lyx_mirror/lib/doc/de/Math.lyx

#LyX 1.5.5svn created this file. For more info see http://www.lyx.org/
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% Folgendes Problem lösen:
% Besteht die Kapitelnummer aus zu vielen Ziffern, wird  die
% Kapitelüberschrift im Inhaltsverzeichnis direkt an oder über
% die Kapitelnummer geschrieben.
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% Damit die Zeichen ° und · in LyX direkt eingegeben werden können,
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% Linkfläche für Querverweise vergrößern und automatisch benennen,
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% damit die Seiten des Inhaltsverzeichnisses römisch
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% provides caption formatting
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% benutzt in Kap. 22.4
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% benutzt in Kap. 22.6
\usepackage[samesize]{cancel}

% enables calculation of values,
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% für Mehrfachzeilen und -spalten
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\usepackage{multicol}

% für Diagramme
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% benutzt in Kap. 19.4
\usepackage{remreset}

%Mehrfachzeilen zentriert ausrichten (z.B. in Kap. 13.3)
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% Farbdefinition aus Kap. 9.3
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% Operatoren deklarieren (siehe Kap. 10.4 und 15.2)
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\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}{$#3$}}
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% 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
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% Damit der Index einen anderen Namen erhält.
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% testen ob das Paket eurosym installiert ist
% wird benutzt für das Euro-Symbol
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\IfFileExists{eurosym.sty}
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% benutzt in Kap. 22.4
% testen ob Paket braket installiert ist
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% benutzt in Kap. 22.10
% testen ob Paket upgreek installiert ist
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% benötigt für Kommas in Formeln, siehe Kap. 22.3
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LyXs detailliertes Mathe Handbuch
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vom LyX Team
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Für Anmerkungen oder Korrekturen senden sie bitte eine Email an LyXs Dokumentati
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Verfasser: Uwe Stöhr
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e
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In LyX gibt es drei 
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T
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Befehlsschema
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Die meisten LaTeX-Befehle für mathematische Konstruktionen besitzen folgendes
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{
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immer
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Zeichenerklärung
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Das Symbol
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\backslash
leer 
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Ein Pfeil wie z.\InsetSpace \thinspace{}
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Verwendete Einheiten
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\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" 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 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 Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
hspace{0mm}
\series default
 dient nur zur Trennung,da sonst im Ausdruck ¡ bzw.
 ¿ erscheinen würde.
\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

\backslash
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 $\textrm{\o}$
\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
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 $\textrm{\O}$
\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
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">
<cell 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.
 Die Befehle müssen dazu im TeX-Modus eingegeben 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

\begin_inset Quotes grd
\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
"e
\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
`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
`e
\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
^
\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
^e
\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
=e
\end_layout

\end_inset
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<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
=e
\end_layout

\end_inset


\end_layout

\end_inset
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<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\backslash
u
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
leer 
\end_layout

\end_inset

e
\end_layout

\end_inset
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<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
u e
\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
b
\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
b 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
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
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</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">
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\begin_inset Text

\begin_layout Standard
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\end_layout

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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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\begin_layout Standard
Ergebnis
\end_layout

\end_inset
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<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\backslash
H
\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
H e
\end_layout

\end_inset


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</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\backslash
'e
\end_layout

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<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


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'e
\end_layout

\end_inset


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</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\backslash
~e
\begin_inset LatexCommand index
name "Tilde"

\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 ERT
status collapsed

\begin_layout Standard


\backslash
~e
\end_layout

\end_inset


\end_layout

\end_inset
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</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\backslash
.e
\end_layout

\end_inset
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<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
.e
\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
v
\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
v 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
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.
\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 auf 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.
 Hier ist eine Übersicht der Synonymbefehle:
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\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
äquivalent zu
\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
ast
\end_layout

\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{-1.2mm}{
\end_layout

\end_inset

*
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\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
choose
\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
binom
\end_layout

\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
geq
\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
ge
\end_layout

\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
lbrace
\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
lbracket
\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
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

\backslash
gets
\end_layout

\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
leq
\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
le
\end_layout

\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
lor
\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
vee
\end_layout

\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
neq
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\backslash
not=
\end_layout

\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
slash
\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" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\backslash
vert
\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


\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
äquivalent zu
\end_layout

\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

\backslash

\backslash

\end_layout

\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
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

\backslash
dashrightarrow
\end_layout

\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
land
\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
wedge
\end_layout

\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
rbrace
\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
rbracket
\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
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

\backslash
to
\end_layout

\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
lnot
\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
neg
\end_layout

\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
ne
\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
not=
\end_layout

\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
owns
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\backslash
ni
\end_layout

\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
square
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard

\backslash
Box
\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
Vert
\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>
</lyxtabular>

\end_inset


\hfill

\end_layout

\begin_layout Standard

\newpage

\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "TLC2"

\end_inset


\shape smallcaps
Mittelbach, F.
 ; Goossens, M.
\shape default
: 
\shape italic
The LaTeX Companion
\shape default
.
 Addison Wesley, 2004
\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "Mathmode"

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{ftp://ftp.dante.de/tex-archive/info/math/voss/mathmode/Mathmode.pdf}{
\end_layout

\end_inset

Beschreibung
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

 der mathematischen Fähigkeiten von LaTeX
\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "Voss"

\end_inset

LaTeX Tipps- und Tricks-
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://tug.org/TeXnik/}{
\end_layout

\end_inset

Seite
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "AMS"

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{ftp://ftp.ams.org/pub/tex/doc/amsmath/amsldoc.pdf}{
\end_layout

\end_inset

Beschreibung
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

 von 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
AmS
\end_layout

\end_inset

-LaTeX
\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "Symbole"

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{ftp://ftp.dante.de/tex-archive/info/symbols/comprehensive/symbols-a4.pdf}{
\end_layout

\end_inset

Auflistung
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

 aller über LaTeX-Pakete verfügbare Symbole
\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "hyperref"

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://www.tug.org/applications/hyperref/ftp/doc/manual.pdf}{
\end_layout

\end_inset

Dokumentation
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

 des LaTeX-Pakets 
\series bold
hyperref
\series default

\begin_inset LatexCommand index
name "Pakete ! hyperref"

\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "Mathclap"

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf}{
\end_layout

\end_inset

Beschreibung
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

 des in 
\begin_inset LatexCommand ref
reference "sub:Operatorgrenzen"

\end_inset

 vorgestellten Befehls 
\series bold

\backslash
mathclap
\series default

\begin_inset LatexCommand index
name "Befehle ! 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