#LyX 1.5.5svn created this file. For more info see http://www.lyx.org/ \lyxformat 276 \begin_document \begin_header \textclass scrartcl \begin_preamble % DO NOT ALTER THIS PREAMBLE!!! % % This preamble is designed to ensure that the file prints % out as advertised. If you mess with this preamble, % parts of this document may not print out as expected. If you % have problems LaTeXing this file, please contact % the documentation team % email: lyx-docs@lists.lyx.org % if pdflatex is used \usepackage{ifpdf} \ifpdf % set fonts for nicer pdf view \IfFileExists{lmodern.sty} {\usepackage{lmodern}}{} % link all cross references and URLs % in pdf output \usepackage[colorlinks=true, bookmarks, bookmarksnumbered, bookmarksopen, bookmarksopenlevel=1, linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false, pdfpagelabels, pdfauthor={LyX Team}, pdftex, pdftitle={LyXs Mathehandbuch}, pdfsubject={LyX-Dokumentation der Mathefunktionen}, pdfkeywords={LyX, Mathed}]{hyperref} \else % if dvi or ps is produced % link all cross references and URLs in DVI output \usepackage[ps2pdf, colorlinks=true, linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue]{hyperref} \fi % end if pdflatex is used % Folgendes Problem lösen: % Besteht die Kapitelnummer aus zu vielen Ziffern, wird die % Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über % die Kapitelnummer geschrieben. % Als Lösung wird mehr Platz zwischen Nummer und % Überschrift eingefügt. \renewcommand{\l@subsection}{\@dottedtocline{2}{1.5em}{2.8em}} \renewcommand{\l@subsubsection}{\@dottedtocline{3}{4.3em}{3.6em}} % Damit die Zeichen ° und · in LyX direkt eingegeben werden können, % siehe Kap. 22.11 \DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi} \DeclareInputText{183}{\ifmmode\cdot\else\textperiodcentered\fi} % Linkfläche für Querverweise vergrößern und automatisch benennen, % siehe Kap. 22.18.1 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}} \renewcommand{\sectionautorefname}{Kap.\negthinspace} \renewcommand{\subsectionautorefname}{Kap.\negthinspace} \renewcommand{\subsubsectionautorefname}{Kap.\negthinspace} \newlength{\abc} \settowidth{\abc}{\space} \renewcommand{\equationautorefname}{\hspace{-\abc}} % Makros damit Pakete nicht doppelt geladen werden. % siehe erste Fußnote in Kap. 9.3 \@ifundefined{textcolor}{\usepackage{color}}{} % damit die Seiten des Inhaltsverzeichnisses römisch % nummeriert werden und damit das Inhaltsverzeichnis % ein eigenes pdf-Lesezeichen erhält \pagenumbering{Roman} \let\myTOC\tableofcontents \renewcommand{\tableofcontents}{% \vspace{1cm} \pdfbookmark[1]{Inhaltsverzeichnis}{} \myTOC \cleardoublepage \pagenumbering{arabic}} % Damit die Fußnoten einen zusätzlichen vertikalen Abstand von 1,5 mm haben, % siehe Kap. 22.16 \let\myFoot\footnote \renewcommand{\footnote}[1]{\myFoot{#1\vspace{1.5mm}}} % provides caption formatting \setkomafont{captionlabel}{\bfseries} % benutzt in Kap. 22.4 \usepackage{braket} % benutzt in Kap. 22.6 \usepackage[samesize]{cancel} % enables calculation of values, \usepackage{calc} % für Mehrfachzeilen und -spalten \usepackage{multirow} \usepackage{multicol} % für Diagramme \usepackage{amscd} % benutzt in Kap. 19.4 \usepackage{remreset} %Mehrfachzeilen zentriert ausrichten (z.B. in Kap. 13.3) \renewcommand{\multirowsetup}{\centering} % Farbdefinition aus Kap. 9.3 \definecolor{dunkelgruen}{cmyk}{0.5, 0, 1, 0.5} % Operatoren deklarieren (siehe Kap. 10.4 und 15.2) \DeclareMathOperator*{\Raute}{\blacklozenge} \DeclareMathOperator{\sgn}{sgn} \newcommand{\leer}{\textvisiblespace} % Beispielbefehle aus Kap. 20.1 \newcommand{\gr}{\Longrightarrow} \newcommand{\us}[1]{\underline{#1}} \newcommand{\fb}[3]{\framebox#1#2{$#3$}} \newcommand{\cb}[3][white]{\fcolorbox{#2}{#1}{$#3$}} \newcommand{\fracS}[3][]{\genfrac{}{}{#1}{}{#2}{#3}} % Beispielmakro aus Kap. 19.4 %\def\tagform@#1{\maketag@@@{|#1|}} % Makro aus Kap. 10.2 \def\clap#1{\hbox to 0pt{\hss #1\hss}} \def\mathclap {\mathpalette \mathclapinternal} \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}} % Grauschrift Notiz umdefinieren \renewenvironment{lyxgreyedout} {\textcolor{blue}\bgroup}{\egroup} % Damit der Index einen anderen Namen erhält. \usepackage[ngerman]{babel} \addto\captionsngerman {\renewcommand{\indexname} {Stichwort- und Befehlsverzeichnis}} % testen ob das Paket eurosym installiert ist % wird benutzt für das Euro-Symbol \newboolean{eurosym} \IfFileExists{eurosym.sty} {\usepackage[gennarrow]{eurosym} \setboolean{eurosym}{true}} {\setboolean{eurosym}{false}} % benutzt in Kap. 22.4 % testen ob Paket braket installiert ist \newboolean{braket} \IfFileExists{braket.sty} {\usepackage{braket} \setboolean{braket}{true}} {\setboolean{braket}{false}} % benutzt in Kap. 22.10 % testen ob Paket upgreek installiert ist \newboolean{upgreek} \IfFileExists{upgreek.sty} {\usepackage{upgreek} \setboolean{upgreek}{true}} {\setboolean{upgreek}{false}} % benötigt für Kommas in Formeln, siehe Kap. 22.3 \IfFileExists{icomma.sty} {\usepackage{icomma}}{} \end_preamble \options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove \language ngerman \inputencoding auto \font_roman default \font_sans default \font_typewriter default \font_default_family default \font_sc false \font_osf false \font_sf_scale 100 \font_tt_scale 100 \graphics default \paperfontsize 12 \spacing single \papersize a4paper \use_geometry false \use_amsmath 2 \use_esint 1 \cite_engine basic \use_bibtopic false \paperorientation portrait \secnumdepth 4 \tocdepth 3 \paragraph_separation skip \defskip medskip \quotes_language german \papercolumns 1 \papersides 2 \paperpagestyle plain \bullet 1 0 6 -1 \bullet 2 2 35 -1 \bullet 3 2 7 -1 \tracking_changes false \output_changes false \author "" \author "" \end_header \begin_body \begin_layout Title LyXs detailliertes Mathe Handbuch \end_layout \begin_layout Author vom LyX Team \begin_inset Foot status collapsed \begin_layout Standard \noindent Für Anmerkungen oder Korrekturen senden sie bitte eine Email an LyXs Dokumentati ons-Liste: \family typewriter \begin_inset ERT status collapsed \begin_layout Standard \backslash href{mailto:lyx-docs@lists.lyx.org?subject=LyXs Mathehandbuch}{ \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 Verfasser: Uwe Stöhr \end_layout \end_inset \newline \newline \family sans Version 1.5.5 \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 Um diese Datei als PDF, PS oder DVI zu exportieren, müssen die LaTeX-Pakete \series bold eurosym, \series default \series bold multirow, \series default und \series bold was \series default installiert sein. Wenn sie nicht installiert sind, kann das Dokument trotzdem exportiert werden, die Abschnitte in denen die Pakete benötigt werden, erscheinen dann aber nicht im Ausdruck. \end_layout \end_inset \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Section Einleitung \begin_inset LatexCommand label name "sec:Einleitung" \end_inset \end_layout \begin_layout Standard Dieses Dokument ist eine Zusammenstellung und Erläuterung der wichtigsten LaTeX-Befehle für mathematische Zeichen und Konstruktionen. Die Erläuterungen sind speziell auf die Benutzung der Befehle mit LyX zugeschni tten. Das setzt voraus, dass bereits das Kapitel \family typewriter Mathematische \family default \family typewriter Formeln \family default des Benutzerhandbuchs gelesen worden ist. \end_layout \begin_layout Standard Die meisten Zeichen und viele Konstruktionen sind auch über das Menü \family sans Einfügen \series bold \SpecialChar \menuseparator \series default Mathe \family default oder die \family sans Mathe-Werkzeugleiste \family default aufrufbar. Wer viele Formeln zu schreiben hat, wird jedoch feststellen, dass man mit den LaTeX-Befehlen viel schneller eine Formel setzen kann. Daher wird in diesem Handbuch der Fokus auf Befehle gesetzt wobei entsprechende Werkzeugleistenknöpfe, falls vorhanden, erwähnt werden. \end_layout \begin_layout Standard Sofern nicht anders angegeben, sind Befehle nur in der Formel-Umgebung von LyX verfügbar. Um alle Befehle nutzen zu können, muss die Option \family sans AMS-Mathe-Paket verwenden \family default im Menü \family sans Dokument\SpecialChar \menuseparator Einstellungen\SpecialChar \menuseparator Mathe Optionen \family default aktiviert sein. \begin_inset Foot status collapsed \begin_layout Standard Die \family sans Option \family default \family sans AMS-Mathe-Paket automatisch verwenden \family default verwendet \begin_inset ERT status collapsed \begin_layout Standard \backslash AmS \end_layout \end_inset -Mathe nur wenn im Dokument mathematische Konstrukte gefunden wurden die LyX unterstützt. \end_layout \end_inset \end_layout \begin_layout Standard Es wird in diesem Dokument der Übersichtlichkeit halber auf die Auf\SpecialChar \textcompwordmark{} listung aller \begin_inset ERT status collapsed \begin_layout Standard \backslash AmS \end_layout \end_inset -Mathe Befehle \begin_inset Foot status collapsed \begin_layout Standard Eine Liste mit allen \begin_inset ERT status collapsed \begin_layout Standard \backslash AmS \end_layout \end_inset -Mathe Befehlen findet sich in der Datei \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 , die Teil jeder LaTeX-Standardinstallation ist. \end_layout \end_inset verzichtet. \end_layout \begin_layout Section Allgemeine Hinweise \begin_inset LatexCommand label name "sec:Allgemeine-Hinweise" \end_inset \end_layout \begin_layout Standard Um eine in einer Textzeile eingebettete Formel \begin_inset LatexCommand index name "Formel ! eingebettete" \end_inset zu erstellen, drückt man \family sans Strg-m \family default oder den Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math-mode.png scale 85 \end_inset . \newline Um eine abgesetzte Formel \begin_inset LatexCommand index name "Formel ! abgesetzte" \end_inset zu erstellen, drückt man \family sans Strg-M \family default . \end_layout \begin_layout Standard Um eine abgesetzte Formel in eine eingebettete umzuwandeln, setzt man den Cursor in die Formel und drückt \family sans Strg-M \family default oder benutzt das Menü \family sans Bearbeiten\SpecialChar \menuseparator Mathe\SpecialChar \menuseparator \begin_inset ERT status collapsed \begin_layout Standard \backslash linebreak \end_layout \end_inset Formelart ändern \family default . Auf die selbe Weise lässt sich eine eingebettete in eine abgesetzte Formel umwandeln. \end_layout \begin_layout Standard Um Teile einer eingebetteten Formel in der Größe einer abgesetzten darzustellen, gibt man in die Formel den Befehl \series bold \backslash displaystyle \begin_inset LatexCommand index name "Befehle ! D ! \\textbackslash displaystyle" \end_inset \series default ein. Es erscheint ein neues blaues Kästchen, in das dann der Formelteil eingegeben wird. \end_layout \begin_layout Standard In einer Tabelle dürfen nur eingebettete Formeln verwendet werden. \end_layout \begin_layout Standard Die \family sans Mathe-Werkzeugleiste \family default kann über das Menü \family sans Ansicht\SpecialChar \menuseparator Werkzeugleisten \family default eingeblendet werden. Wenn dort auf \begin_inset Quotes eld \end_inset Mathe \begin_inset Quotes erd \end_inset geklickt wird, wird die Werkzeugleiste permanent am unteren Rand eingeblendet; diese Einstellung wird durch ein Häkchen im Menü \family sans Werkzeugleisten \family default angezeigt. Wenn nun im Menü \family sans Werkzeugleisten \family default nochmal auf \begin_inset Quotes eld \end_inset Mathe \begin_inset Quotes erd \end_inset geklickt wird, wird die Werkzeugleiste nur angezeigt, wenn sich der Cursor in einer Formel befindet; diese Einstellung wird durch die Umbenennung des Menüeintrags von \begin_inset Quotes eld \end_inset Mathe \begin_inset Quotes erd \end_inset zu \begin_inset Quotes eld \end_inset Mathe\InsetSpace ~ (automatisch) \begin_inset Quotes erd \end_inset angezeigt. \end_layout \begin_layout Standard In den TeX-Modus \begin_inset LatexCommand index name "T@\\TeX-Modus" \end_inset gelangt man über den Werkzeugleistenknopf \begin_inset Graphics filename ../../images/ert-insert.png scale 85 \end_inset oder das Menü \family sans Einfügen\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\InsetSpace ~ Code \family default (Tastenkürzel \family sans Strg-l \family default ). \begin_inset Note Note status collapsed \begin_layout Standard In LyX gibt es drei \begin_inset Quotes gld \end_inset Eigennamen \begin_inset Quotes grd \end_inset , die im Ausdruck mit hoch bzw. tief gestellten Großbuchstaben erscheinen: TeX, LaTeX und LyX \end_layout \begin_layout Standard Um zu verhindern, dass diese Wörter als Eigennamen erkannt werden, setzt man einen der Buchstaben in TeX-Klammern. \end_layout \end_inset \end_layout \begin_layout Standard In den LaTeX-Vorspann \begin_inset LatexCommand index name "L@\\LaTeX-Vorspann" \end_inset gelangt man über das Menü \family sans Dokument\SpecialChar \menuseparator Einstellungen\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-Vorspann \family default . \end_layout \begin_layout Standard Zur nachträglichen Bearbeitung von Matrizen, Fallunterscheidungen und mehrzeilig en Formeln kann man die Menüs \family sans Bearbeiten\SpecialChar \menuseparator Mathe \family default und \family sans Bearbeiten\SpecialChar \menuseparator Zeilen\InsetSpace \thinspace{} &\InsetSpace \thinspace{} Spalten \family default oder die \family sans Tabellen-Werkzeugleiste \family default verwenden. Beim Vertauschen von Zeilen und Spalten mit Hilfe dieses Menüs wird immer die Spalte bzw. Zeile, in der der Cursor steht, mit der rechts daneben stehenden Spalte bzw. darunter liegenden Zeile vertauscht. Befindet sich der Cursor in der letzten Spalte bzw. Zeile, wird mit der links daneben stehenden Spalte bzw. darüber liegenden Zeile vertauscht. \end_layout \begin_layout Standard Zum Schreiben von Text in einer Formel \begin_inset Foot status collapsed \begin_layout Standard Bei mehrzeiligen Formeln wird der Befehl \series bold \backslash intertext \series default verwendet, siehe \begin_inset LatexCommand ref reference "sub:Text-in-mehrzeiligen" \end_inset . \end_layout \end_inset verwendet man den \emph on mathematischen Textmodus \emph default \begin_inset LatexCommand index name "Text ! in Formeln" \end_inset \begin_inset LatexCommand index name "Mathematischer Textmodus" \end_inset , in den man mit dem Tastenkürzel \family sans Alt-m\InsetSpace ~ m \family default oder durch Eingabe des Befehls \series bold \backslash text \begin_inset LatexCommand index name "Befehle ! T ! \\textbackslash text" \end_inset \series default gelangt. Der Text erscheint in LyX schwarz und lässt sich dadurch gut vom Rest der Formel unterscheiden. Im fertigen Dokument erscheint mathematischer Text im Gegensatz zu allen anderen Zeichen einer Formel nicht kursiv. \end_layout \begin_layout Subsection* Befehlsschema \end_layout \begin_layout Standard Die meisten LaTeX-Befehle für mathematische Konstruktionen besitzen folgendes Schema: \end_layout \begin_layout Standard \series bold \backslash Befehlsname[optionales \series default \series bold Argument]{anzugebendes \series default \series bold Argument} \end_layout \begin_layout Standard Ein Befehl muss immer mit einem Backslash \begin_inset Quotes gld \end_inset \series bold \backslash \series default \begin_inset Quotes grd \end_inset beginnen. Möchte man ein optionales Argument nicht angeben, müssen auch die zugehörigen eckigen Klammern weggelassen werden. Die geschweiften Klammern werden in diesem Dokument als TeX-Klammern \begin_inset LatexCommand index name "T@\\TeX-Klammern" \end_inset bezeichnet. Hängt man in einer Formel an Befehlsnamen eine linke geschweifte Klammer an, erzeugt LyX automatisch eine TeX-Klammer. Ansonsten werden sie in Formeln mit dem Befehl \series bold \backslash { \series default erzeugt. TeX-Klammern erscheinen in LyX rot, im Gegensatz zu normalen geschweiften Klammern, die blau erscheinen. Im TeX-Modus sind für TeX-Klammern keine Befehle notwendig. TeX-Klammern erscheinen nicht im Ausdruck. \end_layout \begin_layout Standard Werden Befehle ohne Argumente, wie z.\InsetSpace \thinspace{} B. Symbolbefehle, im TeX-Modus eingegeben, muss auf den Befehl \emph on immer \emph default ein Leerzeichen folgen um ihn zu beenden. Dieses Leerzeichen erscheint nicht im Ausdruck. Soll das Leerzeichen auch im Ausdruck erscheinen, muss auf den Befehl im normalen Text ein geschütztes Leerzeichen folgen. \end_layout \begin_layout Standard Ein geschütztes Leerzeichen gibt man mit \family sans Strg-Leertaste \family default ein. \end_layout \begin_layout Subsection* Zeichenerklärung \end_layout \begin_layout Itemize Das Symbol \begin_inset Foot status collapsed \begin_layout Standard Dieses sichtbare Leerzeichen erhält man über den Befehl \series bold \backslash textvisiblespace \series default \begin_inset LatexCommand index name "Befehle ! T ! \\textbackslash textvisiblespace" \end_inset , der im TeX-Modus einzugeben ist. \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \InsetSpace ~ steht für ein einzugebendes Leerzeichen. \end_layout \begin_layout Itemize Ein Pfeil wie z.\InsetSpace \thinspace{} B. \begin_inset Formula $\to$ \end_inset steht für den Druck der jeweiligen Pfeiltaste auf der Tastatur. \end_layout \begin_layout Subsection* Verwendete Einheiten \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:Verwendete-Einheiten" \end_inset Verwendete Einheiten \end_layout \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="13" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Einheit \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Name / Beschreibung \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard mm \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Millimeter \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" 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rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Punkt (72,27\InsetSpace \thinspace{} pt = 1\InsetSpace \thinspace{} in) \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard pc \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Pica (1\InsetSpace \thinspace{} pc = 12\InsetSpace \thinspace{} pt) \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard sp \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard scaled point (65536\InsetSpace \thinspace{} sp = 1\InsetSpace \thinspace{} pt) \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard bp \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard big point (72\InsetSpace \thinspace{} bp = 1\InsetSpace \thinspace{} in) \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard dd \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard cc \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Cicero (1\InsetSpace \thinspace{} cc = 12\InsetSpace \thinspace{} dd) \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard ex \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Höhe des Buchstabens \emph on x \emph default in der aktuellen Schrift \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard em \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Breite des Buchstabens \emph on M \emph default in der aktuellen Schrift \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard mu \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard math unit (1\InsetSpace \thinspace{} mu = \begin_inset Formula $\nicefrac{1}{18}$ \end_inset \InsetSpace \thinspace{} em) \begin_inset Note Note status collapsed \begin_layout Standard Der Befehl \series bold \backslash textfrac \series default ist in Kap. \begin_inset LatexCommand ref reference "sub:Selbstdefinierte-Brüche" \end_inset erklärt. \end_layout \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \end_inset \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Section Grundlegende Funktionen \end_layout \begin_layout Subsection Exponenten \begin_inset LatexCommand index name "Exponenten" \end_inset und Indizes \begin_inset LatexCommand index name "Indizes" \end_inset \begin_inset LatexCommand index name "Hochstellen|see{Exponenten}" \end_inset \begin_inset LatexCommand index name "Tiefstellen|see{Indizes}" \end_inset \end_layout \begin_layout Standard Indizes werden mit dem Unterstrich _ oder mit dem Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math-subscript.png scale 85 \end_inset , Exponenten mit dem Zirkumflexzeichen ^ oder mit dem Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math-superscript.png scale 85 \end_inset erzeugt. \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard B_V \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $B_{V}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard B^V \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}B^{V}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard B^ \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}B^{A}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Da der Zirkumflex ein Akzent ist, werden Selbstlaute akzentuiert statt hochgeste llt \begin_inset Foot status collapsed \begin_layout Standard Je nach Tastatureinstellung werden auch andere Buchstaben akzentuiert. \end_layout \end_inset . Um in diesem Fall Exponenten zu erzeugen, muss nach dem Zirkumflex ein Leerzeichen eingegeben werden, siehe letztes Beispiel. \end_layout \begin_layout Subsection Brüche \begin_inset LatexCommand label name "sub:Brüche" \end_inset \begin_inset LatexCommand index name "Brüche" \end_inset \end_layout \begin_layout Standard Brüche werden mit dem Befehl \series bold \backslash frac \series default \begin_inset LatexCommand index name "Befehle ! F ! \\textbackslash frac" \end_inset oder mit dem Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/frac.png scale 50 \end_inset erstellt. Die Zeichengröße wird automatisch angepasst, je nachdem, ob sich der Bruch in einer eingebetteten oder abgesetzten Formel befindet. Mit dem Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/frac-square.png scale 85 \end_inset können verschieden Bruchtypen gewählt werden. \end_layout \begin_layout Standard Mit dem Befehl \series bold \backslash dfrac \begin_inset LatexCommand index name "Befehle ! D ! \\textbackslash dfrac" \end_inset \series default kann man einen Bruch erzeugen, der immer in der Größe einer abgesetzten Formel erscheint. Mit \series bold \backslash tfrac \begin_inset LatexCommand index name "Befehle ! T ! \\textbackslash tfrac" \end_inset \series default erscheint der Bruch immer in der Größe einer eingebetteten Formel. Ein Beispiel: \end_layout \begin_layout Standard Eine Zeile mit dem Bruch \begin_inset Formula $\frac{1}{2}$ \end_inset , der mit dem Befehl \series bold \backslash frac \series default erstellt wurde. \end_layout \begin_layout Standard Eine Zeile mit dem Bruch \begin_inset Formula $\dfrac{1}{2}$ \end_inset , der mit dem Befehl \series bold \backslash dfrac \series default erstellt wurde. \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash frac \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\frac{A}{B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash dfrac \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{7mm}{}\dfrac{A}{B}\raisebox{-4mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash dfrac \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset e^ \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash frac \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 1 \begin_inset Formula $\downarrow$ \end_inset 2 \begin_inset Formula $\downarrow\downarrow$ \end_inset 3 \end_layout \end_inset </cell> <cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset \newpage Für Mehrfachbrüche gibt es den Befehl \series bold \backslash cfrac \series default \begin_inset LatexCommand index name "Befehle ! C ! \\textbackslash cfrac" \end_inset . Dazu ein Beispiel: \begin_inset VSpace -3mm \end_inset \end_layout \begin_layout Standard \begin_inset Formula \begin{align*} \textrm{mit \textbf{\textbackslash frac} erstellt} & & \textrm{mit \textbf{\textbackslash cfrac} erstellt}\\ \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 Der Befehl für obiges Beispiel lautet: \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 bewirkt, dass der Bruch immer in der Größe einer abgesetzten Formel erscheint, auch wenn er selbst Teil eines Bruches ist. \series bold \backslash cfrac \series default besitzt folgendes Befehlsschema: \end_layout \begin_layout Standard \series bold \backslash cfrac[Zählerposition]{Zähler}{Nenner} \end_layout \begin_layout Standard Zählerposition kann \emph on l \emph default , \emph on c \emph default oder \emph on r \emph default sein. Bei \emph on l \emph default oder \emph on r \emph default wird der Zähler links- bzw.\InsetSpace ~ rechtsbündig am Bruchstrich ausgerichtet. Wird \emph on c \emph default oder keine Position angegeben, erscheint der Zähler wie gewohnt mittig. Diese Brüche demonstrieren die verschiedenen Ausrichtungen: \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 Oftmals ist es am günstigsten \series bold \backslash cfrac \series default und \series bold \backslash frac \series default zu kombinieren: \begin_inset Formula \[ \cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\] \end_inset \end_layout \begin_layout Standard Um Brüche mit schrägem Bruchstrich zu erzeugen, kann der Befehl \series bold \backslash nicefrac \begin_inset LatexCommand index name "Befehle ! N ! \\textbackslash nicefrac" \end_inset \series default benutzt werden: \begin_inset Formula $\nicefrac{5}{31}$ \end_inset \end_layout \begin_layout Standard Wie man eigene Brüche definiert, um die Bruchstrichdicke zu ändern, ist in \begin_inset LatexCommand ref reference "sub:Selbstdefinierte-Brüche" \end_inset erklärt. \end_layout \begin_layout Subsection Wurzeln \begin_inset LatexCommand index name "Wurzeln" \end_inset \end_layout \begin_layout Standard Quadratwurzeln werden mit \series bold \backslash sqrt \series default \begin_inset LatexCommand index name "Befehle ! S ! \\textbackslash sqrt" \end_inset oder dem Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/sqrt.png scale 85 \end_inset gesetzt, alle anderen Wurzeln mit dem Befehl \series bold \backslash root \series default \begin_inset LatexCommand index name "Befehle ! R ! \\textbackslash root" \end_inset oder dem Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/root.png scale 85 \end_inset . \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="3" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sqrt \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A-B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\sqrt{A-B}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash root \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 3 \begin_inset Formula $\downarrow$ \end_inset A-B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\sqrt[3]{A-B}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Eine Quadratwurzel kann man auch mit \series bold \backslash root \series default erstellen, indem man das Feld über der Wurzel frei lässt. \end_layout \begin_layout Standard Bei manchen Indizes ist der Abstand zur Wurzel zu gering, wie bei dieser Formel: \begin_inset Formula $\sqrt[\beta]{B}$ \end_inset \newline Das \begin_inset Formula $\beta$ \end_inset berührt die Wurzel. Um dies zu verhindern, verwendet man die Befehle \series bold \backslash leftroot \series default \begin_inset LatexCommand index name "Befehle ! L ! \\textbackslash leftroot" \end_inset und \series bold \backslash uproot \series default \begin_inset LatexCommand index name "Befehle ! U ! \\textbackslash uproot" \end_inset , die folgendes Schema besitzen: \end_layout \begin_layout Standard \series bold \backslash leftroot{Abstand} \series default bzw. \series bold \backslash uproot{Abstand} \end_layout \begin_layout Standard Abstand ist die Anzahl der Big Points (Einheit bp; \begin_inset Formula $\mathrm{72\, bp=1\, inch}$ \end_inset ), um die der Index nach links bzw. nach oben verschoben werden soll. Die Befehle werden in den Index geschrieben. So ergibt der Befehl \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 leer \end_layout \end_inset \begin_inset Formula $\to$ \end_inset B \newline \series default eine korrekt gesetzte Formel: \begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$ \end_inset \end_layout \begin_layout Subsection Binomialkoeffizienten \begin_inset LatexCommand index name "Binomialkoeffizienten" \end_inset \end_layout \begin_layout Standard Binomialkoeffizienten können mit dem Befehl \series bold \backslash binom \series default \begin_inset LatexCommand index name "Befehle ! B ! \\textbackslash binom" \end_inset oder über das Untermenü des Mathe-Werkzeugleistenknopfs \begin_inset Graphics filename ../../images/math/frac-square.png scale 85 \end_inset eingefügt werden. \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="3" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash binom \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\binom{A}{B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash dbinom{A \begin_inset Formula $\to$ \end_inset \backslash {B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\dbinom{A}{B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Analog zu Brüchen ( \series bold \backslash frac \series default ) gibt es außer \series bold \backslash binom \series default noch die Befehle \series bold \backslash dbinom \begin_inset LatexCommand index name "Befehle ! D ! \\textbackslash dbinom" \end_inset \series default und \series bold \backslash tbinom \series default \begin_inset LatexCommand index name "Befehle ! T ! \\textbackslash tbinom" \end_inset , die folgendes Befehlsschema besitzen: \end_layout \begin_layout Standard \series bold \backslash dbinom{Zähler}{Nenner} \series default bzw. \series bold \backslash tbinom{Zähler}{Nenner} \end_layout \begin_layout Subsection Fallunterscheidungen \begin_inset LatexCommand index name "Fallunterscheidungen" \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="3" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash cases \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset Formula $\to$ \end_inset B>0 \begin_inset LatexCommand index name "Befehle ! C ! \\textbackslash cases" \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\begin{cases} A & B>0\end{cases}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash cases \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset Strg-Enter \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\begin{cases} A & \textrm{für }x>0\\ B & \textrm{für }x=0\end{cases}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Nach der Eingabe von \series bold \backslash cases \series default oder der Benutzung des Mathe-Werkzeugleistenknopfs \begin_inset Graphics filename ../../images/math/cases.png scale 85 \end_inset können mit \family sans Strg-Enter \family default oder dem Tabellen-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/tabular-feature_append-row.png scale 85 \end_inset neue Zeilen erstellt werden. \begin_inset Foot status collapsed \begin_layout Standard Umlaute in Formeln, wie in obiger Tabelle, sind in \begin_inset LatexCommand ref reference "sub:Akzente-für-ein" \end_inset beschrieben. \end_layout \end_inset \end_layout \begin_layout Standard Der Befehl \series bold \backslash cases \series default ist auch über das Menü \family sans Einfügen\SpecialChar \menuseparator Mathe\SpecialChar \menuseparator Cases-Umgebung \family default verfügbar. \end_layout \begin_layout Subsection Verneinungen \begin_inset LatexCommand index name "Verneinungen" \end_inset \end_layout \begin_layout Standard Durch die Eingabe von \series bold \backslash not \series default \begin_inset LatexCommand index name "Befehle ! N ! \\textbackslash not" \end_inset kann jedes beliebige Zeichen durchgestrichen dargestellt werden. Die Zeichen werden quasi mit einem Schrägstrich akzentuiert. \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash not= \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\not=$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash not \backslash le \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\not\le$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash not \backslash parallel \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\not\parallel$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Das letzte Beispiel zeigt, dass nicht alle Verneinungen gut aussehen. Deswegen gibt es für Einige spezielle Befehle (siehe \begin_inset LatexCommand ref reference "sub:Mathematische-Symbole" \end_inset und \begin_inset LatexCommand ref reference "sec:Relationen" \end_inset ). \end_layout \begin_layout Subsection Platzhalter \begin_inset LatexCommand label name "sub:Platzhalter" \end_inset \begin_inset LatexCommand index name "Platzhalter\\vspace{4mm}" \end_inset \begin_inset LatexCommand index name "chemische Zeichen ! Isotope" \end_inset \begin_inset LatexCommand index name "Isotope|see{chemische Zeichen}" \end_inset \end_layout \begin_layout Standard Möchte man z.\InsetSpace \thinspace{} B. Isotope \begin_inset Foot status collapsed \begin_layout Standard Weiteres zu chemischen Symbolen steht in \begin_inset LatexCommand ref reference "sub:Chemische-Symbole-und" \end_inset . \end_layout \end_inset darstellen, tritt folgendes Problem auf: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="2" columns="2"> <features> <column alignment="center" valignment="top" width="0pt"> <column alignment="center" valignment="top" width="0pt"> <row> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard durch Hoch- und Tiefstellen erzeugte Indizes: \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $_{9}^{19}\mathrm{F}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard korrekte Indizes: \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $_{\phantom{1}9}^{19}\mathrm{F}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur \end_layout \begin_layout Standard als Abstandhalter. \end_layout \end_inset \end_layout \begin_layout Standard Der kürzere Index wird standardmäßig unter oder über das erste Zeichen des längeren Index gesetzt. Um das zu verhindern gibt es den Befehl \series bold \backslash phantom \series default \begin_inset LatexCommand index name "Befehle ! P ! \\textbackslash phantom" \end_inset oder den Mathe-Werkzeugleistenknopf\InsetSpace \thinspace{} \begin_inset Foot status collapsed \begin_layout Standard zu finden im Untermenü des Mathe-Werkzeugleistenknopfs \begin_inset Graphics filename ../../images/math/space.png scale 85 \end_inset \end_layout \end_inset \begin_inset Graphics filename ../../images/math/phantom.png scale 85 \end_inset , der ein oder mehrere Phantomzeichen erstellt. Wenn \series bold \backslash phantom \series default eingegeben wird, erscheint ein kleines blaues Kästchen, dass von zwei roten Pfeilen überlagert wird. Die Pfeile geben an, dass die komplette Breite und Höhe des Kästcheninhalts als Leerraum erstellt wird. Phantomzeichen sind dementsprechend Platzhalter mit der Größe der angegebenen Zeichen. \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard ^19 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset _ \backslash phantom \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 1 \begin_inset Formula $\to$ \end_inset 9 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset F \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard ^235 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset _ \backslash phantom \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 23 \begin_inset Formula $\to$ \end_inset 9 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset F \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Lambda^ \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash phantom \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset ii \begin_inset Formula $\to$ \end_inset t \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset _MMt \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Des Weiteren gibt es noch die Befehle \series bold \backslash vphantom \series default \begin_inset LatexCommand index name "Befehle ! V ! \\textbackslash vphantom" \end_inset (Werkzeugleistenknopf \InsetSpace ~ \begin_inset Graphics filename ../../images/math/vphantom.png scale 85 \end_inset ) und \series bold \backslash hphantom \series default \begin_inset LatexCommand index name "Befehle ! H ! \\textbackslash hphantom" \end_inset (Werkzeugleistenknopf \InsetSpace ~ \begin_inset Graphics filename ../../images/math/hphantom.png scale 85 \end_inset ). \series bold \backslash hphantom \series default erzeugt nur Platz für die maximale Höhe der im Kästchen angegebenen Zeichen, nicht jedoch für deren Breite. Bei \series bold \backslash vphantom \series default wird nur Platz mit der Breite des Kästchens erstellt. Daher haben die Kästchen der beiden Befehle nur einen roten Pfeil. \end_layout \begin_layout Standard Zum Beispiel erzeugt \series bold \backslash vphantom \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series bold a \backslash int \series default Platz der Höhe des Integralzeichens, \begin_inset Foot status collapsed \begin_layout Standard Der Befehl \series bold \backslash int \series default erzeugt ein Integralzeichen, siehe \begin_inset LatexCommand ref reference "sub:Große-Operatoren" \end_inset . \end_layout \end_inset da dieses das größere Zeichen ist. Eine Beispielanwendung ist in \begin_inset LatexCommand ref reference "sub:Mehrzeilige-Klammern" \end_inset zu finden. \end_layout \begin_layout Subsection Linien \begin_inset LatexCommand index name "Linien" \end_inset \begin_inset LatexCommand index name "Formel ! unterstrichene" \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash overline \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A+B \begin_inset LatexCommand index name "Befehle ! O ! \\textbackslash overline" \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\overline{A+B}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash underline \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A+B \begin_inset LatexCommand index name "Befehle ! U ! \\textbackslash underline" \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\underline{A+B}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash overline \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash underline \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A+B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\overline{\underline{A+B}}\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Beim letzten Beispiel spielt es keine Rolle, ob man zuerst \series bold \backslash overline \series default oder \series bold \backslash underline \series default eingibt. \end_layout \begin_layout Standard Will man Ergebnisse doppelt unterstreichen, verwendet man zweimal hintereinander \begin_inset ERT status collapsed \begin_layout Standard \backslash linebreak \end_layout \end_inset \series bold \backslash underline \series default . \end_layout \begin_layout Standard Man kann bis zu 6 Striche über oder unter Zeichen setzen. \end_layout \begin_layout Subsection Fortsetzungspunkte \begin_inset LatexCommand index name "Fortsetzungspunkte" \end_inset \end_layout \begin_layout Standard Es gibt unterschiedliche Arten von Fortsetzungspunkten. \begin_inset Foot status collapsed \begin_layout Standard In der Mathe-Werkzeugleiste zu finden im Untermenü des Knopfs \begin_inset Graphics filename ../../images/math/ldots.png scale 85 \end_inset \end_layout \end_inset Für Aufzählungen verwendet man unten sitzende Punkte ( \series bold \backslash ldots \series default \begin_inset LatexCommand index name "Befehle ! L ! \\textbackslash ldots" \end_inset ), während man für Operationen Punkte braucht, die auf der selben Höhe wie die Operatoren sind ( \series bold \backslash cdots \series default \begin_inset LatexCommand index name "Befehle ! C ! \\textbackslash cdots" \end_inset ). Verwendet man den Befehl \series bold \backslash dots \series default \begin_inset LatexCommand index name "Befehle ! D ! \\textbackslash dots" \end_inset , entscheidet LaTeX anhand des nachfolgenden Zeichens, welche Punktart verwendet wird. \newpage \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="8" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard A_1 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset , \backslash dots \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset ,A_n \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A_{1},\dots,A_{n}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard A_1 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset + \backslash dots \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset +A_n \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A_{1}+\dots+A_{n}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard A_1 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset , \backslash ldots \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset ,A_n \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A_{1},\ldots,A_{n}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard A_1 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset + \backslash cdots \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset +A_n \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A_{1}+\cdots+A_{n}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash vdots \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\vdots$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ddots \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\ddots$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 3 \series bold × \series default 3\InsetSpace \thinspace{} Matrix mit obigen Befehlen \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Die im Menü \family sans Einfügen\SpecialChar \menuseparator Sonderzeichen \family default verfügbaren Fortsetzungspunkte sind \series bold \backslash ldots \series default . \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Speziell für Matrizen gibt es Fortsetzungspunkte, die sich über mehrere Spalten erstrecken. Man erhält sie mit dem Befehl \series bold \backslash hdotsfor \series default \begin_inset LatexCommand index name "Befehle ! H ! \\textbackslash hdotsfor" \end_inset , der folgendes Schema besitzt: \end_layout \begin_layout Standard \series bold \backslash hdotsfor[Abstand]{Anzahl der Spalten} \end_layout \begin_layout Standard Anzahl der Spalten gibt an, über wie viele Spalten sich die Punkte erstrecken sollen. Abstand ist ein Faktor, der den Punktabstand festlegt. \end_layout \begin_layout Standard In folgender Matrix wurde in das erste Kästchen der zweiten Zeile der Befehl \series bold \backslash hdotsfor[2]{4} \series default eingegeben, um Fortsetzungspunkte mit doppelt so großem Punktabstand wie beim Befehl \series bold \backslash dots \series default zu erhalten: \begin_inset Formula \[ \left(\begin{array}{cccc} A & B & C & D\\ \hdotsfor[2]{4}\\ q & w & e & r\end{array}\right)\] \end_inset Es ist zu beachten, dass die Matrixfelder über die sich die Punkte erstrecken sollen leer sein müssen, ansonsten kommt es zu LaTeX-Fehlern. \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Des Weiteren kann man mit dem Befehl \series bold \backslash dotfill \series default \begin_inset LatexCommand index name "Befehle ! D ! \\textbackslash dotfill" \end_inset den Rest einer Zeile mit Punkten füllen. Die Wirkungsweise des Befehls entspricht der von \series bold \backslash hfill \series default , siehe \begin_inset LatexCommand ref reference "sub:Variabler-Leerraum" \end_inset . \end_layout \begin_layout Standard Z.\InsetSpace \thinspace{} B. ergibt der Befehl \series bold A \backslash dotfill \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset B \end_layout \begin_layout Standard \begin_inset Formula $A\dotfill B$ \end_inset \end_layout \begin_layout Standard Analog dazu gibt es für eine Linie den Befehl \series bold \backslash hrulefill \series default \begin_inset LatexCommand index name "Befehle ! H ! \\textbackslash hrulefill" \end_inset : \end_layout \begin_layout Standard \begin_inset Formula $A\hrulefill B$ \end_inset \end_layout \begin_layout Standard Um die Befehle für Text zu verwenden, müssen sie im TeX-Modus eingegeben werden. \end_layout \begin_layout Section Matrizen \begin_inset LatexCommand label name "sec:Matrizen" \end_inset \begin_inset LatexCommand index name "Matrizen" \end_inset \end_layout \begin_layout Standard Matrizen können über den Mathe-Werkzeugleistenknopf \family sans \family default \begin_inset Graphics filename ../../images/dialog-show_mathmatrix.png scale 85 \end_inset oder das Menü \family sans Einfügen\SpecialChar \menuseparator Mathe\SpecialChar \menuseparator Matrix \family default eingefügt werden. Sie werden nach der Spalten- und Zeilenanzahl und der Ausrichtung gefragt. Die vertikale Ausrichtung ist dabei nur bei Matrizen in eingebetteten Formeln von Bedeutung: \end_layout \begin_layout Standard Die erste Matrix ist oben \begin_inset Formula $\begin{array}[t]{cccc} A & D & G & J\\ B & E & H & K\\ C & F & I & L\end{array}$ \end_inset , die zweite mittig \begin_inset Formula $\begin{array}{cccc} A & D & G & J\\ B & E & H & K\\ C & F & I & L\end{array}$ \end_inset und die dritte unten \begin_inset Formula $\begin{array}[b]{cccc} A & D & G & J\\ B & E & H & K\\ C & F & I & L\end{array}$ \end_inset ausgerichtet. \end_layout \begin_layout Standard Die horizontale Ausrichtung gibt an, wie die Spalteneinträge ausgerichtet werden sollen. Dazu wird für jede Spalte ein Buchstabe eingegeben. \emph on l \emph default steht für linksbündig, \emph on c \emph default für mittig und \emph on r \emph default für rechtsbündig. Möchte man z.\InsetSpace \thinspace{} B. eine 4 \series bold × \series default 4\InsetSpace ~ Matrix erstellen, bei der der Inhalt der ersten Spalte linksbündig, der Inhalt der zweiten und dritten mittig und der Inhalt der letzten rechtsbündig ausgerichtet ist, gibt man für die horizontale Ausrichtung \series bold lccr \series default an. Normalerweise sind in einer Matrix alle Spalteninhalte zentriert, weswegen die Voreinstellung für jede Spalte ein \series bold c \series default ist. \end_layout \begin_layout Standard Horizontale Ausrichtung: \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 Um nachträglich Zeilen und Spalten hinzuzufügen oder zu entfernen, kann man die Mathe-Werkzeugleistenknöpfe \begin_inset Graphics filename ../../images/tabular-feature_append-row.png scale 85 \end_inset , \begin_inset Graphics filename ../../images/tabular-feature_delete-row.png scale 85 \end_inset , usw.\InsetSpace ~ oder das Menü \family sans Bearbeiten\SpecialChar \menuseparator Zeilen & Spalten \family default verwenden. Neue Zeilen können auch mit \family sans Strg-Enter \family default erstellt werden. \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Klammern um eine Matrix können entweder mit den Befehlen \series bold \backslash left \series default \begin_inset LatexCommand index name "Befehle ! L ! \\textbackslash left" \end_inset und \series bold \backslash right \series default \begin_inset LatexCommand index name "Befehle ! R ! \\textbackslash right" \end_inset erstellt werden (Tastenkürzel \family sans Alt-m\InsetSpace ~ Klammer \family default ), siehe \begin_inset LatexCommand ref reference "sub:Automatische-Klammergrößen" \end_inset , oder man verwendet folgende Befehle: \begin_inset VSpace bigskip \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bmatrix \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} Matrix \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Bmatrix \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} Matrix \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash pmatrix \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} Matrix \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash vmatrix \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} Matrix \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Vmatrix \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} Matrix \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash matrix \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 2 \series bold × \series default 2\InsetSpace \thinspace{} Matrix \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Wurde z.\InsetSpace \thinspace{} B. \series bold \backslash vmatrix \series default eingegeben, erscheint ein blaues Kästchen zwischen zwei senkrechten Strichen, in das die Matrix eingefügt wird. \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Da alle mehrzeiligen Formeln Matrizen sind, kann man die in \begin_inset LatexCommand ref reference "sub:Spaltenabstand" \end_inset beschriebene Länge \series bold \backslash arraycolsep \series default \begin_inset LatexCommand index name "Befehle ! A ! \\textbackslash arraycolsep" \end_inset auch zur Änderung des Spaltenabstands von Matrizen verwenden. \end_layout \begin_layout Standard Möchte man den Zeilenabstand ändern, verwendet man den Befehl \series bold \backslash arraystretch \series default \begin_inset LatexCommand index name "Befehle ! A ! \\textbackslash arraystretch" \end_inset . Dieser wird folgendermaßen benutzt: \end_layout \begin_layout Standard \series bold \backslash renewcommand{ \backslash arraystretch}{Dehnungsfaktor} \begin_inset LatexCommand index name "Befehle ! R ! \\textbackslash renewcommand" \end_inset \end_layout \begin_layout Standard Der Befehl \series bold \backslash renewcommand \series default weist dabei dem vordefinierten Befehl \series bold \backslash arraystretch \series default den Dehnungsfaktor zu. Möchte man z.\InsetSpace \thinspace{} B. den Zeilenabstand verdoppeln, gibt man für den Faktor eine 2 an. Dieser wird dann für alle folgenden Matrizen verwendet. Um wieder zum ursprünglichen Abstand zurückzukehren, weist man \series bold \backslash arraystretch \series default den Faktor 1 zu. \end_layout \begin_layout Standard Um Matrizen in eine Textzeile zu setzen, benutzt man den Befehl \series bold \backslash smallmatrix \series default \begin_inset LatexCommand index name "Befehle ! S ! \\textbackslash smallmatrix" \end_inset . Gibt man ihn in eine Formel ein, erscheint ein blaues Kästchen mit zwei gestrichelten Linien. In dieses Kästchen wird die Matrix eingegeben. Man verwendet stattdessen das Menü \family sans Bearbeiten\SpecialChar \menuseparator Zeilen\InsetSpace ~ &\InsetSpace ~ Spalten \family default oder die Mathe-Werkzeugleiste um neue Spalten zu erstellen. Neue Zeilen können auch mit \family sans Strg-Enter \family default erstellt werden. \end_layout \begin_layout Standard Dies ist eine Matrix \begin_inset Formula $\left(\begin{smallmatrix}A & B\\ C & D\end{smallmatrix}\right)$ \end_inset in einer Textzeile. \end_layout \begin_layout Section Klammern und Begrenzungszeichen \begin_inset LatexCommand index name "Klammern" \end_inset \begin_inset LatexCommand index name "Begrenzungszeichen" \end_inset \end_layout \begin_layout Subsection Vertikale Klammern und Begrenzungszeichen \begin_inset LatexCommand index name "Klammern ! vertikale" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="9" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard ( \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $($ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard { \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\{$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard [ \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $[$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash langle \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\langle$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash lceil \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\lceil$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash lfloor \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\lfloor$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard / \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $/$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard | \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $|$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="9" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard ) \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $)$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard } \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard ] \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $]$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash rangle \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\rangle$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash rceil \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\rceil$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash rfloor \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\rfloor$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash \backslash \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\backslash$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash | \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\|$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard \series medium \begin_inset Note Greyedout status open \begin_layout Standard \series bold Achtung: \series default Im TeX-Modus muss für den Backslash der Befehl \series bold \backslash textbackslash \series default \begin_inset LatexCommand index name "Befehle ! T ! \\textbackslash textbackslash" \end_inset verwendet werden, denn der Befehl \series bold \backslash \backslash \series default steht dort für einen Zeilenumbruch. \end_layout \end_inset \end_layout \begin_layout Standard Für alle oben aufgelisteten Zeichen kann die Größe mit den in den folgenden zwei Unterkapiteln beschriebenen Befehlen eingestellt werden. Dabei können dann statt den Befehlen \series bold \backslash langle \series default und \series bold \backslash rangle \series default direkt die Zeichen < und > verwendet werden. \end_layout \begin_layout Subsubsection Manuelle Klammergrößen \begin_inset LatexCommand label name "sub:Manuelle-Klammergrößen" \end_inset \begin_inset LatexCommand index name "Klammergrößen ! manuelle" \end_inset \end_layout \begin_layout Standard Möchte man die Klammergröße manuell festlegen, kann man dies mittels der LaTeX-Befehle \series bold \backslash big \series default \begin_inset LatexCommand index name "Befehle ! B ! \\textbackslash big" \end_inset , \series bold \backslash Big \series default , \series bold \backslash bigg \series default und \series bold \backslash Bigg \series default tun. \series bold \backslash big \series default steht hierbei für die kleinste und \series bold \backslash Bigg \series default für die größte Klammergröße. \end_layout \begin_layout Standard Diese Befehle werden benutzt um Klammerebenen optisch hervorzuheben: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="2" columns="2"> <features> <column alignment="center" valignment="top" width="0pt"> <column alignment="center" valignment="top" width="0pt"> <row> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard einheitliche Klammergröße: \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $((A+B)(A-B))^{C}\raisebox{-4mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard besser sieht das so aus: \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Big((A+B)(A-B)\Big)^{C}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur \end_layout \begin_layout Standard als Abstandhalter. \end_layout \end_inset \end_layout \begin_layout Standard Für die zweite Formel wurde der Befehl \series bold \backslash Big((A+B)(A-B) \backslash Big)^ \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset C \series default verwendet. \end_layout \begin_layout Standard Hier alle Klammergrößen in der Übersicht: \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 leer \end_layout \end_inset \backslash sin(x) \backslash Big]^ \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \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 Es gibt außer den \series bold \backslash big \series default -Befehlen noch die Variante \series bold \backslash bigm \series default \begin_inset LatexCommand index name "Befehle ! B ! \\textbackslash bigm" \end_inset , die etwas mehr Leerraum zwischen Klammer und Klammerinhalt erzeugt und die Variante \series bold \backslash bigl \series default - \series bold \backslash bigr \series default \begin_inset LatexCommand index name "Befehle ! B ! \\textbackslash bigl - \\textbackslash bigr" \end_inset , die keinen zusätzlichen Leerraum erzeugt. Das \emph on l \emph default am Ende des Befehls \series bold \backslash bigl \series default steht für eine linke Klammer; für eine rechte Klammer wird dieses durch ein \emph on r \emph default ersetzt. Eine linke oder rechte Klammer kann je eine öffnende oder schließende Klammer sein. \end_layout \begin_layout Standard In der folgenden Tabelle sind die Varianten miteinander verglichen: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="5" columns="2"> <features> <column alignment="center" valignment="middle" leftline="true" width="0"> <column alignment="center" valignment="middle" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Bigm( \backslash bigm( \backslash ln(3x) \backslash bigm)^2 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash Bigm) \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Big( \backslash big( \backslash ln(3x) \backslash big)^2 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash Big) \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Bigl( \backslash bigl( \backslash ln(3x) \backslash bigr)^2 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash Bigr) \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigl) \backslash ln(3x) \backslash bigr( \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\bigl)\ln(3x)\bigr(\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Subsubsection Automatische Klammergrößen \begin_inset LatexCommand label name "sub:Automatische-Klammergrößen" \end_inset \begin_inset LatexCommand index name "Klammergrößen ! automatische" \end_inset \end_layout \begin_layout Standard Klammern variabler Größe können mit den Befehlen \series bold \backslash left \series default \begin_inset LatexCommand index name "Befehle ! L ! \\textbackslash left" \end_inset und \series bold \backslash right \series default \begin_inset LatexCommand index name "Befehle ! R ! \\textbackslash right" \end_inset oder über den Mathe-Werkzeugleistenknopf \family sans \family default \begin_inset Graphics filename ../../images/dialog-show_mathdelimiter.png scale 85 \end_inset eingefügt werden. Auf \series bold \backslash left \series default und \series bold \backslash right \series default muss unmittelbar die gewünschte Klammer folgen. Die Klammergröße wird dann bei der Ausgabe automatisch berechnet. \end_layout \begin_layout Standard \align center normale Klammer: Der Befehl \series bold \backslash ln( \backslash frac \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset C \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset ) \series default ergibt \begin_inset Formula \[ \ln(\frac{A}{C})\] \end_inset \end_layout \begin_layout Standard \align center mehrzeilige Klammer: Der Befehl \series bold \backslash ln \backslash left( \backslash frac \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset C \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash right) \series default ergibt \begin_inset Formula \[ \ln\left(\frac{A}{C}\right)\] \end_inset \end_layout \begin_layout Standard An Stelle von \series bold \backslash left \series default und \series bold \backslash right \series default kann man die Tastenkürzel \family sans Alt-m\InsetSpace ~ Klammer \family default verwenden. Das hat den Vorteil, dass man in LyX sofort die wahre Klammergröße sieht und dass die rechte Klammer gleich mit erstellt wird. \newline Der Befehl für das letzte Beispiel würde dann lauten: \series bold \backslash ln Alt-m \series default \series bold ( \backslash frac \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset C \end_layout \begin_layout Standard Will man nur eine Klammerhälfte erstellen, schreibt man für die weggelassene Klammer einen Punkt. So ergibt z.\InsetSpace \thinspace{} B. der Befehl \series bold \backslash left. \backslash frac \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash right} \series default \InsetSpace \thinspace{} : \series bold \begin_inset Formula \[ \left.\frac{A}{B}\right\} \] \end_inset \series default Die Befehle \series bold \backslash left \series default und \series bold \backslash right \series default werden beim Neu laden des Dokuments von LyX in Klammern der richtigen Größe umgewandelt. Für eine weggelassene Klammer erscheint in LyX eine gestrichelte Linie. \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Da alle gängigen LaTeX-Distributionen eTeX, eine Erweiterung von LaTeX, verwenden, steht für alle Klammern und Begrenzungszeichen zusätzlich der Befehl \series bold \backslash middle \series default \begin_inset LatexCommand index name "Befehle ! M ! \\textbackslash middle" \end_inset zur Verfügung. Durch diesen wird das folgende Zeichen an die Höhe der umgebenden Klammern angepasst, was z.\InsetSpace \thinspace{} B. für physikalische Vektoren von Nutzen ist: \begin_inset Formula \[ \left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \] \end_inset Für physikalische Vektoren gibt es ein spezielles LaTeX-Paket, das in \begin_inset LatexCommand ref reference "sub:Physikalische-Vektoren" \end_inset beschrieben ist. \end_layout \begin_layout Subsection Horizontale Klammern \begin_inset LatexCommand index name "Klammern ! horizontale" \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 leer \end_layout \end_inset A+B \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset ^ \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 3 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \begin_inset LatexCommand index name "Befehle ! O ! \\textbackslash overbrace" \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\overbrace{A+B}^{3}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 leer \end_layout \end_inset A+B \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset _5 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \begin_inset LatexCommand index name "Befehle ! U ! \\textbackslash underbrace" \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\underbrace{A+B}_{5}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash overbrace \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash underbrace \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A+B_w \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset _7 \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset ^ \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset C \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\overbrace{\underbrace{A+B_{w}}_{7}}^{C}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Beim letzten Beispiel spielt es keine Rolle, ob man zuerst \series bold \backslash overbrace \series default oder \series bold \backslash underbrace \series default eingibt. \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Benötigt man Klammern, die sich überschneiden, muss man die in \begin_inset LatexCommand ref reference "sec:Mehrzeilige-Formeln" \end_inset beschriebenen mehrzeiligen Formeln verwenden: \begin_inset Formula \begin{eqnarray*} A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\ & & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*} \end_inset In die erste Zeile wird die Formel zusammen mit der ersten Klammer eingegeben. Dabei ist es wichtig, dass vor dem ersten \begin_inset Formula $d$ \end_inset der Abstandsbefehl \begin_inset Foot status collapsed \begin_layout Standard Abstandsbefehle sind in \begin_inset LatexCommand ref reference "sub:Vordefinierter-Leerraum" \end_inset erklärt. \end_layout \end_inset \series bold \backslash : \series default eingegeben wird, denn die nach dem \begin_inset Formula $q$ \end_inset endende Klammer verhindert, dass das nachfolgende \begin_inset Quotes gld \end_inset + \begin_inset Quotes grd \end_inset von Leerraum umgeben ist. \begin_inset Foot status collapsed \begin_layout Standard weil eine Klammer nicht als Zeichen gilt, siehe \begin_inset LatexCommand ref reference "sub:Binäre-Operatoren" \end_inset \end_layout \end_inset In die zweite Zeile wird die zweite Klammer eingegeben. Da sie vor dem \begin_inset Formula $b$ \end_inset beginnen soll, gibt man zuerst \series bold \backslash hphantom{gggg+ \backslash :} \series default ein. \begin_inset Foot status collapsed \begin_layout Standard mehr zu \series bold \backslash hphantom \series default siehe \begin_inset LatexCommand ref reference "sub:Platzhalter" \end_inset . \end_layout \end_inset Dieser Leerraum wird benötigt, weil das \begin_inset Quotes gld \end_inset + \begin_inset Quotes grd \end_inset in der Formel auch von Leerraum umgeben ist. Die Klammer wird unter den Befehl \series bold \backslash hphantom{bbqq+dddd} \series default gesetzt. \end_layout \begin_layout Standard Komplizierter wird es, wenn sich Klammern über und unter der Formel überschneide n, wie in folgendem Beispiel: \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 Die erste Formelzeile ist gleich der zweiten Zeile des vorigen Beispiels, mit dem Unterschied, dass sich die Klammer oben befindet. Die zweite Zeile enthält die Formel zusammen mit der zweiten Klammer. Damit sich zwischen oberer Klammer in der ersten Zeile und der Formel in der zweiten Zeile kein Leerraum befindet, muss der Zeilenabstand verändert werden. Aufgrund eines Fehlers in LyX ist dies nicht ohne Weiteres möglich \begin_inset Foot status collapsed \begin_layout Standard \begin_inset ERT status open \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{ \end_layout \end_inset LyX-Fehler #1505 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset . Es muss als Lösung des Problems der globale Formelzeilenabstand \series bold \backslash jot \series default \begin_inset LatexCommand index name "Befehle ! J ! \\textbackslash jot" \end_inset vor der Formel mit dem Befehl \series bold \backslash setlength{ \backslash jot}{-6pt} \series default im TeX-Modus auf den Wert -6\InsetSpace \thinspace{} pt geändert. Nach der Formel wird \series bold \backslash jot \series default mit demselben Befehl wieder auf den Standardwert 3\InsetSpace \thinspace{} pt zurückgesetzt. Genaueres zum Zeilenabstand in Formeln ist in \begin_inset LatexCommand ref reference "sub:Zeilenabstand" \end_inset erklärt. \end_layout \begin_layout Section Pfeile \begin_inset LatexCommand index name "Pfeile" \end_inset \end_layout \begin_layout Standard Pfeile können über den Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/leftarrow.png scale 85 \end_inset oder mit den Befehlen eingefügt werden, die in den folgenden Unterkapiteln aufgelistet sind. \end_layout \begin_layout Subsection Horizontale Pfeile \begin_inset LatexCommand index name "Pfeile ! horizontale" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="8" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash gets \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\gets$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Leftarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Leftarrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash longleftarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\longleftarrow$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Longleftarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Longleftarrow$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash leftharpoonup \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\leftharpoonup$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash leftharpoondown \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\leftharpoondown$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash hookleftarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\hookleftarrow$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="8" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash to \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\to$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Rightarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Rightarrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash longrightarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\longrightarrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Longrightarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Longrightarrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash rightharpoonup \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\rightharpoonup$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash rightharpoondown \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\rightharpoondown$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash hookrightarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\hookrightarrow$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="6" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash leftrightarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\leftrightarrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Leftrightarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Leftrightarrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash longleftrightarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\longleftrightarrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Longleftrightarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Longleftrightarrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash rightleftharpoons \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\rightleftharpoons$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{25pt} \end_layout \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="5" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mapsto \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mapsto$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash longmapsto \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\longmapsto$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash leadsto \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\leadsto$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash dasharrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\dasharrow$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Als Akzent verwendete Pfeile, wie z.\InsetSpace \thinspace{} B. Vektorpfeile, sind in \begin_inset LatexCommand ref reference "sec:Akzente" \end_inset aufgelistet. \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Des Weiteren gibt es die beschriftbaren Pfeile \begin_inset LatexCommand index name "Pfeile ! beschriftbare" \end_inset \series bold \backslash xleftarrow \series default \begin_inset LatexCommand index name "Befehle ! X ! \\textbackslash xleftarrow" \end_inset und \series bold \backslash xrightarrow \series default \begin_inset LatexCommand index name "Befehle ! X ! \\textbackslash xrightarrow\\vspace{4mm}" \end_inset . Gibt man einen dieser Befehle in eine Formel ein, erscheint ein Pfeil mit zwei blauen Kästchen, in die man die Beschriftung eingeben kann. Die Pfeillänge passt sich der Breite der Beschriftung an. \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="3" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard F(a) \backslash xleftarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \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 </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard F(x) \backslash xrightarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \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 </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Subsection Vertikale und diagonale Pfeile \begin_inset LatexCommand index name "Pfeile ! diagonale" \end_inset \begin_inset LatexCommand index name "Pfeile ! vertikale" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="7" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash uparrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\uparrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Uparrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Uparrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash updownarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\updownarrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Updownarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Updownarrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Downarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Downarrow$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash downarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\downarrow$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="5" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash nearrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\nearrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash searrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\searrow$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash swarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\swarrow$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash nwarrow \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\nwarrow$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Vertikale Pfeile können auch als Begrenzungszeichen zusammen mit den in \begin_inset LatexCommand ref reference "sub:Manuelle-Klammergrößen" \end_inset und \begin_inset LatexCommand ref reference "sub:Automatische-Klammergrößen" \end_inset beschriebenen Befehlen verwendet werden. \end_layout \begin_layout Section Akzente \begin_inset LatexCommand label name "sec:Akzente" \end_inset \begin_inset LatexCommand index name "Akzente" \end_inset \end_layout \begin_layout Standard Akzente können über den Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/hat.png scale 85 \end_inset oder mit den Befehlen eingefügt werden, die in den folgenden Unterkapiteln aufgelistet sind. \end_layout \begin_layout Subsection Akzente für ein Zeichen \begin_inset ERT status collapsed \begin_layout Standard \backslash texorpdfstring{ \end_layout \end_inset \begin_inset Foot status collapsed \begin_layout Standard Akzente im Text siehe \begin_inset LatexCommand ref reference "sub:Sonderzeichen-Akzente" \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 \series bold \backslash texorpdfstring \series default dient dazu, dass die Fußnote nicht im PDF-Lesezeichen erscheint. \end_layout \begin_layout Standard Näheres zu \series bold \backslash texorpdfstring \series default steht in Kapitel \begin_inset LatexCommand ref reference "sub:Formeln-in-Überschriften" \end_inset . \end_layout \end_inset \begin_inset LatexCommand label name "sub:Akzente-für-ein" \end_inset \begin_inset LatexCommand index name "Akzente ! für ein Zeichen" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="8" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash dot \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\dot{A}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ddot \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\ddot{A}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash dddot \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\dddot{A}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ddddot{A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\ddddot{A}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash vec \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset LatexCommand index name "Vektoren" \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\vec{A}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bar \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\bar{A}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mathring \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\mathring{A}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="7" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash tilde \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\tilde{A}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash hat \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\hat{A}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash check \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\check{A}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash acute \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\acute{A}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash grave \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\grave{A}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash breve \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\breve{A}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Wenn man in einer Formel Umlaute \begin_inset LatexCommand index name "Umlaute" \end_inset erstellen will, schreibt man ein Anführungszeichen vor den Selbstlaut. Diese beiden Zeichen bilden dann für LaTeX \emph on ein \emph default Zeichen. Im Gegensatz zu \series bold \backslash ddot \series default entstehen damit \begin_inset Quotes gld \end_inset echte \begin_inset Quotes grd \end_inset Umlaute, was folgendes Beispiel zeigt: \end_layout \begin_layout Standard \begin_inset VSpace -2mm \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="3" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Quotes grd \end_inset i \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $"i$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ddot \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset i \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\ddot{i}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Ein weiterer Vorteil gegenüber \series bold \backslash ddot \series default ist, dass man Umlaute direkt in mathematischen Text konvertieren kann, denn die obigen Akzentbefehle sind \emph on im mathematischen Text\SpecialChar \- modus nicht erlaubt \emph default . Um ein akzentuiertes Zeichen in mathematischen Text zu überführen, darf nur das Zeichen unter dem Akzent umgewandelt werden. Das gilt auch für alle anderen Umwandlungen wie z.\InsetSpace \thinspace{} B. in kursiv oder fett. \end_layout \begin_layout Standard Im mathematischen Textmodus können Umlaute und andere akzentuierten Zeichen direkt eingegeben werden. \end_layout \begin_layout Subsection Akzente für Operatoren \begin_inset LatexCommand index name "Akzente ! für Operatoren" \end_inset \end_layout \begin_layout Standard Zum Akzentuieren von Operatoren gibt es die Befehle \series bold \backslash overset \series default \begin_inset LatexCommand index name "Befehle ! O ! \\textbackslash overset" \end_inset und \series bold \backslash underset \series default \begin_inset LatexCommand index name "Befehle ! U ! \\textbackslash underset" \end_inset , mit denen man Zeichen über bzw. unter einen Operator setzen kann. Mit dem Befehl \series bold \backslash sideset \series default \begin_inset LatexCommand index name "Befehle ! S ! \\textbackslash sideset" \end_inset können Zeichen vor und nach einen Operator gesetzt werden. Das Befehlsschema lautet: \end_layout \begin_layout Standard \series bold \backslash sideset{Zeichen \series default \series bold davor}{Zeichen \series default \series bold dahinter} \end_layout \begin_layout Standard \series bold \backslash sideset \series default mussen immer vor dem zu akzentuierenden Operator stehen. Es kann auch mit mehreren Zeichen und sogar mit anderen Operatoren und Symbolen akzentuiert werden. Will man mit \series bold \backslash sideset \series default z.\InsetSpace \thinspace{} B. nur Zeichen hinter einen Operator setzen, schreibt man nichts zwischen die ersten geschweiften Klammern, lässt die Klammern aber nicht weg. \end_layout \begin_layout Standard Z.\InsetSpace \thinspace{} B. ergibt der Befehl \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 leer \end_layout \end_inset \series default ^ \series bold n \series default : \begin_inset Formula \[ \sideset{}{'}\sum_{k=1}^{n}\] \end_inset \end_layout \begin_layout Standard Der Befehl \series bold \backslash overset \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash maltese \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default \begin_inset Formula $\uparrow$ \end_inset \series bold a \series default ergibt: \begin_inset Formula \[ \overset{a}{\maltese}\] \end_inset Wie man am letzten Beispiel sieht, kann man mit \series bold \backslash overset \series default bzw. \series bold \backslash underset \series default außer Operatoren auch Symbole und Zeichen akzentuieren; mit \series bold \backslash sideset \series default ist dies nicht möglich. \end_layout \begin_layout Subsection Akzente für mehrere Zeichen \begin_inset LatexCommand label name "sub:Akzente-für-mehrere" \end_inset \begin_inset LatexCommand index name "Akzente ! für mehrere Zeichen" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="5" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash overleftarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\overleftarrow{A=B}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash underleftarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\underleftarrow{A=B}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash overleftrightarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\overleftrightarrow{A=B}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash underleftrightarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\underleftrightarrow{A=B}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="5" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash overrightarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\overrightarrow{A=B}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash underrightarrow \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{5mm}{}\underrightarrow{A=B}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash widetilde \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\widetilde{A=B}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash widehat \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\widehat{A=B}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Mit diesen Befehlen können beliebig viele Zeichen akzentuiert werden. Die Akzente \begin_inset ERT status collapsed \begin_layout Standard \backslash linebreak \end_layout \end_inset \series bold \backslash widetilde \series default und \series bold \backslash widehat \series default werden aber im Ausdruck nur mit einer Länge von etwa drei Zeichen gesetzt, was folgendes Beispiel verdeutlicht: \begin_inset Formula \[ \widetilde{A+B=C-D}\] \end_inset \end_layout \begin_layout Standard Mit den im vorigen Kapitel beschriebenen Befehlen \series bold \backslash overset \series default \begin_inset LatexCommand index name "Befehle ! O ! \\textbackslash overset" \end_inset und \series bold \backslash underset \series default \begin_inset LatexCommand index name "Befehle ! U ! \\textbackslash underset" \end_inset ist es auch möglich mehrere Zeichen zu akzentuieren. Der Befehl \series bold \backslash underset \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \begin_inset Formula $\downarrow$ \end_inset *** \series default ergibt: \begin_inset Formula \[ \underset{***}{A=B}\] \end_inset \end_layout \begin_layout Section Leerraum \begin_inset LatexCommand label name "sub:Leerraum" \end_inset \begin_inset LatexCommand index name "Leerraum ! horizontaler" \end_inset \end_layout \begin_layout Subsection Vordefinierter Leerraum \begin_inset LatexCommand label name "sub:Vordefinierter-Leerraum" \end_inset \begin_inset LatexCommand index name "Leerraum ! horizontaler ! vordefiniert" \end_inset \end_layout \begin_layout Standard Ab und an ist es notwendig in einer Formel horizontalen Leerraum einzufügen. Dazu gibt man ein geschütztes Leerzeichen ein. Es erscheint ein blaues \begin_inset Quotes gld \end_inset \series bold \color blue \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default \color inherit \begin_inset Quotes grd \end_inset und man kann durch mehrfaches Drücken der Leertaste aus acht verschiedenen Leerraum-Größen wählen. Man kann die Leerräume auch über den Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/space.png scale 85 \end_inset oder mit einzelnen Befehlen aufrufen. Unabhängig vom eingegebenen Befehl kann man durch Drücken der Leertaste danach wieder aus allen Größen wählen. \end_layout \begin_layout Standard \align center \begin_inset VSpace -5mm \end_inset \begin_inset Tabular <lyxtabular version="3" rows="3" columns="7"> <features> <column alignment="center" valignment="middle" leftline="true" width="6.8cm"> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash , \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash : \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ; \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash quad \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash qquad \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ! \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" leftline="true" usebox="none" width="7cm"> \begin_inset Text \begin_layout Standard Anzahl der Leertastendrücke nach Eingabe des geschützten Leerzeichens \end_layout \end_inset </cell> <cell alignment="center" valignment="top" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 0 \end_layout \end_inset </cell> <cell alignment="center" valignment="top" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 1 \end_layout \end_inset </cell> <cell alignment="center" valignment="top" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 2 \end_layout \end_inset </cell> <cell alignment="center" valignment="top" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 3 \end_layout \end_inset </cell> <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard 4 \end_layout \end_inset </cell> <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard 5 \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\, B$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\: B$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\; B$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\quad B$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\qquad B$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\! B$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Die letzte Größe scheint überhaupt keinen Leerraum zu produzieren. In LyX ist diese allerdings auch im Gegensatz zu allen anderen rot eingefärbt, denn sie erstellt negativen Leerraum. Es gibt noch zwei weitere negative Leerräume: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="3" columns="3"> <features> <column alignment="center" valignment="middle" leftline="true" width="6.8cm"> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash negmedspace \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash negthickspace \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Anzahl der Leertastendrücke nach Eingabe des geschützten Leerzeichens \end_layout \end_inset </cell> <cell alignment="center" valignment="top" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 6 \end_layout \end_inset </cell> <cell alignment="center" valignment="top" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard 7 \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\negmedspace B$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\negthickspace B$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Negative Leerräume bewirken, dass sich benachbarte Zeichen überschneiden. Man kann auf diese Weise Ligaturen erzwingen, was z.\InsetSpace \thinspace{} B. für Summenzeichen von Nutzen ist: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="3" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sum \backslash sum \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset f_kl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sum \backslash negmedspace \backslash sum \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset f_kl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Relationen, wie z.\InsetSpace \thinspace{} B. Gleichheitszeichen, sind immer von Leerraum umgeben. Will man dies unterdrücken, schreibt man das Gleichheitszeichen in eine TeX-Klammer. Die Wirkung kann man an folgendem Beispiel gut erkennen: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="2" columns="2"> <features> <column alignment="center" valignment="top" width="0pt"> <column alignment="center" valignment="top" width="0pt"> <row> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard normale Gleichung \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A=B$ \end_inset \end_layout \end_inset </cell> </row> <row> <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \begin_inset Formula $\raisebox{5mm}{}$ \end_inset Gleichung ohne Leerraum \end_layout \end_inset </cell> <cell multicolumn="1" alignment="center" valignment="top" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A{=}B$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Der Befehl für die letzte Formel lautet: \series bold A \backslash {= \begin_inset Formula $\to$ \end_inset B \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Leerräumen werden für physikalische Einheiten benötigt, denn zwischen Wert und Einheit ist der kleinste Leerraum und kein normales Leerzeichen. Bei Einheiten im Text fügt man den kleinsten Leerraum über das Menü \family sans Einfügen\SpecialChar \menuseparator Formatierung\SpecialChar \menuseparator Kleiner\InsetSpace ~ Abstand \family default (Tastenkürzel \family sans Strg-Shift-Leertaste \family default ) ein. \end_layout \begin_layout Standard Ein Beispiel zur Veranschaulichung: \end_layout \begin_layout Standard \begin_inset Tabular <lyxtabular version="3" rows="2" columns="2"> <features> <column alignment="left" valignment="top" width="0"> <column alignment="left" valignment="top" width="0"> <row> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 24 kW \begin_inset Formula $\cdot$ \end_inset h \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Leerzeichen zwischen Wert und Einheit \end_layout \end_inset </cell> </row> <row> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 24\InsetSpace \thinspace{} kW \begin_inset Formula $\cdot$ \end_inset h \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard kleinster Leerraum zwischen Wert und Einheit \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Subsection Variabler Leerraum \begin_inset ERT status collapsed \begin_layout Standard \backslash texorpdfstring{ \end_layout \end_inset \begin_inset Foot status collapsed \begin_layout Standard für vertikalen Leerraum in Formeln siehe \begin_inset LatexCommand ref reference "sub:Zeilenabstand" \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 \series bold \backslash texorpdfstring \series default dient dazu, dass die Fußnote nicht mit im PDF-Lesezeichen erscheint. \end_layout \begin_layout Standard Näheres zu \series bold \backslash texorpdfstring \series default steht in Kapitel \begin_inset LatexCommand ref reference "sub:Formeln-in-Überschriften" \end_inset . \end_layout \end_inset \begin_inset LatexCommand label name "sub:Variabler-Leerraum" \end_inset \begin_inset LatexCommand index name "Leerraum ! horizontaler ! variabel" \end_inset \end_layout \begin_layout Standard Leerraum mit vorgegebener Länge lässt sich in LyX mit dem Befehl \series bold \backslash hspace{Länge} \series default \begin_inset LatexCommand index name "Befehle ! H ! \\textbackslash hspace" \end_inset einfügen. Dabei können alle Längeneinheiten verwendet werden, die in \begin_inset LatexCommand ref reference "tab:Verwendete-Einheiten" \end_inset aufgelistet sind, mit Ausnahme der Einheit \begin_inset Quotes gld \end_inset mu \begin_inset Quotes grd \end_inset . Die Länge darf auch negativ sein. Um so viel Leerraum einzufügen, dass die Formel allen verfügbaren Platz einnimmt, benutzt man den Befehl \series bold \backslash hfill \series default \begin_inset LatexCommand index name "Befehle ! H ! \\textbackslash hfill" \end_inset . \end_layout \begin_layout Standard \begin_inset VSpace -1mm \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A=B\hspace{3cm}A\not=C$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard A \backslash hspace{-1mm \begin_inset Formula $\to$ \end_inset A \backslash not=A \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\hspace{-1mm}A\not=A$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard A=A \backslash hfill \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset B=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A=A\hfill B=B$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Im letzten Beispiel ist der verfügbare Platz durch die Länge des längsten Spalteneintrags der Tabelle vorgegeben. In einer eingebetteten Formel ist der Platz von der Länge der Zeile abhängig, in die \series bold \backslash hfill \series default eingegeben wird. Füllt eine Zeile die Breite komplett aus, wird demnach kein Leerraum erstellt. \series bold \backslash hfill \series default wirkt in abgesetzten Formeln nur, wenn der Formelstil \series bold Eingerückt \series default eingestellt ist. (Formelstile sind in \begin_inset LatexCommand ref reference "sec:Formelstile" \end_inset erklärt.) \end_layout \begin_layout Standard Die Befehle \series bold \backslash hspace \series default und \series bold \backslash hfill \series default können auch im TeX-Modus eingegeben werden, um sie für Text zu verwenden: \end_layout \begin_layout Standard Dies ist eine Zeile mit \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{2cm} \end_layout \end_inset 2\InsetSpace \thinspace{} cm Leerraum. \end_layout \begin_layout Standard Dies ist eine Zeile mit \hfill maximalem Leerraum. \end_layout \begin_layout Standard Im letzten Beispiel wurde \series bold \backslash hfill \series default über das Menü \family sans Einfügen\SpecialChar \menuseparator Formatierung\SpecialChar \menuseparator Variabler horiz. Abstand \family default eingefügt, was in Formeln nicht möglich ist. Das hat den Vorteil, dass man in LyX direkt sieht, dass es sich um einen gedehnten Leerraum handelt. \end_layout \begin_layout Standard Befinden sich die Befehle am Anfang einer Zeile, jedoch nicht am Anfang eines Absatzes, werden sie von LaTeX ignoriert. Um das zu verhindern, verwendet man statt \series bold \backslash hspace \series default den Befehl \series bold \backslash hspace* \series default . Bei \series bold \backslash hfill \series default fügt man vor dem Befehl einen Zeilenumbruch und im TeX-Modus mit dem Befehl \series bold \backslash vphantom{} \series default einen leeren Platzhalter \series bold \begin_inset Foot status collapsed \begin_layout Standard Platzhalter siehe \begin_inset LatexCommand ref reference "sub:Platzhalter" \end_inset \end_layout \end_inset \series default ein. \end_layout \begin_layout Subsection Leerraum neben eingebetteten Formeln \begin_inset LatexCommand index name "Leerraum ! neben eingebetteten Formeln" \end_inset \end_layout \begin_layout Standard Über die Länge \series bold \backslash mathsurround \begin_inset LatexCommand index name "Befehle ! M ! \\textbackslash mathsurround" \end_inset \series default lässt sich der Leerraum einstellen, der neben eingebettete Formeln gesetzt wird. Der Wert einer Länge wird mit dem Befehl \series bold \backslash setlength \begin_inset LatexCommand index name "Befehle ! S ! \\textbackslash setlength" \end_inset \series default gesetzt. Dieser besitzt folgendes Befehlsschema: \end_layout \begin_layout Standard \series bold \backslash setlength{Längenname}{Wert} \end_layout \begin_layout Standard Um \series bold \backslash mathsurround \series default den Wert 5\InsetSpace \thinspace{} mm zuzuweisen, gibt man im TeX-Modus den Befehl \end_layout \begin_layout Standard \series bold \backslash setlength{ \backslash mathsurround}{5mm} \end_layout \begin_layout Standard ein. Neben alle eingebetteten Formeln, die auf den Befehl folgen, wird nun 5\InsetSpace \thinspace{} mm Leerraum gesetzt: \begin_inset ERT status collapsed \begin_layout Standard \backslash setlength{ \backslash mathsurround}{5mm} \end_layout \end_inset \end_layout \begin_layout Standard Dies ist eine Zeile in der sich \begin_inset Formula $A=B$ \end_inset eine Formel mit 5\InsetSpace \thinspace{} mm umgebendem Leerraum befindet. \begin_inset ERT status collapsed \begin_layout Standard \backslash setlength{ \backslash mathsurround}{0pt} \end_layout \end_inset \end_layout \begin_layout Standard Um wieder zum voreingestellten Wert zurückzukehren, setzt man \series bold \backslash mathsurround \series default auf den Wert 0\InsetSpace \thinspace{} pt. \end_layout \begin_layout Section Boxen und Rahmen \begin_inset LatexCommand index name "Boxen" \end_inset \begin_inset LatexCommand index name "Rahmen | see {Boxen}" \end_inset \end_layout \begin_layout Standard Boxen für Text sind im Kapitel \family typewriter Boxen \family default im Handbuch \family typewriter Eingebettete\InsetSpace ~ Objekte \family default beschrieben. \end_layout \begin_layout Subsection Boxen mit Rahmen \begin_inset LatexCommand label name "sub:Boxen-mit-Rahmen" \end_inset \begin_inset LatexCommand index name "Boxen ! mit Rahmen" \end_inset \end_layout \begin_layout Standard Es ist möglich Formeln oder Teile davon mit den Befehlen \series bold \backslash fbox \series default \begin_inset LatexCommand index name "Befehle ! F ! \\textbackslash fbox" \end_inset und \series bold \backslash boxed \series default \begin_inset LatexCommand index name "Befehle ! B ! \\textbackslash boxed" \end_inset zu umranden. \end_layout \begin_layout Standard Gibt man einen dieser Befehle in eine Formel ein, erscheint ein Eingabefeld in einem Rahmen. Bei \series bold \backslash fbox \series default muss in diesem Eingabefeld mit \family sans Strg-m \family default noch eine Formel erstellt werden \begin_inset Foot status collapsed \begin_layout Standard Aufgrund eines Fehlers in LyX ist es nicht möglich mit \family sans Strg-m \family default eine neue Formel zu erzeugen, siehe \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{ \end_layout \end_inset LyX-Fehler #1435 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset . \end_layout \end_inset , denn der Inhalt dieser Box wird sonst als mathematischer Text behandelt. Verwendet man \series bold \backslash boxed \series default , wird automatisch im Rahmen eine neue Formel erzeugt. \end_layout \begin_layout Standard Der Befehl \series bold \backslash fbox \series default ist nicht zur Umrandung von abgesetzten Formeln geeignet, denn die Formel wird dann immer in Textzeilengröße gesetzt. Im Gegensatz dazu ist \series bold \backslash boxed \series default nicht zur Umrandung von Formeln in einer Textzeile geeignet, denn die Formel wird dann immer in der Größe einer abgesetzten Formel gesetzt. \end_layout \begin_layout Standard Als Erweiterung zu \series bold \backslash fbox \series default gibt es den Befehl \series bold \backslash framebox \series default \begin_inset LatexCommand index name "Befehle ! F ! \\textbackslash framebox" \end_inset , bei dem man zusätzlich die Rahmenbreite und die Ausrichtung einstellen kann. \series bold \backslash framebox \series default wird nach folgendem Schema verwendet: \end_layout \begin_layout Standard \series bold \backslash framebox[Rahmenbreite][Position]{Boxinhalt} \end_layout \begin_layout Standard Die Position kann entweder \emph on l \emph default oder \emph on r \emph default sein. \emph on l \emph default bewirkt linksbündige, \emph on r \emph default rechtsbündige Ausrichtung der Formel in der Box. Gibt man keine Position an, wird die Formel zentriert. \newline Gibt man keine Breite an, darf auch keine Position angegeben werden. In diesem Falle wird die Rahmenbreite wie bei \series bold \backslash fbox \series default an den Boxinhalt angepasst. \end_layout \begin_layout Standard Wenn man den Befehl \series bold \backslash framebox \series default eingibt, erscheint eine Box mit drei Eingabefeldern. Die ersten beiden sind von eckigen Klammern umgeben und stehen für die beiden optionalen Argumente. In das dritte Feld wird wie bei \series bold \backslash fbox \series default die Formel eingegeben. \end_layout \begin_layout Standard \align center \begin_inset Note Note status open \begin_layout Standard Die Tabelle wurde in eine Minibox gesetzt damit die Fußnote der Tabelle auch erscheint. Denn sonst würde der Fußnotentext im Ausdruck nicht angezeigt werden. \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 <lyxtabular version="3" rows="5" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \begin_inset Foot status collapsed \begin_layout Standard Durch einen Fehler in LyX ist es momentan nicht möglich mit \family sans Strg-m \family default eine neue Formel zu erzeugen, siehe \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{ \end_layout \end_inset LyX-Fehler #1435 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash fbox \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \family sans Strg-m \family default \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula \raisebox{6mm}{}\fbox{$\int A=B$}\raisebox{-4mm}{} \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash boxed \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard A+ \backslash fbox \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}A+\fbox{B}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash framebox \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 20mm \begin_inset Formula $\to$ \end_inset \begin_inset Formula $\to$ \end_inset \family sans Strg-m \family default \backslash frac \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset Formula $\downarrow$ \end_inset B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Die Rahmendicke kann ebenfalls eingestellt werden. Dazu müssen vor der Formel im TeX-Modus die Befehle \end_layout \begin_layout Standard \series bold \backslash fboxrule \series default \series bold \begin_inset Quotes gld \end_inset Dicke \begin_inset Quotes grd \end_inset \series default \series bold \backslash fboxsep \series default \series bold \begin_inset Quotes gld \end_inset Abstand \begin_inset Quotes grd \end_inset \end_layout \begin_layout Standard eingegeben werden. \begin_inset Quotes gld \end_inset Abstand \begin_inset Quotes grd \end_inset legt dabei den minimalen Abstand zwischen Rahmen und dem ersten Zeichen in der Box fest. Ein Beispiel dafür ist folgende umrandete Formel: \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 Vor dieser Formel wurde im TeX-Modus \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 eingegeben. Diese angegeben Werte werden für alle folgenden Boxen verwendet. \end_layout \begin_layout Standard Möchte man wieder zur Standardrahmengröße zurückkehren, gibt man vor der nächsten Formel im TeX-Modus folgende Befehle ein: \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 Subsection Boxen ohne Rahmen \begin_inset LatexCommand label name "sub:Boxen-ohne-Rahmen" \end_inset \begin_inset LatexCommand index name "Boxen ! ohne Rahmen" \end_inset \end_layout \begin_layout Standard Für Boxen ohne Rahmen gibt es folgende Box-Befehle: \series bold \backslash mbox \series default \begin_inset LatexCommand index name "Befehle ! M ! \\textbackslash mbox" \end_inset , \series bold \backslash makebox \series default \begin_inset LatexCommand index name "Befehle ! M ! \\textbackslash makebox" \end_inset und \begin_inset ERT status collapsed \begin_layout Standard \backslash linebreak \end_layout \end_inset \series bold \backslash raisebox \series default \begin_inset LatexCommand index name "Befehle ! R ! \\textbackslash raisebox" \end_inset \end_layout \begin_layout Standard Mit \series bold \backslash raisebox \series default kann man eine Box hoch- oder tiefstellen. Allerdings behalten die Zeichen in der Box im Gegensatz zum normalen Hochstelle n die Schriftgröße bei. \series bold \backslash raisebox \series default wird dabei mit folgendem Schema benutzt: \end_layout \begin_layout Standard \series bold \backslash raisebox{Höhe}{Boxinhalt} \end_layout \begin_layout Standard Soll in der Box eine Formel stehen, muss man wie bei \series bold \backslash fbox \series default eine weitere Formel erstellen. \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $H\raisebox{2mm}{al}lo$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $H\raisebox{-2mm}{al}lo$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard A= \backslash raisebox{-2mm \begin_inset Formula $\to$ \end_inset \backslash { \family sans Strg-m \family default \backslash sqrt \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Die letzte Formel kann derzeit nur im TeX-Modus erstellt werden, da LyX statt der benötigten weiteren Formel eine Box einfügt. \begin_inset Foot status collapsed \begin_layout Standard siehe \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{ \end_layout \end_inset LyX-Fehler #1435 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Der Befehl \series bold \backslash mbox \series default ist äquivalent zu \series bold \backslash fbox \series default und \series bold \backslash makebox \series default ist äquivalent zu \series bold \backslash framebox \series default , nur dass es keinen Rahmen gibt. \end_layout \begin_layout Subsection Farbige Boxen \begin_inset LatexCommand label name "sub:Farbige-Boxen" \end_inset \begin_inset LatexCommand index name "Boxen ! farbige" \end_inset \end_layout \begin_layout Standard Damit die in diesem Kapitel angegebenen Befehle benutzt werden können, muss im LaTeX-Vorspann das LaTeX-Paket \series bold color \series default \begin_inset Foot status collapsed \begin_layout Standard Das Paket \series bold color \series default ist Teil jeder LaTeX-Standardinstallation. \end_layout \end_inset \begin_inset LatexCommand index name "Pakete ! color" \end_inset mit der Zeile \end_layout \begin_layout Standard \series bold \backslash usepackage{color} \end_layout \begin_layout Standard geladen werden \begin_inset Foot status collapsed \begin_layout Standard Wird irgendwo im Dokument Text mit einer vordefinierten Farbe gefärbt, lädt LyX das LaTeX-Paket \series bold color \series default automatisch. Dadurch kann es vorkommen, dass das Paket doppelt geladen wird, was aber keine Probleme hervorruft. \end_layout \end_inset \begin_inset Note Note status collapsed \begin_layout Standard Damit das Paket nicht doppelt geladen werden kann, wurde im LaTeX-Vorspann ein Makro eingefügt. \end_layout \end_inset . \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Um Boxen einzufärben, verwendet man den Befehl \series bold \backslash colorbox \series default \begin_inset LatexCommand index name "Befehle ! C ! \\textbackslash colorbox" \end_inset nach folgendem Schema: \end_layout \begin_layout Standard \series bold \backslash colorbox{Farbe}{Boxinhalt} \end_layout \begin_layout Standard Der Boxinhalt kann auch wieder eine Box sein und eine \series bold \backslash colorbox \series default kann auch ein Teil einer anderen Box sein (siehe 2. und 3. Beispiel). Soll in der Box eine Formel stehen, muss wie bei \series bold \backslash fbox \series default eine weitere Formel erstellt werden. \begin_inset Foot status collapsed \begin_layout Standard Das gilt auch für den Befehl \series bold \backslash fcolorbox \series default . Dabei ist \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{ \end_layout \end_inset LyX-Fehler #1435 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset zu beachten. \end_layout \end_inset \end_layout \begin_layout Standard Aus folgenden vordefinierten Farben kann gewählt werden: \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 und \series bold yellow \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash colorbox{yellow \begin_inset Formula $\to$ \end_inset \backslash {A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\colorbox{yellow}{A=B}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\colorbox{green}{\fbox{A=B}}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash fbox \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash colorbox{green \begin_inset Formula $\to$ \end_inset \backslash {A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\fbox{\colorbox{green}{A=B}}\raisebox{-3mm}{}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard \series bold \backslash colorbox \series default färbt nur die Box, nicht aber die Zeichen in der Box ein. Um alle Zeichen zu färben, markiert man die ganze Formel und wählt im Dialog \family sans Textstil \family default die gewünschte Farbe aus. Der Dialog kann mit dem Werkzeugleistenknopf \begin_inset Graphics filename ../../images/dialog-show_character.png scale 85 \end_inset oder dem Menü \family sans Bearbeiten\SpecialChar \menuseparator Textstil\SpecialChar \menuseparator Benutzerdefiniert \family default aufgerufen werden. Die Formelnummer hat dann dieselbe Farbe wie die Formel. Soll die Formelnummer eine andere Farbe als die Formelzeichen haben, muss innerhalb der Formel die Farbe geändert werden. \end_layout \begin_layout Standard Ein Beispiel: \end_layout \begin_layout Standard \color red \begin_inset Formula \begin{equation} \int A=B\label{eq:rot}\end{equation} \end_inset \color green \begin_inset Formula \begin{equation} \textcolor{red}{\int A=B}\label{eq:rotgruen}\end{equation} \end_inset \end_layout \begin_layout Standard Formel \begin_inset LatexCommand eqref reference "eq:rot" \end_inset ist komplett rot gefärbt. \newline Formel \begin_inset LatexCommand eqref reference "eq:rotgruen" \end_inset wurde zuerst komplett grün gefärbt, um die Farbe der Formelnummer festzulegen. Anschließend wurden die Formelzeichen rot gefärbt. \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Möchte man den Rahmen anders als den Rest der Box färben, verwendet man den Befehl \series bold \backslash fcolorbox \series default \begin_inset LatexCommand index name "Befehle ! F ! \\textbackslash fcolorbox" \end_inset nach folgendem Schema: \end_layout \begin_layout Standard \series bold \backslash fcolorbox{Rahmenfarbe}{Farbe}{Boxinhalt} \end_layout \begin_layout Standard \series bold \backslash fcolorbox \series default stellt also eine Erweiterung des Befehls \series bold \backslash colorbox \series default dar. Die Rahmenbreite wird, wie bei \series bold \backslash framebox \series default , mit \series bold \backslash fboxrule \series default und \series bold \backslash fboxsep \series default festgelegt. Ein Beispiel: \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 Diese Formel wurde mit folgendem Befehl erstellt: \newline \series bold \backslash fcolorbox{cyan \begin_inset Formula $\to$ \end_inset \backslash {magenta \begin_inset Formula $\to$ \end_inset \backslash {A=B \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Um andere als die vordefinierten Farben zu verwenden, muss man diese zuerst selbst definieren. \end_layout \begin_layout Standard Man kann z.\InsetSpace \thinspace{} B. mit folgender LaTeX-Vorspannzeile die Farbe \begin_inset Quotes gld \end_inset \series bold dunkelgruen \series default \begin_inset Quotes grd \end_inset \begin_inset Foot status collapsed \begin_layout Standard In Befehlen darf kein Umlaut stehen, siehe \begin_inset LatexCommand ref reference "sec:Benutzerdefinierte-Befehle" \end_inset . \end_layout \end_inset definieren: \end_layout \begin_layout Standard \series bold \backslash definecolor{dunkelgruen}{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 "Befehle ! D ! \\textbackslash definecolor" \end_inset \end_layout \begin_layout Standard \series bold cmyk \series default ist der Farbraum und steht für die Farben \series bold cyan \series default , \series bold magenta \series default , \series bold yellow \series default und \series bold black \series default . Die vier Zahlen geben der Reihe nach den Anteil der vier Farben an. Für den Anteil kann man Werte im Bereich 0\InsetSpace \thinspace{} -\InsetSpace \thinspace{} 1 angeben. Anstelle von \series bold cmyk \series default kann man zur Definition auch den Farbraum \series bold rgb \series default verwenden. \series bold rgb \series default steht für \series bold red \series default , \series bold green \series default und \series bold blue \series default , so dass man dann mit drei Zahlen die Anteile dieser Farben festlegen kann. Des Weiteren gibt es noch den Farbraum \series bold gray \series default , bei dem man mit einer Zahl den Graustufenanteil festlegen kann. \end_layout \begin_layout Standard Als Beispiel eine gerahmte Box mit der neu definierten Farbe \series bold darkgreen \series default , bei der die Zeichenfarbe \series bold yellow \series default gewählt wurde: \begin_inset Formula \begin{equation} \colorbox{dunkelgruen}{\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 Selbst definierte Farben können mit dem Befehl \series bold \backslash textcolor \series default auch für Text \begin_inset LatexCommand index name "Text ! farbiger" \end_inset verwendet werden: \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash textcolor{dunkelgruen}{ \end_layout \end_inset Dieser Satz ist \begin_inset Quotes gld \end_inset dunkelgruen \begin_inset Quotes grd \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 "Befehle ! T ! \\textbackslash textcolor" \end_inset wird nach dem Schema \series bold \backslash textcolor{Farbe}{zu \series default \series bold färbende \series default \series bold Zeichen} \series default verwendet. \end_layout \begin_layout Subsection Absatzboxen \begin_inset LatexCommand label name "sub:Absatzboxen" \end_inset \begin_inset LatexCommand index name "Boxen ! Absatz-" \end_inset \end_layout \begin_layout Standard Mit dem Menü \family sans Einfügen\SpecialChar \menuseparator Box \family default oder dem Werkzeugleistenknopf \begin_inset Graphics filename ../../images/box-insert.png scale 85 \end_inset kann man eine Box erstellen, die mehrere Zeilen und Absätze enthalten kann, eine so genannte \emph on Parbox \emph default (Absatzbox). \end_layout \begin_layout Standard Das folgende Beispiel zeigt eine umrahmte Absatzbox in einer Zeile: \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Dies ist eine Zeile \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 Dies ist die Absatzbox. Sie ist genau 5\InsetSpace \thinspace{} cm lang und kann auch Formeln enthalten: \begin_inset Formula $\int A\,\mathrm{d}s=C$ \end_inset \end_layout \end_inset mit einer Absatzbox. \begin_inset VSpace medskip \end_inset \end_layout \begin_layout Standard Solch eine Box wird erstellt, indem man mit der rechten Maustaste auf die graue Box mit dem Namen \begin_inset Quotes gld \end_inset Box(Gerahmt) \begin_inset Quotes grd \end_inset klickt. Es erscheint dann ein Fenster in dem man die Boxeigenschaften festlegt. In diesem Fall: \emph on Verzierung \emph default : Rechteckige Box, \emph on Innere Box \emph default : Parbox, \emph on Breite \emph default : 5\InsetSpace \thinspace{} cm, \emph on Vertikale Box Ausrichtung \emph default : Mitte \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset In LaTeX wird eine Absatzbox mit dem Befehl \series bold \backslash parbox \series default \begin_inset LatexCommand index name "Befehle ! P ! \\textbackslash parbox" \end_inset erstellt, welcher folgendes Schema besitzt: \end_layout \begin_layout Standard \series bold \backslash parbox[Position]{Breite}{Boxinhalt} \end_layout \begin_layout Standard Die Positionen \emph on b \emph default und \emph on t \emph default sind möglich. \emph on b \emph default steht für bottom und bedeutet, dass die letzte Absatzzeile in den umstehenden Text eingepasst wird. Bei \emph on t \emph default wie top geschieht dies für die erste Zeile. Wird keine Position angegeben, wird der Absatz in mittlerer Höhe eingepasst, siehe das Kapitel \emph on Boxen \emph default des Handbuchs \emph on Eingebettete\InsetSpace ~ Objekte \emph default für Beispiele. \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Möchte man Formeln komplett mit Formelnummer umranden, muss man die Formel in eine Absatzbox setzen. Dazu schreibt man im TeX-Modus vor die Formel den Befehl \series bold \backslash fbox{ \backslash parbox{ \backslash linewidth-2 \backslash fboxsep-2 \backslash fboxrule}{ \series default . Hierbei steht \series bold \backslash linewidth \begin_inset LatexCommand index name "Befehle ! L ! \\textbackslash linewidth" \end_inset \series default für die im Dokument eingestellte Zeilenbreite. Da sich der Rahmen außerhalb der Absatzbox befindet, muss man von der Zeilenbre ite zweimal die Rahmendicke und den Rahmenabstand abziehen. Da dies LyX aufgrund eines Fehlers \begin_inset Foot status collapsed \begin_layout Standard \begin_inset ERT status open \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{ \end_layout \end_inset LyX-Fehler #4483 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset nicht automatisch macht, muss der TeX-Modus verwendet werden. Damit man in Argumenten multiplizieren und subtrahieren kann, muss im LaTeX-Vor spann das LaTeX-Paket \series bold calc \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold calc \series default ist Teil jeder LaTeX-Standardinstallation. \end_layout \end_inset \begin_inset LatexCommand index name "Pakete ! calc" \end_inset mit der Zeile \end_layout \begin_layout Standard \series bold \backslash usepackage{calc} \end_layout \begin_layout Standard geladen werden. Nach der Formel werden beide Boxen geschlossen, indem man \series bold }} \series default im TeX-Modus eingibt. Dazu ein Beispiel: \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 Da im Argument von \series bold \backslash fbox \series default eine Absatzbox verwendet wird, gibt es in diesem Fall bei der Formelgröße keinen Unterschied zwischen \series bold \backslash fbox \series default und \series bold \backslash boxed \series default . \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Sehr nützlich sind Absatzboxen, wenn man Formeln direkt kommentieren möchte. Dazu verwendet man \series bold \backslash parbox \series default in Verbindung mit dem Befehl \series bold \backslash tag \series default . (mehr zu \series bold \backslash tag \series default siehe \begin_inset LatexCommand ref reference "sub:Benutzerdefinierte-Nummerierung" \end_inset ) \end_layout \begin_layout Standard Ein Beispiel einer mit Hilfe von \series bold \backslash parbox \series default kommentierten Formel: \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 Dies ist eine Beschreibung. Sie ist deutlich von der Formel getrennt und mehrzeilig. \begin_inset ERT status collapsed \begin_layout Standard }} \backslash ] \end_layout \end_inset \end_layout \begin_layout Standard So eine Formel muss komplett im TeX-Modus eingegeben werden, da LyX den Befehl \series bold \backslash parbox \series default in Formeln noch nicht unterstützt. Die Formel wird mit folgender Befehlssequenz erstellt: \end_layout \begin_layout Standard Der Befehl \series bold \backslash [5x-7b=3b \backslash tag* \backslash { \backslash parbox{5cm}{ \series default wird im TeX-Modus eingegeben. \begin_inset Foot status collapsed \begin_layout Standard Ist der Formelstil \series bold Eingerückt \series default aktiviert, kann \series bold \backslash tag* \backslash { \series default auch durch \series bold \backslash hfill \series default ersetzt werden. (Formelstile siehe \begin_inset LatexCommand ref reference "sec:Formelstile" \end_inset ) \end_layout \end_inset Dann folgt die Beschreibung als normaler Text und zuletzt gibt man \series bold }} \backslash ] \series default im TeX-Modus ein. Die Befehle \series bold \backslash [ \series default und \series bold \backslash ] \series default erstellen hierbei eine abgesetzte Formel. \end_layout \begin_layout Standard Die Vorteile von \series bold \backslash parbox \series default erkennt man an folgendem Beispiel, in dem mit Hilfe des mathematischen Textmodus \begin_inset Quotes gld \end_inset kommentiert \begin_inset Quotes grd \end_inset wurde: \begin_inset Formula \[ 5x-7b=3b\textrm{Dies ist eine Beschreibung. Sie ist nicht von der Formel getrennt ...}\] \end_inset \end_layout \begin_layout Section Operatoren \begin_inset LatexCommand index name "Operatoren" \end_inset \end_layout \begin_layout Subsection Große Operatoren \begin_inset LatexCommand label name "sub:Große-Operatoren" \end_inset \begin_inset LatexCommand index name "Operatoren ! große" \end_inset \begin_inset LatexCommand index name "Summen" \end_inset \begin_inset LatexCommand index name "Integrale" \end_inset \end_layout \begin_layout Standard Um alle großen Integraloperatoren nutzen zu können, die im Folgenden aufgelistet sind, muss die Option \family sans esint-Paket automatisch verwenden \family default in den Dokumenteinstellungen unter \family sans Mathe-Optionen \family default gewählt sein. \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="11" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sum \begin_inset LatexCommand index name "Befehle ! S ! \\textbackslash sum" \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\sum$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash int \begin_inset LatexCommand index name "Befehle ! I ! \\textbackslash int" \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\int$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash intop \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\intop$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash oint \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\oint$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ointop \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\ointop$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ointctrclockwise \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\ointctrclockwise$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ointclockwise \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\ointclockwise$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sqint \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\sqint$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigcap \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigcap$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigcup \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigcup$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="10" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash prod \begin_inset LatexCommand index name "Befehle ! P ! \\textbackslash prod" \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\prod$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash coprod \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\coprod$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigodot \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigodot$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigotimes \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigotimes$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigoplus \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigoplus$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigwedge \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigwedge$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigvee \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigvee$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigsqcup \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigsqcup$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash biguplus \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\biguplus$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard Alle großen Operatoren können auch über den Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/intop.png scale 85 \end_inset eingefügt werden. \end_layout \begin_layout Standard Die Operatoren werden als groß bezeichnet, da sie größer sind als die zum Teil gleich aussehenden binären Operatoren. Zu allen großen Operatoren kann man Grenzen angeben, wie im nächsten Abschnitt beschrieben. \end_layout \begin_layout Standard Die Operatoren \series bold \backslash intop \series default und \series bold \backslash ointop \series default unterscheiden sich von \series bold \backslash int \series default bzw. \series bold \backslash oint \series default in der Art wie die Operatorgrenzen dargestellt werden, siehe \begin_inset LatexCommand ref reference "sub:Operatorgrenzen" \end_inset . \end_layout \begin_layout Subsubsection* Hinweise zu Integralen \end_layout \begin_layout Standard Der Buchstabe \emph on d \emph default in einer Integralen ist ein Operator, der deswegen aufrecht erscheinen muss. Dazu markiert man das \emph on d \emph default und wandelt es mit der Tastenkombination \family sans Alt-z\InsetSpace ~ r \family default \begin_inset Foot status collapsed \begin_layout Standard Schriftstile siehe \begin_inset LatexCommand ref reference "sub:Schriftstile" \end_inset \end_layout \end_inset um. Anschließend fügt man vor dem \emph on d \emph default , wie bei Operatoren üblich, den kleinsten Leerraum ein. Dazu ein Beispiel: \end_layout \begin_layout Standard inkorrekt: \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 korrekt: \begin_inset Formula $\int A(x)\,\mathrm{d}x$ \end_inset \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Für Mehrfachintegrale gibt es folgende Befehle: \begin_inset VSpace medskip \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash iint \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\iint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash oiint \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\oiint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sqiint \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\sqiint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash iiint \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\iiint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash iiiint \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\iiiint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash dotsint \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\dotsint\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \newpage \end_layout \begin_layout Subsection Operatorgrenzen \begin_inset LatexCommand label name "sub:Operatorgrenzen" \end_inset \begin_inset LatexCommand index name "Operatoren ! Grenzen" \end_inset \end_layout \begin_layout Standard Grenzen werden durch Hoch- bzw. Tiefstellen erzeugt: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="2" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash prod^ \backslash infty \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \begin_inset Formula $\to$ \end_inset _0 \begin_inset Formula $\to$ \end_inset A(x) \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Bei einer Formel in einer Textzeile werden die Grenzen rechts neben den Operator gesetzt. In einer abgesetzten Formel werden, außer bei Integralen, die Grenzen über bzw. unter den Operator gesetzt. \end_layout \begin_layout Standard Um zu erzwingen, dass die Grenzen neben den Operator gesetzt werden, setzt man den Cursor direkt hinter den Operator und setzt über das Menü \family sans Bearbeiten\SpecialChar \menuseparator Mathe\SpecialChar \menuseparator Art der Operatorgrenzen ändern \family default die Grenzen auf \series bold Eingebettet \series default (Tastenkombination \family sans Alt-m\InsetSpace ~ l \family default ). Dazu folgendes Beispiel: \end_layout \begin_layout Standard Die normalen Grenzen sehen so aus: \begin_inset Formula \[ \sum_{x=0}^{\infty}\frac{1}{x^{2}}\] \end_inset So sieht die Formel aus, wenn man die Grenzen neben das Summenzeichen setzt: \begin_inset Formula \[ \sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\] \end_inset Bei Integralen werden mit Ausnahme von \series bold \backslash intop \series default und \series bold \backslash ointop \series default die Grenzen standardmäßig neben den Operator gesetzt. Bei Mehrfachintegralen werden die Grenzen jedoch meistens unter den Operator gesetzt. Im folgenden Beispiel wurde die Grenze deswegen auf \series bold Anzeige \series default gesetzt und damit unter die Integrale geschrieben: \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 Um Bedingungen für Grenzen anzugeben, gibt es die Befehle \series bold \backslash subarray \series default \begin_inset LatexCommand index name "Befehle ! S ! \\textbackslash subarray" \end_inset und \series bold \backslash substack \series default \begin_inset LatexCommand index name "Befehle ! S ! \\textbackslash substack" \end_inset . Um z.\InsetSpace \thinspace{} B. diesen Ausdruck \begin_inset Formula \begin{equation} \sum_{\begin{subarray}{c} 0<k<1000\\ \\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation} \end_inset zu erstellen, muss man Folgendes tun: \newline Zuerst gibt man den Befehl \series bold \backslash sum \series default ^ \series bold n \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset _ \series default ein. Man befindet sich nun in einem blauen Kästchen unter dem Summenzeichen. In dieses gibt man den Befehl \series bold \backslash subarray \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default ein. Das blaue Kästchen hat nun eine lila Umrahmung und man kann jetzt mehrere Zeilen untereinander schreiben. Mit Eingabe des Zeilenumbruchs ( \family sans Strg-Enter \family default ) wird eine neue Zeile erstellt. Gibt man \newline \series bold 0<k<1000 Strg-Enter \newline \series default ein, erscheint darunter ein Kästchen für die neue Zeile. \end_layout \begin_layout Standard Die Ausrichtung der Zeilen kann mit der \family sans Tabellen-Werkzeugleiste \family default oder dem Menü \family sans Bearbeiten\SpecialChar \menuseparator Zeilen & Spalten \family default auf links geändert werden. Um rechts ausgerichtete Zeilen zu erhalten, wird am Anfang der Zeile \series bold \backslash hfill \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default eingegeben. \end_layout \begin_layout Standard Der Befehl \series bold \backslash substack \series default ist äquivalent zu \series bold \backslash subarray \series default , mit dem Unterschied dass die Zeilen immer zentriert ausgerichtet sind. \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Wie bei Formel \begin_inset LatexCommand eqref reference "eq:substack" \end_inset kann es vorkommen, dass sich neben dem Operator zu viel Leerraum befindet, denn das dem Operator folgende Zeichen wird neben die Grenzen gesetzt. \end_layout \begin_layout Standard Um das zu verhindern, kann man folgendes Makro in den LaTeX-Vorspann einfügen: \end_layout \begin_layout Standard \series bold \backslash def \backslash clap#1{ \backslash hbox to 0pt{ \backslash hss #1 \backslash hss}} \newline \backslash def \backslash mathclap { \backslash mathpalette \backslash mathclapinternal} \newline \backslash def \backslash mathclapinternal #1#2{ \backslash clap{$ \backslash mathsurround =0pt #1{#2}$}} \end_layout \begin_layout Standard Dadurch wird der Befehl \series bold \backslash mathclap \series default \begin_inset LatexCommand index name "Befehle ! M ! \\textbackslash mathclap" \end_inset definiert, der die Breite der Grenze auf 0\InsetSpace \thinspace{} pt setzt. Das Befehlsschema lautet \end_layout \begin_layout Standard \series bold \backslash mathclap{Grenze} \end_layout \begin_layout Standard wobei die Grenze auch aus mehreren Bedingungen bestehen kann. \end_layout \begin_layout Standard Auf Formel \begin_inset LatexCommand eqref reference "eq:substack" \end_inset angewandt, gibt man also den Befehl \end_layout \begin_layout Standard \series bold \backslash sum_ \backslash mathclap{ \backslash substack \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset 0<k<1000 Strg-Enter \end_layout \begin_layout Standard ein, um die untere Grenze zu erstellen. Der Summand befindet sich nun direkt hinter dem Summenzeichen: \begin_inset Formula \[ \sum_{\mathclap{\substack{0<k<1000\\ \\k\,\in\,\mathbb{N}} }}^{n}k^{-2}\] \end_inset \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset In \begin_inset LatexCommand ref reference "sub:Selbstdefinierte-Operatoren" \end_inset ist beschrieben, wie man eine Grenze für mehrere Operatoren verwenden kann. \end_layout \begin_layout Subsection Binäre Operatoren \begin_inset LatexCommand label name "sub:Binäre-Operatoren" \end_inset \begin_inset LatexCommand index name "Operatoren ! binäre" \end_inset \end_layout \begin_layout Standard Binäre Operatoren sind von Leerraum umgeben, wenn sich vor und hinter ihnen ein Zeichen befindet. \begin_inset VSpace medskip \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="13" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard + \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $+$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard - \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $-$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash pm \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\pm$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mp \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mp$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash cdot \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\cdot$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash times \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\times$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash div \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\div$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $*$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash star \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\star$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash circ \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\circ$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash diamond \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\diamond$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bullet \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bullet$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="13" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash nabla \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\nabla$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigtriangledown \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigtriangledown$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigtriangleup \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigtriangleup$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Box \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Box$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash cap \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\cap$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash cup \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\cup$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash dagger \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\dagger$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ddagger \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\ddagger$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash wr \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\wr$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigcirc \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigcirc$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash wedge \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\wedge$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash vee \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\vee$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="13" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash oplus \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\oplus$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ominus \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\ominus$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash otimes \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\otimes$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash oslash \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\oslash$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash odot \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\odot$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash amalg \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\amalg$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash uplus \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\uplus$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash setminus \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\setminus$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sqcap \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\sqcap$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sqcup \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\sqcup$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash triangleleft \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\triangleleft$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash triangleright \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\triangleright$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard Alle binären Operatoren können auch über den Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/pm.png scale 85 \end_inset eingefügt werden. \end_layout \begin_layout Standard Um den Laplace-Operator darzustellen, kann man statt \series bold \backslash bigtriangleup \series default auch \series bold \backslash Delta \series default verwenden oder man benutzt \series bold \backslash nabla \series default ^ \series bold 2 \series default ( \begin_inset Formula $\nabla^{2}$ \end_inset ). \end_layout \begin_layout Standard Das Zeichen \family sans Menütrenner \family default im Menü \family sans Einfügen\SpecialChar \menuseparator Sonderzeichen \family default ist der Operator \series bold \backslash triangleright \series default . \end_layout \begin_layout Subsection Selbst definierte Operatoren \begin_inset LatexCommand label name "sub:Selbstdefinierte-Operatoren" \end_inset \begin_inset LatexCommand index name "Operatoren ! selbstdefinierte" \end_inset \end_layout \begin_layout Standard Mit Hilfe des Befehls \series bold \backslash DeclareMathOperator \series default \begin_inset LatexCommand index name "Befehle ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator" \end_inset kann man im LaTeX-Vorspann eigene Operatoren definieren. Das Befehlsschema dazu lautet: \end_layout \begin_layout Standard \series bold \backslash DeclareMathOperator{neuer Befehl}{Anzeige} \end_layout \begin_layout Standard Anzeige können Zeichen und Symbole sein, die festlegen, wie der Operator im Ausdruck aussieht. Will man einen großen Operator definieren, setzt man hinter den Befehl ein \series bold * \series default . Zu allen selbst definierten großen Operatoren kann man Grenzen angeben, wie in \begin_inset LatexCommand ref reference "sub:Operatorgrenzen" \end_inset beschrieben. \end_layout \begin_layout Standard Beispielsweise definiert die LaTeX-Vorspannzeile \end_layout \begin_layout Standard \series bold \backslash DeclareMathOperator*{ \backslash Raute}{ \backslash blacklozenge} \end_layout \begin_layout Standard den Befehl \series bold \backslash Raute \series default , mit dem man einen großen Operator aufrufen kann, der aus dem Raute Symbol aus \begin_inset LatexCommand ref reference "sub:Sonstige-Symbole" \end_inset besteht: \begin_inset Formula \[ \Raute_{n=1}^{\infty}\] \end_inset Der Befehl für diese Formel lautet: \series bold \backslash Raute \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 Benötigt man eigene Operatoren nicht mehrfach im Dokument, kann man diese auch mit den Befehlen \series bold \backslash mathop \series default \begin_inset LatexCommand index name "Befehle ! M ! \\textbackslash mathop" \end_inset und \series bold \backslash mathbin \series default \begin_inset LatexCommand index name "Befehle ! M ! \\textbackslash mathbin" \end_inset definieren, die folgendes Schema besitzen: \end_layout \begin_layout Standard \series bold \backslash mathop{Anzeige} \series default bzw. \series bold \backslash mathbin{Anzeige} \end_layout \begin_layout Standard \series bold \backslash mathop \series default definiert große, \series bold \backslash mathbin \series default binäre Operatoren. \end_layout \begin_layout Standard \series bold \backslash mathop \series default lässt sich z.\InsetSpace \thinspace{} B. nutzen, um eine Grenze für mehrere Operatoren zu verwenden: \begin_inset Formula \[ \mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\] \end_inset \end_layout \begin_layout Standard Der Befehl für obige Formel lautet: \newline \series bold \backslash mathop{ \backslash sum \backslash negmedspace \backslash sum \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series bold \begin_inset Formula $\to$ \end_inset ^N \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series bold _i,j=1 \end_layout \begin_layout Section Schriften \begin_inset LatexCommand index name "Schriften" \end_inset \end_layout \begin_layout Subsection Schriftstile \begin_inset LatexCommand label name "sub:Schriftstile" \end_inset \begin_inset LatexCommand index name "Schriften ! Schriftstile" \end_inset \end_layout \begin_layout Standard Lateinische Buchstaben in einer Formel können in folgenden Schriftstilen gesetzt werden: \begin_inset VSpace -2mm \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="6" columns="3"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Tastenkürzel \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mathbb \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default ABC \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathbb{ABC}$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Alt-z k \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mathbf \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default AbC \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathbf{AbC}$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Alt-z f \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash boldsymbol \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default AbC \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\boldsymbol{AbC}$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard - \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mathcal \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default ABC \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathcal{ABC}$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Alt-z h \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mathfrak \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default AbC \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathfrak{AbC}$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard - \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="5" columns="3"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Tastenkürzel \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mathit \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default AbC \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathit{AbC}$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard - \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mathrm \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default AbC \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathrm{AbC}$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Alt-z r \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mathsf \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default AbC \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathsf{AbC}$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Alt-z s \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mathtt \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series default AbC \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathtt{AbC}$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Alt-z c \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard \begin_inset Note Greyedout status open \begin_layout Standard \series bold Achtung: \series default Die Stile \series bold \backslash mathbb \series default und \series bold \backslash mathcal \series default können nur für Großbuchstaben verwendet werden. \end_layout \end_inset \end_layout \begin_layout Standard Voreingestellt ist der Stil \series bold \backslash mathnormal \series default . \end_layout \begin_layout Standard Die Stilbefehle wirken auch auf Buchstaben in mathematischen Konstruktionen: \begin_inset Formula \[ \mathfrak{A=\frac{b}{C}}\] \end_inset \end_layout \begin_layout Standard Zeichen im mathematischen Textmodus erscheinen nicht in einem der Matheschriftst ile, sondern in dem Textschriftstil \series bold \backslash textrm \series default . Dass ihr Stil nicht über den Textstil Dialog geändert werden kann ist ein Fehler 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-Fehler #4091 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Anstelle der Stilbefehle kann man auch den Dialog \family sans Bearbeiten\SpecialChar \menuseparator Mathe\SpecialChar \menuseparator Text-Stil \family default oder den Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/font.png scale 85 \end_inset verwenden. \end_layout \begin_layout Subsection Fett gedruckte Formeln \begin_inset LatexCommand label name "sub:Fett-gedruckte-Formeln" \end_inset \begin_inset LatexCommand index name "Formel ! fett gedruckte" \end_inset \end_layout \begin_layout Standard Möchte man komplette Formeln fett setzen, kann man nicht den im vorigen Kapitel angegebenen Befehl \series bold \backslash mathbf \series default verwenden, denn dieser wirkt nicht auf kleine griechische Buchstaben. Außerdem setzt er lateinische Buchstaben immer aufrecht, was man an folgender Formel gut erkennt: \end_layout \begin_layout Standard \begin_inset Formula \[ \mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{Formel mit \textbackslash mathbf}\] \end_inset \end_layout \begin_layout Standard Um die Formel korrekt darzustellen, verwendet man den Befehl \series bold \backslash boldsymbol \series default : \begin_inset Formula \[ \boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{Formel mit \textbackslash boldsymbol}}\] \end_inset Es gibt auch die Möglichkeit die Formel in eine \series bold boldmath-Umgebung \series default zu setzen. Diese Umgebung wird erzeugt, indem man im TeX-Modus den Befehl \series bold \backslash boldmath \begin_inset LatexCommand index name "Befehle ! B ! \\textbackslash boldmath" \end_inset \series default eingibt. Um die Umgebung wieder zu beenden, gibt man im TeX-Modus den Befehl \series bold \backslash unboldmath \begin_inset LatexCommand index name "Befehle ! U ! \\textbackslash unboldmath" \end_inset \series default ein. \begin_inset ERT status collapsed \begin_layout Standard \backslash boldmath \end_layout \end_inset \begin_inset Formula \[ \int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{Formel in boldmath-Umgebung}\] \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash unboldmath \end_layout \end_inset \end_layout \begin_layout Subsection Schriftgrößen \begin_inset LatexCommand label name "sub:Schriftgrößen" \end_inset \begin_inset LatexCommand index name "Schriften ! Schriftgrößen" \end_inset \end_layout \begin_layout Standard Für Zeichen in einer Formel gibt es, analog zu Textzeichen, folgende Größenbefeh le: \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 , \series bold \backslash footnotesize \series default , \begin_inset ERT status collapsed \begin_layout Standard \backslash linebreak \end_layout \end_inset \series bold \backslash scriptsize \series default und \series bold \backslash tiny \end_layout \begin_layout Standard Welche Größe die Befehle produzieren, hängt von der Dokumentschriftgröße ab, die dem Befehl \series bold \backslash normalsize \series default entspricht. Die anderen Befehle produzieren kleinere oder größere Schriften als \series bold \backslash normalsize \series default . Die Schriftgröße kann jedoch einen bestimmten Wert nicht übertreffen. Beträgt z.\InsetSpace \thinspace{} B. die Dokumentschriftgröße 12\InsetSpace \thinspace{} pt, produziert der Befehl \series bold \backslash Huge \series default dasselbe wie \series bold \backslash huge \series default . \end_layout \begin_layout Standard Ein Größenbefehl wird im TeX-Modus vor der Formel eingegeben und legt die Größe aller nachfolgenden Formel- und Textzeichen fest. Um wieder zur Ausgangsgröße zurückzukehren, gibt man nach der Formel im TeX-Modus den Befehl \series bold \backslash normalsize \series default ein. \end_layout \begin_layout Standard Innerhalb einer Formel kann die Größe nur für Symbole oder Buchstaben im mathematischen Text geändert werden. Dazu wird der Größenbefehl im mathematischen Textmodus eingegeben. Alle diesem Befehl folgenden Zeichen bis zum Ende des mathematischen Textes oder bis zu einem anderen Größenbefehl haben dann die angegebene Größe. Dazu zwei Beispiele: \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 Vor beiden Formeln wurde der Befehl \series bold \backslash huge \series default eingegeben. Der Befehl für die zweite Formel lautet: \newline \series bold \backslash maltese \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A M-m m \backslash Large \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash maltese \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash textit \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \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 M-m \series default \series bold m \backslash tiny \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash maltese \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash textit \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \end_layout \begin_layout Standard Kann ein Symbol nicht in verschiedenen Größen dargestellt werden, wird es immer in der Standardgröße dargestellt. \end_layout \begin_layout Section Griechische Buchstaben \begin_inset LatexCommand index name "griechische Buchstaben" \end_inset \end_layout \begin_layout Standard Alle griechischen Buchstaben können auch über den Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/alpha.png scale 85 \end_inset eingefügt werden. \end_layout \begin_layout Subsection Kleine Buchstaben \begin_inset LatexCommand label name "sub:Kleine-Buchstaben" \end_inset \begin_inset LatexCommand index name "griechische Buchstaben ! kleine" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="11" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash alpha \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\alpha$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash beta \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\beta$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash gamma \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\gamma$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash delta \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\delta$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash epsilon \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\epsilon$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash varepsilon \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\varepsilon$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash zeta \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\zeta$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash eta \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\eta$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash theta \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\theta$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash vartheta \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\vartheta$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="12" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash iota \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\iota$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash kappa \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\kappa$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash varkappa \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\varkappa$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash lambda \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\lambda$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mu \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mu$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash nu \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\nu$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash xi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\xi$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard o \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $o$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash pi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\pi$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash varpi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\varpi$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash rho \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\rho$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="11" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash varrho \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\varrho$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sigma \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\sigma$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash varsigma \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\varsigma$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash tau \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\tau$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash upsilon \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\upsilon$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash phi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\phi$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash varphi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\varphi$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash chi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\chi$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash psi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\psi$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash omega \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\omega$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Wie man aufrechte griechische Buchstaben erstellt, ist in \begin_inset LatexCommand ref reference "sub:Aufrechte-kleine-griechische" \end_inset beschrieben. \end_layout \begin_layout Subsection Große Buchstaben \begin_inset LatexCommand index name "griechische Buchstaben ! große" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="7" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Gamma \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Gamma$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Delta \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Delta$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Theta \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Theta$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Lambda \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Lambda$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Xi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Xi$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Pi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Pi$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="6" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Sigma \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Sigma$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Upsilon \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Upsilon$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Phi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Phi$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Psi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Psi$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Omega \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Omega$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Dass die großen griechischen Buchstaben aufrecht erscheinen, ist einem Fehler geschuldet, der während der Entwicklung von TeX gemacht wurde. Um korrekte kursive Großbuchstaben zu erhalten, beginnt man einen Befehl mit \series bold var \series default . So ergibt z.\InsetSpace \thinspace{} B. der Befehl \series bold \backslash varGamma \series default : \begin_inset Formula $\varGamma$ \end_inset \end_layout \begin_layout Subsection Fett gedruckte Buchstaben \begin_inset LatexCommand index name "griechische Buchstaben ! fett gedruckte" \end_inset \end_layout \begin_layout Standard Griechische lassen sich nicht wie lateinische Buchstaben in verschiedenen Schriftstilen darstellen. Es besteht nur die Möglichkeit, sie mit dem Befehl \series bold \backslash boldsymbol \series default \begin_inset LatexCommand index name "Befehle ! B ! \\textbackslash boldsymbol" \end_inset fett gedruckt auszugeben. \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="3" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Upsilon \backslash boldsymbol \backslash Upsilon \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Upsilon\boldsymbol{\Upsilon}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash theta \backslash boldsymbol \backslash theta \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\theta\boldsymbol{\theta}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Section Symbole \begin_inset ERT status collapsed \begin_layout Standard \backslash texorpdfstring{ \end_layout \end_inset \begin_inset Foot status collapsed \begin_layout Standard Eine Liste mit sämtlichen Symbolen der meisten LaTeX-Pakete findet man 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 \series bold \backslash texorpdfstring \series default dient dazu, dass die Fußnote nicht mit im pdf-Lesezeichen erscheint. \end_layout \begin_layout Standard Näheres zu \series bold \backslash texorpdfstring \series default steht in Kapitel \begin_inset LatexCommand ref reference "sub:Formeln-in-Überschriften" \end_inset . \end_layout \end_inset \begin_inset LatexCommand index name "Symbole" \end_inset \end_layout \begin_layout Standard Viele der im Folgenden aufgelisteten Symbole können auch über die Mathe-Werkzeug\SpecialChar \- leistenknöpfe \begin_inset Graphics filename ../../images/math/nabla.png scale 85 \end_inset und \begin_inset Graphics filename ../../images/math/digamma.png scale 85 \end_inset eingefügt werden. \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Subsection Mathematische Symbole \begin_inset LatexCommand label name "sub:Mathematische-Symbole" \end_inset \begin_inset LatexCommand index name "Symbole ! mathematische" \end_inset \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="10" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash neg \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\neg$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Im \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Im$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Re \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Re$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash aleph \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\aleph$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash partial \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\partial$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash infty \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\infty$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash wp \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\wp$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash imath \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\imath$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash jmath \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\jmath$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="10" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash forall \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\forall$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash exists \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\exists$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash nexists \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\nexists$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash emptyset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\emptyset$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash varnothing \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\varnothing$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash dag \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\dag$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ddag \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\ddag$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash complement \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Bbbk \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Bbbk$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="10" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash prime \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\prime$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash backprime \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\backprime$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mho \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mho$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash triangle \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\triangle$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash angle \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\angle$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash measuredangle \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\measuredangle$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sphericalangle \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\sphericalangle$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash top \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\top$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bot \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bot$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Subsection Sonstige Symbole \begin_inset LatexCommand label name "sub:Sonstige-Symbole" \end_inset \begin_inset LatexCommand index name "Symbole ! sonstige" \end_inset \end_layout \begin_layout Standard \noindent \align center \begin_inset Tabular <lyxtabular version="3" rows="10" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash flat \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\flat$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash natural \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\natural$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sharp \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\sharp$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash surd \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\surd$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash checkmark \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\checkmark$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash yen \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\yen$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash pounds \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\pounds$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard $ \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\$$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard § \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $§$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \begin_inset Tabular <lyxtabular version="3" rows="10" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash hbar \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\hbar$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash hslash \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\hslash$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash clubsuit \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\clubsuit$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash spadesuit \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\spadesuit$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bigstar \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bigstar$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash blacklozenge \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\blacklozenge$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash blacktriangle \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\blacktriangle$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash blacktiangledown \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\blacktriangledown$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bullet \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bullet$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \begin_inset Tabular <lyxtabular version="3" rows="10" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash diamondsuit \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\diamondsuit$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Diamond \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Diamond$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash heartsuit \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\heartsuit$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash P \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\P$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash copyright \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\copyright$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash circledR \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\circledR$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash maltese \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\maltese$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash diagup \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\diagup$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash diagdown \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\diagdown$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Weitere Symbole sind in \begin_inset LatexCommand ref reference "sub:Sonstige-Sonderzeichen" \end_inset aufgelistet. \end_layout \begin_layout Standard Einige Symbole können in unterschiedlicher Größe dargestellt werden, siehe \begin_inset LatexCommand ref reference "sub:Schriftgrößen" \end_inset . \end_layout \begin_layout Subsection Das Euro-Symbol € \begin_inset LatexCommand index name "Symbole ! Euro-Symbol" \end_inset \begin_inset LatexCommand index name "\\textcent@\\officialeuro" \end_inset \end_layout \begin_layout Standard Wenn man in einer Formel das Euro-Symbol verwenden will, muss man das LaTeX-Pake t \series bold eurosym \series default \begin_inset LatexCommand index name "Pakete ! eurosym" \end_inset installieren und dieses mit der LaTeX-Vorspannzeile \end_layout \begin_layout Standard \series bold \backslash usepackage[gennarrow]{eurosym} \end_layout \begin_layout Standard aktivieren. Das Euro-Symbol kann man nun mit dem Befehl \series bold \backslash euro \series default \begin_inset LatexCommand index name "Befehle ! E ! \\textbackslash euro" \end_inset aufrufen. \end_layout \begin_layout Standard Das Euro-Symbol kann man direkt übder die Tastatur in mathematischen Text eingeben, ohne \series bold eurosym \series default installiert zu haben. Ist \series bold eurosym \series default installiert, kann man \series bold \backslash euro \series default auch im TeX-Modus eingeben. Das offizielle Währungssymbol erhält man dann über den Befehl \series bold \backslash officialeuro \series default \begin_inset LatexCommand index name "Befehle ! O ! \\textbackslash officialeuro" \end_inset , der nur im TeX-Modus verfügbar ist. \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 Die folgende Tabelle erscheint nur im Ausdruck wenn das LaTeX-Paket \series bold eurosym \series default installiert ist: \end_layout \end_inset \end_layout \begin_layout Standard Eine Übersicht der verschiedenen Euro-Symbole: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="3"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell multicolumn="1" alignment="center" valignment="top" bottomline="true" usebox="none"> \begin_inset Text \begin_layout Standard \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Formel \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash euro \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\euro$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard mathematischer Text \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard € \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mbox{€}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard TeX-Modus \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash officialeuro \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash officialeuro \end_layout \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \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 Folgendes erscheint im Ausdruck wenn das LaTeX-Paket \series bold eurosym \series default nicht installiert ist: \end_layout \end_inset \end_layout \begin_layout Standard Das LaTeX-Paket \series bold eurosym \series default muss installiert sein, um den Rest dieses Abschnitts im Ausdruck zu sehen. \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash fi \end_layout \end_inset \end_layout \begin_layout Section Relationen \begin_inset LatexCommand label name "sec:Relationen" \end_inset \begin_inset LatexCommand index name "Relationen" \end_inset \begin_inset LatexCommand index name "Vergleiche|see{Relationen}" \end_inset \end_layout \begin_layout Standard Alle griechischen Buchstaben können auch über den Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/leq.png scale 85 \end_inset eingefügt werden. \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="17" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard < \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $<$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash le \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\le$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ll \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\ll$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash prec \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\prec$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash preceq \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\preceq$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash subset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\subset$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash subseteq \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\subseteq$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sqsubseteq \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\sqsubseteq$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash in \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\in$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash vdash \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\vdash$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash smile \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\smile$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash lhd \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\lhd$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash unlhd \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\unlhd$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash gtrless \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\gtrless$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash mid \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mid$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash nmid \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\nmid$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="17" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard = \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $=$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash not= \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\not=$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash equiv \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\equiv$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sim \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\sim$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash simeq \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\simeq$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash approx \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\approx$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash cong \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\cong$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bowtie \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\bowtie$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash notin \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\notin$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash perp \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\perp$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash propto \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\propto$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash asymp \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\asymp$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash doteq \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\doteq$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash circeq \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\circeq$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash models \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\models$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash widehat= \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\widehat{=}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="17" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard > \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $>$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ge \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\ge$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash gg \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\gg$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash succ \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\succ$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash succeq \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\succeq$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash supset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\supset$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash supseteq \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\supseteq$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sqsupseteq \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\sqsupseteq$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ni \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\ni$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash dashv \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\dashv$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash frown \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\frown$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash rhd \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\rhd$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash unrhd \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\unrhd$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash lessgtr \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\lessgtr$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash parallel \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\parallel$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash nparallel \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\nparallel$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Die Zeichen \series bold \backslash lhd \series default bzw. \series bold \backslash rhd \series default sind größer als die gleich aussehenden Operatoren \begin_inset ERT status collapsed \begin_layout Standard \backslash linebreak \end_layout \end_inset \series bold \backslash triangleleft \series default bzw. \series bold \backslash triangleright \series default . \end_layout \begin_layout Standard Relationen sind im Gegensatz zu Symbolen immer von Leerraum umgeben. \end_layout \begin_layout Standard Relationen mit Beschriftungen können mit Hilfe des Befehls \series bold \backslash stackrel \series default \begin_inset LatexCommand index name "Befehle ! S ! \\textbackslash stackrel" \end_inset erstellt werden: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="2" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard A(r) \backslash stackrel \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset r \backslash to \backslash infty \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \begin_inset Formula $\downarrow$ \end_inset \backslash approx \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Section Funktionen \end_layout \begin_layout Subsection Vordefinierte Funktionen \begin_inset LatexCommand label name "sub:Vordefinierte-Funktionen" \end_inset \begin_inset LatexCommand index name "Funktionen ! vordefinierte" \end_inset \end_layout \begin_layout Standard Allgemein werden in mathematischen Ausdrücken Variablen \shape italic kursiv \shape default gesetzt, Funktionsnamen hingegen nicht, denn \begin_inset Formula $sin$ \end_inset könnte als \begin_inset Formula $s\cdot i\cdot n$ \end_inset missverstanden werden. Aus diesem Grund gibt es vordefinierte Funktionen, die zusätzlich von Vorfaktor en etwas abgesetzt sind. Sie werden als Befehle mit einem Backslash vor dem Funktionsnamen eingefügt. \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="2" columns="4"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Asin(x)+B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $Asin(x)+B$ \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard A \backslash sin(x)+B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\sin(x)+B$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Folgende Funktionen sind vordefiniert: \end_layout \begin_layout Standard \begin_inset VSpace -2mm \end_inset \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="9" columns="4"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sin \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sinh \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash arcsin \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sup \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash cos \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash cosh \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash arccos \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash inf \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash tan \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash tanh \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash arctan \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash lim \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash cot \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash coth \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash arg \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash liminf \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash sec \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash min \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash deg \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash limsup \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash csc \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash max \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash det \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Pr \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ln \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash exp \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash dim \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash hom \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash lg \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash log \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ker \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash gcd \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Sie können auch über den Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/functions.png scale 85 \end_inset eingefügt werden. \end_layout \begin_layout Subsection Selbst definierte Funktionen \begin_inset LatexCommand index name "Funktionen ! selbstdefinierte" \end_inset \end_layout \begin_layout Standard Will man eine Funktion verwenden, die nicht vordefiniert ist, wie z.\InsetSpace \thinspace{} B. die Signumfunktion sgn(x), hat man zwei Möglichkeiten: \end_layout \begin_layout Itemize Man definiert die Funktion selbst. Dazu gibt man im LaTeX-Vorspann die Zeile \newline \begin_inset VSpace -3mm \end_inset \newline \series bold \backslash DeclareMathOperator{ \backslash sgn}{sgn} \series default \begin_inset LatexCommand index name "Befehle ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator" \end_inset \newline \begin_inset VSpace -2mm \end_inset \newline ein \begin_inset Foot status collapsed \begin_layout Standard Näheres zu \series bold \backslash DeclareMathOperator \series default siehe \begin_inset LatexCommand ref reference "sub:Selbstdefinierte-Operatoren" \end_inset . \end_layout \end_inset . Nun kann man mit dem Befehl \series bold \backslash sgn \series default die neu definierte Funktion aufrufen. \end_layout \begin_layout Itemize Man schreibt die Formel wie gewohnt, markiert den Formelnamen, also in unserem Beispiel die Buchstaben \emph on sgn \emph default , und wandelt ihn in in mathematischen Text um. Zwischen Vorfaktor und Funktion fügt man einen kleinen Leerraum ein. \end_layout \begin_layout Standard Das Ergebnis ist bei beiden Methoden dasselbe wie bei einer vordefinierten Funktion \begin_inset Foot status collapsed \begin_layout Standard Selbst definierte Funktionen werden in LyX rot, vordefinierte schwarz angezeigt. \end_layout \end_inset : \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="3" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0pt"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0pt"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard A \backslash sgn(x)+B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\sgn(x)+B$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\,\textrm{sgn}(x)+B$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Die erste Methode ist besser geeignet, wenn die selbst definierte Funktion mehrfach verwendet werden soll. \end_layout \begin_layout Subsection Grenzwerte \begin_inset LatexCommand index name "Grenzwerte" \end_inset \end_layout \begin_layout Standard Für Grenzwerte sind außer \series bold \backslash lim \series default \begin_inset LatexCommand index name "Befehle ! L ! \\textbackslash lim" \end_inset , \series bold \backslash liminf \series default und \series bold \backslash limsup \series default noch folgende Funktionen definiert: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="5" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash varliminf \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\varliminf$ \end_inset \end_layout \end_inset </cell> </row> <row> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash varlimsup \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\varlimsup$ \end_inset \end_layout \end_inset </cell> </row> <row> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash varprojlim \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\varprojlim$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash varinjlim \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\varinjlim$ \end_inset \begin_inset Formula $\raisebox{-2.5mm}{}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Der Grenzwert wird durch Tiefstellen erzeugt. Bei einer eingebetteten Formel wird er rechts neben die Funktion gesetzt: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="2" columns="2"> <features> <column alignment="center" valignment="top" width="0pt"> <column alignment="center" valignment="top" width="0pt"> <row> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{1cm} \end_layout \end_inset Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash hspace \series default und \series bold \backslash raisebox \series default dienen nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash lim_x \backslash to \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset x=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard In einer abgesetzten Formel steht der Grenzwert wie gewohnt darunter: \begin_inset Formula \[ \lim_{x\to A}x=B\] \end_inset \end_layout \begin_layout Subsection Modulo-Funktionen \begin_inset LatexCommand index name "Funktionen ! Modulo-" \end_inset \end_layout \begin_layout Standard Eine Besonderheit stellt die Modulo-Funktion dar, denn es gibt sie in vier Varianten. \newpage \end_layout \begin_layout Standard Die Varianten in einer abgesetzten Formel: \begin_inset Formula \begin{align*} \underline{\textrm{Befehl}\raisebox{-0.9mm}{}} & & \underline{\textrm{Ergebnis}}\\ \mathrm{a\backslash mod\textrm{\leer}b} & & a\mod b\\ \mathrm{a\backslash pmod\textrm{\leer}b} & & a\pmod b\\ \mathrm{a\backslash bmod\textrm{\leer}b} & & a\bmod b\\ \mathrm{a\backslash pod\textrm{\leer}b} & & a\pod b\end{align*} \end_inset \end_layout \begin_layout Standard In einer eingebetteten Formel wird bei allen Varianten vor den Funktionsnamen weniger Leerraum gesetzt. \end_layout \begin_layout Section Sonderzeichen \begin_inset LatexCommand index name "Sonderzeichen" \end_inset \end_layout \begin_layout Subsection Sonderzeichen im mathematischen Text \end_layout \begin_layout Standard Die folgenden Befehle können nur im mathematischen Textmodus oder im TeX-Modus verwendet werden: \end_layout \begin_layout Standard \hfill \begin_inset Tabular <lyxtabular version="3" rows="8" columns="2"> <features> <column alignment="block" valignment="top" leftline="true" width="0"> <column alignment="block" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash oe \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\oe}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash OE \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\OE}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ae \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\ae}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash AE \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\AE}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash aa \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\aa}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash AA \begin_inset LatexCommand index name "\\@\\textrm{\\AA}" \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\AA}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash i \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\i}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="8" columns="2"> <features> <column alignment="block" valignment="top" leftline="true" width="0"> <column 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alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash L \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\L}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 leer \end_layout \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{!`}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 leer \end_layout \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{?`}$ \end_inset \end_layout \end_inset </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash j \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\textrm{\j}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard Die Zeichen \begin_inset Formula $\textrm{\textrm{Å}}$ \end_inset und \begin_inset Formula $\textrm{\textrm{Ø}}$ \end_inset können auch über den Mathe-Werkzeugleistenknopf \begin_inset Graphics filename ../../images/math/digamma.png scale 85 \end_inset eingefügt werden. \end_layout \begin_layout Standard Eine Ausnahme bilden die Befehle \series bold ! \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{0mm} \end_layout \end_inset ` \series default und \series bold ? \begin_inset ERT status collapsed \begin_layout Standard \backslash hspace{0mm} \end_layout \end_inset ` \series default , denn man kann sie in LyX direkt in den Text eingeben. \end_layout \begin_layout Subsection Akzente im Text \begin_inset LatexCommand label name "sub:Sonderzeichen-Akzente" \end_inset \begin_inset LatexCommand index name "Akzente ! im Text" \end_inset \end_layout \begin_layout Standard Man kann mit den folgenden Befehlen sämtliche Buchstaben akzentuieren. 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topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash t \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset ee \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \hfill \begin_inset Tabular <lyxtabular version="3" rows="8" columns="2"> <features> <column alignment="block" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell 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\backslash d \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset e \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash c \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset e \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \hfill \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Mit dem Befehl \series bold \backslash t \series default können auch zwei verschiedene Zeichen akzentuiert werden. Der Befehl \series bold \backslash t \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset sz \series default ergibt: \begin_inset ERT status collapsed \begin_layout Standard \backslash t sz \end_layout \end_inset \end_layout \begin_layout Standard Die Akzente \series bold ` \series default , \series bold ' \series default und \series bold ^ \series default können in Verbindung mit Selbstlauten auch direkt über die Tastatur eingegeben werden ohne den TeX-Modus zu benutzen. Dasselbe gilt für die Tilde \begin_inset Foot status collapsed \begin_layout Standard Gilt nur für Tastaturen, bei denen die Tilde als Akzent definiert ist. \end_layout \end_inset \series bold ~ \series default in Verbindung mit \emph on a \emph default , \emph on n \emph default oder \emph on o \emph default . \end_layout \begin_layout Standard Die Befehle \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 und direkt über die Tastatur eingegebene Akzente sind auch im mathematischen Textmodus verfügbar. Für die restlichen Akzente gibt es in Formeln spezielle Mathebefehle, siehe \begin_inset LatexCommand ref reference "sub:Akzente-für-ein" \end_inset . \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Des Weiteren kann man mit dem Befehl \series bold \backslash textcircled \series default \begin_inset LatexCommand index name "Befehle ! T ! \\textbackslash textcircled" \end_inset , ähnlich dem Copyrightsymbol, sämtliche Zahlen und Buchstaben in einen Kreis setzen, quasi mit einem Kreis akzentuieren. \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="3" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default in der Formel dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash textcircled{w} \end_layout \end_inset </cell> <cell multicolumn="1" alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Large \backslash textcircled{ \backslash normalsize \backslash protect \backslash raisebox{-1.5pt}{W}} \end_layout \end_inset </cell> <cell multicolumn="1" alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Man muss darauf achten, dass das Zeichen in einen Kreis passt. \series bold \backslash Large \series default \begin_inset Foot status collapsed \begin_layout Standard siehe \begin_inset LatexCommand ref reference "sub:Schriftgrößen" \end_inset \end_layout \end_inset bestimmt dabei die Größe des Kreises. Mit Hilfe von \series bold \backslash raisebox \series default \begin_inset Foot status collapsed \begin_layout Standard siehe \begin_inset LatexCommand ref reference "sub:Boxen-ohne-Rahmen" \end_inset \end_layout \end_inset kann man das Zeichen zentrieren. \end_layout \begin_layout Subsection Minuskelziffern \begin_inset LatexCommand index name "Minuskelziffern" \end_inset \end_layout \begin_layout Standard Minuskelziffern werden mit dem Befehl \series bold \backslash oldstylenums \series default \begin_inset LatexCommand index name "Befehle ! O ! \\textbackslash oldstylenums" \end_inset erzeugt. Der Befehl ist sowohl in einer Formel als auch im TeX-Modus verwendbar. Das Befehlsschema lautet: \end_layout \begin_layout Standard \series bold \backslash oldstylenums{Ziffer} \end_layout \begin_layout Standard Der Befehl \series bold \backslash oldstylenums{0123456789 \series default ergibt: \begin_inset Formula $\oldstylenums{0123456789}$ \end_inset \end_layout \begin_layout Subsection Sonstige Sonderzeichen \begin_inset LatexCommand label name "sub:Sonstige-Sonderzeichen" \end_inset \begin_inset LatexCommand index name "Sonderzeichen ! sonstige" \end_inset \end_layout \begin_layout Standard Folgende Zeichen können in eine Formel nur mit Befehlen eingegeben werden: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash ^ \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\mathcircumflex$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash _ \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\_$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard ^ \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \backslash circ \begin_inset LatexCommand index name "°" \end_inset \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $^{\circ}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Das Gradzeichen ° kann dennoch direkt eingegeben werden, wenn der LaTeX-Vorspann folgende Zeile enthält \begin_inset Foot status collapsed \begin_layout Standard Mehr dazu ist in \begin_inset LatexCommand ref reference "sub:Textzeichen-in-Formeln" \end_inset beschrieben. \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 Die Tilde \begin_inset LatexCommand index name "Tilde" \end_inset ist nur für Akzente gedacht, weswegen sie alleine deplatziert wirkt: ~ \newline Aber für Webadressen (URLs) wird manchmal eine einzelne Tilde benötigt. Man verwendet in diesem Fall das Relationszeichen \series bold \backslash sim \begin_inset Foot status collapsed \begin_layout Standard siehe \begin_inset LatexCommand ref reference "sec:Relationen" \end_inset \end_layout \end_inset \series default in einer Formel. Da in einer URL-Box (Menü \family sans Einfügen\SpecialChar \menuseparator URL \family default ) keine Formel erstellt werden kann, gibt man die URL als normalen Text in der Stilart ' \family typewriter Schreibmaschine \family default ' ein. Soll die URL in der DVI- oder PDF-Ausgabe einen Link produzieren, verwendet man den Befehl \series bold \backslash href \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold \backslash href \series default kann nur zusammen mit dem LaTeX-Paket \series bold hyperref \series default \begin_inset LatexCommand index name "Pakete ! hyperref" \end_inset verwendet werden. Mehr zu \series bold \backslash href \series default steht im Kapitel \family typewriter URL \family default im Handbuch \family typewriter Eingebettete\InsetSpace ~ Objekte \family default . \end_layout \end_inset . \begin_inset LatexCommand index name "Befehle ! H ! \\textbackslash href" \end_inset \end_layout \begin_layout Standard Als Beispiel eine URL mit einer Tilde: \end_layout \begin_layout Standard als Text: \family typewriter http://www.lyx.org/ \begin_inset Formula $\sim$ \end_inset mustermann \end_layout \begin_layout Standard mit \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 Formelstile \begin_inset LatexCommand label name "sec:Formelstile" \end_inset \begin_inset LatexCommand index name "Formel ! Stile" \end_inset \end_layout \begin_layout Itemize Für abgesetzte Formeln gibt es zwei verschiedene Anordnungsstile: \end_layout \begin_deeper \begin_layout Description Zentriert ist der voreingestellte Standard \end_layout \begin_layout Description Eingerückt dazu muss im Menü \family sans Dokument\SpecialChar \menuseparator Einstellungen \family default unter \family sans Dokumentklasse \family default die Option \series bold fleqn \series default eingeben werden \end_layout \begin_layout Standard Wird \series bold Eingerückt \series default verwendet, kann mit der Länge \series bold \backslash mathindent \series default \begin_inset LatexCommand index name "Befehle ! M ! \\textbackslash mathindent" \end_inset die Einrückung eingestellt werden. Soll der Abstand 15\InsetSpace \thinspace{} mm betragen, gibt man im LaTeX-Vorspann die Zeile \end_layout \begin_layout Standard \series bold \backslash setlength{ \backslash mathindent}{15mm} \end_layout \begin_layout Standard ein. Wenn keine Länge vorgegeben wird, wird der voreingestellte Wert von 30\InsetSpace \thinspace{} pt verwendet. \end_layout \end_deeper \begin_layout Itemize Und zwei verschiedene Nummerierungsstile: \end_layout \begin_deeper \begin_layout Description Rechts ist der voreingestellte Standard \end_layout \begin_layout Description Links dazu muss im Menü \family sans Dokument\SpecialChar \menuseparator Einstellungen \family default unter \family sans Dokumentklasse \family default die Option \series bold leqno \series default eingeben werden \end_layout \end_deeper \begin_layout Standard \series bold fleqn \series default und \series bold leqno \series default können auch gemeinsam verwendet werden. Dazu werden beide Optionen, durch ein Komma getrennt, hintereinander geschriebe n. \end_layout \begin_layout Standard Die eingestellten Stile gelten für alle abgesetzten Formeln eines Dokuments. Möchte man jedoch in einem Dokument sowohl zentrierte als auch eingerückte ausgerichtete Formeln setzen, verwendet man den Stil \series bold Zentriert \series default . Die einzurückenden Formeln setzt man dann in eine flalign-Umgebung, siehe \begin_inset LatexCommand ref reference "sub:Flalign-Umgebung" \end_inset . \end_layout \begin_layout Section Mehrzeilige Formeln \begin_inset LatexCommand label name "sec:Mehrzeilige-Formeln" \end_inset \begin_inset LatexCommand index name "Formel ! mehrzeilige" \end_inset \end_layout \begin_layout Subsection Allgemeines \end_layout \begin_layout Standard In LyX werden mehrzeilige Formeln erstellt, wenn man in einer Formel \family sans \series bold Strg-Enter \family default \series default drückt. Dies erzeugt eine \series bold align-Umgebung \series default , die in \begin_inset LatexCommand ref reference "sub:Standard-align-Umgebung" \end_inset beschrieben ist. \end_layout \begin_layout Standard Es gibt noch weitere mehrzeilige Formelumgebungen, die über das Menü \family sans Einfügen\SpecialChar \menuseparator Mathe \family default erstellt werden können. Diese Umgebungen werden in den folgenden Kapiteln beschrieben. \end_layout \begin_layout Standard In allen mehrzeiligen Formelumgebungen erstellt man eine neue Zeile, indem man \family sans Strg-Enter \family default drückt. Um Spalten hinzuzufügen oder zu entfernen, können die Mathe-Werkzeugleistenknöp fe \begin_inset Graphics filename ../../images/tabular-feature_append-row.png scale 85 \end_inset bzw.\InsetSpace ~ \begin_inset Graphics filename ../../images/tabular-feature_delete-row.png scale 85 \end_inset oder das Menü \family sans Bearbeiten\SpecialChar \menuseparator Zeilen & Spalten \family default verwendet werden. \end_layout \begin_layout Subsubsection Zeilenabstand \begin_inset LatexCommand label name "sub:Zeilenabstand" \end_inset \begin_inset LatexCommand index name "Formel ! mehrzeilige ! Zeilenabstand" \end_inset \end_layout \begin_layout Standard Bei mehrzeiligen Formeln fehlt manchmal etwas Platz zwischen den Zeilen: \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 wird zusätzlicher Zeilenabstand als optionales Argument des Zeilenumbru chbefehls angegeben. Dies ist in LyX aber nicht möglich \begin_inset Foot status collapsed \begin_layout Standard siehe \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{ \end_layout \end_inset LyX-Fehler #1505 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset , weshalb man die ganze Formel im TeX-Modus eingeben muss. Um für unser Beispiel Leerraum einzufügen, gibt man am Ende der ersten Zeile den Befehl \series bold \backslash \backslash [3mm] \series default ein. Damit erhält man: \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 Möchte man den Zeilenabstand für alle Zeilen einer Formel festlegen, verändert man die Länge \series bold \backslash jot \series default \begin_inset LatexCommand index name "Befehle ! J ! \\textbackslash jot" \end_inset . Es gilt \begin_inset Formula $\mbox{Zeilenabstand}=\mathrm{6\, pt+\backslash jot}$ \end_inset . Voreingestellt ist für \series bold \backslash jot \series default der Wert 3\InsetSpace \thinspace{} pt. Um wie im vorigen Beispiel 3\InsetSpace \thinspace{} mm zusätzlichen Zeilenabstand zu erzeugen, gibt man den Befehl \end_layout \begin_layout Standard \series bold \backslash setlength{ \backslash jot}{3mm+3pt} \end_layout \begin_layout Standard im TeX-Modus vor der Formel ein. Das setzt voraus, dass das LaTeX-Paket \series bold calc \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold calc \series default ist Teil jeder LaTeX-Standardinstallation. \end_layout \end_inset \begin_inset LatexCommand index name "Pakete ! calc" \end_inset im LaTeX-Vorspann mit der Zeile \end_layout \begin_layout Standard \series bold \backslash usepackage{calc} \end_layout \begin_layout Standard geladen wurde. \end_layout \begin_layout Standard Man erhält: \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 Um wieder zum voreingestellten Abstand zu wechseln, setzt man \series bold \backslash jot \series default auf den Wert 3\InsetSpace \thinspace{} pt. \end_layout \begin_layout Subsubsection Spaltenabstand \begin_inset LatexCommand label name "sub:Spaltenabstand" \end_inset \begin_inset LatexCommand index name "Formel ! mehrzeilige ! Spaltenabstand" \end_inset \end_layout \begin_layout Standard Mehrzeilige Formeln bilden eine Matrix. Eine Formel in der Eqnarray-Umgebung ist z.\InsetSpace \thinspace{} B. eine dreispaltige Matrix. Durch Änderung des Spaltenabstands in dieser Umgebung, kann man den Leerraum neben den Relationszeichen ändern. \end_layout \begin_layout Standard Der Spaltenabstand wird mit der Länge \series bold \backslash arraycolsep \series default \begin_inset LatexCommand index name "Befehle ! A ! \\textbackslash arraycolsep" \end_inset festgelegt, wobei gilt: \newline Spaltenabstand = 2\InsetSpace \thinspace{} \series bold \backslash arraycolsep \series default . \newline Der im TeX-Modus eingegebene Befehl \end_layout \begin_layout Standard \series bold \backslash setlength{ \backslash arraycolsep}{1cm} \end_layout \begin_layout Standard bewirkt also für alle folgenden Formeln einen Spaltenabstand von 2\InsetSpace \thinspace{} cm. Um wieder zum voreingestellten Abstand zurückzukehren, setzt man \series bold \backslash arraycolsep \series default auf 5\InsetSpace \thinspace{} pt. \end_layout \begin_layout Standard Eine Formel mit 2\InsetSpace \thinspace{} cm Spaltenabstand: \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 Eine Formel mit dem für Matrizen voreingestellten Spaltenabstand von 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 Lange Formeln \begin_inset LatexCommand index name "Formel ! lange" \end_inset \end_layout \begin_layout Standard Lange Formeln kann man wie folgt setzen: \end_layout \begin_layout Itemize Ist eine Seite der Gleichung deutlich kürzer als die Zeilenbreite, wählt man man diese als linke Seite und schreibt die rechte über zwei Zeilen: \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 Das Minuszeichen zu Beginn der zweiten Zeile erscheint eigentlich nicht als Operator, da es das erste Zeichen der Zeile ist. Deswegen wäre es nicht von Leerraum umgeben und ließe sich schlecht vom Bruchstrich unterscheiden. Um das zu verhindern, wurde mit dem Befehl \series bold \backslash hspace{3pt} \series default \begin_inset Foot status collapsed \begin_layout Standard mehr zu \series bold \backslash hspace \series default siehe \begin_inset LatexCommand ref reference "sub:Variabler-Leerraum" \end_inset \end_layout \end_inset \begin_inset LatexCommand index name "Befehle ! H ! \\textbackslash hspace" \end_inset Leerraum hinter das Minuszeichen eingefügt. \end_layout \begin_layout Itemize Sind beide Seiten der Gleichung zu lang, verwendet man den Befehl \series bold \backslash lefteqn \series default \begin_inset LatexCommand index name "Befehle ! L ! \\textbackslash lefteqn" \end_inset . Dieser wird in die erste Spalte der ersten Zeile eingegeben und bewirkt, dass alle weiteren Eingaben die folgenden Spalten überschreiben: \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 Nachdem man \series bold \backslash lefteqn \series default eingegeben hat, befindet sich der Cursor in einem pinkfarbenen Kästchen, das gegenüber dem blauen leicht verschoben ist. In dieses wird die Formel eingegeben. \begin_inset ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \newline Der Inhalt der weiteren Zeilen wird in die zweite oder eine andere Formelspalte eingegeben. Je größer die Spaltennummer in die eingegeben wurde, desto größer ist die Einrückung. \begin_inset ERT status collapsed \begin_layout Standard \backslash medskip \end_layout \end_inset \newline \begin_inset Note Greyedout status open \begin_layout Standard Bei der Verwendung von \series bold \backslash lefteqn \series default ist Folgendes zu beachten: \end_layout \begin_layout Itemize Die Formel nutzt nicht die gesamte Seitenbreite aus. Würde man in obigem Beispiel der ersten Zeile den Term \begin_inset Formula $-B^{2}$ \end_inset anfügen, befände sich dieser außerhalb des Seitenrands. Um die Breite besser auszunutzen, kann man zu Beginn der ersten Zeile negativen Leerraum einfügen. \end_layout \begin_layout Itemize Aufgrund eines Fehlers in LyX kann der Cursor nicht mit der Maus in die erste Zeile gesetzt werden. \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-Fehler #1429 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \end_layout \end_inset Man kann den Cursor nur an den Anfang der Zeile setzen und ihn mit den Pfeiltasten bewegen. \end_layout \end_inset \end_layout \begin_layout Itemize Weitere Möglichkeiten lange Formeln zu setzen, bieten die in \begin_inset LatexCommand ref reference "sub:Multline-Umgebung" \end_inset und \begin_inset LatexCommand ref reference "sub:Mehrzeilige-Formelteile" \end_inset beschriebenen Umgebungen. \end_layout \begin_layout Subsubsection Mehrzeilige Klammern \begin_inset LatexCommand label name "sub:Mehrzeilige-Klammern" \end_inset \begin_inset LatexCommand index name "Klammern ! mehrzeilige" \end_inset \end_layout \begin_layout Standard Bei Klammern, die über mehrere Zeilen gehen, tritt folgendes Problem auf: \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 Die schließende Klammer ist kleiner als die öffnende, denn Klammern variabler Größe dürfen nicht über mehrere Zeilen gehen. \end_layout \begin_layout Standard Um die Größe für die Klammer der zweiten Zeile anzupassen, beendet man die erste Zeile mit \series bold \backslash right. \series default \begin_inset LatexCommand index name "Befehle ! R ! \\textbackslash right" \end_inset und beginnt die zweite Zeile mit \series bold \backslash left. \begin_inset Foot status collapsed \begin_layout Standard mehr zu \series bold \backslash left \series default und \series bold \backslash right \series default siehe \begin_inset LatexCommand ref reference "sub:Automatische-Klammergrößen" \end_inset \end_layout \end_inset \series default \begin_inset LatexCommand index name "Befehle ! L ! \\textbackslash left" \end_inset . Nach \series bold \backslash left. \series default gibt man den Befehl \series bold \backslash vphantom \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series bold \backslash prod \series default ^ \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series bold \backslash infty \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series bold \begin_inset Formula $\downarrow$ \end_inset _R=1} \series default \begin_inset LatexCommand index name "Befehle ! V ! \\textbackslash vphantom" \end_inset ein, denn der Multiplikationsoperator mit seinen Grenzen ist das größte Symbol der ersten Zeile, und daran soll die zweite Klammer angepasst werden. \end_layout \begin_layout Standard Das Ergebnis sieht so aus: \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-Umgebungen \end_layout \begin_layout Standard Align-Umgebungen können für jede Art von mehrzeiligen Formeln verwendet werden. Sie sind besonders geeignet um mehrere Formeln nebeneinander zu setzen. \end_layout \begin_layout Standard Align-Umgebungen bestehen aus Spalten. Die ungeradzahligen Spalten sind rechts-, die geradzahligen linksbündig ausgerichtet. Jede Zeile einer Align-Umgebung kann nummeriert werden. \end_layout \begin_layout Standard Align-Umgebung werden über das Menü \family sans Einfügen\SpecialChar \menuseparator Mathe \family default erstellt. Über das Menü \family sans Bearbeiten\SpecialChar \menuseparator Mathe\SpecialChar \menuseparator Formelart\InsetSpace ~ ändern \family default können bereits existierende Formeln in Align-Umgebungen umgewandelt werden. \end_layout \begin_layout Standard Um Spalten hinzuzufügen oder zu entfernen, können die Mathe-Werkzeugleistenknöpf e \begin_inset Graphics filename ../../images/tabular-feature_append-column.png scale 85 \end_inset bzw.\InsetSpace ~ \begin_inset Graphics filename ../../images/tabular-feature_delete-column.png scale 85 \end_inset oder das Menü \family sans Bearbeiten\SpecialChar \menuseparator Zeilen & Spalten \family default verwendet werden. \end_layout \begin_layout Subsubsection Standard align-Umgebung \begin_inset LatexCommand label name "sub:Standard-align-Umgebung" \end_inset \begin_inset LatexCommand index name "Formel ! mehrzeilige ! align-Umgebung" \end_inset \end_layout \begin_layout Standard Diese Align-Umgebung wird erstellt, indem man in einer Formel \family sans Strg-Enter \family default drückt oder das Menü \family sans Einfügen\SpecialChar \menuseparator Mathe\SpecialChar \menuseparator AMS align-Umge\SpecialChar \- bung \family default aufruft. \end_layout \begin_layout Standard Ein Beispiel für zwei nebeneinander stehende Formeln, die mit einer vierspaltige n align-Umgebung erzeugt wurden: \begin_inset Formula \begin{align*} A & =\sin(B) & C & =D\\ C & \ne A & B & \ne D\end{align*} \end_inset Wie man sieht, werden die Formeln in dieser Umgebung so angeordnet, als würde sich vor der ersten und hinter jeder geraden Spalte ein \series bold \backslash hfill \begin_inset Foot status collapsed \begin_layout Standard mehr zu \series bold \backslash hfill \series default siehe \begin_inset LatexCommand ref reference "sub:Variabler-Leerraum" \end_inset \end_layout \end_inset \series default befinden. Ist der Formelstil \series bold Eingerückt \begin_inset Foot status collapsed \begin_layout Standard Formelstile siehe \begin_inset LatexCommand ref reference "sec:Formelstile" \end_inset \end_layout \end_inset \series default gewählt, wird die Formel ohne den \series bold \backslash hfill \series default vor der ersten Spalte gesetzt. \end_layout \begin_layout Subsubsection Alignat-Umgebung \begin_inset LatexCommand index name "Formel ! mehrzeilige ! alignat-Umgebung" \end_inset \end_layout \begin_layout Standard In der alignat-Umgebung gibt es keinen vordefinierten Spaltenabstand. Man kann ihn manuell durch die in \begin_inset LatexCommand ref reference "sub:Leerraum" \end_inset beschriebenen Leerräume einfügen. \end_layout \begin_layout Standard Das vorige Beispiel in der alignat-Umgebung, bei dem zu Beginn der zweiten Formel 1\InsetSpace \thinspace{} cm Leerraum eingefügt wurde: \begin_inset Formula \begin{alignat*}{2} A & =\sin(B) & \hspace{1cm}C & =D\\ C & \ne A & B & \ne D\end{alignat*} \end_inset Weil man den Spaltenabstand für jede Spalte einzeln einstellen kann, eignet sich diese Umgebung besonders für drei und mehr nebeneinander gesetzte Formeln. \end_layout \begin_layout Subsubsection Flalign-Umgebung \begin_inset LatexCommand label name "sub:Flalign-Umgebung" \end_inset \begin_inset LatexCommand index name "Formel ! mehrzeilige ! flalign-Umgebung" \end_inset \end_layout \begin_layout Standard Bei dieser Umgebung werden die ersten beiden Spalten immer so weit links und die letzten beiden Spalten so weit rechts wie möglich gesetzt. Dazu ein Beispiel: \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 Erzeugt man eine flalign-Umgebung mit ungerader Spaltenanzahl und gibt in die letzte Spalte eine leere TeX-Klammer ein, kann man einzelne Formeln im Dokument links setzen obwohl der Formelstil \series bold Zentriert \series default eingestellt ist. Als Beispiel die eingerückte ausgerichtete Formel \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 In den ersten beiden Spalten befindet sich die Formel. Damit sie wie beim Formelstil \series bold Eingerückt \series default vom Rand etwas abgesetzt ist, wurde zu Beginn der ersten Spalte 30\InsetSpace \thinspace{} pt Leerraum eingefügt. \end_layout \begin_layout Subsection Eqnarray-Umgebung \begin_inset LatexCommand index name "Formel ! mehrzeilige ! Eqnarray-Umgebung" \end_inset \end_layout \begin_layout Standard Hat man diese Umgebung erzeugt, erscheinen drei blaue Kästchen. Der Inhalt des ersten Kästchens wird rechtsbündig, der des letzten linksbündig ausgerichtet. Der Inhalt des mittleren Kästchens erscheint zentriert und etwas kleiner, da dieses Kästchen nur für Relationzeichen gedacht ist. \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-Umgebung \begin_inset LatexCommand index name "Formel ! mehrzeilige ! Gather-Umgebung" \end_inset \end_layout \begin_layout Standard Diese Umgebung besteht nur aus einer Spalte, deren Inhalt zentriert ist. Jede Zeile kann nummeriert werden. \begin_inset Formula \begin{gather} A=1\\ X=\textrm{-}1\end{gather} \end_inset \end_layout \begin_layout Subsection Multline-Umgebung \begin_inset LatexCommand label name "sub:Multline-Umgebung" \end_inset \begin_inset LatexCommand index name "Formel ! mehrzeilige ! Multline-Umgebung" \end_inset \end_layout \begin_layout Standard Die multline-Umgebung besteht wie die Gather-Umgebung nur aus einer Spalte. Jedoch ist die erste Zeile links, die letzte rechts ausgerichtet. Alle anderen Zeilen sind zentriert. Dadurch eignet sich diese Umgebung besonders für lange Formeln. Als Beispiel Formel \begin_inset LatexCommand eqref reference "eq:lefteqn" \end_inset in der multline-Umgebung: \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 der Ausgabe erscheint nur die letzte (erste) Zeile einer multline-Umgebung nummeriert, wenn rechts (links) nummeriert wird. \begin_inset Foot status collapsed \begin_layout Standard Nummerierungsstile siehe \begin_inset LatexCommand ref reference "sec:Formelstile" \end_inset \end_layout \end_inset Dies gilt auch wenn in LyX hinter jeder Zeile eine Formelnummer angezeigt wird. \begin_inset Foot status collapsed \begin_layout Standard Dies ist \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{ \end_layout \end_inset LyX-Fehler #518 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset . \end_layout \end_inset \end_layout \begin_layout Standard Mit den Befehlen \series bold \backslash shoveright \begin_inset LatexCommand index name "Befehle ! S ! \\textbackslash shoveright" \end_inset \series default und \series bold \backslash shoveleft \begin_inset LatexCommand index name "Befehle ! S ! \\textbackslash shoveleft" \end_inset \series default kann eine zentrierte Zeile rechts bzw. links ausgerichtet werden. Die Befehle werden folgendermaßen verwendet: \end_layout \begin_layout Standard \series bold \backslash shoveright{Zeileninhalt} \series default bzw. \series bold \backslash shoveleft{Zeileninhalt} \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Die Länge \series bold \backslash multlinegap \begin_inset LatexCommand index name "Befehle ! M ! \\textbackslash multlinegap" \end_inset \series default legt den Abstand der ersten Zeile vom linken Seitenrand fest. Voreingestellt ist die Länge 0\InsetSpace \thinspace{} pt. \end_layout \begin_layout Standard Als Beispiel obige Formel, vor der im TeX-Modus der Befehl \end_layout \begin_layout Standard \series bold \backslash setlength{ \backslash multlinegap}{2cm} \end_layout \begin_layout Standard eingegeben wurde: \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 \end_layout \begin_layout Standard Die zweite Zeile wurde mit \series bold \backslash shoveleft \series default linksbündig ausgerichtet. \end_layout \begin_layout Subsection Mehrzeilige Formelteile \begin_inset LatexCommand label name "sub:Mehrzeilige-Formelteile" \end_inset \begin_inset LatexCommand index name "Formel ! mehrzeilige ! Formelteile" \end_inset \end_layout \begin_layout Standard Möchte man nur Teile einer Formel mehrzeilig darstellen, verwendet man eine der folgenden Umgebungen: \series bold aligned \series default , \series bold alignedat \series default , \series bold gathered \series default oder \series bold split \series default . Sie können über das Menü \family sans Einfügen\SpecialChar \menuseparator Mathe \family default oder mit Befehlen eingefügt werden, wie in diesem Abschnitt beschrieben. \end_layout \begin_layout Standard Die ersten drei haben dieselben Eigenschaften wie die entsprechenden mehrzeilige n Formel\SpecialChar \- umgebungen. Man kann jedoch zusätzlich weitere Formelteile daneben setzen. Dazu ein Beispiel: \begin_inset Formula \[ \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\ \Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned} \right\} \textrm{Unbestimmtheitsrelationen}\] \end_inset \end_layout \begin_layout Standard Um diese Formel zu erhalten, wird eine abgesetzte Formel erstellt, in die der Befehl \series bold \backslash aligned \begin_inset LatexCommand index name "Befehle ! A ! \\textbackslash aligned" \end_inset \series default eingegeben wird. Es erscheint eine lila Box um das blaue Formelkästchen in der man nun Spalten und Zeilen hinzufügen kann. Außerhalb der mehrzeiligen Umgebung können Formelteile, wie die Klammer, gesetzt werden. \end_layout \begin_layout Standard Die aligned-Umgebung eignet sich auch für lange Formeln, deren Zeilen horizontal ausgerichtet sind. Verwendet man aligned in einer abgesetzten Formel, hat das den Vorteil, dass die Formelnummer vertikal mittig hinter den Zeilen steht. Als Beispiel Formel \begin_inset LatexCommand eqref reference "eq:kurzlang" \end_inset in der aligned-Umgebung: \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 Möchte man die Umgebung \series bold alignedat \series default , \series bold gathered \series default oder \series bold split \series default verwenden, gibt man den Befehl \series bold \backslash alignedat \series default , \begin_inset LatexCommand index name "Befehle ! A ! \\textbackslash alignedat" \end_inset \series bold \backslash gathered \series default \begin_inset LatexCommand index name "Befehle ! G ! \\textbackslash gathered" \end_inset bzw. \series bold \backslash split \series default \begin_inset LatexCommand index name "Befehle ! S ! \\textbackslash split" \end_inset ein. Die split-Umgebung hat dieselben Eigenschaften wie die aligned-Umgebung, jedoch darf sie nur zwei Spalten enthalten. \end_layout \begin_layout Subsection Text in mehrzeiligen Formeln \begin_inset LatexCommand label name "sub:Text-in-mehrzeiligen" \end_inset \begin_inset LatexCommand index name "Text ! in Formeln" \end_inset \begin_inset LatexCommand index name "Formel ! mehrzeilige ! Text" \end_inset \end_layout \begin_layout Standard Bei den Align-Umgebungen sowie der multline- und gather-Umgebung besteht die Möglichkeit Text einzufügen, der in einer eigenen Zeile erscheint und die Ausrichtung der Spalten nicht beeinflusst. Dazu wird der Befehl \series bold \backslash intertext \begin_inset LatexCommand index name "Befehle ! I ! \\textbackslash intertext" \end_inset \series default nach folgendem Schema benutzt: \end_layout \begin_layout Standard \series bold \backslash intertext{Text} \end_layout \begin_layout Standard Der Text sollte nicht länger als eine Zeile sein, da er nicht umgebrochen werden kann. Weil LyX \series bold \backslash intertext \series default noch nicht direkt unterstützt, schreibt man den Text als mathematischen Text. \series bold \backslash intertext \series default muss dabei zu Beginn einer Zeile stehen und erscheint in der Ausgabe über dieser Zeile. Ein Beispiel bei dem der Text zu Beginn der zweiten Zeile eingegeben wurde: \begin_inset Formula \begin{align} I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\ \intertext{\text{Integrand ist symmetrisch zu $\phi=\pi$, daher}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align} \end_inset \end_layout \begin_layout Section Formelnummerierung \begin_inset LatexCommand index name "Formelnummerierung" \end_inset \begin_inset LatexCommand index name "Formel ! Nummerierung|see{Formelnummerierung}" \end_inset \end_layout \begin_layout Subsection Allgemeines \end_layout \begin_layout Standard Nummerierte Formeln können mit dem Menü \family sans Einfügen\SpecialChar \menuseparator Mathe\SpecialChar \menuseparator Nummerierte\InsetSpace ~ Formel \family default (Tastenkürzel \family sans Strg-Alt\InsetSpace ~ n \family default ) erstellt, bestehende Formeln über das Menü \family sans Bearbeiten\SpecialChar \menuseparator Mathe\SpecialChar \menuseparator Nummerierung\InsetSpace ~ an/aus \family default (Tastenkürzel \family sans Alt-m\InsetSpace ~ n \family default ) nummeriert werden. Die Formelnummer erscheint in LyX hinter der Formel als Raute in runden Klammern. Im Ausdruck erscheint anstelle der Raute die Formelnummer. \end_layout \begin_layout Standard Wird in mehrzeiligen Formeln die Nummerierung angeschaltet, werden alle Zeilen nummeriert. Man kann jedoch über das Menü \family sans Bearbeiten\SpecialChar \menuseparator Mathe\SpecialChar \menuseparator Zeilennummerierung an/aus \family default (Tastenkürzel \family sans Alt-m\InsetSpace ~ N \family default ) für jede Zeile die Nummerierung festlegen. \end_layout \begin_layout Standard Außer eingebetteten können alle Formeln in zwei verschiedenen Stilen nummeriert werden, siehe \begin_inset LatexCommand ref reference "sec:Formelstile" \end_inset . \end_layout \begin_layout Subsection Querverweise \begin_inset LatexCommand label name "sub:Querverweise" \end_inset \begin_inset LatexCommand index name "Querverweise ! auf Formeln" \end_inset \end_layout \begin_layout Standard Es kann auf alle Formeln verwiesen werden, die eine Marke besitzen. Eine Marke wird mit dem Menü \family sans Einfügen\SpecialChar \menuseparator Marke \family default oder dem Werkzeugleistenknopf \begin_inset Graphics filename ../../images/label-insert.png scale 85 \end_inset gesetzt. Dabei muss sich der Cursor in einer abgesetzten Formel befinden. Es erscheint ein Eingabefeld mit dem voreingestellten Eintrag \series bold eq: \series default , nachdem der eigentliche Markenname eingegeben wird. Der voreingestellte Eintrag steht für \begin_inset Quotes gld \end_inset equation \begin_inset Quotes grd \end_inset und erleichtert bei größeren Dokumenten die Zuordnung, dass die Marke zu einer Formel und nicht zu einem Kapitel gehört. Um eine Marke zu ändern, wählt man wieder das Menü \family sans Einfügen\SpecialChar \menuseparator Marke \family default . \end_layout \begin_layout Standard Der Name der Marke erscheint in LyX in zwei runden Klammern hinter der Formel. Eine Formel mit Marke wird immer nummeriert. Wird die Nummerierung abgeschaltet, wird die Marke gelöscht. Dies ist momentan die einzige Möglichkeit eine Marke zu löschen, siehe \begin_inset ERT status collapsed \begin_layout Standard \backslash href{http://bugzilla.lyx.org/show_bug.cgi?id=2556}{ \end_layout \end_inset LyX-Fehler #2556 \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset . \end_layout \begin_layout Standard Querverweise werden mit dem Menü \family sans Einfügen\SpecialChar \menuseparator Querverweis \family default oder dem Werkzeugleistenknopf \begin_inset Graphics filename ../../images/dialog-show-new-inset_ref.png scale 85 \end_inset eingefügt. Ein Querverweis uaf Formeln erscheint im Ausdruck als Formelnummer. Wenn man im Querverweis Dialogfenster das Format \series bold (<Querverweis>) \series default wählt, erscheint der Querverweis als Formelnummer in Klammern. \newline Drückt man in LyX mit der rechten Maustaste auf einen Querverweis, gelangt man zur Formel auf die verwiesen wird. \end_layout \begin_layout Standard Als Beispiel folgen Querverweise zu Formeln aus diesem Kapitel: \begin_inset Note Note status open \begin_layout Standard Man beachte die unterschiedlichen Querverweistypen. \end_layout \end_inset \end_layout \begin_layout Standard Die Gleichungen \begin_inset LatexCommand eqref reference "eq:tag" \end_inset und \begin_inset LatexCommand eqref reference "eq:c" \end_inset sind äquivalent. In ( \begin_inset LatexCommand ref reference "eq:Lat" \end_inset ) werden im Gegensatz zu ( \begin_inset LatexCommand ref reference "eq:Roem" \end_inset ) große lateinische Buchstaben zur Nummerierung verwendet. \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Ist im Argument von \series bold \backslash tag \begin_inset Foot status collapsed \begin_layout Standard \series bold \backslash tag \series default ist in \begin_inset LatexCommand ref reference "sub:Benutzerdefinierte-Nummerierung" \end_inset beschrieben. \end_layout \end_inset \series default wie in \begin_inset LatexCommand ref reference "sub:Absatzboxen" \end_inset eine Box angegeben, kann nicht auf die Formel verwiesen werden. \end_layout \begin_layout Subsection Unternummerierung \begin_inset LatexCommand index name "Formelnummerierung ! Unternummerierung" \end_inset \end_layout \begin_layout Standard Möchte man Formeln weiter untergliedern, kann man das mit Hilfe der Befehle \newline \series bold \backslash begin{subequations} \series default und \series bold \backslash end{subequations} \series default erreichen. Beide Befehle werden im TeX-Modus eingegeben. \end_layout \begin_layout Standard Dazu ein Beispiel: \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 Um das Beispiel zu erstellen, geht man folgendermaßen vor: \end_layout \begin_layout Enumerate erste Formel eingeben \end_layout \begin_layout Enumerate \series bold \backslash addtocounter{equation}{-1} \backslash begin{subequations} \begin_inset LatexCommand index name "Befehle ! A ! \\textbackslash addtocounter" \end_inset \newline \series default nach der ersten Formel einfügen \end_layout \begin_layout Enumerate zweite Formel eingeben \end_layout \begin_layout Enumerate dritte Formel eingeben \end_layout \begin_layout Enumerate \series bold \backslash end{subequations} \series default nach der dritten Formel einfügen \end_layout \begin_layout Standard Jede Formel, die zwischen den Befehlen \series bold \backslash begin \series default und \series bold \backslash end \series default steht, wird mit a, b, c, \SpecialChar \ldots{} untergliedert. Bei mehrzeiligen Formeln wird jede Zeile untergliedert. Alle untergliederten Formeln gelten als \emph on eine \emph default nummerierte Formel. Da jede nummerierte Formel den Formelzähler \series bold equation \series default um Eins erhöht, ist der Befehl \series bold \backslash addtocounter \series default notwendig um den Zähler wieder zu erniedrigen. Ansonsten würden die Formeln \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 als \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 nummeriert werden. \end_layout \begin_layout Standard Durch die Eingabe der Befehle im TeX-Modus wird zwischen den ersten beiden Formeln automatisch etwas Leerraum erstellt. Um dies rückgängig zu machen, fügt man nach dem Befehl \series bold \backslash begin{subequations} \series default -5\InsetSpace \thinspace{} mm vertikalen Leerraum ein. Ist der Formelstil \series bold Eingerückt \begin_inset Foot status collapsed \begin_layout Standard Formelstile siehe \begin_inset LatexCommand ref reference "sec:Formelstile" \end_inset \end_layout \end_inset \series default gewählt, fügt man -7\InsetSpace \thinspace{} mm Leerraum ein. \end_layout \begin_layout Standard Hier ist ein Beispiel für mehrzeilige Formeln, bei dem die Nummerierung der zweiten Zeile abgeschaltet wurde: \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 Benutzerdefinierte Nummerierung \begin_inset LatexCommand label name "sub:Benutzerdefinierte-Nummerierung" \end_inset \begin_inset LatexCommand index name "Formelnummerierung ! benutzerdefinierte" \end_inset \end_layout \begin_layout Standard \begin_inset LatexCommand index name "Formelnummerierung ! eigene Klammern" \end_inset Bei der Standardnummerierung werden um die Formelnummern runde Klammern gesetzt. Will man diese Klammern z.\InsetSpace \thinspace{} B. durch senkrechte Striche ersetzen, gibt man im LaTeX-Vorspann Folgendes an: \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 Dieses Makro ist zum Testen bereits im LaTeX-Vorspann angegeben. Damit es wirksam wird, muss das Prozentzeichen am Zeilenbeginn entfernt werden. \end_layout \end_inset \end_layout \begin_layout Standard Möchte man andere Zeichen haben, ersetzt man die Striche neben \series bold #1 \series default durch ein oder mehrere gewünschte Zeichen. Möchte man nur die Formelnummer haben, lässt man die Striche weg. \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Soll statt einer fortlaufenden Nummer ein beliebiger Ausdruck in den Klammern hinter der Formel stehen, benutzt man den Befehl \series bold \backslash tag \series default \begin_inset LatexCommand index name "Befehle ! T ! \\textbackslash tag" \end_inset : \begin_inset Formula \begin{equation} A+B=C\tag{etwas}\label{eq:tag}\end{equation} \end_inset In diesem Beispiel wurde in der Formel der Befehl \series bold \backslash tag \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series bold etwas \series default eingegeben. \end_layout \begin_layout Standard Gibt man stattdessen \series bold \backslash tag* \series default \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset \series bold etwas \series default ein, verhindert der Stern die Klammern um den Ausdruck: \begin_inset Formula \[ A+B=C\tag*{etwas}\] \end_inset \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Möchte man die Formelnummerierung neu starten wenn ein neuer Dokumentteil oder \begin_inset ERT status collapsed \begin_layout Standard \backslash mbox{ \end_layout \end_inset -abschnitt \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \begin_inset Note Note status collapsed \begin_layout Standard Der Befehl \series bold \backslash mbox \series default verhindert, dass am Bindestrich umgebrochen wird. Mehr zu \series bold \backslash mbox \series default siehe Kap.\InsetSpace \thinspace{} \begin_inset LatexCommand ref reference "sub:Worttrennungen" \end_inset . \end_layout \end_inset beginnt, verwendet man folgende LaTeX-Vorspannzeile: \end_layout \begin_layout Standard \series bold \backslash @addtoreset{equation}{part} \series default \begin_inset LatexCommand index name "Befehle ! \"@\" ! \\textbackslash \"@\"addtoreset" \end_inset \newline bzw. \newline \series bold \backslash @addtoreset{equation}{section} \end_layout \begin_layout Standard Um diese Befehle im TeX-Modus benutzen zu können, muss das \begin_inset Quotes gld \end_inset @ \begin_inset Quotes grd \end_inset Zeichen für LaTeX mit dem Befehl \series bold \backslash makeatletter \series default \begin_inset Quotes gld \end_inset aktiv \begin_inset Quotes grd \end_inset gemacht werden. Der Befehl \series bold \backslash makeatother \series default macht dies wieder rückgängig. Daher ist die Befehlssequenz im TeX-Modus: \end_layout \begin_layout Standard \series bold \backslash makeatletter \newline \backslash @addtoreset{equation}{section} \newline \backslash makeatother \end_layout \begin_layout Standard Im LaTeX-Vorspann können \series bold \backslash makeatletter \series default und \series bold \backslash makeatother \series default weggelassen werden, da LyX sie automatisch intern einfügt. \end_layout \begin_layout Standard Um \series bold \backslash @addtoreset \series default rückgängig zu machen, muss die Datei \series bold remreset.sty \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold remreset \series default ist Teil des LaTeX-Paketes \series bold carlisle \series default \begin_inset LatexCommand index name "Pakete ! carlisle" \end_inset , das Teil jeder LaTeX-Standardinstallation ist. \end_layout \end_inset \begin_inset LatexCommand index name "Pakete ! remreset" \end_inset im LaTeX-Vorspann mit der Zeile \end_layout \begin_layout Standard \series bold \backslash usepackage{remreset} \end_layout \begin_layout Standard geladen werden. Dann kann der Befehl \series bold \backslash @removefromreset \series default \begin_inset LatexCommand index name "Befehle ! \"@\" ! \\textbackslash \"@\"removefromreset" \end_inset mit dem selben Schema wie \series bold \backslash @addtoreset \series default benutzt werden. \end_layout \begin_layout Standard \begin_inset VSpace bigskip \end_inset Oftmals möchte man Formeln in folgender Art nummerieren: \end_layout \begin_layout Standard \family typewriter (Kapitelnummer.Formelnummer) \end_layout \begin_layout Standard Dabei soll die Formelnummer bei jedem Kapitel wieder mit Eins beginnen. \end_layout \begin_layout Standard Für diesen Fall gibt es den Befehl \series bold \backslash numberwithin \series default \begin_inset LatexCommand index name "Befehle ! N ! \\textbackslash numberwithin" \end_inset , der nach folgendem Schema benutzt wird: \end_layout \begin_layout Standard \series bold \backslash numberwithin{Zähler}{Gliederung} \end_layout \begin_layout Standard Zähler gibt an, welche Nummerierung betroffen ist. Gliederung gibt an, welche Nummer vor dem Punkt steht. \end_layout \begin_layout Standard In unserem Fall gibt man demnach folgende LaTeX-Vorspann- oder ERT-zeile ein: \end_layout \begin_layout Standard \series bold \backslash numberwithin{equation}{section} \end_layout \begin_layout Standard Das ist das Ergebnis: \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 Möchte man z.\InsetSpace \thinspace{} B. Tabellen nummerieren, so dass die Nummer des Teils vor dem Punkt steht, gibt man \series bold \backslash numberwithin{table}{part} \series default ein. \end_layout \begin_layout Standard Um wieder auf Standardnummerierung umzuschalten oder um diese Art der Nummerieru ng zu vermeiden wenn sie von der Dokumentklasse vorgegeben ist, gibt man folgenden Befehl als ERT oder als LaTeX-Vorspannzeile ein: \end_layout \begin_layout Standard \series bold \backslash renewcommand{ \backslash theequation}{ \backslash arabic{equation}} \begin_inset LatexCommand index name "Befehle ! 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 bzw. \series bold \newline \backslash renewcommand{ \backslash thetable}{ \backslash arabic{table}} \end_layout \begin_layout Standard \series bold \backslash numberwithin \series default benutzt intern den oben beschriebenen Befehl \series bold \backslash @addtoreset \series default , der ebenfalls rückgängig gemacht werden muss. \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 Nummerierung mit römischen Zahlen und Buchstaben \begin_inset LatexCommand label name "sub:Nummerierung-mit-römischen" \end_inset \begin_inset LatexCommand index name "Formelnummerierung ! mit Buchstaben" \end_inset \begin_inset LatexCommand index name "Formelnummerierung ! mit römischen Zahlen" \end_inset \end_layout \begin_layout Standard Formeln können auch mit römischen Zahlen und lateinischen Buchstaben nummeriert werden. Um z.\InsetSpace \thinspace{} B. mit kleinen römischen Zahlen zu nummerieren, gibt man vor der Formel im TeX-Modus den Befehl \end_layout \begin_layout Standard \series bold \backslash renewcommand{ \backslash theequation}{ \backslash roman{equation}} \end_layout \begin_layout Standard ein. \series bold \backslash renewcommand \series default \begin_inset LatexCommand index name "Befehle ! R ! \\textbackslash renewcommand" \end_inset weist dem vordefinierten Befehl \series bold \backslash theequation \series default den Befehl \begin_inset ERT status collapsed \begin_layout Standard \backslash linebreak \end_layout \end_inset \series bold \backslash roman{equation} \series default zu \begin_inset Foot status collapsed \begin_layout Standard Der Befehl \series bold \backslash renewcommand \series default besitzt dasselbe Schema wie der in \begin_inset LatexCommand ref reference "sec:Benutzerdefinierte-Befehle" \end_inset beschriebene Befehl \newline \series bold \backslash newcommand \series default . \end_layout \end_inset . \series bold equation \series default ist der Formelzähler. Stellt man einem Zähler den Befehl \series bold \backslash the \series default voran, bewirkt dies, dass der Wert des Zählers als arabische Zahl ausgegeben wird. Gibt man an, dass eine Formel nummeriert wird, setzt LaTeX intern den Befehl \series bold \backslash theequation \series default hinter die Formel. \series bold \backslash roman{equation} \begin_inset LatexCommand index name "Befehle ! R ! \\textbackslash roman" \end_inset \series default bewirkt, dass der Formelzähler als kleine römische Zahl erscheint. \end_layout \begin_layout Standard Alle Formeln nach dem \series bold \backslash renewcommand \series default -Befehl werden nun römisch nummeriert. Um auf Nummerierung mit großen römischen Zahlen umzuschalten, gibt man den Befehl erneut ein, ersetzt aber \series bold \backslash roman \series default durch \series bold \backslash Roman \series default \begin_inset LatexCommand index name "Befehle ! R ! \\textbackslash roman@\\textbackslash Roman" \end_inset . Für die \begin_inset Quotes gld \end_inset Nummerierung \begin_inset Quotes grd \end_inset mit lateinischen Buchstaben gibt es den Befehl \series bold \backslash alph \series default \begin_inset LatexCommand index name "Befehle ! A ! \\textbackslash alph" \end_inset für kleine und \series bold \backslash Alph \series default \begin_inset LatexCommand index name "Befehle ! A ! \\textbackslash alph@\\textbackslash Alph" \end_inset für große Buchstaben. \end_layout \begin_layout Standard \begin_inset Note Greyedout status open \begin_layout Standard \series bold Achtung: \series default Es können nur maximal 26 Formeln in einem Dokument mit lateinischen Buchstaben nummeriert werden. \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{römisch}\label{eq:roem}\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{Römisch}\label{eq:Roem}\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{lateinisch}\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{Lateinisch}\label{eq:Lat}\end{equation} \end_inset \end_layout \begin_layout Standard Um wieder auf Standardnummerierung umzuschalten, gibt man folgenden Befehl ein: \end_layout \begin_layout Standard \series bold \backslash renewcommand{ \backslash theequation}{ \backslash arabic{equation}} \begin_inset LatexCommand index name "Befehle ! 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{arabisch}\label{eq:arab}\end{equation} \end_inset \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Wie man sieht, werden die Formeln unabhängig von der Nummerierungsart durchnumme riert. Soll beim Wechsel der Nummerierungsart die Nummerierung wieder mit Eins beginnen, müssen neue Formelzähler angelegt werden. Eine Beschreibung dazu findet man in der Datei \begin_inset ERT status collapsed \begin_layout Standard \backslash href{Formelnummerierung.lyx}{ \end_layout \end_inset Formelnummerierung.lyx \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset . \end_layout \begin_layout Section Benutzerdefinierte Befehle \begin_inset LatexCommand label name "sec:Benutzerdefinierte-Befehle" \end_inset \begin_inset LatexCommand index name "benutzerdefinierte Befehle" \end_inset \end_layout \begin_layout Standard Viele der LaTeX-Befehle sind für den ständigen Gebrauch viel zu lang. Man kann sich aber mit dem Befehl \series bold \backslash newcommand \series default \begin_inset LatexCommand index name "Befehle ! N ! \\textbackslash newcommand" \end_inset neue kürzere Befehle definieren. \end_layout \begin_layout Standard Das Befehlsschema von \series bold \backslash newcommand \series default lautet: \end_layout \begin_layout Standard \series bold \backslash newcommand{neuer Befehlsname}[Argumentanzahl][optionaler \series default \series bold Wert] \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 {Befehlsdefinition} \end_layout \begin_layout Standard \begin_inset Note Greyedout status open \begin_layout Standard \series bold Achtung: \series default Es muss darauf geachtet werden, dass der Befehlsname nicht schon im Dokument oder von benutzten LaTeX-Paketen verwendet wird. Definiert man beispielsweise für \series bold \backslash Leftarrow \series default den Befehl \series bold \backslash le \series default , erhält man eine Fehlermeldung, denn \series bold \backslash le \series default ist schon für \begin_inset Quotes gld \end_inset \begin_inset Formula $\le$ \end_inset \begin_inset Quotes grd \end_inset definiert. \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Note Greyedout status open \begin_layout Standard \series bold Achtung: \series default Die Namen von selbst definierten Befehlen dürfen nur aus lateinischen Buchstaben bestehen. \end_layout \end_inset \end_layout \begin_layout Standard Die Argumentanzahl ist eine ganze Zahl im Bereich 0\InsetSpace \thinspace{} -\InsetSpace \thinspace{} 9 und gibt an, wie viele Argumente der neue Befehl haben soll. Als optionalen Wert kann man den Wert für ein optionales Argument voreinstellen. Wenn man dies macht, bedeutet das gleichzeitig, dass das \emph on erste \emph default Argument des neuen Befehls ein optionales ist. \end_layout \begin_layout Standard Es folgen einige Beispiele: \end_layout \begin_layout Itemize Will man für \series bold \backslash Longrightarrow \series default den Befehl \series bold \backslash gr \series default definieren, lautet die LaTeX-Vor\SpecialChar \- spannzeile: \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 Um für den Befehl \series bold \backslash underline \series default den Befehl \series bold \backslash us \series default zu definieren, muss das Argument (was unterstrichen werden soll) berücksichtigt werden. Dazu sieht die Vorspannzeile wie folgt aus: \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 Das Zeichen \series bold # \series default fungiert als Argumentplatzhalter, die \series bold 1 \series default dahinter gibt an, dass es der Platzhalter für das erste Argument ist. \end_layout \begin_layout Itemize Für \series bold \backslash framebox \series default kann man z.\InsetSpace \thinspace{} B. den Befehl \series bold \backslash fb \series default definieren: \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 Die beiden Dollarzeichen erstellen hierbei die für \series bold \backslash framebox \series default geforderte weitere Formel, siehe \begin_inset LatexCommand ref reference "sub:Boxen-mit-Rahmen" \end_inset . \end_layout \begin_layout Itemize Um einen neuen Befehl für \series bold \backslash fcolorbox \series default zu erstellen, bei dem die Farbe der Box nicht mehr angegeben werden muss, definiert man das Argument für die Farbe als 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 Gibt man bei der Verwendung von \series bold \backslash cb \series default die Farbe nicht an, wird die voreingestellte Farbe \series bold white \series default verwendet. \begin_inset ERT status collapsed \begin_layout Standard \backslash pagebreak \end_layout \end_inset \end_layout \begin_layout Standard Ein Test der neu definierten Befehle: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="6" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash raisebox \series default dient nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard A \backslash gr \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $A\gr B$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash us{ABcd \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{4.5mm}{}\us{ABcd}\raisebox{-2mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\fb{[2cm]}{}{\int A=B}\raisebox{-4mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\raisebox{6mm}{}\cb{red}{\int A=B}\raisebox{-4mm}{}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Section Diagramme \begin_inset LatexCommand index name "Diagramme" \end_inset \end_layout \begin_layout Standard Um Diagramme zu erstellen, wird das LaTeX-Paket \series bold amscd \begin_inset Foot status collapsed \begin_layout Standard \series bold amscd \series default ist Teil jeder LaTeX-Standardinstallation. \end_layout \end_inset \series default \begin_inset LatexCommand index name "Pakete ! amscd" \end_inset benötigt. Es wird im LaTeX-Vorspann mit der Zeile \end_layout \begin_layout Standard \series bold \backslash usepackage{amscd} \end_layout \begin_layout Standard geladen. \end_layout \begin_layout Standard Diagramme stellen Beziehungen dar und sehen folgendermaßen aus: \begin_inset Formula \[ \begin{CD}A@>>>B@>>>C\\ @AAA@.@VVV\\ F@<<<E@<<<D\end{CD}\] \end_inset \end_layout \begin_layout Standard Um sie zu erstellen, gibt man in einer Formel den Befehl \series bold \backslash CD \begin_inset LatexCommand index name "Befehle ! C ! \\textbackslash CD" \end_inset \series default ein. Es erscheint ein blaues Kästchen mit zwei gestrichelten Linien, in das man die weiteren Befehle eingibt. Mit \series bold \begin_inset ERT status collapsed \begin_layout Standard \backslash mbox{ \end_layout \end_inset \family sans \series default Strg-Enter \family default \series bold \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset \series default wird eine neue Zeile erstellt. Horizontale Beziehungen werden in ungerade Zeilen, vertikale in gerade Zeilen der Formel eingegeben. \end_layout \begin_layout Standard Zum Erstellen der Beziehungen gibt es folgende Befehle: \end_layout \begin_layout Itemize \series bold @<<< \series default erstellt einen Linkspfeil, \series bold @>>> \series default einen Rechtspfeil und \series bold @= \series default ein langes Gleichheitszeichen \end_layout \begin_layout Itemize \series bold @AAA \series default erstellt einen Pfeil nach oben, \series bold @VVV \series default einen Pfeil nach unten und \series bold @| \series default ein senkrechtes Gleichheitszeichen \end_layout \begin_layout Itemize \series bold @. \series default dient als Platzhalter für nicht vorhandene Beziehungen \end_layout \begin_layout Standard Alle Pfeile sind wie folgt beschriftbar: \end_layout \begin_layout Itemize Wird bei horizontalen Pfeilen zwischen dem ersten und zweiten < bzw. > Text eingegeben, erscheint er über dem Pfeil. Wird der Text zwischen dem zweiten und dritten < bzw. > eingegeben, erscheint er unter dem Pfeil. \end_layout \begin_layout Itemize Wird bei vertikalen Pfeilen Text zwischen erstem und zweitem A bzw. V eingegeben, erscheint er links neben dem Pfeil. Bei Eingabe zwischen zweitem und drittem A bzw. V erscheint er rechts daneben. Enthält der Text ein A oder V, müssen diese Buchstaben in eine TeX-Klammer gesetzt werden. \end_layout \begin_layout Standard Als Beispiel ein Diagramm mit allen möglichen Beziehungen: \end_layout \begin_layout Standard \begin_inset Formula \[ \begin{CD}A@>j>>B@>>k>C@=F\\ @AmAA@.@VV{V}V@|\\ D@<<j<E@>k>>F@=C\end{CD}\] \end_inset \end_layout \begin_layout Standard Der Befehl dazu lautet: \newline \series bold \backslash CD \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A@>j>>B@>>k>C@=F Strg-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 leer \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@| Strg-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 leer \end_layout \end_inset \begin_inset ERT status collapsed \begin_layout Standard } \end_layout \end_inset D@<<j<E@>k>>F@=C \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Section Tipps \begin_inset ERT status collapsed \begin_layout Standard \backslash texorpdfstring{ \end_layout \end_inset \begin_inset Foot status collapsed \begin_layout Standard Weitere gute Tipps gibt es unter \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 \series bold \backslash texorpdfstring \series default dient dazu, dass die Fußnote nicht mit im pdf-Lesezeichen erscheint. \end_layout \begin_layout Standard Näheres zu \series bold \backslash texorpdfstring \series default steht in Kapitel \begin_inset LatexCommand ref reference "sub:Formeln-in-Überschriften" \end_inset . \end_layout \end_inset \begin_inset LatexCommand index name "Tipps" \end_inset \begin_inset LatexCommand index name "Ionen|see{chemische Zeichen}" \end_inset \end_layout \begin_layout Subsection Chemische Symbole und Reaktionsgleichungen \begin_inset LatexCommand label name "sub:Chemische-Symbole-und" \end_inset \begin_inset LatexCommand index name "chemische Zeichen ! Symbole" \end_inset \begin_inset LatexCommand index name "Reaktionsgleichungen" \end_inset \begin_inset LatexCommand index name "Symbole ! chemische" \end_inset \end_layout \begin_layout Standard Ein Beispieltext aus der Chemie: \end_layout \begin_layout Quote Das \begin_inset Formula $\mathrm{SO_{4}^{2-}}$ \end_inset -Ion verbindet sich mit zwei \begin_inset Formula $\mathrm{Na^{+}}$ \end_inset -Ionen zu Natriumsulfat \begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$ \end_inset . Die Reaktionsgleichung dazu lautet: \begin_inset Formula \[ \mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\] \end_inset \end_layout \begin_layout Standard Diese Reaktionsgleichung kann direkt als Formel erstellt werden. Damit die Symbole nicht kursiv erscheinen, markiert man sämtliche Zeichen in der Formel und wandelt diese mit der Tastenkombination \family sans Alt-z\InsetSpace ~ r \family default in den aufrechten Schriftstil um. \begin_inset Foot status collapsed \begin_layout Standard Schriftstile siehe \begin_inset LatexCommand ref reference "sub:Schriftstile" \end_inset \end_layout \end_inset \end_layout \begin_layout Subsection Negative Zahlen \begin_inset LatexCommand index name "Zahlen ! negative" \end_inset \end_layout \begin_layout Standard Negative Zahlen sehen im Formelmodus oft schlecht aus, denn das Minuszeichen vor der Ziffer wird mit der gleichen Länge wie das Zeichen der Minus-Operation dargestellt. Schreibt man dagegen eine negative Zahl im normalen Text, erscheint das Minuszeichen korrekt. \end_layout \begin_layout Standard Wandelt man also das Minuszeichen in mathematischen Text um, tritt das Problem nicht mehr auf. \end_layout \begin_layout Standard Ein Beispiel zur Veranschaulichung der Problematik: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="3" columns="2"> <features> <column alignment="right" valignment="top" leftline="true" width="0"> <column alignment="left" valignment="top" rightline="true" width="0"> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard normaler Text: \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard x = -2 \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Formelmodus: \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $x=-2$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Lösung: \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $x=\textrm{-}2$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Subsection Komma als Dezimaltrennzeichen \begin_inset LatexCommand index name "Komma" \end_inset \end_layout \begin_layout Standard In LaTeX fungiert das Komma in einer Formel, gemäß englischer Konvention, als Gruppentrennzeichen. Es wird demnach automatisch hinter allen Kommas in Formeln ein Leerraum eingefügt. \end_layout \begin_layout Standard Um dies zu verhindern, markiert man das Komma und wandelt es in mathematischen Text um (Tastenkürzel \family sans Alt-m\InsetSpace ~ m \family default ). \end_layout \begin_layout Standard Um hingegen alle Formelkommas des Dokuments als Dezimaltrennzeichen zu setzen, lädt man die Datei \series bold icomma.sty \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold icomma \series default ist Teil des LaTeX-Paketes \series bold was \series default \begin_inset LatexCommand index name "Pakete ! was\\vspace{4mm}" \end_inset . \end_layout \end_inset \begin_inset LatexCommand index name "Pakete ! icomma" \end_inset mit der LaTeX-Vorspannzeile \end_layout \begin_layout Standard \series bold \backslash usepackage{icomma} \end_layout \begin_layout Subsection Physikalische Vektoren \begin_inset LatexCommand label name "sub:Physikalische-Vektoren" \end_inset \begin_inset LatexCommand index name "Vektoren ! physikalische" \end_inset \end_layout \begin_layout Standard Vordefinierte Vektoren bietet das LaTeX-Paket \series bold braket \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold braket \series default sollte Teil jeder LaTeX-Standardinstallation sein. \end_layout \end_inset \begin_inset LatexCommand index name "Pakete ! braket" \end_inset , das mit der LaTeX-Vorspannzeile \end_layout \begin_layout Standard \series bold \backslash usepackage{braket} \end_layout \begin_layout Standard geladen wird. \begin_inset ERT status collapsed \begin_layout Standard \backslash ifbraket \end_layout \end_inset \begin_inset Note Note status open \begin_layout Standard Die folgende Tabelle erscheint nur im Ausdruck wenn das LaTeX-Paket \series bold braket \series default installiert ist: \end_layout \end_inset \end_layout \begin_layout Standard Folgende Befehle sind definiert: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="4" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Bra{ \backslash psi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Bra{\psi}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Ket{ \backslash psi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Ket{\psi}$ \end_inset \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash Braket{ \backslash psi| \backslash phi \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard \begin_inset Formula $\Braket{\psi|\phi}$ \end_inset \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Der Befehl \series bold \backslash Braket \series default stellt sicher, dass alle senkrechten Striche in der Größe der umgebenden Klammern gesetzt werden: \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 Folgendes erscheint im Ausdruck wenn das LaTeX-Paket \series bold braket \series default nicht installiert ist: \end_layout \end_inset \end_layout \begin_layout Standard Das LaTeX-Paket \series bold braket \series default muss installiert sein, um den Rest dieses Abschnitts im Ausdruck zu sehen. \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash fi \end_layout \end_inset \end_layout \begin_layout Standard Der Effekt von \series bold \backslash Braket \series default kann auch mit dem Befehl \series bold \backslash middle \series default erzielt werden, der in \begin_inset LatexCommand ref reference "sub:Automatische-Klammergrößen" \end_inset beschrieben ist. \end_layout \begin_layout Subsection Selbst definierte Brüche \begin_inset LatexCommand label name "sub:Selbstdefinierte-Brüche" \end_inset \begin_inset LatexCommand index name "Brüche ! selbstdefinierte" \end_inset \end_layout \begin_layout Standard Um eigene Befehle für Brüche zu definieren, verwendet man den Befehl \series bold \backslash genfrac \series default \begin_inset LatexCommand index name "Befehle ! G ! \\textbackslash genfrac" \end_inset in folgendem Schema: \end_layout \begin_layout Standard \series bold \backslash genfrac{linke \series default \series bold Klammer}{rechte \series default \series bold Klammer}{Bruchstrichdicke}{Ansichtsstil} \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 {Zähler}{Nenner} \end_layout \begin_layout Standard Der Ansichtsstil wird mit einer ganzen Zahl im Bereich 0\InsetSpace \thinspace{} -\InsetSpace \thinspace{} 3 angegeben. \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="5" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Nummer \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ansichtsstil \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 0 \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard abgesetzte Formel \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 1 \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard eingebettete Formel \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 2 \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard klein \end_layout \end_inset </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard 3 \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard winzig \end_layout \end_inset </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard Wird nichts für den Ansichtsstil angegeben, passt sich die Größe wie bei \series bold \backslash frac \series default der Umgebung an. \end_layout \begin_layout Standard Wird keine Bruchstrichdicke angegeben, wird der voreingestellte Wert von 0.4\InsetSpace \thinspace{} pt verwendet. \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset Zum Beispiel sind die Befehle \series bold \backslash dfrac \series default und \series bold \backslash tbinom \series default aus \begin_inset LatexCommand ref reference "sub:Brüche" \end_inset folgendermaßen definiert: \end_layout \begin_layout Standard \series bold \backslash newcommand{ \backslash dfrac}[2]{ \backslash genfrac{}{}{}{0}{#1}{#2}} \end_layout \begin_layout Standard und \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 Um einen Bruch zu definieren, bei dem man die Bruchstrichdicke als optionales Argument angeben kann, gibt man im LaTeX-Vorspann folgenden Befehl ein: \end_layout \begin_layout Standard \series bold \backslash newcommand{ \backslash fracS}[3][]{ \backslash genfrac{}{}{#1}{}{#2}{#3}} \end_layout \begin_layout Standard Dazu ein Test: \begin_inset Formula \begin{align*} \text{Befehl} & & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} & & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\ \text{Ergebnis} & & \fracS[1mm]{A}{B} & & \fracS[5mm]{A}{B}\end{align*} \end_inset Wie man sieht, entspricht der Abstand des Zählers und Nenners vom Strich in etwa der dreifachen Strichdicke. \end_layout \begin_layout Subsection Durchgestrichene Formeln \begin_inset LatexCommand label name "sub:Durchgestrichene-Formeln" \end_inset \begin_inset LatexCommand index name "Formel ! durchgestrichene" \end_inset \end_layout \begin_layout Standard Um Formeln oder Formelteile durchzustreichen, muss das LaTeX-Paket \series bold cancel \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold cancel \series default ist Teil jeder LaTeX-Standardinstallation. \end_layout \end_inset \begin_inset LatexCommand index name "Pakete ! cancel" \end_inset mit der LaTeX-Vorspannzeile \end_layout \begin_layout Standard \series bold \backslash usepackage[samesize]{cancel} \end_layout \begin_layout Standard geladen werden. \begin_inset ERT status collapsed \begin_layout Standard \backslash pagebreak \end_layout \end_inset \end_layout \begin_layout Standard Es gibt vier verschiedene Arten durchzustreichen: \end_layout \begin_layout Standard \align center \begin_inset Tabular <lyxtabular version="3" rows="5" columns="2"> <features> <column alignment="center" valignment="top" leftline="true" width="0"> <column alignment="center" valignment="top" leftline="true" rightline="true" width="0"> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard Befehl \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \begin_inset Text \begin_layout Standard Ergebnis \begin_inset Note Note status collapsed \begin_layout Standard \series bold \backslash hspace \series default und \series bold \backslash raisebox \series default dienen nur als Abstandhalter. \end_layout \end_inset \end_layout \end_inset </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash cancel{ \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash bcancel{ \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \begin_inset Text \begin_layout Standard \backslash xcancel{ \backslash int \begin_inset ERT status collapsed \begin_layout Standard \backslash leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> <row topline="true" bottomline="true"> <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none"> \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 leer \end_layout \end_inset A=B \end_layout \end_inset </cell> <cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> \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 </cell> </row> </lyxtabular> \end_inset \end_layout \begin_layout Standard \series bold \backslash cancelto \series default eignet sich besonders, wenn man das Kürzen innerhalb einer Formel darstellen will: \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 Formeln in Überschriften \begin_inset LatexCommand label name "sub:Formeln-in-Überschriften" \end_inset \begin_inset LatexCommand index name "Formel ! in Überschriften" \end_inset \end_layout \begin_layout Standard Benutzt man Formeln in Überschriften, ist auf Folgendes zu achten: \end_layout \begin_layout Standard \begin_inset Note Greyedout status open \begin_layout Standard Verwendet man das LaTeX-Paket \series bold hyperref \series default \begin_inset LatexCommand index name "Pakete ! hyperref" \end_inset , werden automatisch PDF-Lesezeichen für jede Überschrift aus dem Inhaltsverzeic hnis erzeugt. Enthält eine Überschrift Formeln, werden diese im Lesezeichentext falsch dargestellt. Denn Formeln in Lesezeichen verstoßen gegen die PDF-Konventionen. \end_layout \end_inset \end_layout \begin_layout Standard Beide Probleme lassen sich lösen, indem man am Ende der Überschrift einen Kurztitel über das Menü \family sans Einfügen\SpecialChar \menuseparator Kurztitel \family default einfügt. Kurztitel werden als Alternative für mehrzeilige Überschriften verwendet, um das Inhaltsverzeichnis übersichtlich zu halten. Nur der Kurztitel erscheint im Inhaltsverzeichnis und damit auch im PDF-Lesezei chen. \end_layout \begin_layout Standard Möchte man im Inhaltsverzeichnis eine Formel verwenden, benutzt aber \series bold hyperref \series default , verwendet man im TeX-Modus den Befehl \end_layout \begin_layout Standard \series bold \backslash texorpdfstring{Teil}{Alternative} \begin_inset LatexCommand index name "Befehle ! T ! \\textbackslash texorpdfstring" \end_inset \end_layout \begin_layout Standard Teil ist der Überschriftsteil, der nicht im PDF-Lesezeichen erscheinen solle. Das können Zeichen, Formeln, Fußnoten aber auch Querverweise sein. Als Alternative kann man angeben, was stattdessen im Lesezeichen erscheinen soll. \end_layout \begin_layout Standard Es folgen zwei Beispielüberschriften: \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 Überschrift ohne Formel im Inhaltsverzeichnis \begin_inset Formula $\sqrt{-1}=\mathrm{i}$ \end_inset \begin_inset OptArg status collapsed \begin_layout Standard Überschrift ohne Formel im Inhaltsverzeichnis \end_layout \end_inset \end_layout \begin_layout Subsubsection Überschrift mit Formel im Inhaltsverzeichnis \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 der ersten Überschrift wurde ein Kurztitel verwendet. In der zweiten \series bold \backslash texorpdfstring \series default . \end_layout \begin_layout Standard Damit die Formeln so wie der Rest der Überschrift formatiert werden, wurde die komplette Überschrift in eine \series bold boldmath-Umgebung \series default \begin_inset Foot status collapsed \begin_layout Standard siehe \begin_inset LatexCommand ref reference "sub:Fett-gedruckte-Formeln" \end_inset \end_layout \end_inset gesetzt. \end_layout \begin_layout Subsection Formeln im mehrspaltigen Text \begin_inset LatexCommand index name "Formel ! im mehrspaltigen Text" \end_inset \end_layout \begin_layout Standard Formeln im mehrspaltigen Text sind oftmals zu breit für eine Spalte und müssen daher über die gesamte Seitenbreite gesetzt werden. Dazu verwendet man das LaTeX-Paket \series bold multicol \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold multicol \series default ist Teil jeder LaTeX-Standardinstallation. \end_layout \end_inset \begin_inset LatexCommand index name "Pakete ! multicol" \end_inset , das mit der LaTeX-Vorspannzeile \end_layout \begin_layout Standard \series bold \backslash usepackage{multicol} \end_layout \begin_layout Standard geladen wird. \end_layout \begin_layout Standard \begin_inset Note Greyedout status open \begin_layout Standard Dabei ist zu beachten, dass im Menü \family sans Dokument\SpecialChar \menuseparator Einstellungen \family default unter \family sans Textformat \family default \emph on nicht \emph default \family sans Zweispaltiges\InsetSpace ~ Dokument \family default ausgewählt sein darf. \end_layout \end_inset \end_layout \begin_layout Standard Vor den mehrspaltigen Text schreibt man im TeX-Modus den Befehl \end_layout \begin_layout Standard \series bold \backslash begin{multicols}{Spaltenanzahl} \end_layout \begin_layout Standard wobei die Spaltenanzahl eine Zahl im Bereich 2\InsetSpace \thinspace{} -\InsetSpace \thinspace{} 10 ist. Vor der Formel beendet man den mehrspaltigen Text mit dem Befehl \end_layout \begin_layout Standard \series bold \backslash end{multicols} \end_layout \begin_layout Standard der im TeX-Modus eingegeben wird. \end_layout \begin_layout Standard Durch den Befehl wird vor der Formel automatisch etwas Leerraum erstellt. Um dies rückgängig zu machen, fügt man vor der Formel -6\InsetSpace \thinspace{} mm vertikalen Leerraum ein. Ist der Formelstil \series bold Eingerückt \begin_inset Foot status collapsed \begin_layout Standard Formelstile siehe \begin_inset LatexCommand ref reference "sec:Formelstile" \end_inset \end_layout \end_inset \series default gewählt, fügt man stattdessen -9\InsetSpace \thinspace{} mm Leerraum ein. \end_layout \begin_layout Standard Als Beispiel ein mehrspaltiger Text mit einer abgesetzten Formel: \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. Die Fouriertransformation wird verwendet, um die überlagerten Signale (Netzwerk , Lösungsmittel) zu trennen. Nachdem wir die Phasenverschiebung bestimmen konnten, interessiert uns nun das Aussehen des Ausgangssignals. Im Experiment haben wir es mit sehr vielen Teilchen zu tun, so dass man über alle Phasen integrieren muss. Sei nun \begin_inset Formula $S$ \end_inset unser normiertes Ausgangssignal und \begin_inset Formula $P$ \end_inset die Phasenverteilungsfunktion, so ergibt sich die Beziehung \begin_inset ERT status collapsed \begin_layout 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 und die Normierungsbedingung \begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$ \end_inset gilt. Nun dürfen wir aber nicht den Relaxationsprozess außer Acht lassen. Direkt nach dem \begin_inset Formula $\nicefrac{\pi}{2}$ \end_inset \InsetSpace \thinspace{} -rf-Puls beginnt sich die Magnetisierung zu entfokussieren, wodurch sich das Signal zusätzlich abschwächt. Diese Abschwächung verläuft exponentiell in Abhängigkeit der so genannten \begin_inset Formula $T_{2}$ \end_inset -Zeit. \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash end{multicols} \end_layout \end_inset \end_layout \begin_layout Subsection Formeln mit Beschreibung der Variablen \begin_inset LatexCommand index name "Formel ! mit Variablenbeschreibung" \end_inset \end_layout \begin_layout Standard Möchte man wie in Formel \begin_inset LatexCommand eqref reference "eq:innerhalb" \end_inset , Variablen innerhalb einer Formel beschreiben, verwendet man eine 2 \series bold × \series default \begin_inset Formula $n$ \end_inset \InsetSpace ~ Matrix mit links ausgerichteten Spalten für die verwendeten \begin_inset Formula $n$ \end_inset Variablen. \begin_inset Foot status collapsed \begin_layout Standard Matrizen siehe \begin_inset LatexCommand ref reference "sec:Matrizen" \end_inset \end_layout \end_inset Um die Beschreibung kleiner zu setzen, gibt man vor der Matrix z.\InsetSpace \thinspace{} B. den Befehl \series bold \backslash footnotesize \series default ein. \begin_inset Foot status collapsed \begin_layout Standard Schriftgrößen siehe \begin_inset LatexCommand ref reference "sub:Schriftgrößen" \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Wird der Formelstil \series bold Eingerückt \begin_inset Foot status collapsed \begin_layout Standard Formelstile siehe \begin_inset LatexCommand ref reference "sec:Formelstile" \end_inset \end_layout \end_inset \series default verwendet, fügt man vor und nach der Matrix ein \series bold \backslash hfill \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold \backslash hfill \series default wirkt nur in Formeln mit dem Stil \series bold Eingerückt \series default , siehe \begin_inset LatexCommand ref reference "sub:Variabler-Leerraum" \end_inset . \end_layout \end_inset ein, damit der Abstand der Matrix von der Gleichung und vom Seitenrand gleich ist. \end_layout \begin_layout Standard Ist der Formelstil \series bold Zentriert \series default gewählt, nutzt man die in \begin_inset LatexCommand ref reference "sub:Flalign-Umgebung" \end_inset beschriebene Möglichkeit, Formeln einzurücken. Formel \begin_inset LatexCommand eqref reference "eq:innerhalb" \end_inset besteht aus fünf Spalten, wobei in den ersten beiden die Gleichung, in der dritten die Matrix und in der letzten die leere TeX-Klammer steht. \begin_inset Formula \begin{flalign} \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll} \rho & \textrm{Dichte}\\ V & \textrm{Volumen}\\ g & \textrm{Fallbeschleunigung}\end{array} & & {}\label{eq:innerhalb}\end{flalign} \end_inset \end_layout \begin_layout Subsection Aufrechte kleine griechische Buchstaben \begin_inset LatexCommand label name "sub:Aufrechte-kleine-griechische" \end_inset \begin_inset LatexCommand index name "griechische Buchstaben ! aufrechte" \end_inset \end_layout \begin_layout Standard Die meisten Mathe-Schriften stellen nur kursive kleine griechische Buchstaben zur Verfügung. Für Symbole der Elementarteilchen, wie Pionen und Neutrinos werden jedoch aufrechte griechische Buchstaben benötigt. Die Datei \series bold upgreek.sty \series default \begin_inset Foot status collapsed \begin_layout Standard \series bold upgreek \series default ist Teil des LaTeX-Paketes \series bold was \series default \begin_inset LatexCommand index name "Pakete ! was\\vspace{4mm}" \end_inset . \end_layout \end_inset \begin_inset LatexCommand index name "Pakete ! upgreek" \end_inset , die mit der LaTeX-Vorspannzeile \end_layout \begin_layout Standard \series bold \backslash usepackage{upgreek} \end_layout \begin_layout Standard geladen wird, stellt diese Buchstaben zur Verfügung. \begin_inset ERT status collapsed \begin_layout Standard \backslash ifupgreek \end_layout \end_inset \begin_inset Note Note status open \begin_layout Standard Die folgende Tabelle erscheint nur im Ausdruck wenn das LaTeX-Paket \series bold upgreek \series default installiert ist: \end_layout \end_inset Sie werden erzeugt, wenn der Befehl für einen griechischen Buchstaben mit \series bold up \series default begonnen wird. So erzeugt z.\InsetSpace \thinspace{} B. der Befehl \series bold \backslash uptau \series default dies: \begin_inset Formula $\uptau$ \end_inset \end_layout \begin_layout Standard Damit kann man Elementarteilchenreaktionen erstellen: \begin_inset Formula \[ \uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\] \end_inset \end_layout \begin_layout Standard Die aufrechten Buchstaben sind fetter und breiter als die kursiven. Sie sollten daher nicht für Einheiten wie \begin_inset Quotes gld \end_inset µm \begin_inset Quotes grd \end_inset verwendet werden. \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 Folgendes erscheint im Ausdruck wenn das LaTeX-Paket \series bold upgreek \series default nicht installiert ist: \end_layout \end_inset \end_layout \begin_layout Standard Das LaTeX-Paket \series bold upgreek \series default muss installiert sein, um den Rest dieses Abschnitts im Ausdruck zu sehen. \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Standard \backslash fi \end_layout \end_inset \end_layout \begin_layout Subsection Textzeichen in Formeln \begin_inset LatexCommand label name "sub:Textzeichen-in-Formeln" \end_inset \begin_inset LatexCommand index name "Text ! in Formeln" \end_inset \end_layout \begin_layout Standard In einigen Fällen möchte man Textzeichen direkt in Formeln eingeben. Benötigt man z.\InsetSpace \thinspace{} B. den mittigen Punkt · in Formeln wie \begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$ \end_inset , müsste man dafür jedes Mal den Befehl \series bold \backslash cdot \series default eingeben \begin_inset Foot status collapsed \begin_layout Standard siehe \begin_inset LatexCommand ref reference "sub:Binäre-Operatoren" \end_inset \end_layout \end_inset , da dieses Zeichen in allen Kodierungen als Textzeichen definiert ist. Man kann jedoch die Kodierung mit folgender LaTeX-Vorspannzeile ändern: \end_layout \begin_layout Standard \series bold \backslash DeclareInputText{183}{ \backslash ifmmode \backslash cdot \backslash else \backslash textperiodcentered \backslash f\SpecialChar \textcompwordmark{} i} \end_layout \begin_layout Standard Die Zeichenkodierung (Menü \family sans Dokument\SpecialChar \menuseparator Einstellungen\SpecialChar \menuseparator Sprache \family default ) legt fest, welches Zeichen beim Druck einer bestimmten Taste erscheint. Wenn man die Taste für das Zeichen '·' drückt, wird intern der Befehl \series bold \backslash textperiodcentered \series default verwendet. Dieser Befehl ist in einer Formel jedoch nicht verfügbar, so dass es zu LaTeX-Fehlern kommen würde. Durch die geänderte Kodierung wird hingegen automatisch der richtige Befehl gewählt, je nachdem ob das Zeichen in eine Formel eingegeben wurde oder nicht. \end_layout \begin_layout Standard Die Kodierung der einzelnen Zeichen ist in Definitionsdateien abgespeichert. Z.\InsetSpace \thinspace{} B. ist die Kodierung \series bold latin9 \series default in der Datei \series bold latin9.def \series default definiert, die sich im Installationsverzeichnis von LaTeX befindet. Kodierungen sollten nur über den LaTeX-Vorspann und nicht in den Definitionsdat eien geändert werden. Ansonsten können eigene Dokumente von anderen LyX-Nutzern auf anderen Computern nicht ohne Weiteres bearbeitet werden. \end_layout \begin_layout Standard \begin_inset VSpace medskip \end_inset In diesem Dokument wurde außerdem mittigen Punkt noch das Gradzeichen ° mit folgenden LaTeX-Vorspannzeilen so definiert, dass sie direkt in eine Formel eingegeben werden können: \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 Typographische Hinweise \begin_inset LatexCommand index name "Typographische Hinweise" \end_inset \end_layout \begin_layout Standard Dieses Kapitel ist eine Zusammenfassung der wichtigsten typographischen Regeln, die teilweise auch im Duden \begin_inset LatexCommand cite key "Duden" \end_inset unter \family typewriter Textverarbeitung \family default aufgelistet sind. \end_layout \begin_layout Itemize Physikalische Einheiten werden \emph on immer \emph default aufrecht gesetzt \begin_inset Foot status collapsed \begin_layout Standard wird durch Schriftstile erreicht, siehe \begin_inset LatexCommand ref reference "sub:Schriftstile" \end_inset \end_layout \end_inset : 30\InsetSpace \thinspace{} km/h \newline Zwischen Wert und Einheit befindet sich der kleinste Leerraum, siehe \begin_inset LatexCommand ref reference "sub:Vordefinierter-Leerraum" \end_inset . \end_layout \begin_layout Itemize Prozent- und Promillezeichen werden wie physikalische Einheiten gesetzt: \newline 1,2\InsetSpace \thinspace{} \begin_inset ERT status collapsed \begin_layout Standard \backslash textperthousand \end_layout \end_inset \InsetSpace ~ Alkohol im Blut \newline Sie folgen jedoch direkt auf die Zahl, wenn sie in einer Zusammensetzung oder Ableitung stehen: 3%-ige Rendite, 20%-Grenze \end_layout \begin_layout Itemize Das Grad-Symbol folgt immer unmittelbar auf die Zahl: 15°, es sei denn es wird in einer Einheit verwendet: 15\InsetSpace \thinspace{} °C \end_layout \begin_layout Itemize In Zahlen mit mehr als vier Ziffern wird zur Gruppierung vor jeder dritten Ziffer der kleinste Leerraum eingefügt: 18\InsetSpace \thinspace{} 473\InsetSpace \thinspace{} 588 \end_layout \begin_layout Itemize Für Bemaßungen wie z.\InsetSpace \thinspace{} B. 120×90×40\InsetSpace \thinspace{} cm, verwendet man das gelegte Kreuz \begin_inset Quotes gld \end_inset × \begin_inset Quotes grd \end_inset , dass über den LaTeX-Befehl \series bold \backslash texttimes \series default verfügbar ist, mit einigen Tastaturdefinitionen aber auch direkt eingegeben werden kann. \end_layout \begin_layout Itemize Bei Datumsangaben befindet sich zwischen Tag und Monat der kleinste Leerraum, zwischen Monat und Jahr ein geschütztes Leerzeichen: 23.\InsetSpace \thinspace{} 6.\InsetSpace ~ 1979 \end_layout \begin_layout Itemize Funktionen, deren Name aus mehreren Buchstaben besteht, werden aufrecht gesetzt um Verwechslungen mit Variablen zu vermeiden, siehe \begin_inset LatexCommand ref reference "sub:Vordefinierte-Funktionen" \end_inset . \end_layout \begin_layout Itemize Indizes, die aus mehreren Buchstaben bestehen, werden aufrecht gesetzt: \begin_inset Formula $E_{\mathrm{kin}}$ \end_inset \newline Komponenten von Matrizen werden kursiv gesetzt: \begin_inset Formula $\hat{H}_{kl}$ \end_inset \end_layout \begin_layout Itemize Der Ableitungs-/Integrationsoperator 'd', die Eulersche Zahl 'e' und die Imaginäre Zahl 'i' sollten aufrecht gesetzt werden, um sie nicht mit anderen Variablen zu verwechseln. \end_layout \begin_layout Standard \newpage \end_layout \begin_layout Section Synonyme \begin_inset LatexCommand index name "Synonyme" \end_inset \end_layout \begin_layout Standard Einige Zeichen und Symbole können mit mehreren Befehlen erstellt werden. 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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 Verlag 2001 \end_layout \begin_layout Subsubsection* \begin_inset Note Note status collapsed \begin_layout Standard Damit der Index den Namen \begin_inset Quotes gld \end_inset Stichwortverzeichnis \begin_inset Quotes grd \end_inset erhält, wurde im LaTeX-Vorspann \end_layout \begin_layout Standard \series bold \backslash usepackage[ngerman]{babel} \newline \backslash addto \backslash captionsngerman{ \backslash renewcommand{ \backslash indexname}{Stichwortverzeichnis}} \end_layout \begin_layout Standard eingefügt. \end_layout \begin_layout Standard Das Paket \series bold babel \series default sorgt dafür, dass die Beschriftungen in der ausgewählten Sprache erscheinen. Ehe man Beschriftungen ändern kann, muss es geladen werden. Außerdem wird \series bold babel \series default von LyX automatisch nach dem LaTeX-Vorspann geladen. Das ruft aber keine Probleme hervor, solange im LaTeX-Vorspann die Dokumentspra che verwendet wurde. \end_layout \begin_layout Standard Möchte man andere Beschriftungen ändern, ersetzt man \series bold \backslash indexname \series default durch \series bold \backslash <Beschriftungs>name \series default . Eine Auflistung der möglichen Namen findet man unter \end_layout \begin_layout Standard \family typewriter http://www.tex.ac.uk/cgi-bin/texfaq2html?label=fixnam \end_layout \begin_layout Standard Möchte man Beschriftungen für andere Sprachen ändern, ersetzt man \series bold ngerman \series default durch die Dokumentsprache und \end_layout \begin_layout Standard \series bold \backslash captionsgerman \series default durch \series bold \backslash captions<Dokumentsprache> \series default . \end_layout \end_inset \begin_inset LatexCommand printindex \end_inset \end_layout \end_body \end_document