documentation: the macro chapter for the Math manual

(The adoption of the UserGuide will follow later.)

git-svn-id: svn://svn.lyx.org/lyx/lyx-devel/trunk@27796 a592a061-630c-0410-9148-cb99ea01b6c8
This commit is contained in:
Uwe Stöhr 2008-12-07 16:49:53 +00:00
parent 1e3e6b88ea
commit 10be14c280
2 changed files with 1078 additions and 69 deletions

View File

@ -1,4 +1,4 @@
#LyX 1.6.0 created this file. For more info see http://www.lyx.org/
#LyX 1.6.1svn created this file. For more info see http://www.lyx.org/
\lyxformat 345
\begin_document
\begin_header
@ -154,6 +154,7 @@
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
\graphics default
\paperfontsize 12
\spacing single
@ -192,8 +193,8 @@
\bullet 3 2 7 -1
\tracking_changes false
\output_changes false
\author ""
\author ""
\author ""
\author ""
\end_header
\begin_body
@ -27986,7 +27987,7 @@ medskip
\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}
& & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:shortlong}\end{eqnarray}
\end_inset
@ -29090,7 +29091,7 @@ The aligned environment is also suitable for long formulas whose lines are
As example formula
\begin_inset CommandInset ref
LatexCommand eqref
reference "eq:kurzlang"
reference "eq:shortlong"
\end_inset
@ -30641,7 +30642,7 @@ theequation
\backslash
roman{equation}
\series default
.
\begin_inset Foot
status collapsed
@ -30661,7 +30662,7 @@ newcommand
that is described in
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:User-defined-Commands"
reference "sub:The-Command-newcommand"
\end_inset
@ -30670,7 +30671,6 @@ reference "sec:User-defined-Commands"
\end_inset
.
\series bold
equation
@ -30997,9 +30997,43 @@ target "Formula-numbering.lyx"
\begin_layout Section
User-defined Commands
\begin_inset Index
status collapsed
\begin_layout Plain Layout
User-defined commands
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Greyedout
status open
\begin_layout Plain Layout
\series bold
Note:
\series default
The names of user-defined commands and macros may only consist of Latin
letters.
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
The Command
\backslash
newcommand
\begin_inset CommandInset label
LatexCommand label
name "sec:User-defined-Commands"
name "sub:The-Command-newcommand"
\end_inset
@ -31008,7 +31042,21 @@ name "sec:User-defined-Commands"
status collapsed
\begin_layout Plain Layout
User-defined commands
User-defined commands !
\backslash
newcommand
\end_layout
\end_inset
\begin_inset Index
status collapsed
\begin_layout Plain Layout
Commands ! N !
\backslash
newcommand
\end_layout
\end_inset
@ -31024,18 +31072,6 @@ Many LaTeX-commands are too long to be used frequently.
\backslash
newcommand
\series default
\begin_inset Index
status collapsed
\begin_layout Plain Layout
Commands ! N !
\backslash
newcommand
\end_layout
\end_inset
new shorter commands.
\end_layout
@ -31138,23 +31174,6 @@ le
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Greyedout
status open
\begin_layout Plain Layout
\series bold
Note:
\series default
The names of user-defined commands may only consist of Latin letters.
\end_layout
\end_inset
\end_layout
\begin_layout Standard
@ -31710,6 +31729,475 @@ A=B
\end_layout
\begin_layout Subsection
Math Macros
\begin_inset Index
status collapsed
\begin_layout Plain Layout
User-defined commands! Math Macros
\end_layout
\end_inset
\begin_inset Index
status collapsed
\begin_layout Plain Layout
Macros
\end_layout
\end_inset
\end_layout
\begin_layout Standard
User-defined commands are especially convenient for complex expressions.
When you are for example dealing in a document with quadratic equations,
the same solution type occurs several times.
The general form of a quadratic equation is
\begin_inset Formula \[
0=\lambda^{2}+p\lambda+q\]
\end_inset
The general form of the solution is
\begin_inset Formula \[
\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
\end_inset
\end_layout
\begin_layout Standard
To define a command for the solution formula where only the three parameters
\begin_inset Formula $\lambda$
\end_inset
,
\begin_inset Formula $p$
\end_inset
, and
\begin_inset Formula $q$
\end_inset
need to be specified and the index of
\begin_inset Formula $\lambda$
\end_inset
can be given optionally, the LaTeX-preamble line is
\begin_inset Newline newline
\end_inset
\series bold
\backslash
newcommand{
\backslash
qG}[4][1,
\backslash
,2]{#2_{#1}=-
\backslash
frac{#3}{2}
\backslash
pm
\begin_inset Newline newline
\end_inset
\begin_inset ERT
status collapsed
\begin_layout Plain Layout
\backslash
hphantom{
\end_layout
\end_inset
\backslash
newcommand
\begin_inset ERT
status collapsed
\begin_layout Plain Layout
}
\end_layout
\end_inset
\backslash
sqrt{
\backslash
frac{#3^{2}}{4}-#4}}
\end_layout
\begin_layout Standard
To create with this the solution formula, the command
\begin_inset Newline newline
\end_inset
\series bold
\backslash
qG{
\backslash
lambda
\begin_inset Formula $\to$
\end_inset
\backslash
{p
\begin_inset Formula $\to$
\end_inset
\backslash
{q
\series default
is inserted to a formula
\series bold
.
\end_layout
\begin_layout Standard
The definition of the new command is unintuitive because one has to know
the schemes of all used LaTeX commands, e.
\begin_inset space \thinspace{}
\end_inset
g.
\begin_inset space \space{}
\end_inset
that a fraction is inserted in LaTeX as
\series bold
\backslash
frac{numerator}{denominator}
\series default
.
Furthermore one can easily forget a brace in the definition and cannot
see in LyX what the new command is doing.
To avoid these problems LyX offers the possibility to use math macros instead
of the command
\series bold
\backslash
newcommand
\series default
.
\end_layout
\begin_layout Standard
A math macro is created by using the menu
\family sans
Insert\SpecialChar \menuseparator
Math\SpecialChar \menuseparator
Macro
\family default
or the toolbar button
\begin_inset Graphics
filename ../images/math-macro_newmacroname_newcommand.png
scale 85
\end_inset
.
The math macro toolbar appears together with the following box where the
macro is defined:
\begin_inset Newline newline
\end_inset
\begin_inset space \hspace*{\fill}
\end_inset
\begin_inset Graphics
filename clipart/macrobox.png
lyxscale 90
scale 90
\end_inset
\begin_inset space \hspace*{\fill}
\end_inset
\begin_inset Newline newline
\end_inset
\begin_inset FormulaMacro
\newcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
\end_inset
\backslash
newmacroname is the default name of the macro that should be changed to
something sensible.
The wanted formula is inserted in the first blue box.
An argument placeholder is inserted with the command
\series bold
\backslash
#argumentnumber
\series default
, e.
\begin_inset space \thinspace{}
\end_inset
g
\begin_inset space \space{}
\end_inset
\series bold
\backslash
#1
\series default
or by using the macro toolbar button
\begin_inset Graphics
filename ../images/math-macro-add-param.png
scale 85
\end_inset
.
Argument placeholders are displayed red.
Maximum 9 arguments are possible.
Optional arguments are created with the toolbar button
\begin_inset Graphics
filename ../images/math-macro-add-optional-param.png
scale 85
\end_inset
.
The first non-optional argument can be transformed to an optional one with
the toolbar button
\begin_inset Graphics
filename ../images/math-macro-make-optional.png
scale 85
\end_inset
.
In the second blue box the appearance of the macro in LyX can be defined.
Normally you want to see it as it is defined, so the box is kept empty.
But when you have created a macro that needs lot of space on the screen,
you can insert in the box for example
\begin_inset Newline newline
\end_inset
\series bold
qG:
\backslash
#1
\series default
\series bold
,
\series default
\series bold
\backslash
#2
\series default
\series bold
,
\series default
\series bold
\backslash
#3,
\backslash
#4
\begin_inset Newline newline
\end_inset
\series default
For the macro only the arguments with the macro name in front of them will
then be displayed in LyX, leading to a better overview.
The formula appears in the output as defined in the first box.
\begin_inset Newline newline
\end_inset
The appearance of macros in formulas can furthermore be changed for single
macros by setting the cursor in the macro and using the menu
\family sans
View\SpecialChar \menuseparator
(Un)fold
\begin_inset space ~
\end_inset
Math
\begin_inset space ~
\end_inset
Macro
\family default
.
\end_layout
\begin_layout Standard
To use a macro, the macro name is inserted as command to a formula, in our
case
\series bold
\backslash
qG
\series default
.
Our macro looks in LyX like this:
\begin_inset Newline newline
\end_inset
\begin_inset space \hspace*{\fill}
\end_inset
\begin_inset Graphics
filename clipart/macrouse.png
lyxscale 75
scale 75
\end_inset
\begin_inset space \hspace*{\fill}
\end_inset
\begin_inset Newline newline
\end_inset
Here is our macro example with the arguments
\begin_inset Formula $x$
\end_inset
,
\begin_inset Formula $\ln(x)$
\end_inset
, and
\begin_inset Formula $B$
\end_inset
:
\end_layout
\begin_layout Standard
\begin_inset Formula \[
\qG x{\ln(x)}B\]
\end_inset
\end_layout
\begin_layout Standard
A math macro is transformed internally to a
\series bold
\backslash
newcommand
\series default
command when exporting the document.
The created
\series bold
\backslash
newcommand
\series default
command is not placed in the LaTeX-preamble, therefore macros can only
be used in formulas that are in the document below the macro definition
box.
\end_layout
\begin_layout Standard
Math macros can also be directly be created from a
\series bold
\backslash
newcommand
\series default
command.
When writing for example the command
\series bold
\begin_inset Newline newline
\end_inset
\backslash
newcommand{
\backslash
larrow}[2]{
\backslash
xleftarrow[#2]{#1}}
\begin_inset Newline newline
\end_inset
\series default
in LyX as normal text, highlighting it completely and using then the shortcut
\family sans
Ctrl-m
\family default
, the command will be transformed to a math macro.
Using this method you need to be careful that the
\series bold
\backslash
newcommand
\series default
command is typed correctly, otherwise you get a faulty macro leading to
LaTeX errors.
\end_layout
\begin_layout Standard
Math macros currently yet have the problem that further formulas in macro
definitions are handled wrongly.
Therefore the example
\series bold
\backslash
fb
\series default
from
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:The-Command-newcommand"
\end_inset
cannot be created as macro.
\end_layout
\begin_layout Section
Diagrams
\end_layout
@ -33836,7 +34324,7 @@ end{multicols}
\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}
S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
\end_inset

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@ -1,4 +1,4 @@
#LyX 1.6.0 created this file. For more info see http://www.lyx.org/
#LyX 1.6.1svn created this file. For more info see http://www.lyx.org/
\lyxformat 345
\begin_document
\begin_header
@ -163,6 +163,7 @@
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
\graphics default
\paperfontsize 12
\spacing single
@ -201,8 +202,8 @@
\bullet 3 2 7 -1
\tracking_changes false
\output_changes false
\author ""
\author ""
\author ""
\author ""
\end_header
\begin_body
@ -30699,7 +30700,7 @@ theequation
\backslash
roman{equation}
\series default
zu
zu.
\begin_inset Foot
status collapsed
@ -30713,7 +30714,7 @@ renewcommand
besitzt dasselbe Schema wie der in
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:Benutzerdefinierte-Befehle"
reference "sub:Der-Befehl-newcommand"
\end_inset
@ -30732,7 +30733,6 @@ newcommand
\end_inset
.
\series bold
equation
@ -31071,13 +31071,45 @@ benutzerdefinierte Befehle
\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
\begin_inset Note Greyedout
status open
\begin_layout Plain Layout
\series bold
Achtung:
\series default
Die Namen von benutzerdefinierten Befehlen und Makros dürfen nur aus lateinische
n Buchstaben bestehen.
\end_layout
\end_inset
\end_layout
\begin_layout Subsection
Der Befehl
\backslash
newcommand
\series default
\begin_inset CommandInset label
LatexCommand label
name "sub:Der-Befehl-newcommand"
\end_inset
\begin_inset Index
status collapsed
\begin_layout Plain Layout
benutzerdefinierte Befehle !
\backslash
newcommand
\end_layout
\end_inset
\begin_inset Index
status collapsed
@ -31090,6 +31122,17 @@ newcommand
\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
neue kürzere Befehle definieren.
\end_layout
@ -31192,24 +31235,6 @@ le
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Greyedout
status open
\begin_layout Plain Layout
\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
@ -31760,6 +31785,502 @@ A=B
\end_layout
\begin_layout Subsection
Mathe-Makros
\begin_inset Index
status collapsed
\begin_layout Plain Layout
benutzerdefinierte Befehle ! Mathe-Makros
\end_layout
\end_inset
\begin_inset Index
status collapsed
\begin_layout Plain Layout
Makros
\end_layout
\end_inset
\end_layout
\begin_layout Standard
Besonders praktisch sind eigene Befehle für komplexe Ausdrücke.
Hat man es in einem Dokument z.
\begin_inset space \thinspace{}
\end_inset
B.
häufiger mit quadratischen Gleichungen zu tun, tritt immer derselbe Lösungstyp
auf.
Die allgemeine Form einer quadratischen Gleichung ist
\begin_inset Formula \[
0=\lambda^{2}+p\lambda+q\]
\end_inset
Die allgemeine Form der Lösung lautet
\begin_inset Formula \[
\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
\end_inset
\end_layout
\begin_layout Standard
Um für die Lösungsformel einen Befehl zu definieren, bei dem nur noch die
drei Parameter
\begin_inset Formula $\lambda$
\end_inset
,
\begin_inset Formula $p$
\end_inset
und
\begin_inset Formula $q$
\end_inset
angegeben werden müssen und der Index von
\begin_inset Formula $\lambda$
\end_inset
optional angeben werden kann, lautet die LaTeX-Vorspannzeile
\begin_inset Newline newline
\end_inset
\series bold
\backslash
newcommand{
\backslash
qG}[4][1,
\backslash
,2]{#2_{#1}=-
\backslash
frac{#3}{2}
\backslash
pm
\begin_inset Newline newline
\end_inset
\begin_inset ERT
status collapsed
\begin_layout Plain Layout
\backslash
hphantom{
\end_layout
\end_inset
\backslash
newcommand
\begin_inset ERT
status collapsed
\begin_layout Plain Layout
}
\end_layout
\end_inset
\backslash
sqrt{
\backslash
frac{#3^{2}}{4}-#4}}
\end_layout
\begin_layout Standard
Um damit die Lösungsformel zu erstellen, gibt man in einer Formel den Befehl
\begin_inset Newline newline
\end_inset
\series bold
\backslash
qG{
\backslash
lambda
\begin_inset Formula $\to$
\end_inset
\backslash
{p
\begin_inset Formula $\to$
\end_inset
\backslash
{q
\series default
ein.
\end_layout
\begin_layout Standard
Die Definition des neuen Befehls ist unintuitiv, denn man muss die Schemata
aller verwendeten LaTeX-Befehle kennen, z.
\begin_inset space \thinspace{}
\end_inset
B.
dass ein Bruch in LaTeX mit
\series bold
\backslash
frac{Zähler}
\begin_inset Newline linebreak
\end_inset
{Nenner}
\series default
eingegeben wird.
Außerdem kann man leicht eine geschweifte Klammer vergessen und man kann
in LyX nicht sehen, was der neue Befehl macht.
Um diesen Problemen aus dem Weg zu gehen, gibt es in LyX die Möglichkeit
Mathe-Makros statt den Befehl
\series bold
\backslash
newcommand
\series default
zu verwenden.
\end_layout
\begin_layout Standard
Ein Mathe-Makro wird erstellt, indem man das Menü
\family sans
Einfügen\SpecialChar \menuseparator
Mathe\SpecialChar \menuseparator
Makro
\family default
oder den Werkzeugleistenknopf
\begin_inset Graphics
filename ../../images/math-macro_newmacroname_newcommand.png
scale 85
\end_inset
verwendet.
Es erscheint die Mathe-Makro-Werkzeugleiste und folgende Box, in der das
Makro definiert wird:
\begin_inset Newline newline
\end_inset
\lang english
\begin_inset space \hspace*{\fill}
\end_inset
\lang ngerman
\begin_inset Graphics
filename ../clipart/macrobox.png
lyxscale 90
scale 90
\end_inset
\lang english
\begin_inset space \hspace*{\fill}
\end_inset
\lang ngerman
\begin_inset Newline newline
\end_inset
\begin_inset FormulaMacro
\renewcommand{\qG}[4][1,\,2]{#2_{#1}=-\frac{#3}{2}\pm\sqrt{\frac{#3^{2}}{4}-#4}}
\end_inset
\backslash
newmacroname ist der voreingestellte Makroname, der auf etwas sinnvolles
geändert werden sollte.
In das erste blaue Kästchen gibt man die gewünschte Formel ein.
Einen Argumentplatzhalter fügt man mit dem Befehl
\series bold
\backslash
#Argumentnummer
\series default
ein, z.
\begin_inset space \thinspace{}
\end_inset
B.
\series bold
\backslash
#1
\series default
oder man verwendet den Makro-Werkzeugleistenknopf
\begin_inset Graphics
filename ../../images/math-macro-add-param.png
scale 85
\end_inset
.
Argumentplatzhalter werden rot dargestellt.
Es sind maximal 9 Argumente möglich.
Optionale Argumente werden mit dem Werkzeugleistenknopf
\begin_inset Graphics
filename ../../images/math-macro-add-optional-param.png
scale 85
\end_inset
erstellt.
Mit dem Werkzeugleistenknopf
\begin_inset Graphics
filename ../../images/math-macro-make-optional.png
scale 85
\end_inset
kann das erste nicht-optionale Argument in ein optionales verwandelt werden.
Im zweiten Kästchen kann man definieren wie das Makro in LyX angezeigt
werden soll.
Normalerweise will man es so sehen, wie es definiert wurde, wozu man das
Kästchen leer lässt.
Hat man hingegen ein Makro erstellt, der auf dem Bildschirm viel Platz
einnimmt, kann man in das Kästchen z.
\begin_inset space \thinspace{}
\end_inset
B.
\begin_inset Newline newline
\end_inset
\series bold
qG:
\backslash
#1
\series default
\series bold
,
\series default
\series bold
\backslash
#2
\series default
\series bold
,
\series default
\series bold
\backslash
#3,
\backslash
#4
\begin_inset Newline newline
\end_inset
\series default
eingeben.
Für das Makro werden dann in LyX nur die Argumente mit dem davor stehenden
Makronamen angezeigt, was für mehr Überblick im Dokument sorgt.
Im Ausdruck erscheint die Formel so, wie sie im ersten Kästchen definiert
wurde.
\begin_inset Newline newline
\end_inset
Das Erscheinungsbild von Makros in Formeln lässt sich außerdem für einzelne
Makros ändern, indem man den Cursor in das Makro setzt und das Menü
\family sans
Ansicht\SpecialChar \menuseparator
Mathe-Makro
\begin_inset space ~
\end_inset
auf/zuklappen
\family default
verwendet.
\end_layout
\begin_layout Standard
Um ein Makro zu verwenden, gibt man in eine Formel den Makronamen als Befehl
ein, in unserem Fall
\series bold
\backslash
qG
\series default
.
Unser Makro sieht in LyX folgendermaßen aus:
\begin_inset Newline newline
\end_inset
\lang english
\begin_inset space \hspace*{\fill}
\end_inset
\lang ngerman
\begin_inset Graphics
filename ../clipart/macrouse.png
lyxscale 75
scale 75
\end_inset
\lang english
\begin_inset space \hspace*{\fill}
\end_inset
\lang ngerman
\begin_inset Newline newline
\end_inset
Hier ist unser Makro-Beispiel mit den Argumenten
\begin_inset Formula $x$
\end_inset
,
\begin_inset Formula $\ln(x)$
\end_inset
und
\begin_inset Formula $B$
\end_inset
:
\end_layout
\begin_layout Standard
\begin_inset Formula \[
\qG x{\ln(x)}B\]
\end_inset
\end_layout
\begin_layout Standard
Ein Mathe-Makro wird beim Exportieren des Dokuments intern in einen
\series bold
\backslash
new\SpecialChar \-
command
\series default
-Befehl umgewandelt.
Der
\series bold
\backslash
newcommand
\series default
-Befehl wird dabei nicht in den LaTeX-Vorspann gesetzt, so dass man daher
Makros nur in Formeln verwenden kann, die sich im Dokument unterhalb der
Makrodefinitionsbox befinden.
\end_layout
\begin_layout Standard
Mathe-Makros können auch direkt aus einem
\series bold
\backslash
newcommand
\series default
-Befehl erstellt werden.
Schreibt man z.
\begin_inset space \thinspace{}
\end_inset
B.
den Befehl
\series bold
\begin_inset Newline newline
\end_inset
\backslash
newcommand{
\backslash
larrow}[2]{
\backslash
xleftarrow[#2]{#1}}
\begin_inset Newline newline
\end_inset
\series default
in LyX als normalen Text, markiert ihn komplett und verwendet dann das Tastenkür
zel
\family sans
Strg-m
\family default
, wird der Befehl in ein Mathe-Makro umgewandelt.
Bei dieser Methode muss man jedoch aufpassen, dass der
\series bold
\backslash
newcommand
\series default
-Befehl richtig geschrieben wurde, ansonsten wird ein fehlerhaftes Makro
erstellt, dass später LaTeX-Fehler hervorruft.
\end_layout
\begin_layout Standard
Mathe-Makros haben im Moment noch das Problem, dass weitere Formeln in einer
Makrodefinition fehlerhaft behandelt werden.
Dadurch kann das Beispiel
\series bold
\backslash
fb
\series default
aus
\begin_inset CommandInset ref
LatexCommand ref
reference "sub:Der-Befehl-newcommand"
\end_inset
nicht als Makro erzeugt werden.
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\begin_layout Section
Diagramme
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@ -33936,7 +34457,7 @@ end{multicols}
\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}
S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
\end_inset