ! \\textbackslash underset" \end_inset characters can be placed above or below an operator, respectively, to accent it. With the command \series bold \backslash sideset \series default \begin_inset LatexCommand index name "Commands ! S ! \\textbackslash sideset" \end_inset characters can be set before and behind an operator. The command scheme is: \end_layout \begin_layout Standard \series bold \backslash sideset{character \series default \series bold before}{character \series default \series bold behind} \end_layout \begin_layout Standard \series bold \backslash sideset \series default must always be before the operator that should be accented. You can accent with several characters and even with other operators and symbols. To place with \series bold \backslash sideset \series default for example only characters behind an operator, write nothing between the first braces but don't omit the braces. \end_layout \begin_layout Standard For example the command \series bold \backslash sideset{ \begin_inset Formula $\to$ \end_inset \backslash { \series default ' \series bold \begin_inset Formula $\to$ \end_inset \backslash sum_k=1 \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default ^ \series bold n \series default produces: \begin_inset Formula \[ \sideset{}{'}\sum_{k=1}^{n}\] \end_inset \end_layout \begin_layout Standard The command \series bold \backslash overset \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash maltese \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default \begin_inset Formula $\uparrow$ \end_inset \series bold a \series default produces: \begin_inset Formula \[ \overset{a}{\maltese}\] \end_inset As seen in the last example, with \series bold \backslash overset \series default and \series bold \backslash underset \series default also symbols and characters can be accented; with \series bold \backslash sideset \series default this is not possible. \end_layout \begin_layout Subsection Accents for several Characters \begin_inset LatexCommand label name "sub:Accents-for-several" \end_inset \begin_inset LatexCommand index name "Accents ! for several characters" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash overleftarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash underleftarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash overleftrightarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash underleftrightarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash overrightarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash underrightarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash widetilde \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash widehat \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset \end_inset \hfill \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 LatexCommand index name "Commands ! O ! \\textbackslash overset" \end_inset and \series bold \backslash underset \series default \begin_inset LatexCommand index name "Commands ! U ! \\textbackslash underset" \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 Standard \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 Section Space \begin_inset LatexCommand label name "sub:Space" \end_inset \begin_inset LatexCommand index name "Space ! horizontal" \end_inset \end_layout \begin_layout Subsection Predefined Space \begin_inset LatexCommand label name "sub:Predefined-Space" \end_inset \begin_inset LatexCommand index name "Space ! horizontal ! predefined" \end_inset \end_layout \begin_layout Standard Sometimes it is necessary to insert horizontal space to a formula. This is done by inserting a protected space (shortcut \family sans Ctrl-Space \family default ). A blue \begin_inset Quotes eld \end_inset \series bold \color blue \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default \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.xpm 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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash , \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash : \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ; \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash quad \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash qquad \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ! \end_layout \end_inset \begin_inset Text \begin_layout Standard Number of \family sans Space \family default keystrokes after inserting the protected space \end_layout \end_inset \begin_inset Text \begin_layout Standard 0 \end_layout \end_inset \begin_inset Text \begin_layout Standard 1 \end_layout \end_inset \begin_inset Text \begin_layout Standard 2 \end_layout \end_inset \begin_inset Text \begin_layout Standard 3 \end_layout \end_inset \begin_inset Text \begin_layout Standard 4 \end_layout \end_inset \begin_inset Text \begin_layout Standard 5 \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A\, B$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A\: B$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A\; B$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A\quad B$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A\qquad B$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash negmedspace \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash negthickspace \end_layout \end_inset \begin_inset Text \begin_layout Standard Number of \family sans Space \family default keystrokes after inserting the protected space \end_layout \end_inset \begin_inset Text \begin_layout Standard 6 \end_layout \end_inset \begin_inset Text \begin_layout Standard 7 \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A\negmedspace B$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \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, what is e.\InsetSpace \thinspace{} g.\InsetSpace ~ useful for summation operators: \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sum \backslash sum \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset f_kl \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\sum\sum f_{kl}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sum \backslash negmedspace \backslash sum \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset f_kl \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard normal equation \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A=B$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Standard \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 Standard \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\InsetSpace ~ Space \family default (shortcut \family sans Ctrl-Shift-Space \family default ). \end_layout \begin_layout Standard An example to visualize the difference: \end_layout \begin_layout Standard \begin_inset Tabular \begin_inset Text \begin_layout Standard 24 kW \begin_inset Formula $\cdot$ \end_inset h \end_layout \end_inset \begin_inset Text \begin_layout Standard space between value and unit \end_layout \end_inset \begin_inset Text \begin_layout Standard 24\InsetSpace \thinspace{} kW \begin_inset Formula $\cdot$ \end_inset h \end_layout \end_inset \begin_inset Text \begin_layout Standard 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 Standard \backslash texorpdfstring{ \end_layout \end_inset \begin_inset Foot status collapsed \begin_layout Standard for vertical space in formulas see \begin_inset LatexCommand ref reference "sub:Line-Separation" \end_inset \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard }{} \end_layout \end_inset \begin_inset Note Note status collapsed \begin_layout Standard \backslash texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. \end_layout \begin_layout Standard More about \backslash texorpdfstring is in section \begin_inset LatexCommand ref reference "sub:Formulas-in-Section" \end_inset . \end_layout \end_inset \begin_inset LatexCommand label name "sub:Variable-Space" \end_inset \begin_inset LatexCommand index name "Space ! horizontal ! variable" \end_inset \end_layout \begin_layout Standard Space with a defined length can be inserted in LyX with the command \newline \series bold \backslash hspace{length} \series default \begin_inset LatexCommand index name "Commands ! H ! \\textbackslash hspace" \end_inset . For the length all units listed in \begin_inset LatexCommand ref reference "tab:Used-units" \end_inset are allowed, except of the unit \begin_inset Quotes eld \end_inset mu \begin_inset Quotes erd \end_inset . The length may also be negative. To insert so many space that the formula uses all available space, the command \series bold \backslash hfill \series default \begin_inset LatexCommand index name "Commands ! H ! \\textbackslash hfill" \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard A=B \backslash hspace{3cm \begin_inset Formula $\to$ \end_inset A \backslash not=C \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A=B\hspace{3cm}A\not=C$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard A \backslash hspace{-1mm \begin_inset Formula $\to$ \end_inset A \backslash not=A \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A\hspace{-1mm}A\not=A$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard A=A \backslash hfill \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset B=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 has only an effect on displayed formulas when the formula style \series bold Indented \series default is used. (Formula styles are explained in \begin_inset LatexCommand ref reference "sec:Formula-Styles" \end_inset .) \end_layout \begin_layout Standard The commands \series bold \backslash hspace \series default and \series bold \backslash hfill \series default can also be inserted in TeX-mode to use them for text: \end_layout \begin_layout Standard This is a line with \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{2cm} \end_layout \end_inset 2\InsetSpace \thinspace{} cm space. \end_layout \begin_layout Standard This is a line with \hfill maximum space. \end_layout \begin_layout Standard In the last example \series bold \backslash hfill \series default was inserted via the menu \family sans Insert\SpecialChar \menuseparator Formatting\SpecialChar \menuseparator Horizontal\InsetSpace ~ Fill \family default , what is not possible in formulas. This has the advantage that one can directly see in LyX that this is a stretch space. \end_layout \begin_layout Standard When the commands are at the begin of a text line but not at the beginning of a paragraph, they will be ignored by LaTeX. To avoid that, the command \series bold \backslash hspace* \series default is used instead of \series bold \backslash hspace \series default . To get the same with \series bold \backslash hfill \series default , a line break and an empty placeholder \series bold \begin_inset Foot status collapsed \begin_layout Standard for placeholders see \begin_inset LatexCommand ref reference "sub:Placeholders" \end_inset \end_layout \end_inset \series default is inserted in TeX-mode with the command \series bold \backslash vphantom{} \series default before \series bold \backslash hfill \series default . \end_layout \begin_layout Subsection Space besides inline Formulas \begin_inset LatexCommand index name "Space ! besides inline formulas" \end_inset \end_layout \begin_layout Standard The space that surrounds inline formulas can be adjusted with the length \series bold \backslash mathsurround \begin_inset LatexCommand index name "Commands ! M ! \\textbackslash mathsurround" \end_inset \series default . The value of a length is set with the command \series bold \backslash setlength \begin_inset LatexCommand index name "Commands ! S ! \\textbackslash setlength" \end_inset \series default that 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\InsetSpace \thinspace{} 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\InsetSpace \thinspace{} mm space will now be set around all inline formulas: \begin_inset ERT status collapsed \begin_layout Standard \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\InsetSpace \thinspace{} mm surrounding space. \begin_inset ERT status collapsed \begin_layout Standard \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\InsetSpace \thinspace{} pt. \end_layout \begin_layout Section Boxes and Frames \begin_inset LatexCommand index name "Boxes" \end_inset \begin_inset LatexCommand index name "Frames | see {Boxes}" \end_inset \end_layout \begin_layout Standard Boxes for text are described in chapter \family typewriter Boxes \family default in the \family typewriter Embedded\InsetSpace ~ Objects \family default manual. \end_layout \begin_layout Subsection Boxes with Frame \begin_inset LatexCommand label name "sub:Boxes-with-Frame" \end_inset \begin_inset LatexCommand index name "Boxes ! with frame" \end_inset \end_layout \begin_layout Standard It is possible to frame formulas or parts of it with the commands \series bold \backslash fbox \series default \begin_inset LatexCommand index name "Commands ! F ! \\textbackslash fbox" \end_inset and \series bold \backslash boxed \series default \begin_inset LatexCommand index name "Commands ! B ! \\textbackslash boxed" \end_inset . \end_layout \begin_layout Standard When one of these commands is inserted to 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 \begin_inset Foot status collapsed \begin_layout Standard Due to a bug in LyX it is not possible to create a new formula with \family sans Ctrl-m \family default , see \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{ \end_layout \end_inset LyX-bug #1435 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset . \end_layout \end_inset , because the box content will otherwise be treated as mathematical 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 As extension to \series bold \backslash fbox \series default there is the command \series bold \backslash framebox \series default \begin_inset LatexCommand index name "Commands ! F ! \\textbackslash framebox" \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. \newline Is no width 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 \align center \begin_inset Note Note status open \begin_layout Standard The table has been set into a minipage to make the footnote appearing. Otherwise the footnote text would not be displayed. \end_layout \end_inset \begin_inset Box Frameless position "c" hor_pos "c" has_inner_box 1 inner_pos "c" use_parbox 0 width "100col%" special "none" height "1in" height_special "totalheight" status open \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \begin_inset Foot status collapsed \begin_layout Standard Due to a bug in LyX it is not possible to create a new formula with \family sans Ctrl-m \family default , see \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{ \end_layout \end_inset LyX-bug #1435 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset . \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash fbox \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \family sans Ctrl-m \family default \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{} \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash boxed \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{8.5mm}{}\boxed{\int A=B}\raisebox{-6.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard A+ \backslash fbox \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash framebox \begin_inset ERT status collapsed \begin_layout Standard \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 Standard \backslash spce \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}$ \end_inset \begin_inset Formula $\framebox[20mm]{$\frac{A}{B}$}$ \end_inset \begin_inset Formula $\raisebox{-4mm}{}$ \end_inset \end_layout \end_inset \end_inset \end_layout \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 Standard \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 Standard \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 LatexCommand label name "sub:Boxes-without-Frame" \end_inset \begin_inset LatexCommand index name "Boxes ! without frame" \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 LatexCommand index name "Commands ! M ! \\textbackslash mbox" \end_inset , \series bold \backslash makebox \series default \begin_inset LatexCommand index name "Commands ! M ! \\textbackslash makebox" \end_inset , and \series bold \backslash raisebox \series default \begin_inset LatexCommand index name "Commands ! R ! \\textbackslash raisebox" \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 . \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard 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 Standard \begin_inset Formula $H\raisebox{2mm}{al}lo$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard 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 Standard \begin_inset Formula $H\raisebox{-2mm}{al}lo$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard A= \backslash raisebox{-2mm \begin_inset Formula $\to$ \end_inset \backslash { \family sans Ctrl-m \family default \backslash sqrt \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard $A= \backslash raisebox{-2mm}{$ \backslash sqrt{B}$}$ \end_layout \end_inset \end_layout \end_inset \end_inset \end_layout \begin_layout Standard The last formula can currently only be created using TeX-mode because LyX inserts a box instead of the needed extra formula. \begin_inset Foot status collapsed \begin_layout Standard see \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{ \end_layout \end_inset LyX-bug #1435 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \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 LatexCommand label name "sub:Colored-Boxes" \end_inset \begin_inset LatexCommand index name "Boxes ! colored" \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 Standard The LaTeX-package \series bold color \series default is part of every LaTeX standard installation. \end_layout \end_inset \begin_inset LatexCommand index name "Packages ! color" \end_inset has to be loaded in the LaTeX-preamble with the line \begin_inset Foot status collapsed \begin_layout Standard 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 doesn't arise problems. \end_layout \end_inset \begin_inset Note Note status collapsed \begin_layout Standard 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 LatexCommand index name "Commands ! C ! \\textbackslash colorbox" \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 as for \series bold \backslash fbox \series default . \begin_inset Foot status collapsed \begin_layout Standard This also applies for the command \series bold \backslash fcolorbox \series default . Thereby note \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{ \end_layout \end_inset LyX-bug #1435 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset . \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash colorbox{yellow \begin_inset Formula $\to$ \end_inset \backslash {A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash colorbox{green \begin_inset Formula $\to$ \end_inset \backslash { \backslash fbox \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash fbox \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash colorbox{green \begin_inset Formula $\to$ \end_inset \backslash {A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$ \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 wanted color is chosen in the \family sans Text\InsetSpace ~ Style \family default dialog. The dialog can be called with the toolbar button \begin_inset Graphics filename ../images/dialog-show_character.xpm scale 85 \end_inset or the menu \family sans Edit\SpecialChar \menuseparator Text\InsetSpace ~ Style\SpecialChar \menuseparator Customized \family default . The formula number has then 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 LatexCommand eqref reference "eq:red" \end_inset is completely colored red. \newline Formula \begin_inset 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 LatexCommand index name "Commands ! F ! \\textbackslash fcolorbox" \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 Standard \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 Standard \backslash fboxrule 0.4pt \backslash fboxsep 3pt \end_layout \end_inset \end_layout \begin_layout Standard This formula was created with the command \newline \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 LatexCommand index name "Commands ! D ! \\textbackslash definecolor" \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\InsetSpace \thinspace{} -\InsetSpace \thinspace{} 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 LatexCommand index name "Text ! colored" \end_inset \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \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 Standard } \end_layout \end_inset \end_layout \begin_layout Standard \series bold \backslash textcolor \series default \begin_inset LatexCommand index name "Commands ! T ! \\textbackslash textcolor" \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 LatexCommand label name "sub:Paragraph-Boxes" \end_inset \begin_inset LatexCommand index name "Boxes ! as paragraph" \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.xpm 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 width "5cm" special "none" height "1in" height_special "totalheight" status open \begin_layout Standard This is a paragraph box. It is exactly 5\InsetSpace \thinspace{} 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 : Recangular box, \emph on Inner Box \emph default : Parbox, \emph on Width \emph default : 5\InsetSpace \thinspace{} 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 LatexCommand index name "Commands ! P ! \\textbackslash parbox" \end_inset that 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 bottom means that the box is aligned within the surrounding text with its last line. With \emph on t \emph default for top 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\InsetSpace ~ 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 \begin_inset LatexCommand index name "Commands ! L ! \\textbackslash linewidth" \end_inset \series default is hereby the line width set for the document. Because the frame is outside the parbox, 2\InsetSpace \thinspace{} 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 Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{ \end_layout \end_inset LyX-bug #4483 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \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 Standard \series bold calc \series default is part of every LaTeX standard installation. \end_layout \end_inset \begin_inset LatexCommand index name "Packages ! calc" \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 Standard \backslash fboxsep 5mm \backslash fboxrule 5mm \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \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 Standard }} \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard \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 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 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 Standard \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 Standard }} \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 Standard 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 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 LatexCommand index name "Operators" \end_inset \end_layout \begin_layout Subsection Big Operators \begin_inset LatexCommand label name "sub:Big-Operators" \end_inset \begin_inset LatexCommand index name "Operators ! big" \end_inset \begin_inset LatexCommand index name "Sums" \end_inset \begin_inset LatexCommand index name "Integrals" \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\InsetSpace ~ Options \family default . \end_layout \begin_layout Standard \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sum \begin_inset LatexCommand index name "Commands ! S ! \\textbackslash sum" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\sum$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash int \begin_inset LatexCommand index name "Commands ! I ! \\textbackslash int" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\int$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash intop \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\intop$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash oint \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\oint$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ointop \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\ointop$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ointctrclockwise \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\ointctrclockwise$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ointclockwise \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\ointclockwise$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sqint \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\sqint$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigcap \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigcap$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigcup \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigcup$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash prod \begin_inset LatexCommand index name "Commands ! P ! \\textbackslash prod" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\prod$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash coprod \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\coprod$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigodot \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigodot$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigotimes \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigotimes$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigoplus \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigoplus$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigwedge \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigwedge$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigvee \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigvee$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigsqcup \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigsqcup$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash biguplus \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\biguplus$ \end_inset \end_layout \end_inset \end_inset \hfill \end_layout \begin_layout Standard All big operators can also be inserted via the math toolbar button \begin_inset Graphics filename ../images/math/intop.xpm 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 The operators \series bold \backslash intop \series default and \series bold \backslash ointop \series default are different from \series bold \backslash int \series default and \series bold \backslash oint \series default , resp.\InsetSpace ~ in the style the operator limits are displayed, see \begin_inset LatexCommand ref reference "sub:Operator-Limits" \end_inset . \end_layout \begin_layout Subsubsection* Advices 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 \family sans Alt-c\InsetSpace ~ r \family default \begin_inset Foot status collapsed \begin_layout Standard Font styles \series bold \series default see \begin_inset 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 \newline \begin_inset ERT status collapsed \begin_layout Standard \backslash hphantom{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 \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash iint \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash oiint \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sqiint \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash iiint \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash iiiint \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dotsint \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \end_inset \hfill \end_layout \begin_layout Subsection Operator Limits \begin_inset LatexCommand label name "sub:Operator-Limits" \end_inset \begin_inset LatexCommand index name "Operators ! Limits" \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash prod^ \backslash infty \begin_inset ERT status collapsed \begin_layout Standard \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 Standard \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 of 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 \family sans Alt-m\InsetSpace ~ l \family default ). 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 of \series bold \backslash intop \series default and \series bold \backslash ointop \series default , 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 LatexCommand index name "Commands ! S ! \\textbackslash subarray" \end_inset and \series bold \backslash substack \series default \begin_inset LatexCommand index name "Commands ! S ! \\textbackslash substack" \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 Standard Command \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard + \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $+$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard - \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $-$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash pm \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\pm$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mp \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mp$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cdot \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\cdot$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash times \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\times$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash div \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\div$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash raisebox{-1.2mm}{ \end_layout \end_inset * \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $*$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash star \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\star$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash circ \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\circ$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash diamond \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\diamond$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bullet \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bullet$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash nabla \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\nabla$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigtriangledown \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigtriangledown$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigtriangleup \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigtriangleup$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Box \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Box$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cap \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\cap$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cup \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\cup$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dagger \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\dagger$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ddagger \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\ddagger$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash wr \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\wr$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigcirc \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigcirc$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash wedge \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\wedge$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash vee \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\vee$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash oplus \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\oplus$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ominus \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\ominus$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash otimes \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\otimes$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash oslash \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\oslash$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash odot \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\odot$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash amalg \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\amalg$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash uplus \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\uplus$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash setminus \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\setminus$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sqcap \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\sqcap$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sqcup \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\sqcup$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash triangleleft \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\triangleleft$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash triangleright \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\triangleright$ \end_inset \end_layout \end_inset \end_inset \hfill \end_layout \begin_layout Standard All binary operators can also be inserted via the math toolbar button \begin_inset Graphics filename ../images/math/pm.xpm 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 LatexCommand label name "sub:Self-defined-Operators" \end_inset \begin_inset LatexCommand index name "Operators ! self-defined" \end_inset \end_layout \begin_layout Standard With the help of the command \series bold \backslash DeclareMathOperator \series default \begin_inset LatexCommand index name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator" \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 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 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 LatexCommand index name "Commands ! M ! \\textbackslash mathop" \end_inset and \series bold \backslash mathbin \series default \begin_inset LatexCommand index name "Commands ! M ! \\textbackslash mathbin" \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.\InsetSpace \thinspace{} g.\InsetSpace ~ 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: \newline \series bold \backslash mathop{ \backslash sum \backslash negmedspace \backslash sum \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series bold \begin_inset Formula $\to$ \end_inset ^N \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series bold _i,j=1 \end_layout \begin_layout Section Fonts \begin_inset LatexCommand index name "Fonts" \end_inset \end_layout \begin_layout Subsection Font Styles \begin_inset LatexCommand label name "sub:Font-Styles" \end_inset \begin_inset LatexCommand index name "Font ! style" \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard shortcut \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mathbb \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default ABC \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathbb{ABC}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard Alt-c c \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mathbf \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default AbC \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathbf{AbC}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard Alt-c b \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash boldsymbol \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default AbC \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\boldsymbol{AbC}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard - \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mathcal \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default ABC \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathcal{ABC}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard Alt-c e \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mathfrak \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default AbC \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathfrak{AbC}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard - \end_layout \end_inset \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard shortcut \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mathit \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default AbC \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathit{AbC}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard - \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mathrm \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default AbC \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathrm{AbC}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard Alt-c r \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mathsf \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default AbC \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathsf{AbC}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard Alt-c s \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mathtt \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series default AbC \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathtt{AbC}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard Alt-c p \end_layout \end_inset \end_inset \end_layout \begin_layout Standard \begin_inset Note Greyedout status open \begin_layout Standard \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 Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{ \end_layout \end_inset LyX-bug #4091 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \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.xpm scale 85 \end_inset can be used. \end_layout \begin_layout Subsection Bold Formulas \begin_inset LatexCommand label name "sub:Bold-Formulas" \end_inset \begin_inset LatexCommand index name "Formula ! bold" \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 \begin_inset LatexCommand index name "Commands ! B ! \\textbackslash boldmath" \end_inset \series default in TeX-mode. To end the environment, the command \series bold \backslash unboldmath \begin_inset LatexCommand index name "Commands ! U ! \\textbackslash unboldmath" \end_inset \series default is inserted in TeX-mode. \begin_inset ERT status collapsed \begin_layout Standard \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 Standard \backslash unboldmath \end_layout \end_inset \end_layout \begin_layout Subsection Font Sizes \begin_inset LatexCommand label name "sub:Font-Sizes" \end_inset \begin_inset LatexCommand index name "Font ! size" \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 , \newline \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, that corresponds with 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\InsetSpace \thinspace{} 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 only be changed for symbols or letters in mathematical text. To do this, the size command 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 Standard \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 Standard \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: \newline \series bold \backslash maltese \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A Alt-m m \backslash Large \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash maltese \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash textit \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \begin_inset Formula $\to$ \end_inset \begin_inset Formula $\to$ \end_inset \newline \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace*{1cm} \end_layout \end_inset Alt-m \series default \series bold m \backslash tiny \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash maltese \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash textit \begin_inset ERT status collapsed \begin_layout Standard \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 LatexCommand index name "Greek letters" \end_inset \end_layout \begin_layout Standard All Greek letters can also be inserted via the toolbar button \begin_inset Graphics filename ../images/math/alpha.xpm scale 85 \end_inset . \end_layout \begin_layout Subsection Small Letters \begin_inset LatexCommand label name "sub:Small-Letters" \end_inset \begin_inset LatexCommand index name "Greek letters ! small" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash alpha \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\alpha$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash beta \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\beta$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash gamma \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\gamma$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash delta \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\delta$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash epsilon \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\epsilon$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash varepsilon \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\varepsilon$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash zeta \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\zeta$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash eta \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\eta$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash theta \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\theta$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash vartheta \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\vartheta$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash iota \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\iota$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash kappa \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\kappa$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash varkappa \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\varkappa$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash lambda \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\lambda$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mu \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mu$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash nu \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\nu$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash xi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\xi$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard o \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $o$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash pi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\pi$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash varpi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\varpi$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash rho \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\rho$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash varrho \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\varrho$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sigma \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\sigma$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash varsigma \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\varsigma$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash tau \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\tau$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash upsilon \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\upsilon$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash phi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\phi$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash varphi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\varphi$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash chi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\chi$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash psi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\psi$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash omega \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\omega$ \end_inset \end_layout \end_inset \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset \end_layout \begin_layout Standard How to create upright Greek letters is explained in \begin_inset LatexCommand ref reference "sub:Upright-small-Greek" \end_inset . \end_layout \begin_layout Subsection Big Letters \begin_inset LatexCommand index name "Greek letters ! big" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Gamma \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Gamma$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Delta \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Delta$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Theta \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Theta$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Lambda \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Lambda$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Xi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Xi$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Pi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Pi$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Sigma \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Sigma$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Upsilon \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Upsilon$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Phi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Phi$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Psi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Psi$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Omega \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Omega$ \end_inset \end_layout \end_inset \end_inset \hfill \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 \end_layout \begin_layout Subsection Bold Letters \begin_inset LatexCommand index name "Greek letters ! bold" \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 LatexCommand index name "Commands ! B ! \\textbackslash boldsymbol" \end_inset . \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Upsilon \backslash boldsymbol \backslash Upsilon \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash theta \backslash boldsymbol \backslash theta \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \backslash texorpdfstring{ \end_layout \end_inset \begin_inset Foot status collapsed \begin_layout Standard A list with all symbols of most of the LaTeX-packages can be found in \begin_inset LatexCommand cite key "Symbole" \end_inset . \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard }{} \end_layout \end_inset \begin_inset Note Note status collapsed \begin_layout Standard \backslash texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. \end_layout \begin_layout Standard More about \backslash texorpdfstring is in section \begin_inset LatexCommand ref reference "sub:Formulas-in-Section" \end_inset . \end_layout \end_inset \begin_inset LatexCommand index name "Symbols" \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.xpm scale 85 \end_inset and \begin_inset Graphics filename ../images/math/digamma.xpm scale 85 \end_inset . \end_layout \begin_layout Subsection Mathematical Symbols \begin_inset LatexCommand label name "sub:Mathematical-Symbols" \end_inset \begin_inset LatexCommand index name "Symbols ! mathematical" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash neg \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\neg$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Im \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Im$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Re \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Re$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash aleph \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\aleph$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash partial \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\partial$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash infty \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\infty$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash wp \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\wp$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash imath \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\imath$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash jmath \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\jmath$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash forall \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\forall$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash exists \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\exists$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash nexists \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\nexists$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash emptyset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\emptyset$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash varnothing \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\varnothing$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dag \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\dag$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ddag \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\ddag$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash complement \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash raisebox{-0.8mm}{ \end_layout \end_inset \begin_inset Formula $\complement$ \end_inset \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Bbbk \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Bbbk$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash prime \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\prime$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash backprime \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\backprime$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mho \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mho$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash triangle \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\triangle$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash angle \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\angle$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash measuredangle \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\measuredangle$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sphericalangle \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\sphericalangle$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash top \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\top$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bot \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bot$ \end_inset \end_layout \end_inset \end_inset \hfill \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Subsection Miscellaneous Symbols \begin_inset LatexCommand label name "sub:Miscellaneous-Symbols" \end_inset \begin_inset LatexCommand index name "Symbols ! miscellaneous" \end_inset \end_layout \begin_layout Standard \noindent \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash flat \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\flat$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash natural \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\natural$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sharp \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\sharp$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash surd \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\surd$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash checkmark \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\checkmark$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash yen \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\yen$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash pounds \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\pounds$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard $ \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\$$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard § \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $§$ \end_inset \end_layout \end_inset \end_inset \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash hbar \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\hbar$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash hslash \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\hslash$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash clubsuit \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\clubsuit$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash spadesuit \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\spadesuit$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bigstar \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigstar$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash blacklozenge \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\blacklozenge$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash blacktriangle \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\blacktriangle$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash blacktiangledown \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\blacktriangledown$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bullet \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bullet$ \end_inset \end_layout \end_inset \end_inset \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash diamondsuit \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\diamondsuit$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Diamond \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Diamond$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash heartsuit \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\heartsuit$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash P \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\P$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash copyright \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\copyright$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash circledR \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\circledR$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash maltese \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\maltese$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash diagup \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\diagup$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash diagdown \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 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 LatexCommand ref reference "sub:Font-Sizes" \end_inset . \end_layout \begin_layout Subsection The Euro-Symbol € \begin_inset LatexCommand index name "Symbols ! Euro-symbol" \end_inset \begin_inset LatexCommand index name "\\officialeuro" \end_inset \end_layout \begin_layout Standard To use the Euro symbol in formulas, the LaTeX-package \series bold eurosym \series default \begin_inset LatexCommand index name "Packages ! eurosym" \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 LatexCommand index name "Commands ! E ! \\textbackslash euro" \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 LatexCommand index name "Commands ! O ! \\textbackslash officialeuro" \end_inset , that is only available in TeX-mode. \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash ifeurosym \end_layout \end_inset \begin_inset Note Note status open \begin_layout Standard 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 Standard \end_layout \end_inset \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard formula \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash euro \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\euro$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard mathematical text \end_layout \end_inset \begin_inset Text \begin_layout Standard € \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mbox{€}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard TeX-mode \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash officialeuro \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash officialeuro \end_layout \end_inset \end_layout \end_inset \end_inset \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash else \end_layout \end_inset \begin_inset Note Note status open \begin_layout Standard 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 Standard \backslash fi \end_layout \end_inset \end_layout \begin_layout Section Relations \begin_inset LatexCommand label name "sec:Relations" \end_inset \begin_inset LatexCommand index name "Relations" \end_inset \begin_inset LatexCommand index name "Comparisons|see{Relations}" \end_inset \end_layout \begin_layout Standard All relations can also be inserted via the toolbar button \begin_inset Graphics filename ../images/math/leq.xpm scale 85 \end_inset . \end_layout \begin_layout Standard \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard < \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $<$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash le \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\le$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ll \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\ll$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash prec \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\prec$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash preceq \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\preceq$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash subset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\subset$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash subseteq \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\subseteq$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sqsubseteq \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\sqsubseteq$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash in \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\in$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash vdash \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\vdash$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash smile \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\smile$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash lhd \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\lhd$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash unlhd \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\unlhd$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash gtrless \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\gtrless$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash mid \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mid$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash nmid \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\nmid$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard = \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $=$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash not= \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\not=$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash equiv \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\equiv$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sim \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\sim$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash simeq \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\simeq$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash approx \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\approx$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cong \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\cong$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bowtie \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\bowtie$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash notin \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\notin$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash perp \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\perp$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash propto \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\propto$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash asymp \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\asymp$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash doteq \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\doteq$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash circeq \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\circeq$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash models \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\models$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash widehat= \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\widehat{=}$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard > \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $>$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ge \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\ge$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash gg \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\gg$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash succ \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\succ$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash succeq \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\succeq$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash supset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\supset$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash supseteq \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\supseteq$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sqsupseteq \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\sqsupseteq$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ni \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\ni$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dashv \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\dashv$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash frown \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\frown$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash rhd \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\rhd$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash unrhd \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\unrhd$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash lessgtr \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\lessgtr$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash parallel \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\parallel$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash nparallel \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\nparallel$ \end_inset \end_layout \end_inset \end_inset \hfill \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 LatexCommand index name "Commands ! S ! \\textbackslash stackrel" \end_inset : \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard A(r) \backslash stackrel \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset r \backslash to \backslash infty \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \begin_inset Formula $\downarrow$ \end_inset \backslash approx \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset B \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 LatexCommand label name "sub:Predefined-Functions" \end_inset \begin_inset LatexCommand index name "Functions ! predefined" \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 functions, that 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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard Asin(x)+B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $Asin(x)+B$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard A \backslash sin(x)+B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A\sin(x)+B$ \end_inset \end_layout \end_inset \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash pagebreak \end_layout \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sin \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sinh \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash arcsin \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sup \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cos \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cosh \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash arccos \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash inf \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash tan \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash tanh \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash arctan \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash lim \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cot \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash coth \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash arg \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash liminf \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash sec \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash min \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash deg \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash limsup \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash csc \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash max \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash det \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Pr \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ln \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash exp \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dim \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash hom \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash lg \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash log \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ker \end_layout \end_inset \begin_inset Text \begin_layout Standard \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.xpm scale 85 \end_inset . \end_layout \begin_layout Subsection Self-defined Functions \begin_inset LatexCommand index name "Functions ! self-defined" \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 Standard For more about \series bold \backslash DeclareMathOperator \series default see \begin_inset LatexCommand ref reference "sub:Self-defined-Operators" \end_inset . \end_layout \end_inset \newline \begin_inset VSpace -3mm \end_inset \newline \series bold \backslash DeclareMathOperator{ \backslash sgn}{sgn} \series default \begin_inset LatexCommand index name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator" \end_inset \newline \begin_inset VSpace -2mm \end_inset \newline Now the new defined function can be called with the command \series bold \backslash sgn \series default . \end_layout \begin_layout Itemize Write the the formula as usual, mark the formula name, in our example the letters \emph on sgn \emph default , and change it to mathematical text. At last 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 Standard 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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard A \backslash sgn(x)+B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A\sgn(x)+B$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard 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 Standard \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 LatexCommand index name "Limits" \end_inset \end_layout \begin_layout Standard For limits there are defined besides \series bold \backslash lim \series default \begin_inset LatexCommand index name "Commands ! L ! \\textbackslash lim" \end_inset , \series bold \backslash liminf \series default and \series bold \backslash limsup \series default furthermore the following functions: \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash varliminf \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\varliminf$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash varlimsup \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\varlimsup$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash varprojlim \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\varprojlim$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash varinjlim \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{1cm} \end_layout \end_inset Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash hspace \series default 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 Standard \backslash lim_x \backslash to \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset x=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 LatexCommand index name "Functions ! modulo-" \end_inset \end_layout \begin_layout Standard The modulo-function is special, because it exists in four variants. \end_layout \begin_layout Standard The variants in a displayed formula: \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. \end_layout \begin_layout Section Special Characters \begin_inset LatexCommand index name "Special characters" \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 \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash oe \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\oe}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash OE \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\OE}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ae \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\ae}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash AE \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\AE}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash aa \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\aa}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash AA \begin_inset LatexCommand index name "\\@\\textrm{\\AA}" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\AA}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash i \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\i}$ \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard command \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash hspace{0mm} \series default is used for separation, because otherwise the output will be ¡ and ¿ respective ly. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash o \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\o}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash O \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\O}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash l \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\l}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash L \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\L}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard ! \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{0mm} \end_layout \end_inset ` \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{!`}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard ? \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{0mm} \end_layout \end_inset ` \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{?`}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash j \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\j}$ \end_inset \end_layout \end_inset \end_inset \hfill \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.xpm scale 85 \end_inset . \end_layout \begin_layout Standard An exception are the commands \series bold ! \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{0mm} \end_layout \end_inset ` \series default and \series bold ? \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{0mm} \end_layout \end_inset ` \series default , because they can be inserted in LyX directly to text. \end_layout \begin_layout Subsection Accents in Text \begin_inset LatexCommand label name "sub:Accents-in-Text" \end_inset \begin_inset LatexCommand index name "Accents ! in text" \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 \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash \begin_inset Quotes grd \end_inset e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash "e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash `e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash `e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ^ \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash ^e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash =e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash =e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash u \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash u e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash b \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash b e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash t \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset ee \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash t ee \end_layout \end_inset \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash H \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash H e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash 'e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash 'e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ~e \begin_inset LatexCommand index name "Tilde" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash ~e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash .e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash .e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash v \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash v e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash d \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash d e \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash c \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset e \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash c e \end_layout \end_inset \end_layout \end_inset \end_inset \hfill \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 Standard \backslash spce \end_layout \end_inset sz \series default creates: \begin_inset ERT status collapsed \begin_layout Standard \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 Standard 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 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 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 LatexCommand index name "Commands ! T ! \\textbackslash textcircled" \end_inset all numbers and letters can be set into a circle, quasi accented with a circle, similar to the the copyright symbol. \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash textcircled{w} \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash textcircled{w} \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Large \backslash textcircled{ \backslash normalsize \backslash protect \backslash raisebox{-1.5pt}{W}} \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}$ \end_inset \begin_inset ERT status collapsed \begin_layout Standard \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 Standard see \begin_inset 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 Standard see \begin_inset LatexCommand ref reference "sub:Boxes-without-Frame" \end_inset \end_layout \end_inset the character can be centered. \end_layout \begin_layout Subsection Minuscule Numbers \begin_inset LatexCommand index name "Minuscule numbers" \end_inset \end_layout \begin_layout Standard Minuscule numbers are created with the command \series bold \backslash oldstylenums \series default \begin_inset LatexCommand index name "Commands ! O ! \\textbackslash oldstylenums" \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 LatexCommand label name "sub:Miscellaneous-Special-Characters" \end_inset \begin_inset LatexCommand index name "Special characters ! miscellaneous" \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ^ \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathcircumflex$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash _ \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\_$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard ^ \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \backslash circ \begin_inset LatexCommand index name "°" \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard More about this is described in \begin_inset 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 f\SpecialChar \textcompwordmark{} i} \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset The tilde \begin_inset LatexCommand index name "Tilde" \end_inset is designed as accent, thus is looks alone a bit misplaced: ~ \newline But for web addresses (URLs) sometimes a single tilde is needed. In this case the relation sign \series bold \backslash sim \begin_inset Foot status collapsed \begin_layout Standard see \begin_inset LatexCommand ref reference "sec:Relations" \end_inset \end_layout \end_inset \series default is used in a formula. As a formula cannot be created in an URL-box (menu \family sans Insert\SpecialChar \menuseparator URL \family default ), the URL is inserted as normal text with the font style ' \family typewriter typewriter \family default '. Should the URL be a hyperlink in the DVI- or PDF-output, the command \series bold \backslash href \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold \backslash href \series default can only be used together with the LaTeX-package \series bold hyperref \series default \begin_inset LatexCommand index name "Packages ! hyperref" \end_inset . More about \series bold \backslash href \series default is written in the section \family typewriter URL \family default in the \family typewriter Embedded\InsetSpace ~ Objects \family default manual. \end_layout \end_inset \begin_inset LatexCommand index name "Commands ! H ! \\textbackslash href" \end_inset is used. \end_layout \begin_layout Standard As example an URL with a tilde: \end_layout \begin_layout Standard as text: \family typewriter http://www.lyx.org/ \begin_inset Formula $\sim$ \end_inset mustermann \end_layout \begin_layout Standard with \series bold \backslash href \series default : \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://www.lyx.org/~mustermann}{ \end_layout \end_inset http://www.lyx.org/ \begin_inset Formula $\sim$ \end_inset mustermann \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \begin_layout Section Formula Styles \begin_inset LatexCommand label name "sec:Formula-Styles" \end_inset \begin_inset LatexCommand index name "Formula ! styles" \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\InsetSpace ~ 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 LatexCommand index name "Commands ! M ! \\textbackslash mathindent" \end_inset . Should the distance be 15\InsetSpace \thinspace{} 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\InsetSpace \thinspace{} 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\InsetSpace ~ 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 LatexCommand ref reference "sub:Flalign-Environment" \end_inset . \end_layout \begin_layout Section Multiline Formulas \begin_inset LatexCommand label name "sec:Multiline-Formulas" \end_inset \begin_inset LatexCommand index name "Formula ! multiline" \end_inset \end_layout \begin_layout Subsection General \end_layout \begin_layout Standard In LyX multiline formulas are created by pressing \family sans \series bold Ctrl-Return \family default \series default inside a formula. This creates either an \series bold eqnarray environment \series default that is described in \begin_inset 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 LatexCommand ref reference "sub:Standard-align-Environment" \end_inset . \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 \family sans Ctrl-Return \family default . To add or delete lines, the math toolbar buttons \begin_inset Graphics filename ../images/tabular-feature_append-row.xpm scale 85 \end_inset or \begin_inset Graphics filename ../images/tabular-feature_delete-row.xpm 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 LatexCommand label name "sub:Line-Separation" \end_inset \begin_inset LatexCommand index name "Formula ! multiline ! Line separation" \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 Standard see \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{ \end_layout \end_inset LyX-bug #1505 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \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 Standard \backslash begin{eqnarray*} \end_layout \begin_layout Standard 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 Standard 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 Standard \backslash end{eqnarray*} \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset To set the the line separation for all lines in a formula, the length \series bold \backslash jot \series default \begin_inset LatexCommand index name "Commands ! J ! \\textbackslash jot" \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\InsetSpace \thinspace{} pt. To create 3\InsetSpace \thinspace{} 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 Standard \series bold calc \series default is part of every LaTeX standard installation. \end_layout \end_inset \begin_inset LatexCommand index name "Packages ! calc" \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 Standard \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 Standard \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\InsetSpace \thinspace{} pt. \end_layout \begin_layout Subsubsection Column Separation \begin_inset LatexCommand label name "sub:Column-Separation" \end_inset \begin_inset LatexCommand index name "Formula ! multiline ! Column separation" \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 LatexCommand index name "Commands ! A ! \\textbackslash arraycolsep" \end_inset according to: \newline column separation = 2\InsetSpace \thinspace{} \series bold \backslash arraycolsep \series default \newline 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\InsetSpace \thinspace{} cm. To get back to the predefined distance, \series bold \backslash arraycolsep \series default is set to 5\InsetSpace \thinspace{} pt. \end_layout \begin_layout Standard A formula with 2\InsetSpace \thinspace{} cm column separation: \begin_inset ERT status collapsed \begin_layout Standard \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\InsetSpace \thinspace{} pt: \begin_inset ERT status collapsed \begin_layout Standard \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 LatexCommand index name "Formula ! long" \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 shorther than the line width, this one is chosen for the left side and the right side is typeset over two lines: \begin_inset ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \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:kurzlang}\end{eqnarray} \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash smallskip \end_layout \end_inset \newline The minus sign at the beginning of the second line does normally not appear as 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, space was inserted behind the minus sign with the command \series bold \backslash hspace{3pt} \series default \begin_inset Foot status collapsed \begin_layout Standard more about \series bold \backslash hspace \series default see \begin_inset LatexCommand ref reference "sub:Variable-Space" \end_inset \end_layout \end_inset \begin_inset LatexCommand index name "Commands ! H ! \\textbackslash hspace" \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 LatexCommand index name "Commands ! L ! \\textbackslash lefteqn" \end_inset is used. It is inserted to the first column of the first line and effects that all further insertions overwrite the following columns: \begin_inset ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \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 \begin_inset ERT status collapsed \begin_layout Standard \backslash smallskip \end_layout \end_inset \newline 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 ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \newline 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 ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \newline \begin_inset Note Greyedout status open \begin_layout Standard 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.\InsetSpace \thinspace{} g.\InsetSpace ~ 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 Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{ \end_layout \end_inset LyX-bug #1429 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \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 LatexCommand ref reference "sub:Multline-Environment" \end_inset and \begin_inset LatexCommand ref reference "sub:Multiline-Formula-Parts" \end_inset . \end_layout \begin_layout Subsubsection Multiline Brackets \begin_inset LatexCommand label name "sub:Multiline-Brackets" \end_inset \begin_inset LatexCommand index name "Brackets ! for multiline expressions" \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 LatexCommand index name "Commands ! R ! \\textbackslash right" \end_inset and the second line with \series bold \backslash left. \begin_inset Foot status collapsed \begin_layout Standard for more about \series bold \backslash left \series default and \series bold \backslash right \series default see \begin_inset LatexCommand ref reference "sub:Automatic-Bracket-Size" \end_inset \end_layout \end_inset \series default \begin_inset LatexCommand index name "Commands ! L ! \\textbackslash left" \end_inset . After \series bold \backslash left. \series default the command \series bold \backslash vphantom \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series bold \backslash prod \series default ^ \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series bold \backslash infty \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \series bold \begin_inset Formula $\downarrow$ \end_inset _R=1} \series default \begin_inset LatexCommand index name "Commands ! V ! \\textbackslash vphantom" \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 specially 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.xpm scale 85 \end_inset or \begin_inset Graphics filename ../images/tabular-feature_delete-column.xpm 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 LatexCommand label name "sub:Standard-align-Environment" \end_inset \begin_inset LatexCommand index name "Formula ! multiline ! align environment" \end_inset \end_layout \begin_layout Standard This Align environment is created by presssing \family sans Ctrl-Return \family default 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 Standard more about \series bold \backslash hfill \series default see \begin_inset 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 Standard formula styles see \begin_inset 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 LatexCommand index name "Formula ! multiline ! alignat environment" \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 LatexCommand ref reference "sub:Space" \end_inset . \end_layout \begin_layout Standard The above example in the alignat environment where 1\InsetSpace \thinspace{} 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 LatexCommand label name "sub:Flalign-Environment" \end_inset \begin_inset LatexCommand index name "Formula ! multiline ! flalign environment" \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 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\InsetSpace \thinspace{} pt space was inserted at the beginning of the first column. \end_layout \begin_layout Subsection Eqnarray Environment \begin_inset LatexCommand label name "sub:Eqnarray-Environment" \end_inset \begin_inset LatexCommand index name "Formula ! multiline ! eqnarray environment" \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 LatexCommand index name "Formula ! multiline ! gather environment" \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 LatexCommand label name "sub:Multline-Environment" \end_inset \begin_inset LatexCommand index name "Formula ! multiline ! multline environment" \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 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 Standard numbering styles see \begin_inset LatexCommand ref reference "sec:Formula-Styles" \end_inset \end_layout \end_inset \end_layout \begin_layout Standard With the commands \series bold \backslash shoveright \begin_inset LatexCommand index name "Commands ! S ! \\textbackslash shoveright" \end_inset \series default and \series bold \backslash shoveleft \begin_inset LatexCommand index name "Commands ! S ! \\textbackslash shoveleft" \end_inset \series default 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 \begin_inset LatexCommand index name "Commands ! M ! \\textbackslash multlinegap" \end_inset \series default specifies the distance of the first line from the left page margin. Predefined is the length 0\InsetSpace \thinspace{} 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 Standard \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 Standard \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 LatexCommand label name "sub:Multiline-Formula-Parts" \end_inset \begin_inset LatexCommand index name "Formula ! multiline ! formula parts" \end_inset \end_layout \begin_layout Standard To display only parts of a formula with multiple lines, one of the following environments are 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 \begin_inset LatexCommand index name "Commands ! A ! \\textbackslash aligned" \end_inset \series default 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 LatexCommand eqref reference "eq:kurzlang" \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 LatexCommand index name "Commands ! A ! \\textbackslash alignedat" \end_inset \series bold \backslash gathered \series default \begin_inset LatexCommand index name "Commands ! G ! \\textbackslash gathered" \end_inset , or \series bold \backslash split \series default \begin_inset LatexCommand index name "Commands ! S ! \\textbackslash split" \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 LatexCommand label name "sub:Text-in-multiline" \end_inset \begin_inset LatexCommand index name "Text ! in formulas" \end_inset \begin_inset LatexCommand index name "Formula ! multiline ! text" \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 \begin_inset LatexCommand index name "Commands ! I ! \\textbackslash intertext" \end_inset \series default 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 $\phi=\pi$, 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 LatexCommand index name "Formula numbering" \end_inset \begin_inset LatexCommand index name "Formula ! numbering|see{Formula numbering}" \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\InsetSpace ~ Formula \family default (shortcut \family sans Ctrl-Alt\InsetSpace ~ n \family default ). Existing formulas can be numbered with the menu \family sans Edit\SpecialChar \menuseparator Math\SpecialChar \menuseparator Toggle\InsetSpace ~ Numbering \family default (shortcut \family sans Alt-m\InsetSpace ~ n \family default ). The formula number is displayed in LyX behind the formula as 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\InsetSpace ~ Numbering\InsetSpace ~ of\InsetSpace ~ Line \family default (shortcut \family sans Alt-m\InsetSpace ~ N \family default ) for every line. \end_layout \begin_layout Standard Except of inline formulas, all formulas can be numbered with two different styles, see \begin_inset LatexCommand ref reference "sec:Formula-Styles" \end_inset . \end_layout \begin_layout Subsection Cross-References \begin_inset LatexCommand label name "sub:Cross-References" \end_inset \begin_inset LatexCommand index name "Cross-references ! to formulas" \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.xpm scale 85 \end_inset . The cursor must hereby be inside a displayed formula. 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.\InsetSpace \thinspace{} g.\InsetSpace ~ section labels. To change a label, the menu \family sans Insert\SpecialChar \menuseparator Label \family default is used again. \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.xpm 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. \newline 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 Standard Note the different cross-reference types. \end_layout \end_inset \end_layout \begin_layout Standard The equations \begin_inset LatexCommand eqref reference "eq:tag" \end_inset and \begin_inset LatexCommand eqref reference "eq:c" \end_inset are equivalent. In ( \begin_inset LatexCommand ref reference "eq:Lat" \end_inset ) big Latin letters are used for the numbering in contrary to ( \begin_inset 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 Standard \series bold \backslash tag \series default is described in \begin_inset LatexCommand ref reference "sub:User-defined-Numbering" \end_inset . \end_layout \end_inset \series default contains a box like in \begin_inset LatexCommand ref reference "sub:Paragraph-Boxes" \end_inset , the formula cannot be referenced. \end_layout \begin_layout Subsection Subnumbering \begin_inset LatexCommand index name "Formula numbering ! subnumbering" \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 Standard \backslash addtocounter{equation}{-1} \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard \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 Standard \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 LatexCommand index name "Commands ! A ! \\textbackslash addtocounter" \end_inset \newline \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 ERT status collapsed \begin_layout Standard \backslash linebreak \end_layout \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 LatexCommand eqref reference "eq:a" \end_inset , \begin_inset LatexCommand eqref reference "eq:b" \end_inset , \begin_inset LatexCommand eqref reference "eq:c" \end_inset would be numbered as \begin_inset LatexCommand eqref reference "eq:a" \end_inset , \begin_inset LatexCommand eqref reference "eq:d" \end_inset , \begin_inset 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\InsetSpace \thinspace{} 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 Standard formula styles see \begin_inset LatexCommand ref reference "sec:Formula-Styles" \end_inset \end_layout \end_inset \series default is used, -7\InsetSpace \thinspace{} 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 Standard \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 Standard \backslash end{subequations} \end_layout \end_inset \end_layout \begin_layout Subsection User-defined Numbering \begin_inset LatexCommand label name "sub:User-defined-Numbering" \end_inset \begin_inset LatexCommand index name "Formula numbering ! user-defined" \end_inset \end_layout \begin_layout Standard \begin_inset LatexCommand index name "Formula numbering ! self-defined delimiters" \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 Standard 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 LatexCommand index name "Commands ! T ! \\textbackslash tag" \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 Standard \backslash spce \end_layout \end_inset something \series default was inserted to the formula. \end_layout \begin_layout Standard When the command \series bold \backslash tag* \begin_inset ERT status collapsed \begin_layout Standard \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 LatexCommand index name "Commands ! \"@\" ! \\textbackslash \"@\"addtoreset" \end_inset \newline resp. \newline \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 \newline \backslash @addtoreset{equation}{section} \newline \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 Standard \series bold remreset \series default is part of the LaTeX-package \series bold carlisle \series default \begin_inset LatexCommand index name "Packages ! carlisle" \end_inset that is part of every LaTeX standard installation. \end_layout \end_inset \begin_inset LatexCommand index name "Packages ! remreset" \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 LatexCommand index name "Commands ! \"@\" ! \\textbackslash \"@\"removefromreset" \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 LatexCommand index name "Commands ! N ! \\textbackslash numberwithin" \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 ERT 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 Standard \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.\InsetSpace \thinspace{} g.\InsetSpace ~ tables so that the number of the part is the sectioning, \newline \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 ERT or to the LaTeX-preamble: \end_layout \begin_layout Standard \series bold \backslash renewcommand{ \backslash theequation}{ \backslash arabic{equation}} \begin_inset LatexCommand index name "Commands ! A ! \\textbackslash arabic" \end_inset \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash renewcommand{ \backslash theequation}{ \backslash arabic{equation}} \end_layout \end_inset \series bold \newline \series default or \series bold \newline \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 Standard \backslash makeatletter \end_layout \begin_layout Standard \backslash @removefromreset{equation}{section} \end_layout \begin_layout Standard \backslash makeatother \end_layout \end_inset \end_layout \begin_layout Subsection Numbering with Roman Numbers and Letters \begin_inset LatexCommand label name "sub:Numbering-with-Roman" \end_inset \begin_inset LatexCommand index name "Formula numbering ! with letters" \end_inset \begin_inset LatexCommand index name "Formula numbering ! with Roman numbers" \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 LatexCommand index name "Commands ! R ! \\textbackslash renewcommand" \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 Standard 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 LatexCommand ref reference "sec:User-defined-commands" \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 LatexCommand index name "Commands ! R ! \\textbackslash roman" \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 LatexCommand index name "Commands ! R ! \\textbackslash roman@\\textbackslash Roman" \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 LatexCommand index name "Commands ! A ! \\textbackslash alph" \end_inset , for big ones there is the command \series bold \backslash Alph \series default \begin_inset LatexCommand index name "Commands ! A ! \\textbackslash alph@\\textbackslash Alph" \end_inset . \end_layout \begin_layout Standard \begin_inset Note Greyedout status open \begin_layout Standard \series bold Note: \series default Only maximal 26 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 Standard \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}\label{eq:rom}\end{equation} \end_inset \begin_inset ERT status collapsed \begin_layout Standard \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 Standard \backslash renewcommand{ \backslash theequation}{ \backslash alph{equation}} \end_layout \end_inset \begin_inset Formula \begin{equation} C=\textrm{small Latin}\label{eq:lat}\end{equation} \end_inset \begin_inset ERT status collapsed \begin_layout Standard \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 LatexCommand index name "Commands ! A ! \\textbackslash arabic" \end_inset \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash renewcommand{ \backslash theequation}{ \backslash arabic{equation}} \end_layout \end_inset \begin_inset Formula \begin{equation} E=\textrm{Arabic}\label{eq:arab}\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 ERT status collapsed \begin_layout Standard \backslash href{Formula-numbering.lyx}{ \end_layout \end_inset Formula-numbering.lyx \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset . \end_layout \begin_layout Section User-defined commands \begin_inset LatexCommand label name "sec:User-defined-commands" \end_inset \begin_inset LatexCommand index name "User-defined commands" \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 \begin_inset LatexCommand index name "Commands ! N ! \\textbackslash newcommand" \end_inset 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] \newline \begin_inset ERT status collapsed \begin_layout Standard \backslash phantom{ \end_layout \end_inset \backslash newcommand \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset {command definition} \end_layout \begin_layout Standard \begin_inset Note Greyedout status open \begin_layout Standard \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 \begin_inset Note Greyedout status open \begin_layout Standard \series bold Note: \series default The names of user-defined commands may only consist of Latin letters. \end_layout \end_inset \end_layout \begin_layout Standard The number of arguments is an integer in the range 0\InsetSpace \thinspace{} -\InsetSpace \thinspace{} 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 ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \series bold \newline \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 ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \series bold \newline \backslash newcommand{ \backslash us}[1]{ \backslash underline{#1}} \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \series bold \newline \series default 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.\InsetSpace \thinspace{} g.\InsetSpace ~ define the command \series bold \backslash fb \series default : \begin_inset ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \series bold \newline \backslash newcommand{ \backslash fb}[3]{ \backslash framebox#1#2{$#3$}} \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \series bold \newline \series default The two Dollar signs creates the extra formula needed for \series bold \backslash framebox \series default , see \begin_inset 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 needn't to be specified, the argument for the color is defined optional: \begin_inset ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \series bold \newline \backslash newcommand{ \backslash cb}[3][white]{ \backslash fcolorbox{#2}{#1}{$#3$}} \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \newline 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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard A \backslash gr \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $A\gr B$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash us{ABcd \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cb{red \begin_inset Formula $\to$ \end_inset \backslash { \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cb[green] \backslash {red \begin_inset Formula $\to$ \end_inset \backslash { \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Section Diagrams \begin_inset LatexCommand index name "Diagrams" \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 an 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 Is 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: \newline \series bold \backslash CD \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A@>j>>B@>>k>C@=F Ctrl-Enter \newline \begin_inset ERT status collapsed \begin_layout Standard \backslash hphantom{ \end_layout \end_inset \backslash CD \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset @AmAA@.@VV \backslash {V \series default \begin_inset Formula $\to$ \end_inset \series bold V@| Ctrl-Enter \newline \begin_inset ERT status collapsed \begin_layout Standard \backslash hphantom{ \end_layout \end_inset \backslash CD \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset D@<k>>F@=C \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Section Tips \begin_inset ERT status collapsed \begin_layout Standard \backslash texorpdfstring{ \end_layout \end_inset \begin_inset Foot status collapsed \begin_layout Standard Other useful math tips can be found in \begin_inset LatexCommand cite key "Voss" \end_inset . \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard }{} \end_layout \end_inset \begin_inset Note Note status collapsed \begin_layout Standard \backslash texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark. \end_layout \begin_layout Standard More about \backslash texorpdfstring is in section \begin_inset LatexCommand ref reference "sub:Formulas-in-Section" \end_inset . \end_layout \end_inset \begin_inset LatexCommand index name "Tips" \end_inset \begin_inset LatexCommand index name "Ions|see{Chemical characters}" \end_inset \end_layout \begin_layout Subsection Chemical Symbols and Equations \begin_inset LatexCommand label name "sub:Chemical-Symbols-and" \end_inset \begin_inset LatexCommand index name "Chemical characters ! Symbols" \end_inset \begin_inset LatexCommand index name "Chemical equations" \end_inset \begin_inset LatexCommand index name "Symbols ! chemical" \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 \[ \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\] \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 \family sans Alt-c\InsetSpace ~ r \family default to the upright font style. \begin_inset Foot status collapsed \begin_layout Standard font styles \series bold \series default see \begin_inset LatexCommand ref reference "sub:Font-Styles" \end_inset \end_layout \end_inset \end_layout \begin_layout Subsection Negative Numbers \begin_inset LatexCommand index name "Numbers ! negative" \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 Standard normal text: \end_layout \end_inset \begin_inset Text \begin_layout Standard x = -2 \end_layout \end_inset \begin_inset Text \begin_layout Standard formula: \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $x=-2$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard solution: \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 LatexCommand index name "Comma" \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 \family sans Alt-m\InsetSpace ~ m \family default ). \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 Standard \series bold icomma \series default is part of the LaTeX-package \series bold was \series default \begin_inset LatexCommand index name "Packages ! was\\vspace{4mm}" \end_inset . \end_layout \end_inset \begin_inset LatexCommand index name "Packages ! icomma" \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 LatexCommand label name "sub:Physical-Vectors" \end_inset \begin_inset LatexCommand index name "Vectors ! physical" \end_inset \end_layout \begin_layout Standard Predefined vectors are offered by the LaTeX-package \series bold braket \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold braket \series default should be part of every LaTeX standard installation. \end_layout \end_inset \begin_inset LatexCommand index name "Packages ! braket" \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 Standard \backslash ifbraket \end_layout \end_inset \begin_inset Note Note status open \begin_layout Standard The following table will only be displayed when the LaTeX-package \series bold braket \series default is installed. \end_layout \end_inset The following commands are defined: \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Bra{ \backslash psi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Bra{\psi}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Ket{ \backslash psi \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\Ket{\psi}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Braket{ \backslash psi| \backslash phi \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Standard \backslash else \end_layout \end_inset \begin_inset Note Note status open \begin_layout Standard 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 Standard \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 LatexCommand ref reference "sub:Automatic-Bracket-Size" \end_inset . \end_layout \begin_layout Subsection Self-defined Fractions \begin_inset LatexCommand label name "sub:Self-defined-Fractions" \end_inset \begin_inset LatexCommand index name "Fractions ! self-defined" \end_inset \end_layout \begin_layout Standard To define custom commands for fractions, the command \series bold \backslash genfrac \series default \begin_inset LatexCommand index name "Commands ! G ! \\textbackslash genfrac" \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} \newline \begin_inset ERT status collapsed \begin_layout Standard \backslash phantom{ \end_layout \end_inset \backslash genfrac \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset {numerator}{denominator} \end_layout \begin_layout Standard The style is a number in the range of 0\InsetSpace \thinspace{} -\InsetSpace \thinspace{} 3. \end_layout \begin_layout Standard \align center \begin_inset Tabular \begin_inset Text \begin_layout Standard Number \end_layout \end_inset \begin_inset Text \begin_layout Standard Style (Size) \end_layout \end_inset \begin_inset Text \begin_layout Standard 0 \end_layout \end_inset \begin_inset Text \begin_layout Standard display style formula \end_layout \end_inset \begin_inset Text \begin_layout Standard 1 \end_layout \end_inset \begin_inset Text \begin_layout Standard inline formula \end_layout \end_inset \begin_inset Text \begin_layout Standard 2 \end_layout \end_inset \begin_inset Text \begin_layout Standard small \end_layout \end_inset \begin_inset Text \begin_layout Standard 3 \end_layout \end_inset \begin_inset Text \begin_layout Standard 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\InsetSpace \thinspace{} 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 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 LatexCommand label name "sub:Canceled-Formulas" \end_inset \begin_inset LatexCommand index name "Formula ! canceled" \end_inset \end_layout \begin_layout Standard To cancel formulas or formula parts, the LaTeX-package \series bold cancel \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold cancel \series default is part of every LaTeX standard installation. \end_layout \end_inset \begin_inset LatexCommand index name "Packages ! cancel" \end_inset has to be loaded with the LaTeX-preamble line \end_layout \begin_layout Standard \series bold \backslash usepackage[samesize]{cancel} \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 Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard Result \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash hspace \series default 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 Standard \backslash cancel{ \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\cancel{\int A=B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash bcancel{ \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\bcancel{\int A=B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash xcancel{ \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\xcancel{\int A=B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash cancelto{1 \begin_inset Formula $\to$ \end_inset \backslash { \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash spce \end_layout \end_inset A=B \end_layout \end_inset \begin_inset Text \begin_layout Standard \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 Subsection Formulas in Section Headings \begin_inset LatexCommand label name "sub:Formulas-in-Section" \end_inset \begin_inset LatexCommand index name "Formula ! in section headings" \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 Standard When the LaTeX-package \series bold hyperref \series default \begin_inset LatexCommand index name "Packages ! hyperref" \end_inset is used, PDF-bookmarks are automatically 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\InsetSpace ~ 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 LatexCommand index name "Commands ! T ! \\textbackslash texorpdfstring" \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 Standard \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 OptArg status collapsed \begin_layout Standard 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 Standard \backslash texorpdfstring{ \end_layout \end_inset \begin_inset Formula $\sqrt{-1}=\mathrm{i}$ \end_inset \begin_inset ERT status collapsed \begin_layout Standard }{} \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \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 environment \series default \begin_inset Foot status collapsed \begin_layout Standard see \begin_inset LatexCommand ref reference "sub:Bold-Formulas" \end_inset \end_layout \end_inset . \end_layout \begin_layout Subsection Formulas in multi-column Text \begin_inset LatexCommand index name "Formula ! in multi-column text" \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 Standard \series bold multicol \series default is part of every LaTeX standard installation. \end_layout \end_inset \begin_inset LatexCommand index name "Packages ! multicol" \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 Standard Note herby that the setting \family sans Two-column\InsetSpace ~ document \family default in the menu \family sans Document\SpecialChar \menuseparator Settings \family default under \family sans Text\InsetSpace ~ 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\InsetSpace \thinspace{} -\InsetSpace \thinspace{} 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\InsetSpace \thinspace{} mm vertical space is inserted before the formula. When the formula style \series bold Indented \begin_inset Foot status collapsed \begin_layout Standard formula styles see \begin_inset LatexCommand ref reference "sec:Formula-Styles" \end_inset \end_layout \end_inset \series default is used, -9\InsetSpace \thinspace{} 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 \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{multicols}{2} \end_layout \end_inset Das Spektrum wird fouriertransformiert. the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk , Lösungsmittel) zu trennen. Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns nun das Aussehen des Ausgangssignals. Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man über alle Phasen integrieren muss. Sei nun \begin_inset Formula $S$ \end_inset unser normiertes Ausgangssignal and \begin_inset Formula $P$ \end_inset the Phasenverteilungsfunktion, so ergibt sich the Beziehung \begin_inset ERT status collapsed \begin_layout Standard \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\label{eq:fouriertrafo}\end{equation} \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash begin{multicols}{2} \end_layout \end_inset wobei \begin_inset Formula $S_{0}$ \end_inset das Signal ohne Gradient ist and the Normierungsbedingung \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$ \end_inset gilt. Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen. Direkt nach the \begin_inset Formula $\nicefrac{\pi}{2}$ \end_inset \InsetSpace \thinspace{} -rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich das Signal zusätzlich abschwächt. Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten \begin_inset Formula $T_{2}$ \end_inset -Zeit. \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash end{multicols} \end_layout \end_inset \end_layout \begin_layout Subsection Formulas with Description of Variables \begin_inset LatexCommand index name "Formula ! with description of variables" \end_inset \end_layout \begin_layout Standard To describe variables within a formula, like in formula \begin_inset LatexCommand eqref reference "eq:within" \end_inset , a 2 \series bold × \series default \begin_inset Formula $n$ \end_inset \InsetSpace ~ matrix is used with left aligned columns for the \begin_inset Formula $n$ \end_inset used variables. \begin_inset Foot status collapsed \begin_layout Standard matrices see \begin_inset LatexCommand ref reference "sec:Matrices" \end_inset \end_layout \end_inset To set the description in a smaller size, before the matrix e.\InsetSpace \thinspace{} g.\InsetSpace ~ the command \series bold \backslash footnotesize \series default is inserted. \begin_inset Foot status collapsed \begin_layout Standard font sizes see \begin_inset 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 Standard formula styles see \begin_inset 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 Standard \series bold \backslash hfill \series default only works in formulas with the style \series bold Indented \series default , see \begin_inset 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 LatexCommand ref reference "sub:Flalign-Environment" \end_inset is used to indent formulas. Formula \begin_inset LatexCommand eqref reference "eq:within" \end_inset consists of five columns whereas 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 LatexCommand label name "sub:Upright-small-Greek" \end_inset \begin_inset LatexCommand index name "Greek letters ! upright" \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 Standard \series bold upgreek \series default is part of the LaTeX-package \series bold was \series default \begin_inset LatexCommand index name "Packages ! was\\vspace{4mm}" \end_inset . \end_layout \end_inset \begin_inset LatexCommand index name "Packages ! upgreek" \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 Standard \backslash ifupgreek \end_layout \end_inset \begin_inset Note Note status open \begin_layout Standard 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 letters 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 Standard \backslash else \end_layout \end_inset \begin_inset Note Note status open \begin_layout Standard 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 Standard \backslash fi \end_layout \end_inset \end_layout \begin_layout Subsection Text Characters in Formulas \begin_inset LatexCommand label name "sub:Text-Characters-in" \end_inset \begin_inset LatexCommand index name "Text ! in formulas" \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 Standard see \begin_inset 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. Fore example the encoding \series bold latin9 \series default is defined in the file \series bold latin9.def \series default that is in the installation folder of LaTeX. Encodings should only be changed via the LaTeX-preamble and not in the definition files. Otherwise own 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 directly be inserted to 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 \newpage \end_layout \begin_layout Section \start_of_appendix Typographic Advises \begin_inset LatexCommand index name "Typographic Advises" \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 Standard 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 LatexCommand cite key "Duden" \end_inset that lists some of the ISO rules. \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 Standard done with font styles, see \begin_inset LatexCommand ref reference "sub:Font-Styles" \end_inset \end_layout \end_inset : 30\InsetSpace \thinspace{} km/h \newline Between the value and the unit is the smallest space, see \begin_inset LatexCommand ref reference "sub:Predefined-Space" \end_inset . \end_layout \begin_layout Itemize Percent and perthousand signs are set like physical units: \newline 1,2\InsetSpace \thinspace{} ‰ 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\InsetSpace \thinspace{} °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\InsetSpace \thinspace{} 473\InsetSpace \thinspace{} 588 \end_layout \begin_layout Itemize For dimensionings like 120×90×40\InsetSpace \thinspace{} cm the multiplication sign \begin_inset Quotes eld \end_inset × \begin_inset Quotes erd \end_inset is used. It is available with the LaTeX-command \series bold \backslash texttimes \series default , but can also directly be inserted with some keyboard definitions. \end_layout \begin_layout Itemize Functions with names consisting of several letters are set upright to avoid confusions, see \begin_inset 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 \newline 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 Standard \newpage \end_layout \begin_layout Section Synonyms \begin_inset LatexCommand index name "Synonyms" \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 \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard equivalent to \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default is only used as spacer. \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ast \end_layout \end_inset \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash raisebox{-1.2mm}{ \end_layout \end_inset * \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash choose \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash binom \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash geq \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ge \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash lbrace \end_layout \end_inset \begin_inset Text \begin_layout Standard { \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash lbracket \end_layout \end_inset \begin_inset Text \begin_layout Standard [ \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash leftarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash gets \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash leq \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash le \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash lor \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash vee \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash neq \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash not= \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash slash \end_layout \end_inset \begin_inset Text \begin_layout Standard / \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash vert \end_layout \end_inset \begin_inset Text \begin_layout Standard | \end_layout \end_inset \end_inset \hfill \begin_inset Tabular \begin_inset Text \begin_layout Standard Command \end_layout \end_inset \begin_inset Text \begin_layout Standard equivalent to \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash backslash \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash \backslash \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dasharrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash dashrightarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash land \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash wedge \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash rbrace \end_layout \end_inset \begin_inset Text \begin_layout Standard } \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash rbracket \end_layout \end_inset \begin_inset Text \begin_layout Standard ] \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash rightarrow \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash to \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash lnot \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash neg \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ne \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash not= \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash owns \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash ni \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash square \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Box \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash Vert \end_layout \end_inset \begin_inset Text \begin_layout Standard \backslash | \end_layout \end_inset \end_inset \hfill \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Bibliography \begin_inset 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 LatexCommand bibitem key "Mathmode" \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash href{ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf}{ \end_layout \end_inset Description \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset of LaTeX's math abilities \end_layout \begin_layout Bibliography \begin_inset LatexCommand bibitem key "Voss" \end_inset LaTeX tips and tricks- \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://tug.org/TeXnik/}{ \end_layout \end_inset page \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \begin_layout Bibliography \begin_inset LatexCommand bibitem key "AMS" \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash href{ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf}{ \end_layout \end_inset Description \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset of \begin_inset ERT status collapsed \begin_layout Standard \backslash AmS \end_layout \end_inset -LaTeX \end_layout \begin_layout Bibliography \begin_inset LatexCommand bibitem key "Symbole" \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash href{ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}{ \end_layout \end_inset List \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset of all symbols available with LaTeX-packages \end_layout \begin_layout Bibliography \begin_inset LatexCommand bibitem key "hyperref" \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{ \end_layout \end_inset Documentation \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset of the LaTeX-package \series bold hyperref \series default \begin_inset LatexCommand index name "Packages ! hyperref" \end_inset \end_layout \begin_layout Bibliography \begin_inset LatexCommand bibitem key "Mathclap" \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}{ \end_layout \end_inset Description \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset of the command \series bold \backslash mathclap \series default , described in \begin_inset LatexCommand ref reference "sub:Operator-Limits" \end_inset \begin_inset LatexCommand index name "Commands ! M ! \\textbackslash mathclap" \end_inset \end_layout \begin_layout Bibliography \begin_inset LatexCommand bibitem key "Duden" \end_inset \emph on Duden Band 1 \emph default . 22. Auflage, Duden 2001 \end_layout \begin_layout Subsubsection* \begin_inset LatexCommand printindex \end_inset \end_layout \end_body \end_document