Math.lyx: some fixes for issues spotted by Ignacio

[lyx.git] / lib / doc / Math.lyx

#LyX 1.5.4svn created this file. For more info see http://www.lyx.org/
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% email: lyx-docs@lists.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.
% Als Lösung wird mehr Platz zwischen Nummer und
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% To be able to enter the character ° and · directly in LyX,
% see sec. 22.11
\DeclareInputText{176}{\ifmmode^\circ\else\textdegree\fi}
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% increase link area for cross-references and autoname them,
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% used in Kap. 22.4
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% used in Kap. 22.6
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% enables calculation of values,
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% for multiple table row and column cells
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% needed for diagrams
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% needed in sec. 19.4
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% center multirows (e.g. in sec. 13.3)
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% define a color, used in sec.9.3
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% declare operators (see sec. 10.4 and sec. 15.2)
\DeclareMathOperator*{\Lozenge}{\blacklozenge}
\DeclareMathOperator{\sgn}{sgn}

\newcommand{\spce}{\textvisiblespace}

% example definitions for sec. 20.1 
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% example macro from sec. 19.4
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% macro from sec. 10.2
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\def\mathclap {\mathpalette \mathclapinternal}
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% redefine the greyed out note
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% check for package eurosym
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% needed in sec. 22.4
% check for package braket
\newboolean{braket}
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% needed in sec. 22.10
% check for package upgreek
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\IfFileExists{upgreek.sty}
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\begin_body

\begin_layout Title
LyX's detailed Math manual
\end_layout

\begin_layout Author
by the LyX Team
\begin_inset Foot
status collapsed

\begin_layout Standard
\noindent
If you have comments or error corrections, please send them to the LyX Documenta
tion mailing list: 
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href{mailto:lyx-docs@lists.lyx.org?subject=LyX's Math manual}{
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lyx-docs@lists.lyx.org
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}
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\end_layout

\end_inset


\begin_inset Note Note
status collapsed

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author: Uwe Stöhr
\end_layout

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\newline

\newline

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Version 1.5.4-
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1
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\begin_layout Standard
To export this document to PDF, PS, or DVI the LaTeX-packages 
\series bold
eurosym,
\series default
 
\series bold
multirow,
\series default
 and 
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was
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 must be installed.
 If they are not installed you can export the document anyway but the sections
 where the packages are required won't appear in the output.
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\end_inset


\end_layout

\begin_layout Standard

\newpage

\end_layout

\begin_layout Section
Introduction
\begin_inset LatexCommand label
name "sec:Introduction"

\end_inset


\end_layout

\begin_layout Standard
This document explains LyX's math features and is furthermore a collection
 of LaTeX-commands used for mathematical characters and constructs.
 The explanations are designed for the usage of commands.
 It is therefore required that you have read the section 
\family typewriter
Mathematical\InsetSpace ~
Formulas
\family default
 of the User's Guide.
\end_layout

\begin_layout Standard
Most of the characters and many constructs explained in this manual are
 also accessible via the menu 
\family sans
Insert
\series bold
\SpecialChar \menuseparator

\series default
Math
\family default
, or the 
\family sans
math
\family default
\series bold
 
\family sans
\series default
toolbar
\family default
.
 But everybody who has to write lots of formulas will notice that it is
 much faster to use commands instead of the math toolbar.
 Therefore this manual is focused on commands but also mentions the correspondin
g toolbar buttons when available.
\end_layout

\begin_layout Standard
If not specially mentioned the commands are only available within formulas.
 To be able to use all commands explained in this document, the option 
\family sans
Use AMS math package
\family default
 must be used in the document settings (menu 
\family sans
Document\SpecialChar \menuseparator
Settings\SpecialChar \menuseparator
Math\InsetSpace ~
Options
\family default
).
\begin_inset Foot
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The option 
\family sans
Use AMS math package automatically
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 only uses 
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\backslash
AmS 
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-math when math constructs are found that are supported by LyX.
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\begin_layout Standard
This document doesn't list all 
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\begin_layout Standard


\backslash
AmS 
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-math commands
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\begin_layout Standard
A list with all 
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\begin_layout Standard


\backslash
AmS
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-math commands is in the file 
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href{ftp://ctan.tug.org/tex-archive/macros/amstex/doc/amsguide.ps}{
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amsguide.ps
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, which is part of every LaTeX standard installation.
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 for lucidity reasons.
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General Instructions
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name "sec:General-Instructions"

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\end_layout

\begin_layout Standard
To create an inline formula
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name "Formula ! inline"

\end_inset

 that is embedded into a text line, press 
\family sans
Ctrl-m
\family default
 or the toolbar button 
\begin_inset Graphics
        filename ../images/math-mode.png
        scale 85

\end_inset


\newline
To create a display style formula
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name "Formula ! display style"

\end_inset

 that will appear bigger and in an own paragraph, press 
\family sans
Ctrl-M
\family default
.
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\begin_layout Standard
To change a display style formula to an inline formula, set the cursor into
 the formula and press 
\family sans
Ctrl-M
\family default
 or use the menu 
\family sans
Edit\SpecialChar \menuseparator
Math\SpecialChar \menuseparator
Change formula type
\family default
.
 The same way is used to change an inline formula to a display style formula.
\end_layout

\begin_layout Standard
To display parts of an inline formula in the size of a display style formula,
 enter the command 
\series bold

\backslash
displaystyle
\begin_inset LatexCommand index
name "Commands ! D ! \\textbackslash displaystyle"

\end_inset


\series default
 to a formula.
 Then a new blue box appears in which the desired formula part is inserted.
\end_layout

\begin_layout Standard
Only inline formulas are allowed inside tables.
\end_layout

\begin_layout Standard
The 
\family sans
math toolbar
\family default
 can be turned on in the menu 
\family sans
View\SpecialChar \menuseparator
Toolbars
\family default
.
 When you click there on 
\begin_inset Quotes eld
\end_inset

Math
\begin_inset Quotes erd
\end_inset

 the toolbar will be shown permanently at the bottom; this state is visualized
 in the 
\family sans
Toolbars
\family default
 menu with a checkmark.
 When you click in this state again on 
\begin_inset Quotes eld
\end_inset

Math
\begin_inset Quotes erd
\end_inset

 in the 
\family sans
Toolbars
\family default
 menu, the 
\family sans
math toolbar
\family default
 is only shown when the cursor is within a formula; this state is visualized
 by the renaming of the menu entry from 
\begin_inset Quotes eld
\end_inset

Math
\begin_inset Quotes erd
\end_inset

 to 
\begin_inset Quotes eld
\end_inset

Math\InsetSpace ~
(auto)
\begin_inset Quotes erd
\end_inset

.
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\begin_layout Standard
The TeX-mode
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name "T@\\TeX-mode"

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 is invoked by pressing the toolbar button 
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        scale 85

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 or by using the menu 
\family sans
Insert\SpecialChar \menuseparator
T
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{
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e
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\begin_layout Standard

}
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X Code
\family default
 (shortcut 
\family sans
Ctrl-l
\family default
).
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In LyX there are three 
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proper names
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 that appear in the output with sub- and superscript letters: TeX, LaTeX,
 and LyX
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To avoid that these names are recognized as proper names, TeX-braces are
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\begin_layout Standard
To change the LaTeX-preamble
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name "L@\\LaTeX-preamble"

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Document\SpecialChar \menuseparator
Settings\SpecialChar \menuseparator
La
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\begin_layout Standard

{
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T
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status collapsed

\begin_layout Standard

}
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eX
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\family sans
Preamble
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.
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\begin_layout Standard
To edit matrices, case differentiations, and multiline formulas subsequently,
 the menus 
\family sans
Edit\SpecialChar \menuseparator
Math
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 and 
\family sans
Edit\SpecialChar \menuseparator
Rows\InsetSpace \thinspace{}
&\InsetSpace \thinspace{}
Columns,
\family default
 or the 
\family sans
table toolbar
\family default
 can be used.
 When lines and columns are swapped via the menu, the column or line where
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 below, respectively.
 Is the cursor in the last column or row, the exchange is done with the
 column to the left or the line above.
\end_layout

\begin_layout Standard
To write text in formulas
\begin_inset Foot
status collapsed

\begin_layout Standard
For multiline formulas the command 
\series bold

\backslash
intertext
\series default
 is used, see 
\begin_inset LatexCommand ref
reference "sub:Text-in-multiline"

\end_inset

.
\end_layout

\end_inset

 
\emph on
mathematical text
\emph default

\begin_inset LatexCommand index
name "Text ! in formulas"

\end_inset


\begin_inset LatexCommand index
name "Mathematical text"

\end_inset

 is used.
 This mode is invoked with the the shortcut 
\family sans
Alt-m\InsetSpace ~
m
\family default
 or by the insertion of the command 
\series bold

\backslash
text
\begin_inset LatexCommand index
name "Commands ! T ! \\textbackslash text"

\end_inset


\series default
.
 The text appears black in LyX and can therefore be distinguished from the
 other formula parts that appear blue.
 In the output mathematical text is set upright, in contrary to other formula
 parts.
\end_layout

\begin_layout Subsection*
Command Scheme
\end_layout

\begin_layout Standard
Most of the LaTeX-commands for math constructs have the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
commandname[optional
\series default
 
\series bold
argument]{required
\series default
 
\series bold
argument}
\end_layout

\begin_layout Standard
A command starts always with a backslash 
\begin_inset Quotes gld
\end_inset


\series bold

\backslash

\series default

\begin_inset Quotes grd
\end_inset

.
 To omit optional arguments, also omit the associated brackets.
 The braces around the required arguments are named in this document as
 TeX-braces
\begin_inset LatexCommand index
name "T@\\TeX-braces"

\end_inset

.
 If you add in a formula a left brace to a command name, LyX creates automatical
ly a TeX-brace.
 In all other cases TeX-braces are created in formulas with the command
 
\series bold

\backslash
{
\series default
.
 TeX-braces appear red in LyX, in contrary to normal braces that appear
 blue.
 In TeX-mode no command is needed to get TeX-braces.
 TeX-braces don't appear in the output.
\end_layout

\begin_layout Standard
When commands without arguments, like commands for symbols are entered in
 TeX-mode, a space character must 
\emph on
always
\emph default
 be behind the command to end it.
 This space doesn't appear in the output.
 When the space should appear in the output, the space must be followed
 by a protected space in normal text.
\end_layout

\begin_layout Standard
A protected space is inserted with 
\family sans
Ctrl-Space
\family default
.
\end_layout

\begin_layout Subsection*

\newpage
Syntax Explanation
\end_layout

\begin_layout Itemize
The symbol
\begin_inset Foot
status collapsed

\begin_layout Standard
This visible space character can be created with the command 
\series bold

\backslash
textvisiblespace
\series default

\begin_inset LatexCommand index
name "Commands ! T ! \\textbackslash textvisiblespace"

\end_inset

, inserted in TeX-mode.
\end_layout

\end_inset

 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

\InsetSpace ~
denotes a space character to be input.
\end_layout

\begin_layout Itemize
An arrow like 
\begin_inset Formula $\to$
\end_inset

 denotes the usage of the corresponding arrow key on the keyboard.
\end_layout

\begin_layout Subsection*
Used units
\end_layout

\begin_layout Standard
\align center
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placement H
wide false
sideways false
status open

\begin_layout Standard
\align center
\begin_inset Caption

\begin_layout Standard
\begin_inset LatexCommand label
name "tab:Used-units"

\end_inset

Used units
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="13" columns="2">
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Unit
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\begin_layout Standard
Name / Description
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mm
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\begin_layout Standard
Millimeter
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\begin_layout Standard
cm
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<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
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\begin_layout Standard
Centimeter
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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
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
Inch (1\InsetSpace \thinspace{}
in = 2,54\InsetSpace \thinspace{}
cm)
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\end_inset
</cell>
</row>
<row topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
pt
\end_layout

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

\begin_layout Standard
Point (72.27\InsetSpace \thinspace{}
pt = 1\InsetSpace \thinspace{}
in)
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\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)
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\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

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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
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)
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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
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)
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\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
Height of letter 
\emph on

\begin_inset Quotes eld
\end_inset

x
\emph default

\begin_inset Quotes erd
\end_inset

 in the current font
\end_layout

\end_inset
</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
width of letter 
\begin_inset Quotes eld
\end_inset


\emph on
M
\emph default

\begin_inset Quotes erd
\end_inset

 in the current font
\end_layout

\end_inset
</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
The command 
\series bold

\backslash
textfrac
\series default
 is explained in sec.\InsetSpace \thinspace{}

\begin_inset LatexCommand ref
reference "sub:Self-defined-Fractions"

\end_inset

.
\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
Basic Functions
\end_layout

\begin_layout Subsection
Exponents
\begin_inset LatexCommand index
name "Exponents"

\end_inset

 and Indices
\begin_inset LatexCommand index
name "Indices"

\end_inset


\begin_inset LatexCommand index
name "Superscripts|see{Exponents}"

\end_inset


\begin_inset LatexCommand index
name "Subscripts|see{Indices}"

\end_inset


\end_layout

\begin_layout Standard
Indices are created with an underscore 
\begin_inset Quotes eld
\end_inset

_
\begin_inset Quotes erd
\end_inset

 or via the math toolbar button 
\begin_inset Graphics
        filename ../images/math-subscript.png
        scale 85

\end_inset

 , exponents with a caret 
\begin_inset Quotes eld
\end_inset

^
\begin_inset Quotes erd
\end_inset

 or via the math toolbar button 
\begin_inset Graphics
        filename ../images/math-superscript.png
        scale 85

\end_inset

.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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
As the caret is in some languages an accent, vowels will be accentuated
 in this case and not set as exponents
\begin_inset Foot
status collapsed

\begin_layout Standard
Depending on the used keyboard settings this can also happen for other character
s than vowels.
\end_layout

\end_inset

.
 To get in this case exponents, press 
\family sans
Space
\family default
 after the caret as in the last example.
\end_layout

\begin_layout Subsection
Fractions
\begin_inset LatexCommand label
name "sub:Fractions"

\end_inset


\begin_inset LatexCommand index
name "Fractions"

\end_inset


\end_layout

\begin_layout Standard
Fractions are generated with the command 
\series bold

\backslash
frac
\series default

\begin_inset LatexCommand index
name "Commands ! F ! \\textbackslash frac"

\end_inset

 or via the math toolbar button 
\begin_inset Graphics
        filename ../images/math/frac.png
        scale 50

\end_inset

.
 The font size is adjusted automatically, depending on whether the fraction
 is in an inline or display style formula.
 With the math toolbar button 
\begin_inset Graphics
        filename ../images/math/frac-square.png
        scale 85

\end_inset

 you can select different fraction types.
\end_layout

\begin_layout Standard
With the command 
\series bold

\backslash
dfrac
\begin_inset LatexCommand index
name "Commands ! D ! \\textbackslash dfrac"

\end_inset


\series default
 a fraction can be created that has in any case the size of a display style
 formula.
 With 
\series bold

\backslash
tfrac
\begin_inset LatexCommand index
name "Commands ! T ! \\textbackslash tfrac"

\end_inset


\series default
 the fraction appears always with the size of an inline formula.
 An example:
\end_layout

\begin_layout Standard
A line with the fraction 
\begin_inset Formula $\frac{1}{2}$
\end_inset

 that was created with the command 
\series bold

\backslash
frac
\series default
.
\end_layout

\begin_layout Standard
A line with the fraction 
\begin_inset Formula $\dfrac{1}{2}$
\end_inset

 that was created with the command 
\series bold

\backslash
dfrac
\series default
.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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
spce 
\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
spce 
\end_layout

\end_inset

e^
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\backslash
frac
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

1
\begin_inset Formula $\downarrow$
\end_inset

2
\begin_inset Formula $\downarrow\downarrow$
\end_inset

3
\end_layout

\end_inset
</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
For nested fractions the command 
\series bold

\backslash
cfrac
\series default

\begin_inset LatexCommand index
name "Commands ! C ! \\textbackslash cfrac"

\end_inset

 can be used.
 Here an example:
\begin_inset VSpace -3mm
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula \begin{align*}
\textrm{created with \textbf{\textbackslash frac}} &  & \textrm{created with \textbf{\textbackslash cfrac}}\\
\frac{A}{B+\frac{C+\frac{E}{F}}{D}} &  & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}\end{align*}

\end_inset


\end_layout

\begin_layout Standard
The command for the example above is:
\end_layout

\begin_layout Standard

\series bold

\backslash
cfrac{A
\begin_inset Formula $\to$
\end_inset


\backslash
{B+
\backslash
cfrac{C+
\backslash
cfrac{E
\begin_inset Formula $\to$
\end_inset


\backslash
{F
\begin_inset Formula $\to\to$
\end_inset


\backslash
{D
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard

\series bold

\backslash
cfrac
\series default
 sets the fraction always in the size of a displayed formula, also when
 it is part of another fraction.
 
\series bold

\backslash
cfrac
\series default
 has the following command scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
cfrac[numerator position]{numerator}{denominator}
\end_layout

\begin_layout Standard
The numerator position can be 
\emph on
l
\emph default
 , 
\emph on
c
\emph default
, or 
\emph on
r
\emph default
 .
 l or r aligns the numerator to the left or right, resp.\InsetSpace ~
with the fraction
 stroke.
 When 
\emph on
c
\emph default
 or no position is given, the numerator appears centered.
 These fractions demonstrate the different alignments:
\newline

\series bold

\begin_inset Formula $\cfrac[l]{A}{B+C}$
\end_inset

, 
\begin_inset Formula $\cfrac{A}{B+C}$
\end_inset

, 
\begin_inset Formula $\cfrac[r]{A}{B+C}$
\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

It is often advantageous to combine 
\series bold

\backslash
cfrac
\series default
 and 
\series bold

\backslash
frac
\series default
:
\begin_inset Formula \[
\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]

\end_inset


\end_layout

\begin_layout Standard
For inline fractions with a sloped fraction stroke you can use the command
 
\series bold

\backslash
nicefrac
\begin_inset LatexCommand index
name "Commands ! N ! \\textbackslash nicefrac"

\end_inset


\series default
: 
\begin_inset Formula $\nicefrac{5}{31}$
\end_inset


\end_layout

\begin_layout Standard
How to define own fractions where the fraction stroke can be changed, is
 explained in 
\begin_inset LatexCommand ref
reference "sub:Self-defined-Fractions"

\end_inset

.
\end_layout

\begin_layout Subsection
Roots
\begin_inset LatexCommand index
name "Roots"

\end_inset


\end_layout

\begin_layout Standard
Square roots are created with 
\series bold

\backslash
sqrt
\series default

\begin_inset LatexCommand index
name "Commands ! S ! \\textbackslash sqrt"

\end_inset

 or the math toolbar button 
\begin_inset Graphics
        filename ../images/math/sqrt.png
        scale 85

\end_inset

, all other roots with the command 
\series bold

\backslash
root
\series default

\begin_inset LatexCommand index
name "Commands ! R ! \\textbackslash root"

\end_inset

 or with the math toolbar button 
\begin_inset Graphics
        filename ../images/math/root.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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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
spce 
\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
A square root can also be created with 
\series bold

\backslash
root
\series default
 when the root index field is left empty.
\end_layout

\begin_layout Standard
With certain indices the distance to the root is too small, like in this
 formula: 
\begin_inset Formula $\sqrt[\beta]{B}$
\end_inset


\newline
The 
\begin_inset Formula $\beta$
\end_inset

 touches the root.
 To avoid this, the commands 
\series bold

\backslash
leftroot
\series default

\begin_inset LatexCommand index
name "Commands ! L ! \\textbackslash leftroot"

\end_inset

 and 
\series bold

\backslash
uproot
\series default

\begin_inset LatexCommand index
name "Commands ! U ! \\textbackslash uproot"

\end_inset

 are used with the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
leftroot{distance}
\series default
 and 
\series bold

\backslash
uproot{distance}
\end_layout

\begin_layout Standard
Distance is the number of Big Points (unit bp; 
\begin_inset Formula $\mathrm{72\, bp=1\, inch}$
\end_inset

), that the index should be moved to the left or top, resp..
 The commands are written to the index.
 This way the command
\newline

\series bold

\backslash
root
\backslash
leftroot{-1
\begin_inset Formula $\to$
\end_inset


\backslash
uproot{2
\begin_inset Formula $\to$
\end_inset


\backslash
beta
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\begin_inset Formula $\to$
\end_inset

B
\newline

\series default
produces a correct typeset formula: 
\begin_inset Formula $\sqrt[\leftroot{-1}\uproot{2}\beta]{B}$
\end_inset


\end_layout

\begin_layout Subsection
Binomial coefficients 
\begin_inset LatexCommand index
name "Binomial coefficient s"

\end_inset


\end_layout

\begin_layout Standard
Binomial coefficients are inserted with the command 
\series bold

\backslash
binom
\series default

\begin_inset LatexCommand index
name "Commands ! B ! \\textbackslash binom"

\end_inset

 or with the submenu of the math toolbar button 
\begin_inset Graphics
        filename ../images/math/frac-square.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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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 to fractions (
\series bold

\backslash
frac
\series default
) there are besides 
\series bold

\backslash
binom
\series default
 the commands 
\series bold

\backslash
dbinom
\begin_inset LatexCommand index
name "Commands ! D ! \\textbackslash dbinom"

\end_inset


\series default
 and 
\series bold

\backslash
tbinom
\series default

\begin_inset LatexCommand index
name "Commands ! T ! \\textbackslash tbinom"

\end_inset

 with the following command scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
dbinom{numerator}{denominator}
\series default
 and
\newline

\series bold

\backslash
tbinom{numerator}{denominator}
\end_layout

\begin_layout Subsection
Case differentiations 
\begin_inset LatexCommand index
name "Case differentiations "

\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\to$
\end_inset

B>0
\begin_inset LatexCommand index
name "Commands ! C ! \\textbackslash cases"

\end_inset


\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

Ctrl-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 $\begin{cases}
A & \textrm{for }x>0\\
B & \textrm{for }x=0\end{cases}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
After inserting 
\series bold

\backslash
cases
\series default
 or the usage of the math toolbar button 
\begin_inset Graphics
        filename ../images/math/cases.png
        scale 85

\end_inset

 you can create new lines with the shortcut 
\family sans
Ctrl-Return
\family default
 or the table toolbar button 
\begin_inset Graphics
        filename ../images/tabular-feature_append-row.png
        scale 85

\end_inset

.
\begin_inset Foot
status collapsed

\begin_layout Standard
Umlauts and accents in formulas, like in the table above, are explained
 in 
\begin_inset LatexCommand ref
reference "sub:Accents-for-one"

\end_inset

.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
The command 
\series bold

\backslash
cases
\series default
 is also available via the menu 
\family sans
Insert\SpecialChar \menuseparator
Math\SpecialChar \menuseparator
Cases-Environment
\family default
.
\end_layout

\begin_layout Subsection
Negations
\begin_inset LatexCommand index
name "Negations"

\end_inset


\end_layout

\begin_layout Standard
By inserting of 
\series bold

\backslash
not
\series default

\begin_inset LatexCommand index
name "Commands ! N ! \\textbackslash not"

\end_inset

 every character can be displayed canceled.
 The characters are quasi accentuated by a slash.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
The last example shows, that not all negations look good.
 Therefore there are for some negations special commands (see 
\begin_inset LatexCommand ref
reference "sub:Mathematical-Symbols"

\end_inset

 and 
\begin_inset LatexCommand ref
reference "sec:Relations"

\end_inset

).
\end_layout

\begin_layout Subsection
Placeholders
\begin_inset LatexCommand label
name "sub:Placeholders"

\end_inset


\begin_inset LatexCommand index
name "Placeholders"

\end_inset


\begin_inset LatexCommand index
name "Chemical characters ! Isotopes"

\end_inset


\begin_inset LatexCommand index
name "Isotopes|see{Chemical characters}"

\end_inset


\end_layout

\begin_layout Standard
When displaying e.\InsetSpace \thinspace{}
g.\InsetSpace ~
isotopes
\begin_inset Foot
status collapsed

\begin_layout Standard
More about chemical symbols is written in 
\begin_inset LatexCommand ref
reference "sub:Chemical-Symbols-and"

\end_inset

.
\end_layout

\end_inset

 the following problem occurs:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Indices created with sub- and superscripts:
\end_layout

\end_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
correct indices:
\end_layout

\end_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
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
The shorter index is by default placed below or above the first character
 of the longer index.
 To avoid this there is the command 
\series bold

\backslash
phantom
\series default

\begin_inset LatexCommand index
name "Commands ! P ! \\textbackslash phantom"

\end_inset

 or the math toolbar button\InsetSpace \thinspace{}

\begin_inset Foot
status collapsed

\begin_layout Standard
can be found in the submenu of the toolbar button 
\begin_inset Graphics
        filename ../images/math/space.png
        scale 85

\end_inset


\end_layout

\end_inset

 
\begin_inset Graphics
        filename ../images/math/phantom.png
        scale 85

\end_inset

 that creates one or more phantom characters.
 When inserting 
\series bold

\backslash
phantom
\series default
 a small blue box appears that is superposed with two red arrows.
 The arrows indicate that the complete width and height of the box content
 will be created as placeholder.
 Phantom characters are accordingly placeholders with the size of the characters.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

_
\backslash
phantom
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

1
\begin_inset Formula $\to$
\end_inset

9
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

F
\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

_
\backslash
phantom
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

23
\begin_inset Formula $\to$
\end_inset

9
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

F
\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset


\backslash
phantom
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

ii
\begin_inset Formula $\to$
\end_inset

t
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

_MMt
\end_layout

\end_inset
</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
Furthermore there are the commands 
\series bold

\backslash
vphantom
\series default

\begin_inset LatexCommand index
name "Commands ! V ! \\textbackslash vphantom"

\end_inset

 (toolbar button \InsetSpace ~

\begin_inset Graphics
        filename ../images/math/vphantom.png
        scale 85

\end_inset

) and 
\series bold

\backslash
hphantom
\series default

\begin_inset LatexCommand index
name "Commands ! H ! \\textbackslash hphantom"

\end_inset

 (toolbar button \InsetSpace ~

\begin_inset Graphics
        filename ../images/math/hphantom.png
        scale 85

\end_inset

).
 
\series bold

\backslash
hphantom
\series default
 creates only space for the maximal height of the characters in the box
 but not for its width.
 
\series bold

\backslash
vphantom
\series default
 creates only space for the width of the box content.
 Therefore  the boxes of both commands have only one red arrow.
\end_layout

\begin_layout Standard
For example creates 
\series bold

\backslash
vphantom
\series default

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series bold
a
\backslash
int
\series default
 space for the height of the integral sign,
\begin_inset Foot
status collapsed

\begin_layout Standard
The command 
\series bold

\backslash
int
\series default
 creates an integral sign, see 
\begin_inset LatexCommand ref
reference "sub:Big-Operators"

\end_inset

.
\end_layout

\end_inset

 because this is the larger character.
 An example application is in 
\begin_inset LatexCommand ref
reference "sub:Multiline-Brackets"

\end_inset

.
\end_layout

\begin_layout Subsection
Lines
\begin_inset LatexCommand index
name "Lines"

\end_inset


\begin_inset LatexCommand index
name "Formula ! underlined"

\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

A+B
\begin_inset LatexCommand index
name "Commands ! 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
spce 
\end_layout

\end_inset

A+B
\begin_inset LatexCommand index
name "Commands ! 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
spce 
\end_layout

\end_inset


\backslash
underline
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A+B
\end_layout

\end_inset
</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
In the last example it doesn't matter if first 
\series bold

\backslash
overline
\series default
 or 
\series bold

\backslash
underline
\series default
 is inserted.
\end_layout

\begin_layout Standard
To double underline e.\InsetSpace \thinspace{}
g.
 results, one uses 
\series bold

\backslash
underline
\series default
 twice.
\end_layout

\begin_layout Standard
It is possible to place up to 6 lines above or below characters.
\end_layout

\begin_layout Subsection
Ellipses
\begin_inset LatexCommand index
name "Ellipses"

\end_inset


\end_layout

\begin_layout Standard
There are different types of ellipses available.
\begin_inset Foot
status collapsed

\begin_layout Standard
In the math toolbar in the submenu of the button 
\begin_inset Graphics
        filename ../images/math/ldots.png
        scale 85

\end_inset


\end_layout

\end_inset

 For listings dots at the baseline are used (
\series bold

\backslash
ldots
\series default

\begin_inset LatexCommand index
name "Commands ! L ! \\textbackslash ldots"

\end_inset

), while for operations dots are needed that are on the same height as the
 operators (
\series bold

\backslash
cdots
\series default

\begin_inset LatexCommand index
name "Commands ! C ! \\textbackslash cdots"

\end_inset

).
 When using the command 
\series bold

\backslash
dots
\series default

\begin_inset LatexCommand index
name "Commands ! D ! \\textbackslash dots"

\end_inset

, LaTeX decides on the basis of the next character what type is used.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\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
spce 
\end_layout

\end_inset

,
\backslash
dots
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

,A_n
\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

+
\backslash
dots
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

+A_n
\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

,
\backslash
ldots
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

,A_n
\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

+
\backslash
cdots
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

+A_n
\end_layout

\end_inset
</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
3×3\InsetSpace \thinspace{}
matrix with the different dots
\end_layout

\end_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
The ellipses available in menu 
\family sans
Insert\SpecialChar \menuseparator
Special\InsetSpace ~
Character
\family default
 are 
\series bold

\backslash
ldots
\series default
.
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

Specially for matrices there are ellipses that span over several columns.
 They are created with the command 
\series bold

\backslash
hdotsfor
\series default

\begin_inset LatexCommand index
name "Commands ! H ! \\textbackslash hdotsfor"

\end_inset

, that has the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
hdotsfor[distance]{number of columns}
\end_layout

\begin_layout Standard
The number of columns specifies how many columns should be spanned.
 Distance is a factor for the distance between the dots.
\end_layout

\begin_layout Standard
In the following matrix the command 
\series bold

\backslash
hdotsfor[2]{4}
\series default
 was inserted in the first box of the second line, to get an ellipsis with
 a dot distance twice as long as with the command 
\series bold

\backslash
dots
\series default
:
\begin_inset Formula \[
\left(\begin{array}{cccc}
A & B & C & D\\
\hdotsfor[2]{4}\\
q & w & e & r\end{array}\right)\]

\end_inset

Note that the matrix fields that should be spanned must be empty, otherwise
 you get LaTeX-errors.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

Furthermore you can fill with the command 
\series bold

\backslash
dotfill
\series default

\begin_inset LatexCommand index
name "Commands ! D ! \\textbackslash dotfill"

\end_inset

 the rest of a line with dots.
 The effect of these commands is the same like with 
\series bold

\backslash
hfill
\series default
, see 
\begin_inset LatexCommand ref
reference "sub:Variable-Space"

\end_inset

.
\end_layout

\begin_layout Standard
For example the command 
\series bold
A
\backslash
dotfill
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

B
\series default
 produces
\end_layout

\begin_layout Standard
\begin_inset Formula $A\dotfill B$
\end_inset


\end_layout

\begin_layout Standard
Analog to
\series bold
 
\backslash
dotfill
\series default
 there is for a line the command 
\series bold

\backslash
hrulefill
\series default

\begin_inset LatexCommand index
name "Commands ! H ! \\textbackslash hrulefill"

\end_inset

:
\end_layout

\begin_layout Standard
\begin_inset Formula $A\hrulefill B$
\end_inset


\end_layout

\begin_layout Standard
To use the commands for text, they have to be inserted in TeX-mode.
\end_layout

\begin_layout Section
Matrices
\begin_inset LatexCommand label
name "sec:Matrices"

\end_inset


\begin_inset LatexCommand index
name "Matrices"

\end_inset


\end_layout

\begin_layout Standard
Matrices can be inserted via the math toolbar button 
\begin_inset Graphics
        filename ../images/dialog-show_mathmatrix.png
        scale 85

\end_inset

 or the menu 
\family sans
Insert\SpecialChar \menuseparator
Math\SpecialChar \menuseparator
Matrix
\family default
.
 You will be asked for the number of matrix columns and rows, and the alignment.
 The vertical alignment is hereby only of importance for matrices in inline
 formulas:
\end_layout

\begin_layout Standard
The first matrix is top 
\begin_inset Formula $\begin{array}[t]{cccc}
A & D & G & J\\
B & E & H & K\\
C & F & I & L\end{array}$
\end_inset

, the second middle 
\begin_inset Formula $\begin{array}{cccc}
A & D & G & J\\
B & E & H & K\\
C & F & I & L\end{array}$
\end_inset

, and the third bottom 
\begin_inset Formula $\begin{array}[b]{cccc}
A & D & G & J\\
B & E & H & K\\
C & F & I & L\end{array}$
\end_inset

 aligned.
\end_layout

\begin_layout Standard
The horizontal alignment specifies how the column entries should be aligned.
 It is set by entering a letter for every column.
 
\emph on
l
\emph default
 denotes left aligned, 
\emph on
c
\emph default
 centered, and 
\emph on
r
\emph default
 right aligned.
 To create for example a 4
\series bold
×
\series default
4\InsetSpace ~
matrix where the first column is left aligned, the second and third are
 centered, and the last one is right aligned, one enters for the horizontal
 alignment 
\series bold
lccr
\series default
.
 Normally are in a matrix all columns centered, therefore the default is
 for every column is a 
\series bold
c
\series default
.
\end_layout

\begin_layout Standard
Horizontal alignment:
\end_layout

\begin_layout Standard

\series bold
lll
\series default
 : 
\begin_inset Formula $\begin{array}{lll}
10000 & D & G\\
B & 10000 & H\\
C & F & 10000\end{array}$
\end_inset

 , 
\series bold
ccc
\series default
 : 
\begin_inset Formula $\begin{array}{ccc}
10000 & D & G\\
B & 10000 & H\\
C & F & 10000\end{array}$
\end_inset

 , 
\series bold
rrr
\series default
 : 
\begin_inset Formula $\begin{array}{rrr}
10000 & D & G\\
B & 10000 & H\\
C & F & 10000\end{array}$
\end_inset


\end_layout

\begin_layout Standard
To add or delete rows and columns subsequently, the math toolbar buttons
 
\begin_inset Graphics
        filename ../images/tabular-feature_append-row.png
        scale 85

\end_inset

, 
\begin_inset Graphics
        filename ../images/tabular-feature_delete-row.png
        scale 85

\end_inset

, etc.\InsetSpace \thinspace{}
, or the menu 
\family sans
Edit\SpecialChar \menuseparator
Rows & Columns
\family default
 can be used.
 New rows can also be created with 
\family sans
Ctrl-Return
\family default
.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

Parentheses around a matrix can can either be created with the commands
 
\series bold

\backslash
left
\series default

\begin_inset LatexCommand index
name "Commands ! L ! \\textbackslash left"

\end_inset

 and 
\series bold

\backslash
right
\series default

\begin_inset LatexCommand index
name "Commands ! R ! \\textbackslash right"

\end_inset

 (shortcut 
\family sans
Alt-m\InsetSpace ~
parenthesis
\family default
), see 
\begin_inset LatexCommand ref
reference "sub:Automatic-Bracket-Size"

\end_inset

, or by using the following commands:
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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
spce 
\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
spce 
\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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
spce 
\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
spce 
\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
spce 
\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

When e.\InsetSpace \thinspace{}
g.\InsetSpace ~

\series bold

\backslash
vmatrix
\series default
 is inserted, a blue box appears between two vertical lines where the matrix
 is inserted.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

As all multiline formulas are matrices, the length 
\series bold

\backslash
arraycolsep
\series default

\begin_inset LatexCommand index
name "Commands ! A ! \\textbackslash arraycolsep"

\end_inset

 that is described in 
\begin_inset LatexCommand ref
reference "sub:Column-Separation"

\end_inset

 can also be used to change the column separation of matrices.
\end_layout

\begin_layout Standard
To change the row separation, the command 
\series bold

\backslash
arraystretch
\series default

\begin_inset LatexCommand index
name "Commands ! A ! \\textbackslash arraystretch"

\end_inset

 is used.
 It is used as follows:
\end_layout

\begin_layout Standard

\series bold

\backslash
renewcommand{
\backslash
arraystretch}{stretch factor}
\begin_inset LatexCommand index
name "Commands ! R ! \\textbackslash renewcommand"

\end_inset


\end_layout

\begin_layout Standard
The command 
\series bold

\backslash
renewcommand
\series default
 assigns the stretch factor to the predefined command 
\series bold

\backslash
arraystretch
\series default
.
 To double e.\InsetSpace \thinspace{}
g.\InsetSpace ~
the row separation, use the factor 2.
 This is then used for all following matrices.
 To go back to the original separation, assign the factor 1 to 
\series bold

\backslash
arraystretch
\series default
.
\end_layout

\begin_layout Standard
To set matrices into a text line, the command 
\series bold

\backslash
smallmatrix
\series default

\begin_inset LatexCommand index
name "Commands ! S ! \\textbackslash smallmatrix"

\end_inset

 is used.
 When it is inserted a blue box with two dashed lines appears.
 In this box the matrix is inserted.
\end_layout

\begin_layout Standard
This is a matrix 
\begin_inset Formula $\left(\begin{smallmatrix}A & B\\
C & D\end{smallmatrix}\right)$
\end_inset

 in a text line.
\end_layout

\begin_layout Section
Brackets and Delimiters
\begin_inset LatexCommand index
name "Brackets"

\end_inset


\begin_inset LatexCommand index
name "Delimiters"

\end_inset


\end_layout

\begin_layout Subsection
Vertical Brackets and Delimiters
\begin_inset LatexCommand index
name "Brackets ! vertical"

\end_inset


\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\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
Note:
\series default
 In TeX-mode the command 
\series bold

\backslash
textbackslash
\series default

\begin_inset LatexCommand index
name "Commands ! T ! \\textbackslash textbackslash"

\end_inset

 must be used for the backslash, because the command 
\series bold

\backslash

\backslash

\series default
 produces there a line break.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
For all characters listed above the size can be adjusted with the commands
 described in the following two subsections.
 When using these commands, the characters < and > can directly be used
 instead of the commands 
\series bold

\backslash
langle
\series default
 and 
\series bold

\backslash
rangle
\series default
.
\end_layout

\begin_layout Subsubsection
Manual Bracket Size
\begin_inset LatexCommand label
name "sub:Manual-Bracket-Size"

\end_inset


\begin_inset LatexCommand index
name "Bracket size ! manual"

\end_inset


\end_layout

\begin_layout Standard
The bracket size can be specified manually by the LaTeX-commands 
\series bold

\backslash
big
\series default

\begin_inset LatexCommand index
name "Commands ! B ! \\textbackslash big"

\end_inset

, 
\series bold

\backslash
Big
\series default
, 
\series bold

\backslash
bigg
\series default
, and 
\series bold

\backslash
Bigg
\series default
.
 
\series bold

\backslash
big
\series default
 denotes the smallest and 
\series bold

\backslash
Bigg
\series default
 the largest bracket size.
\end_layout

\begin_layout Standard
These commands are used to emphasize levels of brackets:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
all brackets in the same size:
\end_layout

\end_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
this looks better:
\end_layout

\end_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
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
For the second formula the command 
\series bold

\backslash
Big((A+B)(A-B)
\backslash
Big)^
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

C
\series default
 has been used.
\end_layout

\begin_layout Standard
Here is an overview about all bracket sizes:
\end_layout

\begin_layout Standard
\align center

\backslash
Bigg(
\backslash
exp
\backslash
bigg<
\backslash
Big[
\backslash
big{
\backslash
ln(3x)
\backslash
big}^2
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\backslash
sin(x)
\backslash
Big]^
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\backslash
bigg>
\backslash
Bigg)^0,5
\end_layout

\begin_layout Standard
\align center
\begin_inset Formula $\Bigg(\exp\bigg<\Big[\big\{\ln(3x)\big\}^{2}\sin(x)\Big]^{A}\bigg>\Bigg)^{0,5}$
\end_inset


\end_layout

\begin_layout Standard

\newpage
Besides the 
\series bold

\backslash
big
\series default
-commands there is the variant 
\series bold

\backslash
bigm
\series default

\begin_inset LatexCommand index
name "Commands ! B ! \\textbackslash bigm"

\end_inset

 that adds a bit more space between the bracket and its content, and the
 variant 
\series bold

\backslash
bigl
\series default
-
\series bold

\backslash
bigr
\series default

\begin_inset LatexCommand index
name "Commands ! B ! \\textbackslash bigl - \\textbackslash bigr"

\end_inset

, that don't add additional space.
 The 
\emph on
l
\emph default
 at the end of the command 
\series bold

\backslash
bigl
\series default
 is for a left bracket; for a right bracket this will be replaced by an
 
\emph on
r
\emph default
.
 A left or right bracket can each be an opening or closing bracket.
\end_layout

\begin_layout Standard
In the following table is a comparison of the variants:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
\series bold

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series default

\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
\series bold

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series default

\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
\series bold

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series default

\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
Automatic Bracket Size
\begin_inset LatexCommand label
name "sub:Automatic-Bracket-Size"

\end_inset


\begin_inset LatexCommand index
name "Bracket size ! automatic"

\end_inset


\end_layout

\begin_layout Standard
Brackets with variable size can be inserted with the commands 
\series bold

\backslash
left
\series default

\begin_inset LatexCommand index
name "Commands ! L ! \\textbackslash left"

\end_inset

 and 
\series bold

\backslash
right
\series default

\begin_inset LatexCommand index
name "Commands ! R ! \\textbackslash right"

\end_inset

 or via the math toolbar button 
\begin_inset Graphics
        filename ../images/dialog-show_mathdelimiter.png
        scale 85

\end_inset

.
 Directly behind 
\series bold

\backslash
left
\series default
 and 
\series bold

\backslash
right
\series default
 the wanted bracket must be inserted.
 The bracket size will then automatically be calculated for the output.
\end_layout

\begin_layout Standard
\align center
normal bracket: The command 
\series bold

\backslash
ln(
\backslash
frac
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

C
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

)
\series default
 creates
\begin_inset Formula \[
\ln(\frac{A}{C})\]

\end_inset


\end_layout

\begin_layout Standard
\align center
multiline bracket: The command 
\series bold

\backslash
ln
\backslash
left(
\backslash
frac
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

C
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\backslash
right)
\series default
 creates
\begin_inset Formula \[
\ln\left(\frac{A}{C}\right)\]

\end_inset


\end_layout

\begin_layout Standard
Instead of 
\series bold

\backslash
left
\series default
 and 
\series bold

\backslash
right
\series default
 the shortcut 
\family sans
Alt-m\InsetSpace ~
bracket
\family default
 can be used.
 This has the advantage that you can see in LyX immediately the real bracket
 size and that the matching right bracket will be created too.
\newline
The command
 for the last example would then be: 
\series bold

\backslash
ln Alt-m
\series default
 
\series bold
(
\backslash
frac
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

C
\end_layout

\begin_layout Standard
To omit a left or right bracket, a dot is inserted for the omitted bracket.
 For example the command 
\series bold

\backslash
left.
\backslash
frac
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

B
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\backslash
right}
\series default
 creates:
\series bold

\begin_inset Formula \[
\left.\frac{A}{B}\right\} \]

\end_inset


\series default
The commands 
\series bold

\backslash
left
\series default
 and 
\series bold

\backslash
right
\series default
 will be converted by LyX to brackets in the right size when the document
 is reloaded and an omitted bracket will appear as dashed line.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

Because all popular LaTeX-Distributions use eTeX, an extension to LaTeX,
 the command 
\series bold

\backslash
middle
\series default

\begin_inset LatexCommand index
name "Commands ! M ! \\textbackslash middle"

\end_inset

 is additionally available for all brackets and limits.
 With this command the height of the following character is adapted to the
 one of the surrounding brackets, what is e.\InsetSpace \thinspace{}
g.\InsetSpace ~
needed for physical vectors:
\begin_inset Formula \[
\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]

\end_inset

For physical vectors there is a special LaTeX-package, described in 
\begin_inset LatexCommand ref
reference "sub:Physical-Vectors"

\end_inset

.
\end_layout

\begin_layout Subsection
Horizontal Brackets
\begin_inset LatexCommand index
name "Brackets ! horizontal"

\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

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

\begin_layout Standard
Result
\end_layout

\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
spce 
\end_layout

\end_inset

A+B
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

^
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

3
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Commands ! O ! \\textbackslash overbrace"

\end_inset


\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

A+B
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

_5
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Commands ! U ! \\textbackslash underbrace"

\end_inset


\end_layout

\end_inset
</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
\backslash
underbrace
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A+B_w
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

_7
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

^
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

C
\end_layout

\end_inset
</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
In the last example it doesn't matter if 
\series bold

\backslash
overbrace
\series default
 or 
\series bold

\backslash
underbrace
\series default
 is inserted at first.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

When brackets are needed that overlap each other, multiline formulas, as
 described in 
\begin_inset LatexCommand ref
reference "sec:Multiline-Formulas"

\end_inset

, must be used:
\begin_inset Formula \begin{eqnarray*}
A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
 &  & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}\end{eqnarray*}

\end_inset

In the first row the formula is inserted together with the first brace.
 It is hereby important that the space command
\begin_inset Foot
status collapsed

\begin_layout Standard
Space commands are explained in 
\begin_inset LatexCommand ref
reference "sub:Predefined-Space"

\end_inset

.
\end_layout

\end_inset

 
\series bold

\backslash
:
\series default
 is inserted before the first 
\begin_inset Formula $d$
\end_inset

, because the brace that ends behind the 
\begin_inset Formula $q$
\end_inset

 prevents that the following 
\begin_inset Quotes eld
\end_inset

+
\begin_inset Quotes erd
\end_inset

 is surrounded by space.
\begin_inset Foot
status collapsed

\begin_layout Standard
because a bracket is not handled as character, see 
\begin_inset LatexCommand ref
reference "sub:Binary-Operators"

\end_inset


\end_layout

\end_inset

 In the second row the second brace is inserted.
 As it should begin before the 
\begin_inset Formula $b$
\end_inset

, first the command 
\series bold

\backslash
hphantom{gggg+
\backslash
:}
\series default
 is inserted.
\begin_inset Foot
status collapsed

\begin_layout Standard
more about 
\series bold

\backslash
hphantom
\series default
 see 
\begin_inset LatexCommand ref
reference "sub:Placeholders"

\end_inset


\end_layout

\end_inset

 This space is needed because the 
\begin_inset Quotes eld
\end_inset

+
\begin_inset Quotes erd
\end_inset

 is also surrounded by space in the formula.
 The brace is placed under the command 
\series bold

\backslash
hphantom{bbqq+dddd}
\series default
.
\end_layout

\begin_layout Standard
It gets more complicated when brackets overlap each other, like in the following
 example:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
setlength{
\backslash
jot}{-6pt}
\end_layout

\end_inset


\begin_inset Formula \begin{eqnarray*}
 &  & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\end{eqnarray*}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
setlength{
\backslash
jot}{3pt}
\end_layout

\end_inset

The first formula row is the same as the second row of the previous example,
 with the difference that the brace is above.
 The second row contains the formula together with the second brace.
 To avoid that there is space between the upper brace in the first row and
 the formula, the row spacing need to be reduced.
 This is not easily possible due to a bug in LyX
\begin_inset Foot
status collapsed

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
\end_layout

\end_inset

LyX-bug #1505
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\end_layout

\end_inset

.
 As solution for the problem, the global formula row separation 
\series bold

\backslash
jot
\series default

\begin_inset LatexCommand index
name "Commands ! J ! \\textbackslash jot"

\end_inset

 must be changed to -6\InsetSpace \thinspace{}
pt before the formula with the command 
\series bold

\backslash
setlength{
\backslash
jot}{-6pt}
\series default
 in TeX-mode.
 
\series bold

\backslash
jot
\series default
 is set back after the formula to the standard value of 3\InsetSpace \thinspace{}
pt using the same
 command.
 More about the row separation in formulas is explained in 
\begin_inset LatexCommand ref
reference "sub:Line-Separation"

\end_inset

.
\end_layout

\begin_layout Section
Arrows
\begin_inset LatexCommand index
name "Arrows"

\end_inset


\end_layout

\begin_layout Standard
Arrows can be inserted via the math toolbar button 
\begin_inset Graphics
        filename ../images/math/leftarrow.png
        scale 85

\end_inset

 or the commands listed in the following subsections.
\end_layout

\begin_layout Subsection
Horizontal Arrows
\begin_inset LatexCommand index
name "Arrows ! horizontal"

\end_inset


\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
Command
\end_layout

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

\begin_layout Standard
Result
\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
Command
\end_layout

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

\begin_layout Standard
Result
\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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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

Arrows used as accent like e.\InsetSpace \thinspace{}
g.\InsetSpace ~
vector arrows are listed in 
\begin_inset LatexCommand ref
reference "sec:Accents"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

Furthermore there are the labeled arrows
\begin_inset LatexCommand index
name "Arrows ! labeled"

\end_inset

 
\series bold

\backslash
xleftarrow
\series default

\begin_inset LatexCommand index
name "Commands ! X ! \\textbackslash xleftarrow"

\end_inset

 and 
\series bold

\backslash
xrightarrow
\series default

\begin_inset LatexCommand index
name "Commands ! X ! \\textbackslash xrightarrow\\vspace{4mm}"

\end_inset

.
 When inserting one of these commands in a formula, an arrow with two blue
 boxes appear where the label can be inserted.
 The length of the arrow adapts to the label width.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

x=a
\begin_inset Formula $\downarrow$
\end_inset

x>0
\begin_inset Formula $\to$
\end_inset

F(x)
\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

x=a
\begin_inset Formula $\downarrow$
\end_inset

x>0
\begin_inset Formula $\to$
\end_inset

F(a)
\end_layout

\end_inset
</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
Vertical and diagonal Arrows
\begin_inset LatexCommand index
name "Arrows ! diagonal"

\end_inset


\begin_inset LatexCommand index
name "Arrows ! vertical"

\end_inset


\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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

Vertical arrows can be used also as delimiter together with the commands
 described in 
\begin_inset LatexCommand ref
reference "sub:Manual-Bracket-Size"

\end_inset

 and 
\begin_inset LatexCommand ref
reference "sub:Automatic-Bracket-Size"

\end_inset

.
\end_layout

\begin_layout Standard

\newpage

\end_layout

\begin_layout Section
Accents
\begin_inset LatexCommand label
name "sec:Accents"

\end_inset


\begin_inset LatexCommand index
name "Accents"

\end_inset


\end_layout

\begin_layout Standard
Accents can be inserted via the math toolbar button 
\begin_inset Graphics
        filename ../images/math/hat.png
        scale 85

\end_inset

 or the commands listed in the following subsections.
\end_layout

\begin_layout Subsection
Accents for one Character
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
texorpdfstring{
\end_layout

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Standard
accents in text see 
\begin_inset LatexCommand ref
reference "sub:Accents-in-Text"

\end_inset


\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard

}{}
\end_layout

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Standard

\backslash
texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
\end_layout

\begin_layout Standard
More about 
\backslash
texorpdfstring is in section 
\begin_inset LatexCommand ref
reference "sub:Formulas-in-Section"

\end_inset

.
\end_layout

\end_inset


\begin_inset LatexCommand label
name "sub:Accents-for-one"

\end_inset


\begin_inset LatexCommand index
name "Accents ! for one character"

\end_inset


\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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
spce 
\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
spce 
\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
spce 
\end_layout

\end_inset

A
\begin_inset LatexCommand index
name "Vectors"

\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
spce 
\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
spce 
\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
Command
\end_layout

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

\begin_layout Standard
Result
\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
spce 
\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
spce 
\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
spce 
\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
spce 
\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
spce 
\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
spce 
\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

To create umlauts
\begin_inset LatexCommand index
name "Umlauts"

\end_inset

 in formulas, a quotation mark is inserted before the vowel.
 These two characters are then treated by LaTeX as 
\emph on
one
\emph default
 character when the formula part with the umlaut is marked as German.
 In contrary to 
\series bold

\backslash
ddot
\series default
, with this method 
\begin_inset Quotes eld
\end_inset

real
\begin_inset Quotes erd
\end_inset

 umlauts are created as demonstrated in the following example:
\end_layout

\begin_layout Standard
\begin_inset VSpace -2mm
\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

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

\begin_layout Standard

\lang ngerman
\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

\lang ngerman
\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
spce 
\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
Another advantage to 
\series bold

\backslash
ddot
\series default
 is that umlauts can directly be converted to mathematical text because
 the accent commands above are 
\emph on
not allowed
\emph default
 
\emph on
in mathematical text
\emph default
.
 To convert an accented character to mathematical text, only the character
 under the accent may be converted.
 This applies also for all other conversions, e.\InsetSpace \thinspace{}
g.\InsetSpace ~
to italic or bold.
\end_layout

\begin_layout Standard
In mathematical text, umlauts and other accented characters can directly
 be inserted.
\end_layout

\begin_layout Subsection
Accents for Operators
\begin_inset LatexCommand index
name "Accents ! for operators"

\end_inset


\end_layout

\begin_layout Standard
With the commands 
\series bold

\backslash
overset
\series default

\begin_inset LatexCommand index
name "Commands ! O ! \\textbackslash overset"

\end_inset

 and 
\series bold

\backslash
underset
\series default

\begin_inset LatexCommand index
name "Commands ! U ! \\textbackslash underset"

\end_inset

 characters can be placed above or below an operator, respectively, to accent
 it.
 With the command 
\series bold

\backslash
sideset
\series default

\begin_inset LatexCommand index
name "Commands ! S ! \\textbackslash sideset"

\end_inset

 characters can be set before and behind an operator.
 The command scheme is:
\end_layout

\begin_layout Standard

\series bold

\backslash
sideset{character
\series default
 
\series bold
before}{character
\series default
 
\series bold
behind}
\end_layout

\begin_layout Standard

\series bold

\backslash
sideset
\series default
 must always be before the operator that should be accented.
 You can accent with several characters and even with other operators and
 symbols.
 To place with 
\series bold

\backslash
sideset
\series default
 for example only characters behind an operator, write nothing between the
 first braces but don't omit the braces.
\end_layout

\begin_layout Standard
For example the command 
\series bold

\backslash
sideset{
\begin_inset Formula $\to$
\end_inset


\backslash
{
\series default
'
\series bold

\begin_inset Formula $\to$
\end_inset


\backslash
sum_k=1
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series default
^
\series bold
n
\series default
 produces:
\begin_inset Formula \[
\sideset{}{'}\sum_{k=1}^{n}\]

\end_inset


\end_layout

\begin_layout Standard
The command 
\series bold

\backslash
overset
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\backslash
maltese
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series default

\begin_inset Formula $\uparrow$
\end_inset


\series bold
a
\series default
 produces:
\begin_inset Formula \[
\overset{a}{\maltese}\]

\end_inset

As seen in the last example, with 
\series bold

\backslash
overset
\series default
 and 
\series bold

\backslash
underset
\series default
 also symbols and characters can be accented; with 
\series bold

\backslash
sideset
\series default
 this is not possible.
\end_layout

\begin_layout Subsection
Accents for several Characters
\begin_inset LatexCommand label
name "sub:Accents-for-several"

\end_inset


\begin_inset LatexCommand index
name "Accents ! for several characters"

\end_inset


\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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
spce 
\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
spce 
\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
spce 
\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
Command
\end_layout

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

\begin_layout Standard
Result
\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
spce 
\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
spce 
\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
spce 
\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
spce 
\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

With these commands as many characters as you like can be accented.
 But the accents 
\series bold

\backslash
widetilde
\series default
 and 
\series bold

\backslash
widehat
\series default
 will only be set in the output with a length of three characters, as shown
 in the following example:
\begin_inset Formula \[
\widetilde{A+B=C-D}\]

\end_inset


\end_layout

\begin_layout Standard
With the commands 
\series bold

\backslash
overset
\series default

\begin_inset LatexCommand index
name "Commands ! O ! \\textbackslash overset"

\end_inset

 and 
\series bold

\backslash
underset
\series default

\begin_inset LatexCommand index
name "Commands ! U ! \\textbackslash underset"

\end_inset

 described in the previous subsection it is also possible to accent several
 characters.
 The command 
\series bold

\backslash
underset
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A=B
\begin_inset Formula $\downarrow$
\end_inset

***
\series default
 creates:
\begin_inset Formula \[
\underset{***}{A=B}\]

\end_inset


\end_layout

\begin_layout Section
Space
\begin_inset LatexCommand label
name "sub:Space"

\end_inset


\begin_inset LatexCommand index
name "Space ! horizontal"

\end_inset


\end_layout

\begin_layout Subsection
Predefined Space
\begin_inset LatexCommand label
name "sub:Predefined-Space"

\end_inset


\begin_inset LatexCommand index
name "Space ! horizontal ! predefined"

\end_inset


\end_layout

\begin_layout Standard
Sometimes it is necessary to insert horizontal space to a formula.
 This is done by inserting a protected space (shortcut 
\family sans
Ctrl-Space
\family default
).
 A blue 
\begin_inset Quotes eld
\end_inset


\series bold
\color blue

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series default
\color inherit

\begin_inset Quotes erd
\end_inset

 appears and by pressing 
\family sans
Space
\family default
 several times one can select one of eight different space sizes.
 The spaces can also be inserted using the math toolbar button 
\begin_inset Graphics
        filename ../images/math/space.png
        scale 85

\end_inset

 or special commands.
 Independent from the inserted command, one can select the size again by
 pressing 
\family sans
Space
\family default
 afterwards.
\end_layout

\begin_layout Standard
\noindent
\align center
\begin_inset VSpace -5mm
\end_inset


\begin_inset Tabular
<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="0">
<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" 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">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Command
\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 topline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Number of 
\family sans
Space
\family default
 keystrokes after inserting the protected space
\end_layout

\end_inset
</cell>
<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
1
\end_layout

\end_inset
</cell>
<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
3
\end_layout

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

\begin_layout Standard
4
\end_layout

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

\begin_layout Standard
5
\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
Result
\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
The last size seem to produce no space.
 It is displayed red in LyX contrary to the other sizes, because it is a
 negative space.
 There are two more negative spaces:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\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
Number of 
\family sans
Space
\family default
 keystrokes after inserting the protected space
\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
Result
\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 spaces can lead to characters overlapping each other.
 Thus they can be used to enforce ligatures, what is e.\InsetSpace \thinspace{}
g.\InsetSpace ~
useful for summation
 operators: 
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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
spce 
\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
Relations like for example equal signs, are always surrounded by space.
 To suppress this, the equal sign is placed into a TeX-brace.
 The following example demonstrates this:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
normal equation
\end_layout

\end_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
 is only used as spacer.
\end_layout

\end_inset


\begin_inset Formula $\raisebox{5mm}{}$
\end_inset

equation without space
\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
\noindent
The command for the last formula is: 
\series bold
A
\backslash
{=
\begin_inset Formula $\to$
\end_inset

B
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

Spaces are needed for physical units, because the space between the value
 and the unit is the smallest one and not a normal space.
 For units in text, the smallest space is inserted via the menu 
\family sans
Insert\SpecialChar \menuseparator
Formatting\SpecialChar \menuseparator
Thin\InsetSpace ~
Space
\family default
 (shortcut 
\family sans
Ctrl-Shift-Space
\family default
).
\end_layout

\begin_layout Standard
An example to visualize the difference:
\end_layout

\begin_layout Standard
\begin_inset Tabular
<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
space between value and unit
\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
smallest space between value and unit
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Subsection
Variable Space
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
texorpdfstring{
\end_layout

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Standard
for vertical space in formulas see 
\begin_inset LatexCommand ref
reference "sub:Line-Separation"

\end_inset


\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard

}{}
\end_layout

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Standard

\backslash
texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
\end_layout

\begin_layout Standard
More about 
\backslash
texorpdfstring is in section 
\begin_inset LatexCommand ref
reference "sub:Formulas-in-Section"

\end_inset

.
\end_layout

\end_inset


\begin_inset LatexCommand label
name "sub:Variable-Space"

\end_inset


\begin_inset LatexCommand index
name "Space ! horizontal ! variable"

\end_inset


\end_layout

\begin_layout Standard
Space with a defined length can be inserted in LyX with the command
\newline

\series bold

\backslash
hspace{length}
\series default

\begin_inset LatexCommand index
name "Commands ! H ! \\textbackslash hspace"

\end_inset

.
 For the length all units listed in 
\begin_inset LatexCommand ref
reference "tab:Used-units"

\end_inset

 are allowed, except of the unit 
\begin_inset Quotes eld
\end_inset

mu
\begin_inset Quotes erd
\end_inset

.
 The length may also be negative.
 To insert so many space that the formula uses all available space, the
 command 
\series bold

\backslash
hfill
\series default

\begin_inset LatexCommand index
name "Commands ! H ! \\textbackslash hfill"

\end_inset

 is used.
\end_layout

\begin_layout Standard
\begin_inset VSpace -1mm
\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\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
spce 
\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
In the last example the available space is given by the longest column entry
 of the table.
 In an inline formula the space depends on the length of the line in which
 
\series bold

\backslash
hfill
\series default
 is inserted.
 Thus, when the line uses the full width, no space will be created.
 
\series bold

\backslash
hfill
\series default
 has only an effect on displayed formulas when the formula style 
\series bold
Indented
\series default
 is used.
 (Formula styles are explained in 
\begin_inset LatexCommand ref
reference "sec:Formula-Styles"

\end_inset

.)
\end_layout

\begin_layout Standard
The commands 
\series bold

\backslash
hspace
\series default
 and 
\series bold

\backslash
hfill
\series default
 can also be inserted in TeX-mode to use them for text:
\end_layout

\begin_layout Standard
This is a line with
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
hspace{2cm}
\end_layout

\end_inset

2\InsetSpace \thinspace{}
cm space.
\end_layout

\begin_layout Standard
This is a line with
\hfill
maximum space.
\end_layout

\begin_layout Standard
In the last example 
\series bold

\backslash
hfill
\series default
 was inserted via the menu 
\family sans
Insert\SpecialChar \menuseparator
Formatting\SpecialChar \menuseparator
Horizontal\InsetSpace ~
Fill
\family default
, what is not possible in formulas.
 This has the advantage that one can directly see in LyX that this is a
 stretch space.
\end_layout

\begin_layout Standard
When the commands are at the begin of a text line but not at the beginning
 of a paragraph, they will be ignored by LaTeX.
 To avoid that, the command 
\series bold

\backslash
hspace*
\series default
 is used instead of 
\series bold

\backslash
hspace
\series default
.
 To get the same with 
\series bold

\backslash
hfill
\series default
, a line break and an empty placeholder
\series bold

\begin_inset Foot
status collapsed

\begin_layout Standard
for placeholders see 
\begin_inset LatexCommand ref
reference "sub:Placeholders"

\end_inset


\end_layout

\end_inset


\series default
 is inserted in TeX-mode with the command 
\series bold

\backslash
vphantom{} 
\series default
before 
\series bold

\backslash
hfill
\series default
.
 
\end_layout

\begin_layout Subsection
Space besides inline Formulas
\begin_inset LatexCommand index
name "Space ! besides inline formulas"

\end_inset


\end_layout

\begin_layout Standard
The space that surrounds inline formulas can be adjusted with the length
 
\series bold

\backslash
mathsurround
\begin_inset LatexCommand index
name "Commands ! M ! \\textbackslash mathsurround"

\end_inset


\series default
.
 The value of a length is set with the command 
\series bold

\backslash
setlength
\begin_inset LatexCommand index
name "Commands ! S ! \\textbackslash setlength"

\end_inset


\series default
 that has the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{length name}{value}
\end_layout

\begin_layout Standard
To set 
\series bold

\backslash
mathsurround
\series default
 to the value 5\InsetSpace \thinspace{}
mm, the command
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{
\backslash
mathsurround}{5mm}
\end_layout

\begin_layout Standard
is inserted in TeX-mode.
 5\InsetSpace \thinspace{}
mm space will now be set around all inline formulas:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
setlength{
\backslash
mathsurround}{5mm}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
This is a line with an inline formula 
\begin_inset Formula $A=B$
\end_inset

 with 5\InsetSpace \thinspace{}
mm surrounding space.
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
setlength{
\backslash
mathsurround}{0pt}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
To return to the predefined value, 
\series bold

\backslash
mathsurround
\series default
 is set to the value 0\InsetSpace \thinspace{}
pt.
\end_layout

\begin_layout Section
Boxes and Frames
\begin_inset LatexCommand index
name "Boxes"

\end_inset


\begin_inset LatexCommand index
name "Frames | see {Boxes}"

\end_inset


\end_layout

\begin_layout Standard
Boxes for text are described in chapter 
\family typewriter
Boxes
\family default
 in the 
\family typewriter
Embedded\InsetSpace ~
Objects
\family default
 manual.
\end_layout

\begin_layout Subsection
Boxes with Frame
\begin_inset LatexCommand label
name "sub:Boxes-with-Frame"

\end_inset


\begin_inset LatexCommand index
name "Boxes ! with frame"

\end_inset


\end_layout

\begin_layout Standard
It is possible to frame formulas or parts of it with the commands 
\series bold

\backslash
fbox
\series default

\begin_inset LatexCommand index
name "Commands ! F ! \\textbackslash fbox"

\end_inset

 and 
\series bold

\backslash
boxed
\series default

\begin_inset LatexCommand index
name "Commands ! B ! \\textbackslash boxed"

\end_inset

.
\end_layout

\begin_layout Standard
When one of these commands is inserted to a formula, a blue box appears
 within a frame to enter formula parts.
 For 
\series bold

\backslash
fbox
\series default
 an additional formula has to be created by 
\family sans
Ctrl-m
\family default
 within this box
\begin_inset Foot
status collapsed

\begin_layout Standard
Due to a bug in LyX it is not possible to create a new formula with 
\family sans
Ctrl-m
\family default
, see 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
\end_layout

\end_inset

LyX-bug #1435
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

.
\end_layout

\end_inset

, because the box content will otherwise be treated as mathematical text.
 When 
\series bold

\backslash
boxed
\series default
 is used, a new formula is automatically created inside the frame.
\end_layout

\begin_layout Standard
The command 
\series bold

\backslash
fbox
\series default
 is not suitable to frame displayed formulas, because the formula will always
 be set in the size of the text.
 
\series bold

\backslash
boxed
\series default
 is in contrary not suitable to frame inline formulas, because the formula
 will always be set in the size of a displayed formula.
\end_layout

\begin_layout Standard
As extension to 
\series bold

\backslash
fbox
\series default
 there is the command 
\series bold

\backslash
framebox
\series default

\begin_inset LatexCommand index
name "Commands ! F ! \\textbackslash framebox"

\end_inset

 where additionally the frame width and the alignment can be specified.
 
\series bold

\backslash
framebox
\series default
 is used in the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
framebox[frame width][position]{box content}
\end_layout

\begin_layout Standard
The position can either be 
\emph on
l
\emph default
 or 
\emph on
r
\emph default
.
 
\emph on
l
\emph default
 left aligns, 
\emph on
r
\emph default
 right aligns the formula in the box.
 When no position is given, the formula will be centered.
\newline
Is no width given,
 also no position can be given.
 In this case the frame width is adjusted to the box content like for 
\series bold

\backslash
fbox
\series default
.
\end_layout

\begin_layout Standard
When the command 
\series bold

\backslash
framebox
\series default
 is inserted, a box appears containing three blue boxes.
\begin_inset Foot
status collapsed

\begin_layout Standard
Due to a bug in LyX the cursor has to be placed left beside blue the boxes
 to fill them, see 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=2461}{
\end_layout

\end_inset

LyX-bug #2461
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

.
\end_layout

\end_inset

 The first two boxes are surrounded by brackets and denote the two optional
 arguments.
 The third box is for formula parts like for 
\series bold

\backslash
fbox
\series default
.
\end_layout

\begin_layout Standard
\align center
\begin_inset Note Note
status open

\begin_layout Standard
The table has been set into a minipage to make the footnote appearing.
 Otherwise the footnote text would not be displayed.
\end_layout

\end_inset


\begin_inset Box Frameless
position "c"
hor_pos "c"
has_inner_box 1
inner_pos "c"
use_parbox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\begin_inset Foot
status collapsed

\begin_layout Standard
Due to a bug in LyX it is not possible to create a new formula with 
\family sans
Ctrl-m
\family default
, see 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
\end_layout

\end_inset

LyX-bug #1435
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset


\family sans
Ctrl-m
\family default
 
\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset


\backslash
int
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A=B
\end_layout

\end_inset
</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
spce 
\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
spce 
\end_layout

\end_inset

20mm
\begin_inset Formula $\to$
\end_inset


\begin_inset Formula $\to$
\end_inset


\family sans
Ctrl-m
\family default
 
\backslash
frac
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\downarrow$
\end_inset

B
\end_layout

\end_inset
</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
The frame thickness can also be adjusted.
 To do this the following commands have to be inserted in TeX-mode before
 the formula
\end_layout

\begin_layout Standard

\series bold

\backslash
fboxrule
\series default
 
\series bold

\begin_inset Quotes eld
\end_inset

thickness
\begin_inset Quotes erd
\end_inset


\series default
 
\series bold

\backslash
fboxsep
\series default
 
\series bold

\begin_inset Quotes eld
\end_inset

distance
\begin_inset Quotes erd
\end_inset


\end_layout

\begin_layout Standard
\begin_inset Quotes eld
\end_inset

distance
\begin_inset Quotes erd
\end_inset

 specifies the minimal distance between the frame and the first character
 in the box.
 An example for this is the following framed formula:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
fboxrule 2mm 
\backslash
fboxsep 3mm
\end_layout

\end_inset


\begin_inset Formula \[
\boxed{A+B=C}\]

\end_inset

Before this formula the commands
\end_layout

\begin_layout Standard

\series bold

\backslash
fboxrule
\series default
 
\series bold
2mm
\series default
 
\series bold

\backslash
fboxsep
\series default
 
\series bold
3mm
\end_layout

\begin_layout Standard
were inserted in TeX-mode.
 The given values are used for all following boxes.
\end_layout

\begin_layout Standard
To return to the standard frame size, the command
\end_layout

\begin_layout Standard

\series bold

\backslash
fboxrule
\series default
 
\series bold
0.4pt
\series default
 
\series bold

\backslash
fboxsep
\series default
 
\series bold
3pt
\series default

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
fboxrule 0.4pt 
\backslash
fboxsep 3pt
\end_layout

\end_inset


\end_layout

\begin_layout Standard
is inserted in TeX-mode before the next formula.
\end_layout

\begin_layout Subsection
Boxes without Frame
\begin_inset LatexCommand label
name "sub:Boxes-without-Frame"

\end_inset


\begin_inset LatexCommand index
name "Boxes ! without frame"

\end_inset


\end_layout

\begin_layout Standard
For boxes without a frame there are the following box commands: 
\series bold

\backslash
mbox
\series default

\begin_inset LatexCommand index
name "Commands ! M ! \\textbackslash mbox"

\end_inset

, 
\series bold

\backslash
makebox
\series default

\begin_inset LatexCommand index
name "Commands ! M ! \\textbackslash makebox"

\end_inset

, and 
\series bold

\backslash
raisebox
\series default

\begin_inset LatexCommand index
name "Commands ! R ! \\textbackslash raisebox"

\end_inset


\end_layout

\begin_layout Standard
With 
\series bold

\backslash
raisebox
\series default
 a box can be super- or subscripted.
 But in contrary to normal super- and subscripting, the characters in the
 box keep their font size.
 
\series bold

\backslash
raisebox
\series default
 is used in the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
raisebox{height}{box content}
\end_layout

\begin_layout Standard
When the box should contain a formula, an extra formula is needed like for
 
\series bold

\backslash
fbox
\series default
.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\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
Ctrl-m
\family default
 
\backslash
sqrt
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

B 
\end_layout

\end_inset
</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
The last formula can currently only be created using TeX-mode because LyX
 inserts a box instead of the needed extra formula.
\begin_inset Foot
status collapsed

\begin_layout Standard
see 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
\end_layout

\end_inset

LyX-bug #1435
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
The command 
\series bold

\backslash
mbox
\series default
 is equivalent to 
\series bold

\backslash
fbox
\series default
 and 
\series bold

\backslash
makebox
\series default
 is equivalent to 
\series bold

\backslash
framebox
\series default
, with the difference that there is no frame.
\end_layout

\begin_layout Subsection
Colored Boxes
\begin_inset LatexCommand label
name "sub:Colored-Boxes"

\end_inset


\begin_inset LatexCommand index
name "Boxes ! colored"

\end_inset


\end_layout

\begin_layout Standard
To be able to use all commands explained in this section, the LaTeX-package
 
\series bold
color
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard
The LaTeX-package 
\series bold
color
\series default
 is part of every LaTeX standard installation.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Packages ! color"

\end_inset

 has to be loaded in the LaTeX-preamble with the line
\begin_inset Foot
status collapsed

\begin_layout Standard
When text is colored somewhere in the document with a predefined color,
 LyX loads the LaTeX-package 
\series bold
color
\series default
 automatically.
 Thus it is possible that the package is loaded twice, but this doesn't
 arise problems.
\end_layout

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Standard
To avoid that the package is loaded twice, a macro was inserted to the LaTeX-pre
amble.
\end_layout

\end_inset


\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{color}
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

To color boxes, the command 
\series bold

\backslash
colorbox
\series default

\begin_inset LatexCommand index
name "Commands ! C ! \\textbackslash colorbox"

\end_inset

 is used in the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
colorbox{color}{box content}
\end_layout

\begin_layout Standard
The box content can also be a box and a 
\series bold

\backslash
colorbox
\series default
 can also be part of another box (see the 2nd and 3rd example).
 When the box should contain a formula, an extra formula has to be created,
 the same as for 
\series bold

\backslash
fbox
\series default
.
\begin_inset Foot
status collapsed

\begin_layout Standard
This also applies for the command 
\series bold

\backslash
fcolorbox
\series default
.
 Thereby note 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=1435}{
\end_layout

\end_inset

LyX-bug #1435
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
One of the following predefined colors can be chosen:
\end_layout

\begin_layout Standard

\series bold
black
\series default
, 
\series bold
blue
\series default
, 
\series bold
cyan
\series default
, 
\series bold
green
\series default
, 
\series bold
magenta
\series default
, 
\series bold
red
\series default
, 
\series bold
white
\series default
, and 
\series bold
yellow
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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
spce 
\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
 only colors the box but not the characters in the box.
 To color all characters, the whole formula is highlighted and the wanted
 color is chosen in the 
\family sans
Text\InsetSpace ~
Style
\family default
 dialog.
 The dialog can be called with the toolbar button 
\begin_inset Graphics
        filename ../images/dialog-show_character.png
        scale 85

\end_inset

 or the menu 
\family sans
Edit\SpecialChar \menuseparator
Text\InsetSpace ~
Style\SpecialChar \menuseparator
Customized
\family default
.
 The formula number has then the same color as the formula.
 When the formula number should get another color than the formula characters,
 the color must be changed within the formula.
\end_layout

\begin_layout Standard
An example:
\end_layout

\begin_layout Standard

\color red
\begin_inset Formula \begin{equation}
\int A=B\label{eq:red}\end{equation}

\end_inset


\color green

\begin_inset Formula \begin{equation}
\textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Formula 
\begin_inset LatexCommand eqref
reference "eq:red"

\end_inset

 is completely colored red.
\newline
Formula 
\begin_inset LatexCommand eqref
reference "eq:redgreen"

\end_inset

 was first completely colored green to set the color for the formula number.
 Subsequently the formula characters were colored red.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

To color the frame different than the rest of the box, the command 
\series bold

\backslash
fcolorbox
\series default

\begin_inset LatexCommand index
name "Commands ! F ! \\textbackslash fcolorbox"

\end_inset

 is used in the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
fcolorbox{frame color}{color}{box content}
\end_layout

\begin_layout Standard
So 
\series bold

\backslash
fcolorbox
\series default
 is an extension of the command 
\series bold

\backslash
colorbox
\series default
.
 The frame width is set, like for 
\series bold

\backslash
framebox
\series default
, with 
\series bold

\backslash
fboxrule
\series default
 and 
\series bold

\backslash
fboxsep
\series default
.
 An example:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
fboxrule 1mm 
\backslash
fboxsep 1mm
\end_layout

\end_inset


\begin_inset Formula \[
\fcolorbox{cyan}{magenta}{A=B}\]

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
fboxrule 0.4pt 
\backslash
fboxsep 3pt
\end_layout

\end_inset


\end_layout

\begin_layout Standard
This formula was created with the command
\newline

\series bold

\backslash
fcolorbox{cyan
\begin_inset Formula $\to$
\end_inset


\backslash
{magenta
\begin_inset Formula $\to$
\end_inset


\backslash
{A=B
\series default
.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

To use other colors than the predefined ones, they have to be defined first.
\end_layout

\begin_layout Standard
One can for example define the color 
\begin_inset Quotes eld
\end_inset


\series bold
darkgreen
\series default

\begin_inset Quotes erd
\end_inset

 with the LaTeX-preamble line:
\end_layout

\begin_layout Standard

\series bold

\backslash
definecolor{darkgreen}{cmyk}{0.5,
\series default
 
\series bold
0,
\series default
 
\series bold
1,
\series default
 
\series bold
0.5}
\series default

\begin_inset LatexCommand index
name "Commands ! D ! \\textbackslash definecolor"

\end_inset


\end_layout

\begin_layout Standard

\series bold
cmyk
\series default
 is the color space that denotes the colors 
\series bold
cyan
\series default
, 
\series bold
magenta
\series default
, 
\series bold
yellow
\series default
, and 
\series bold
black
\series default
.
 The four comma separated numbers are the portion factor for the corresponding
 colors of the color space.
 The factors can be in the range of 0\InsetSpace \thinspace{}
-\InsetSpace \thinspace{}
1.
 Instead of 
\series bold
cmyk
\series default
 also the color space 
\series bold
rgb
\series default
 can be used for definitions.
 
\series bold
rgb
\series default
 denotes 
\series bold
red
\series default
, 
\series bold
green
\series default
, and 
\series bold
blue
\series default
, so that there are in this case three portion factors for the corresponding
 colors.
 Furthermore there is the color space 
\series bold
gray
\series default
 with one portion factor for the gray value.
\end_layout

\begin_layout Standard
As example a framed box with the new defined color 
\series bold
darkgreen
\series default
 where the characters have been colored 
\series bold
yellow
\series default
:
\begin_inset Formula \begin{equation}
\colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
Self-defined colors can also be be used for text with the help of the command
 
\series bold

\backslash
textcolor
\series default
:
\begin_inset LatexCommand index
name "Text ! colored"

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
textcolor{darkgreen}{
\end_layout

\end_inset

This sentence is 
\begin_inset Quotes eld
\end_inset

darkgreen
\begin_inset Quotes erd
\end_inset

.
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\end_layout

\begin_layout Standard

\series bold

\backslash
textcolor
\series default

\begin_inset LatexCommand index
name "Commands ! T ! \\textbackslash textcolor"

\end_inset

 is used in the scheme 
\series bold

\backslash
textcolor{color}{characters to color}
\series default
.
\end_layout

\begin_layout Subsection
Paragraph Boxes
\begin_inset LatexCommand label
name "sub:Paragraph-Boxes"

\end_inset


\begin_inset LatexCommand index
name "Boxes ! as paragraph"

\end_inset


\end_layout

\begin_layout Standard
A box that can contain several lines and paragraphs, a so called paragraph
 box (parbox), can be created with the menu 
\family sans
Insert\SpecialChar \menuseparator
Box
\family default
 or the toolbar button 
\begin_inset Graphics
        filename ../images/box-insert.png
        scale 85

\end_inset

.
\end_layout

\begin_layout Standard
The following example shows a framed parbox in a line:
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

This is a line 
\begin_inset Box Boxed
position "c"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 1
width "5cm"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Standard
This is a paragraph box.
 It is exactly 5\InsetSpace \thinspace{}
cm long and can also contain formulas: 
\begin_inset Formula $\int A\,\mathrm{d}s=C$
\end_inset


\end_layout

\end_inset

 with a parbox.
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard
Such a box is created by right-clicking on the gray box inset.
 A dialog pops up showing the box properties.
 In our case set: 
\emph on
Decoration
\emph default
: Recangular box, 
\emph on
Inner Box
\emph default
: Parbox, 
\emph on
Width
\emph default
: 5\InsetSpace \thinspace{}
cm, 
\emph on
Vertical Box Alignment
\emph default
: Middle
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

In LaTeX a parbox is created with the command 
\series bold

\backslash
parbox
\series default

\begin_inset LatexCommand index
name "Commands ! P ! \\textbackslash parbox"

\end_inset

 that has the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
parbox[position]{width}{box content}
\end_layout

\begin_layout Standard
The positions 
\emph on
b
\emph default
 and 
\emph on
t
\emph default
 are possible.
 
\emph on
b
\emph default
 for bottom means that the box is aligned within the surrounding text with
 its last line.
 With 
\emph on
t
\emph default
 for top this is done with the first line.
 When no position is given, the box will be vertically centered, see section
 
\emph on
Boxes
\emph default
 of the 
\emph on
Embedded\InsetSpace ~
Objects
\emph default
 manual for examples.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

To frame formulas completely, including the formula number, the formula
 must be set into a parbox.
 To do this, the command 
\series bold

\backslash
fbox{
\backslash
parbox{
\backslash
linewidth-2
\backslash
fboxsep-2
\backslash
fboxrule}{
\series default
 is inserted in TeX-mode before the formula.
 
\series bold

\backslash
linewidth
\begin_inset LatexCommand index
name "Commands ! L ! \\textbackslash linewidth"

\end_inset


\series default
 is hereby the line width set for the document.
 Because the frame is outside the parbox, 2\InsetSpace \thinspace{}
times the frame separation and
 the frame thickness must be subtracted from the line width.
 As this is not automatically done by LyX due to a bug
\begin_inset Foot
status collapsed

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=4483}{
\end_layout

\end_inset

LyX-bug #4483
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\end_layout

\end_inset

, TeX-mode has to be used.
 To be able to multiply and subtract in arguments, the LaTeX-package 
\series bold
calc
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold
calc
\series default
 is part of every LaTeX standard installation.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Packages ! calc"

\end_inset

 must be loaded in the LaTeX-preamble with the line
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{calc}
\end_layout

\begin_layout Standard
Behind the formula both boxes are closed by entering 
\series bold
}}
\series default
 in TeX-mode.
 Here is an example:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
fboxsep 5mm 
\backslash
fboxrule 5mm
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
fbox{
\backslash
parbox{
\backslash
linewidth-2
\backslash
fboxsep-2
\backslash
fboxrule}{
\end_layout

\end_inset


\begin_inset Formula \begin{equation}
\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard

}}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
fboxrule 0.4pt 
\backslash
fboxsep 3pt
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

As a parbox is used as argument of 
\series bold

\backslash
fbox
\series default
, there is in this case no difference between 
\series bold

\backslash
fbox
\series default
 and 
\series bold

\backslash
boxed
\series default
.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

Paragraph boxes are very useful to comment formulas directly.
 To do this, 
\series bold

\backslash
parbox
\series default
 is used in combination with the command 
\series bold

\backslash
tag
\series default
.
 (more about 
\series bold

\backslash
tag
\series default
 see 
\begin_inset LatexCommand ref
reference "sub:User-defined-Numbering"

\end_inset

)
\end_layout

\begin_layout Standard
An example of a formula commented with 
\series bold

\backslash
parbox
\series default
:
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
[5x-7b=3b
\backslash
tag*{
\backslash
parbox{5cm}{
\end_layout

\end_inset

This is a description.
 It is distinctly separated from the formula and multiline.
\begin_inset ERT
status collapsed

\begin_layout Standard

}}
\backslash
]
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Such a formula must be inserted completely in TeX-mode because LyX does
 not yet support the command 
\series bold

\backslash
parbox
\series default
 in formulas.
 The formula is created with the following command sequence:
\end_layout

\begin_layout Standard
The command 
\series bold

\backslash
[5x-7b=3b
\backslash
tag*
\backslash
{
\backslash
parbox{5cm}{
\series default
 is inserted in TeX-mode.
\begin_inset Foot
status collapsed

\begin_layout Standard
When the formula style 
\series bold
Indented
\series default
 is used, 
\series bold

\backslash
tag*
\backslash
{
\series default
 can also be replaced by 
\series bold

\backslash
hfill
\series default
.
 (formula styles see 
\begin_inset LatexCommand ref
reference "sec:Formula-Styles"

\end_inset

)
\end_layout

\end_inset

 Then the description follows as normal text, and finally 
\series bold
}}
\backslash
]
\series default
 is inserted in TeX-mode.
 The commands 
\series bold

\backslash
[
\series default
 and 
\series bold

\backslash
]
\series default
 hereby create a displayed formula.
\end_layout

\begin_layout Standard
The advantages of 
\series bold

\backslash
parbox
\series default
 can be seen in this example that was 
\begin_inset Quotes eld
\end_inset

commented
\begin_inset Quotes erd
\end_inset

 using the mathematical textmode:
\begin_inset Formula \[
5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]

\end_inset


\end_layout

\begin_layout Section
Operators
\begin_inset LatexCommand index
name "Operators"

\end_inset


\end_layout

\begin_layout Subsection
Big Operators
\begin_inset LatexCommand label
name "sub:Big-Operators"

\end_inset


\begin_inset LatexCommand index
name "Operators ! big"

\end_inset


\begin_inset LatexCommand index
name "Sums"

\end_inset


\begin_inset LatexCommand index
name "Integrals"

\end_inset


\end_layout

\begin_layout Standard
To be able to use all integral operators listed here, the option 
\family sans
Use esint package automatically
\family default
 must be set in the document settings under 
\family sans
Math\InsetSpace ~
Options
\family default
.
\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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 "Commands ! 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 "Commands ! 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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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 "Commands ! 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
All big operators can also be inserted via the math toolbar button 
\begin_inset Graphics
        filename ../images/math/intop.png
        scale 85

\end_inset

.
\end_layout

\begin_layout Standard
The operators are called big because they are bigger than the sometimes
 equal looking binary operators.
 All big operators can have limits as described in the next subsection.
\end_layout

\begin_layout Standard
The operators 
\series bold

\backslash
intop
\series default
 and 
\series bold

\backslash
ointop
\series default
 are different from 
\series bold

\backslash
int
\series default
 and 
\series bold

\backslash
oint
\series default
, resp.\InsetSpace ~
in the style the operator limits are displayed, see 
\begin_inset LatexCommand ref
reference "sub:Operator-Limits"

\end_inset

.
 
\end_layout

\begin_layout Subsubsection*
Advices for Integrals
\end_layout

\begin_layout Standard
The letter 
\emph on
d
\emph default
 in an integral is an operator, that therefore has to be set upright.
 This is done by highlighting the 
\emph on
d
\emph default
 and using the keyboard shortcut 
\family sans
Alt-c\InsetSpace ~
r
\family default

\begin_inset Foot
status collapsed

\begin_layout Standard
Font styles
\series bold
 
\series default
see 
\begin_inset LatexCommand ref
reference "sub:Font-Styles"

\end_inset


\end_layout

\end_inset

.
 Finally the smallest space is inserted before the 
\emph on
d
\emph default
, as this is usual for operators.
 An example:
\end_layout

\begin_layout Standard
incorrect: 
\begin_inset Formula $\int A(x)dx$
\end_inset


\newline

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
hphantom{in}
\end_layout

\end_inset

correct: 
\begin_inset Formula $\int A(x)\,\mathrm{d}x$
\end_inset


\end_layout

\begin_layout Standard
For multiple integrals there are the following commands:
\begin_inset VSpace medskip
\end_inset


\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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

\end_layout

\begin_layout Subsection
Operator Limits
\begin_inset LatexCommand label
name "sub:Operator-Limits"

\end_inset


\begin_inset LatexCommand index
name "Operators ! Limits"

\end_inset


\end_layout

\begin_layout Standard
Limits are created by super- and subscripts:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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
Limits of inline formulas are set right beside the operator.
 Limits in displayed formulas are set above or below the operator, except
 of integral limits.
\end_layout

\begin_layout Standard
To force that the limits are set beside the operator, the cursor is set
 directly behind the operator and the limits type is changed with the menu
 
\family sans
Edit\SpecialChar \menuseparator
Math\SpecialChar \menuseparator
Change Limits Type
\family default
 to 
\family sans
\series bold
Inline
\family default
\series default
 (shortcut 
\family sans
Alt-m\InsetSpace ~
l
\family default
).
 An example:
\end_layout

\begin_layout Standard
The default limits type is this:
\begin_inset Formula \[
\sum_{x=0}^{\infty}\frac{1}{x^{2}}\]

\end_inset

This is how it looks when the limits type was changed to 
\family sans
\series bold
Inline
\family default
\series default
:
\begin_inset Formula \[
\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]

\end_inset

For integrals, except of 
\series bold

\backslash
intop
\series default
 and 
\series bold

\backslash
ointop
\series default
, the limits are by default set beside the operator.
 But for multiple integrals the limits are often set below the operator.
 In the following example the limits type was therefore set to 
\series bold
Display
\series default
 and so set below the integrals:
\begin_inset Formula \begin{equation}
\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

To specify conditions for limits, the commands 
\series bold

\backslash
subarray
\series default

\begin_inset LatexCommand index
name "Commands ! S ! \\textbackslash subarray"

\end_inset

 and 
\series bold

\backslash
substack
\series default

\begin_inset LatexCommand index
name "Commands ! S ! \\textbackslash substack"

\end_inset

 are used.
 To create for example this expression 
\begin_inset Formula \begin{equation}
\sum_{\begin{subarray}{c}
0<k<1000\\
\\k\,\in\,\mathbb{N}\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
the following has to be done:
\newline
First the command 
\series bold

\backslash
sum
\series default
^
\series bold
n
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

_
\series default
 is typed in.
 One is now in a blue box under the summation operator and insert there
 the command 
\series bold

\backslash
subarray
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series default
.
 The blue box is now within a purple box and now several lines can be written
 among each other.
 A new line is created by inserting a line break (
\family sans
Ctrl-Return
\family default
).
 When now
\newline

\series bold
0<k<1000 Ctrl-Return
\newline

\series default
is typed in, a new box appears below for the new line.
\end_layout

\begin_layout Standard
The alignment of the lines can be changed to left aligned with the 
\family sans
table
\family default
 
\family sans
toolbar
\family default
 or the menu 
\family sans
Edit\SpecialChar \menuseparator
Rows &Columns
\family default
.
 To get right alignment, 
\series bold

\backslash
hfill
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series default
 is inserted at the beginning of the line.
\end_layout

\begin_layout Standard
The command 
\series bold

\backslash
substack
\series default
 is equivalent to 
\series bold

\backslash
subarray
\series default
 with the difference that the lines are always centered.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

Like in formula 
\begin_inset LatexCommand eqref
reference "eq:substack"

\end_inset

 there can be too much space beside an operator, because the characters
 following the operator are set beside the limits.
\end_layout

\begin_layout Standard
To avoid this, the following macro can be used in the LaTeX-preamble:
\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
This defines the command 
\series bold

\backslash
mathclap
\series default

\begin_inset LatexCommand index
name "Commands ! M ! \\textbackslash mathclap"

\end_inset

 that sets the width of the limit to 0\InsetSpace \thinspace{}
pt.
 The command scheme is
\end_layout

\begin_layout Standard

\series bold

\backslash
mathclap{limit}
\end_layout

\begin_layout Standard
where the limit can consist of several conditions.
\end_layout

\begin_layout Standard
Applied on formula 
\begin_inset LatexCommand eqref
reference "eq:substack"

\end_inset

, one uses the command
\end_layout

\begin_layout Standard

\series bold

\backslash
sum_
\backslash
mathclap{
\backslash
substack
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

0<k<1000 Ctrl-Enter
\end_layout

\begin_layout Standard
to create the lower limit.
 The summand is now directly behind the summation operator:
\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

How to use one limit for several operators is described in 
\begin_inset LatexCommand ref
reference "sub:Self-defined-Operators"

\end_inset

.
\end_layout

\begin_layout Subsection
Binary Operators
\begin_inset LatexCommand label
name "sub:Binary-Operators"

\end_inset


\begin_inset LatexCommand index
name "Operators ! binary"

\end_inset


\end_layout

\begin_layout Standard
Binary operators are surrounded by space when there is a character before
 and behind them.
\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
Command
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

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

\begin_layout Standard
Result
\end_layout

\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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
All binary operators can also be inserted via the math toolbar button 
\begin_inset Graphics
        filename ../images/math/pm.png
        scale 85

\end_inset

.
\end_layout

\begin_layout Standard
To typeset the Laplace operator also 
\series bold

\backslash
Delta
\series default
 or 
\series bold

\backslash
nabla
\series default
^
\series bold
2
\series default
 (
\begin_inset Formula $\nabla^{2}$
\end_inset

) can be used instead of 
\series bold

\backslash
bigtriangleup
\series default
 .
\end_layout

\begin_layout Standard
The character 
\family sans
Menu Separator
\family default
 from the menu 
\family sans
Insert\SpecialChar \menuseparator
Special Character
\family default
 is the operator 
\series bold

\backslash
triangleright
\series default
.
\end_layout

\begin_layout Subsection
Self-defined Operators
\begin_inset LatexCommand label
name "sub:Self-defined-Operators"

\end_inset


\begin_inset LatexCommand index
name "Operators ! self-defined"

\end_inset


\end_layout

\begin_layout Standard
With the help of the command 
\series bold

\backslash
DeclareMathOperator
\series default

\begin_inset LatexCommand index
name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"

\end_inset

 custom operators can be defined in the LaTeX-preamble.
 Its command scheme is:
\end_layout

\begin_layout Standard

\series bold

\backslash
DeclareMathOperator{new command}{display}
\end_layout

\begin_layout Standard
Display can be characters or symbols that define how the operator looks
 in the output.
 To define a big operator a * is set behind the command.
 All self-defined big operators can have limits as described in 
\begin_inset LatexCommand ref
reference "sub:Operator-Limits"

\end_inset

.
\end_layout

\begin_layout Standard
For example the LaTeX-preamble line
\end_layout

\begin_layout Standard

\series bold

\backslash
DeclareMathOperator*{
\backslash
Lozenge}{
\backslash
blacklozenge}
\end_layout

\begin_layout Standard
defines the command 
\series bold

\backslash
Lozenge
\series default
, that inserts a big operator consisting of the lozenge symbol from 
\begin_inset LatexCommand ref
reference "sub:Miscellaneous-Symbols"

\end_inset

:
\begin_inset Formula \[
\Lozenge_{n=1}^{\infty}\]

\end_inset

The command for this formula is: 
\series bold

\backslash
Lozenge
\series default
^
\series bold

\backslash
infty
\begin_inset Formula $\to$
\end_inset

_n=1
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

When self-defined operators are not used several times in the document,
 they can also be defined with the commands 
\series bold

\backslash
mathop
\series default

\begin_inset LatexCommand index
name "Commands ! M ! \\textbackslash mathop"

\end_inset

 and 
\series bold

\backslash
mathbin
\series default

\begin_inset LatexCommand index
name "Commands ! M ! \\textbackslash mathbin"

\end_inset

, which have the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
mathop{display}
\series default
 and 
\series bold

\backslash
mathbin{display}
\end_layout

\begin_layout Standard

\series bold

\backslash
mathop
\series default
 defines big operators, 
\series bold

\backslash
mathbin
\series default
 binary operators.
\end_layout

\begin_layout Standard

\series bold

\backslash
mathop
\series default
 can e.\InsetSpace \thinspace{}
g.\InsetSpace ~
be used to use one limit for several operators:
\end_layout

\begin_layout Standard
\begin_inset Formula \[
\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]

\end_inset


\end_layout

\begin_layout Standard
The command for the formula above is:
\newline

\series bold

\backslash
mathop{
\backslash
sum
\backslash
negmedspace
\backslash
sum
\series default

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series bold

\begin_inset Formula $\to$
\end_inset

^N
\series default

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series bold
_i,j=1
\end_layout

\begin_layout Section
Fonts
\begin_inset LatexCommand index
name "Fonts"

\end_inset


\end_layout

\begin_layout Subsection
Font Styles
\begin_inset LatexCommand label
name "sub:Font-Styles"

\end_inset


\begin_inset LatexCommand index
name "Font ! style"

\end_inset


\end_layout

\begin_layout Standard
Latin letters in formulas can be set in one of the following font styles:
\begin_inset VSpace -2mm
\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

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

\begin_layout Standard
shortcut
\end_layout

\end_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
spce 
\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
spce 
\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
spce 
\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
spce 
\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
spce 
\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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

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

\begin_layout Standard
shortcut
\end_layout

\end_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
spce 
\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
spce 
\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
spce 
\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
spce 
\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
-
\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
Note:
\series default
 The styles 
\series bold

\backslash
mathbb
\series default
 and 
\series bold

\backslash
mathcal
\series default
 can only be used for big letters.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Predefined is the style 
\series bold

\backslash
mathnormal
\series default
.
\end_layout

\begin_layout Standard
The style commands work also for letters in mathematical constructs:
\begin_inset Formula \[
\mathfrak{A=\frac{b}{C}}\]

\end_inset


\end_layout

\begin_layout Standard
Characters in mathematical text don't appear in a math font style but in
 the text font style 
\series bold

\backslash
textrm
\series default
.
 That their style can't be set correctly via the text style dialog is a
 bug in LyX.
\begin_inset Foot
status collapsed

\begin_layout Standard
 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=4091}{
\end_layout

\end_inset

LyX-bug #4091
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
Instead of the style commands the dialog 
\family sans
Edit\SpecialChar \menuseparator
Math\SpecialChar \menuseparator
Text Style
\family default
 or the toolbar button 
\begin_inset Graphics
        filename ../images/math/font.png
        scale 85

\end_inset

 can be used.
\end_layout

\begin_layout Subsection
Bold Formulas
\begin_inset LatexCommand label
name "sub:Bold-Formulas"

\end_inset


\begin_inset LatexCommand index
name "Formula ! bold"

\end_inset


\end_layout

\begin_layout Standard
To make a complete formula bold, the command 
\series bold

\backslash
mathbf
\series default
 from the previous subsection cannot be used, because it doesn't work for
 small Greek letters.
 Furthermore it prints Latin letters always upright, like in the following
 equation:
\end_layout

\begin_layout Standard
\begin_inset Formula \[
\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]

\end_inset


\end_layout

\begin_layout Standard
To display the formula correctly, the command 
\series bold

\backslash
boldsymbol
\series default
 is used:
\begin_inset Formula \[
\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]

\end_inset

It is also possible to set the formula in a 
\series bold
boldmath environment
\series default
.
 This environment is created by inserting the command 
\series bold

\backslash
boldmath
\begin_inset LatexCommand index
name "Commands ! B ! \\textbackslash boldmath"

\end_inset


\series default
 in TeX-mode.
 To end the environment, the command 
\series bold

\backslash
unboldmath
\begin_inset LatexCommand index
name "Commands ! U ! \\textbackslash unboldmath"

\end_inset


\series default
 is inserted in TeX-mode.
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
boldmath 
\end_layout

\end_inset


\begin_inset Formula \[
\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
unboldmath 
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Font Sizes
\begin_inset LatexCommand label
name "sub:Font-Sizes"

\end_inset


\begin_inset LatexCommand index
name "Font ! size"

\end_inset


\end_layout

\begin_layout Standard
For characters in formulas there are, analog to characters in text, the
 following size commands:
\end_layout

\begin_layout Standard

\series bold

\backslash
Huge
\series default
, 
\series bold

\backslash
huge
\series default
, 
\series bold

\backslash
LARGE
\series default
, 
\series bold

\backslash
Large
\series default
, 
\series bold

\backslash
large
\series default
, 
\series bold

\backslash
normalsize
\series default
, 
\series bold

\backslash
small
\series default
,
\newline

\series bold

\backslash
footnotesize
\series default
, 
\series bold

\backslash
scriptsize
\series default
, and 
\series bold

\backslash
tiny
\end_layout

\begin_layout Standard
The size produced by the commands depends on the document font size, that
 corresponds with the command 
\series bold

\backslash
normalsize
\series default
.
 The other commands produce smaller or larger sizes than 
\series bold

\backslash
normalsize
\series default
.
 The font size can however not exceed a certain value.
 Is for example the document font size 12\InsetSpace \thinspace{}
pt, the command 
\series bold

\backslash
Huge
\series default
 switches to the same size as 
\series bold

\backslash
huge
\series default
.
 
\end_layout

\begin_layout Standard
A size command is inserted in TeX-mode before the formula and sets the size
 for all following formula and text characters.
 To switch back to the initial size, the command 
\series bold

\backslash
normalsize
\series default
 is inserted behind the formula in TeX-mode.
\end_layout

\begin_layout Standard
Within a formula the size can only be changed for symbols or letters in
 mathematical text.
 To do this, the size command is inserted in mathematical text.
 All following characters until the end of the mathematical text or until
 another size command will have the selected size.
 Two examples:
\begin_inset VSpace -2mm
\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
huge 
\end_layout

\end_inset


\begin_inset Formula \[
A=\frac{B}{c}\cdot\maltese\]

\end_inset


\begin_inset Formula \[
\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
normalsize 
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

Before both formulas the command 
\series bold

\backslash
huge
\series default
 was inserted.
 The command for the second formula is:
\newline

\series bold

\backslash
maltese
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A Alt-m m 
\backslash
Large
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\backslash
maltese
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\backslash
textit
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A
\begin_inset Formula $\to$
\end_inset


\begin_inset Formula $\to$
\end_inset


\newline

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
hspace*{1cm}
\end_layout

\end_inset

Alt-m
\series default
 
\series bold
m 
\backslash
tiny
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\backslash
maltese
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\backslash
textit
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A
\end_layout

\begin_layout Standard
If a symbol cannot be displayed in different sizes, it will always be displayed
 in the default size.
\end_layout

\begin_layout Section
Greek Letters
\begin_inset LatexCommand index
name "Greek letters"

\end_inset


\end_layout

\begin_layout Standard
All Greek letters can also be inserted via the toolbar button 
\begin_inset Graphics
        filename ../images/math/alpha.png
        scale 85

\end_inset

.
\end_layout

\begin_layout Subsection
Small Letters
\begin_inset LatexCommand label
name "sub:Small-Letters"

\end_inset


\begin_inset LatexCommand index
name "Greek letters ! small"

\end_inset


\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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


\end_layout

\begin_layout Standard
How to create upright Greek letters is explained in 
\begin_inset LatexCommand ref
reference "sub:Upright-small-Greek"

\end_inset

.
\end_layout

\begin_layout Subsection
Big Letters
\begin_inset LatexCommand index
name "Greek letters ! big"

\end_inset


\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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

That the big Greek letters appear upright is caused by a design bug when
 TeX was developed.
 To get correct italic big letters, begin every command with 
\series bold
var
\series default
.
 For example the command 
\series bold

\backslash
varGamma
\series default
 produces: 
\begin_inset Formula $\varGamma$
\end_inset


\end_layout

\begin_layout Subsection
Bold Letters
\begin_inset LatexCommand index
name "Greek letters ! bold"

\end_inset


\end_layout

\begin_layout Standard
Greek letters cannot be set with different font styles like Latin letters.
 They can only be made bold with the command 
\series bold

\backslash
boldsymbol
\series default

\begin_inset LatexCommand index
name "Commands ! B ! \\textbackslash boldsymbol"

\end_inset

.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
Symbols
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
texorpdfstring{
\end_layout

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Standard
A list with all symbols of most of the LaTeX-packages can be found in 
\begin_inset LatexCommand cite
key "Symbole"

\end_inset

.
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard

}{}
\end_layout

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Standard

\backslash
texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
\end_layout

\begin_layout Standard
More about 
\backslash
texorpdfstring is in section 
\begin_inset LatexCommand ref
reference "sub:Formulas-in-Section"

\end_inset

.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Symbols"

\end_inset


\end_layout

\begin_layout Standard
Many of the symbols listed in this section can also be inserted via the
 toolbar buttons 
\begin_inset Graphics
        filename ../images/math/nabla.png
        scale 85

\end_inset

 and 
\begin_inset Graphics
        filename ../images/math/digamma.png
        scale 85

\end_inset

.
\end_layout

\begin_layout Subsection
Mathematical Symbols
\begin_inset LatexCommand label
name "sub:Mathematical-Symbols"

\end_inset


\begin_inset LatexCommand index
name "Symbols ! mathematical"

\end_inset


\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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 Standard

\newpage

\end_layout

\begin_layout Subsection
Miscellaneous Symbols
\begin_inset LatexCommand label
name "sub:Miscellaneous-Symbols"

\end_inset


\begin_inset LatexCommand index
name "Symbols ! miscellaneous"

\end_inset


\end_layout

\begin_layout Standard
\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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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

More symbols are listed in 
\begin_inset LatexCommand ref
reference "sub:Miscellaneous-Special-Characters"

\end_inset

.
\end_layout

\begin_layout Standard
Some symbols can be displayed in different sizes, see 
\begin_inset LatexCommand ref
reference "sub:Font-Sizes"

\end_inset

.
\end_layout

\begin_layout Subsection
The Euro-Symbol €
\begin_inset LatexCommand index
name "Symbols ! Euro-symbol"

\end_inset


\begin_inset LatexCommand index
name "\\textcent@\\officialeuro"

\end_inset


\end_layout

\begin_layout Standard
To use the Euro symbol in formulas, the LaTeX-package 
\series bold
eurosym
\series default

\begin_inset LatexCommand index
name "Packages ! eurosym"

\end_inset

 must be installed and loaded with the LaTeX-preamble line
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage[gennarrow]{eurosym}
\end_layout

\begin_layout Standard
The Euro symbol can now be inserted with the command 
\series bold

\backslash
euro
\series default

\begin_inset LatexCommand index
name "Commands ! E ! \\textbackslash euro"

\end_inset

.
\end_layout

\begin_layout Standard
The Euro symbol can directly be inserted with the € key in mathematical
 text, without having 
\series bold
eurosym
\series default
 installed.
 When 
\series bold
eurosym
\series default
 is installed, 
\series bold

\backslash
euro
\series default
 can also be inserted in TeX-mode.
 The official currency symbol can then be inserted with the command 
\series bold

\backslash
officialeuro
\series default

\begin_inset LatexCommand index
name "Commands ! O ! \\textbackslash officialeuro"

\end_inset

, that is only available in TeX-mode.
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
ifeurosym 
\end_layout

\end_inset


\begin_inset Note Note
status open

\begin_layout Standard
The following table will only be displayed when the LaTeX-package 
\series bold
eurosym
\series default
 is installed.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
An overview about the different Euro symbols:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command 
\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
Result
\end_layout

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

\begin_layout Standard
formula
\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
mathematical 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-mode
\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
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<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
The following will be displayed when the LaTeX-package 
\series bold
eurosym
\series default
 is not installed:
\end_layout

\end_inset


\end_layout

\begin_layout Standard
You need to install the LaTeX-package 
\series bold
eurosym
\series default
 to see the rest of this subsection in the output.
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
fi 
\end_layout

\end_inset


\end_layout

\begin_layout Section
Relations
\begin_inset LatexCommand label
name "sec:Relations"

\end_inset


\begin_inset LatexCommand index
name "Relations"

\end_inset


\begin_inset LatexCommand index
name "Comparisons|see{Relations}"

\end_inset


\end_layout

\begin_layout Standard
All relations can also be inserted via the toolbar button 
\begin_inset Graphics
        filename ../images/math/leq.png
        scale 85

\end_inset

.
\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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\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

The characters 
\series bold

\backslash
lhd
\series default
 and 
\series bold

\backslash
rhd
\series default
 are bigger than the equal looking operators 
\series bold

\backslash
triangleleft
\series default
 and 
\series bold

\backslash
triangleright
\series default
, respectively.
\end_layout

\begin_layout Standard
Relations are, in contrary to symbols, always surrounded by space.
\end_layout

\begin_layout Standard
Relations with labels can be created with the command 
\series bold

\backslash
stackrel
\series default

\begin_inset LatexCommand index
name "Commands ! S ! \\textbackslash stackrel"

\end_inset

:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

r
\backslash
to
\backslash
infty
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\begin_inset Formula $\downarrow$
\end_inset


\backslash
approx
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

B
\end_layout

\end_inset
</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 Section
Functions
\end_layout

\begin_layout Subsection
Predefined Functions
\begin_inset LatexCommand label
name "sub:Predefined-Functions"

\end_inset


\begin_inset LatexCommand index
name "Functions ! predefined"

\end_inset


\end_layout

\begin_layout Standard
In general, variables are set 
\emph on
italic
\emph default
 in mathematical expressions, but not function names, because 
\begin_inset Formula $sin$
\end_inset

 could be misunderstood as 
\begin_inset Formula $s\cdot i\cdot n$
\end_inset

.
 Therefore there are predefined functions, that are additionally a bit separated
 from prefactors.
 They are inserted as commands starting with a backslash before their name.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

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

\begin_layout Standard
Command
\end_layout

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

\begin_layout Standard
Result
\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


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
pagebreak 
\end_layout

\end_inset


\end_layout

\begin_layout Standard
The following functions are predefined:
\end_layout

\begin_layout Standard
\begin_inset VSpace -2mm
\end_inset


\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Command
\end_layout

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

\begin_layout Standard
Command
\end_layout

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

\begin_layout Standard
Command
\end_layout

\end_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
They can also be inserted with the math toolbar button 
\begin_inset Graphics
        filename ../images/math/functions.png
        scale 85

\end_inset

.
\end_layout

\begin_layout Subsection
Self-defined Functions
\begin_inset LatexCommand index
name "Functions ! self-defined"

\end_inset


\end_layout

\begin_layout Standard
To use a function that is not predefined, like for example the sign function
 sgn(x), there are two possibilities:
\end_layout

\begin_layout Itemize
Define the function by inserting the following line to the LaTeX-preamble
\begin_inset Foot
status collapsed

\begin_layout Standard
For more about 
\series bold

\backslash
DeclareMathOperator
\series default
 see 
\begin_inset LatexCommand ref
reference "sub:Self-defined-Operators"

\end_inset

.
\end_layout

\end_inset


\newline

\begin_inset VSpace -3mm
\end_inset


\newline

\series bold

\backslash
DeclareMathOperator{
\backslash
sgn}{sgn}
\series default

\begin_inset LatexCommand index
name "Commands ! D ! \\textbackslash dbinom@\\textbackslash DeclareMathOperator"

\end_inset


\newline

\begin_inset VSpace -2mm
\end_inset


\newline
Now the new defined function can be called with the command 
\series bold

\backslash
sgn
\series default
.
\end_layout

\begin_layout Itemize
Write the the formula as usual, mark the formula name, in our example the
 letters 
\emph on
sgn
\emph default
, and change it to mathematical text.
 At last a space is inserted between prefactor and function.
\end_layout

\begin_layout Standard
The result is the same with both methods as with a predefined function
\begin_inset Foot
status collapsed

\begin_layout Standard
In LyX self-defined functions are displayed red, predefined ones black.
\end_layout

\end_inset

:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\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
The first method is more suitable when the self-defined function should
 be used several times.
\end_layout

\begin_layout Subsection
Limits
\begin_inset LatexCommand index
name "Limits"

\end_inset


\end_layout

\begin_layout Standard
For limits there are defined besides 
\series bold

\backslash
lim
\series default

\begin_inset LatexCommand index
name "Commands ! L ! \\textbackslash lim"

\end_inset

, 
\series bold

\backslash
liminf
\series default
 and 
\series bold

\backslash
limsup
\series default
 furthermore the following functions:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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

The limit is created by inserting a subscript.
 It is set right beside the function in an inline formula:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\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

Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
hspace
\series default
 and
\series bold
 
\backslash
raisebox
\series default
 are used here as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\end_layout

\end_inset

A
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

x=B
\end_layout

\end_inset
</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 a displayed formula the limit is set below the formula, as usual:
\begin_inset Formula \[
\lim_{x\to A}x=B\]

\end_inset


\end_layout

\begin_layout Subsection
Modulo-Functions
\begin_inset LatexCommand index
name "Functions ! modulo-"

\end_inset


\end_layout

\begin_layout Standard
The modulo-function is special, because it exists in four variants.
\end_layout

\begin_layout Standard
The variants in a displayed formula:
\begin_inset Formula \begin{align*}
\underline{\textrm{Command}\raisebox{-0.9mm}{}} &  & \underline{\textrm{Result}}\\
\mathrm{a\backslash mod\textrm{\spce}b} &  & a\mod b\\
\mathrm{a\backslash pmod\textrm{\spce}b} &  & a\pmod b\\
\mathrm{a\backslash bmod\textrm{\spce}b} &  & a\bmod b\\
\mathrm{a\backslash pod\textrm{\spce}b} &  & a\pod b\end{align*}

\end_inset


\end_layout

\begin_layout Standard
In an inline formula less space is set before the function names for all
 variants.
\end_layout

\begin_layout Section
Special Characters
\begin_inset LatexCommand index
name "Special characters"

\end_inset


\end_layout

\begin_layout Subsection
Special Characters in Mathematical Text
\end_layout

\begin_layout Standard
The following commands can only be used in mathematical text or in TeX-mode:
\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
command
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
hspace{0mm}
\series default
 is used for separation, because otherwise the output will be ¡ and ¿ respective
ly.
\end_layout

\end_inset


\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
spce 
\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
spce 
\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
The characters 
\begin_inset Formula $\textrm{\textrm{Å}}$
\end_inset

 and 
\begin_inset Formula $\textrm{\textrm{Ø}}$
\end_inset

 can also be inserted via the math toolbar button 
\begin_inset Graphics
        filename ../images/math/digamma.png
        scale 85

\end_inset

.
\end_layout

\begin_layout Standard
An exception are the commands 
\series bold
!
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
hspace{0mm}
\end_layout

\end_inset

`
\series default
 and 
\series bold
?
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
hspace{0mm}
\end_layout

\end_inset

`
\series default
, because they can be inserted in LyX directly to text.
\end_layout

\begin_layout Subsection
Accents in Text
\begin_inset LatexCommand label
name "sub:Accents-in-Text"

\end_inset


\begin_inset LatexCommand index
name "Accents ! in text"

\end_inset


\end_layout

\begin_layout Standard
With the following commands all letters can be accented.
 The commands must be inserted in TeX-mode.
\end_layout

\begin_layout Standard

\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
spce 
\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
</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
u
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\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
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
spce 
\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
spce 
\end_layout

\end_inset

ee
\end_layout

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

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
t ee
\end_layout

\end_inset


\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\hfill

\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
<features>
<column alignment="block" valignment="top" leftline="true" width="0">
<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
<row topline="true" bottomline="true">
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Standard
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_inset
</cell>
</row>
<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
spce 
\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


\end_layout

\end_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
~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
</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" 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
spce 
\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
spce 
\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
spce 
\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

With the command 
\series bold

\backslash
t
\series default
 also two different characters can be accented.
 The command 
\series bold

\backslash
t
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

sz
\series default
 creates: 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
t sz
\end_layout

\end_inset


\end_layout

\begin_layout Standard
The accents 
\series bold
`
\series default
 , 
\series bold
'
\series default
 , and 
\series bold
^
\series default
 can in combination with vowels directly be inserted with the keyboard without
 using TeX-mode.
 The same applies for the tilde
\begin_inset Foot
status collapsed

\begin_layout Standard
This only applies for keyboards where the tilde is defined as accent.
\end_layout

\end_inset

 
\series bold
~
\series default
 in combination with 
\emph on
a
\emph default
 , 
\emph on
n
\emph default
 , or 
\emph on
o
\emph default
.
\end_layout

\begin_layout Standard
The commands 
\series bold

\backslash
b
\series default
 , 
\series bold

\backslash
c
\series default
 , 
\series bold

\backslash
d
\series default
 , 
\series bold

\backslash
H
\series default
 , 
\series bold

\backslash
t
\series default
 , 
\series bold

\backslash
u
\series default
 , 
\series bold

\backslash
v
\series default
, and accents inserted directly with the keyboard are also available in
 mathematical text.
 For the other accents there are special math commands to be used in formulas,
 see 
\begin_inset LatexCommand ref
reference "sub:Accents-for-one"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

Furthermore, with the command 
\series bold

\backslash
textcircled
\series default

\begin_inset LatexCommand index
name "Commands ! T ! \\textbackslash textcircled"

\end_inset

 all numbers and letters can be set into a circle, quasi accented with a
 circle, similar to the the copyright symbol.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
One has to take care that the character fits in the circle.
 
\series bold

\backslash
Large
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard
see 
\begin_inset LatexCommand ref
reference "sub:Font-Sizes"

\end_inset


\end_layout

\end_inset

 specifies thereby the size of the circle.
 With the help of 
\series bold

\backslash
raisebox
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard
see 
\begin_inset LatexCommand ref
reference "sub:Boxes-without-Frame"

\end_inset


\end_layout

\end_inset

 the character can be centered.
\end_layout

\begin_layout Subsection
Minuscule Numbers
\begin_inset LatexCommand index
name "Minuscule numbers"

\end_inset


\end_layout

\begin_layout Standard
Minuscule numbers are created with the command 
\series bold

\backslash
oldstylenums
\series default

\begin_inset LatexCommand index
name "Commands ! O ! \\textbackslash oldstylenums"

\end_inset

.
 The command can be used in formulas and in TeX-mode.
 The command scheme is:
\end_layout

\begin_layout Standard

\series bold

\backslash
oldstylenums{number}
\end_layout

\begin_layout Standard
The command 
\series bold

\backslash
oldstylenums{0123456789
\series default
 produces: 
\begin_inset Formula $\oldstylenums{0123456789}$
\end_inset


\end_layout

\begin_layout Subsection
Miscellaneous Special Characters
\begin_inset LatexCommand label
name "sub:Miscellaneous-Special-Characters"

\end_inset


\begin_inset LatexCommand index
name "Special characters ! miscellaneous"

\end_inset


\end_layout

\begin_layout Standard
The following characters can only be inserted to formulas by using commands:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
spce 
\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
spce 
\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
The degree sign ° can nevertheless be directly inserted if the LaTeX-preamble
 contains the following line
\begin_inset Foot
status collapsed

\begin_layout Standard
More about this is described in 
\begin_inset LatexCommand ref
reference "sub:Text-Characters-in"

\end_inset

.
\end_layout

\end_inset

:
\end_layout

\begin_layout Standard

\series bold

\backslash
DeclareInputtext{176}{
\backslash
ifmmode^
\backslash
circ
\backslash
else
\backslash
textdegree
\backslash
f\SpecialChar \textcompwordmark{}
i}
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

The tilde
\begin_inset LatexCommand index
name "Tilde"

\end_inset

 is designed as accent, thus is looks alone a bit misplaced: ~
\newline
But for web
 addresses (URLs) sometimes a single tilde is needed.
 In this case the relation sign 
\series bold

\backslash
sim
\begin_inset Foot
status collapsed

\begin_layout Standard
see 
\begin_inset LatexCommand ref
reference "sec:Relations"

\end_inset


\end_layout

\end_inset


\series default
 is used in a formula.
 As a formula cannot be created in an URL-box (menu 
\family sans
Insert\SpecialChar \menuseparator
URL
\family default
), the URL is inserted as normal text with the font style '
\family typewriter
typewriter
\family default
'.
 Should the URL be a hyperlink in the DVI- or PDF-output, the command 
\series bold

\backslash
href
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold

\backslash
href
\series default
 can only be used together with the LaTeX-package 
\series bold
hyperref
\series default

\begin_inset LatexCommand index
name "Packages ! hyperref"

\end_inset

.
 More about 
\series bold

\backslash
href
\series default
 is written in the section 
\family typewriter
URL
\family default
 in the 
\family typewriter
Embedded\InsetSpace ~
Objects
\family default
 manual.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Commands ! H ! \\textbackslash href"

\end_inset

 is used.
\end_layout

\begin_layout Standard
As example an URL with a tilde:
\end_layout

\begin_layout Standard
as text: 
\family typewriter
http://www.lyx.org/
\begin_inset Formula $\sim$
\end_inset

mustermann
\end_layout

\begin_layout Standard
with 
\series bold

\backslash
href
\series default
: 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://www.lyx.org/~mustermann}{
\end_layout

\end_inset

http://www.lyx.org/
\begin_inset Formula $\sim$
\end_inset

mustermann
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\end_layout

\begin_layout Section
Formula Styles
\begin_inset LatexCommand label
name "sec:Formula-Styles"

\end_inset


\begin_inset LatexCommand index
name "Formula ! styles"

\end_inset


\end_layout

\begin_layout Itemize
There are two different alignment styles:
\end_layout

\begin_deeper
\begin_layout Description
Centered is the predefined standard
\end_layout

\begin_layout Description
Indented for this the option 
\series bold
fleqn
\series default
 must be inserted in the menu 
\family sans
Document\SpecialChar \menuseparator
Settings
\family default
 under 
\family sans
Document\InsetSpace ~
Class
\end_layout

\begin_layout Standard
When 
\series bold
Indented
\series default
 is used, the indentation can be adjusted with the length 
\series bold

\backslash
mathindent
\series default

\begin_inset LatexCommand index
name "Commands ! M ! \\textbackslash mathindent"

\end_inset

.
 Should the distance be 15\InsetSpace \thinspace{}
mm, the following command line is inserted in
 the LaTeX-preamble
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{
\backslash
mathindent}{15mm}
\end_layout

\begin_layout Standard
When no length is specified, the predefined value of 30\InsetSpace \thinspace{}
pt will be used.
\end_layout

\end_deeper
\begin_layout Itemize
And two different numbering styles:
\end_layout

\begin_deeper
\begin_layout Description
Right is the predefined standard
\end_layout

\begin_layout Description
Left for this the option 
\series bold
leqno
\series default
 must be inserted in the menu 
\family sans
Document\SpecialChar \menuseparator
Settings
\family default
 under 
\family sans
Document\InsetSpace ~
Class
\end_layout

\end_deeper
\begin_layout Standard

\series bold
fleqn
\series default
 and 
\series bold
leqno
\series default
 can also be used together.
 In this case both options are inserted, separated by a comma.
\end_layout

\begin_layout Standard
The chosen styles are used for all displayed formulas of the document.
 When both, centered and indented formulas should be created in a document,
 the style 
\series bold
Centered
\series default
 is used.
 The indented formulas are then set in a flalign environment, see 
\begin_inset LatexCommand ref
reference "sub:Flalign-Environment"

\end_inset

.
\end_layout

\begin_layout Section
Multiline Formulas
\begin_inset LatexCommand label
name "sec:Multiline-Formulas"

\end_inset


\begin_inset LatexCommand index
name "Formula ! multiline"

\end_inset


\end_layout

\begin_layout Subsection
General
\end_layout

\begin_layout Standard
In LyX multiline formulas are created by pressing 
\family sans
\series bold
Ctrl-Return
\family default
\series default
 inside a formula.
 This creates an 
\series bold
align environment
\series default
 that is described in 
\begin_inset LatexCommand ref
reference "sub:Standard-align-Environment"

\end_inset

.
\end_layout

\begin_layout Standard
There are other multiline formula environments that can be created via the
 menu 
\family sans
Insert\SpecialChar \menuseparator
Math
\family default
.
 These environments are described in the following sections.
\end_layout

\begin_layout Standard
In all multiline formula environments a new line is created by pressing
 
\family sans
Ctrl-Return
\family default
.
 To add or delete lines, the math toolbar buttons 
\begin_inset Graphics
        filename ../images/tabular-feature_append-row.png
        scale 85

\end_inset

 or 
\begin_inset Graphics
        filename ../images/tabular-feature_delete-row.png
        scale 85

\end_inset

, respectively, or the menu 
\family sans
Edit\SpecialChar \menuseparator
Rows & Columns
\family default
 can be used.
\end_layout

\begin_layout Subsubsection
Line Separation
\begin_inset LatexCommand label
name "sub:Line-Separation"

\end_inset


\begin_inset LatexCommand index
name "Formula ! multiline ! Line separation"

\end_inset


\end_layout

\begin_layout Standard
There is sometimes not enough space in multiline formulas between the lines:
\begin_inset Formula \begin{eqnarray*}
B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Standard
In LaTeX additional line space is specified as optional argument of the
 new line command.
 This is not yet possible in LyX
\begin_inset Foot
status collapsed

\begin_layout Standard
see 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=1505}{
\end_layout

\end_inset

LyX-bug #1505
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\end_layout

\end_inset

, therefore the whole formula must be inserted in TeX-mode.
 To add in our example space, the command 
\series bold

\backslash

\backslash
[3mm]
\series default
 is inserted at the end of the first line.
 One gets: 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
begin{eqnarray*}
\end_layout

\begin_layout Standard

B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD &
 = & 
\backslash
textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}
\backslash

\backslash
[3mm]
\end_layout

\begin_layout Standard

4x^{2}
\backslash
left(B^{2}+x_{0}^{2}
\backslash
right)+4x_{0}x
\backslash
left(D-B^{2}
\backslash
right)+B^{2}
\backslash
left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}
\backslash
right) & = & 0
\end_layout

\begin_layout Standard


\backslash
end{eqnarray*}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

To set the the line separation for all lines in a formula, the length 
\series bold

\backslash
jot
\series default

\begin_inset LatexCommand index
name "Commands ! J ! \\textbackslash jot"

\end_inset

 is changed.
 The definition is: 
\begin_inset Formula $\mbox{line separation}=\mathrm{6\, pt+\backslash jot}$
\end_inset

.
 Predefined for 
\series bold

\backslash
jot
\series default
 is the value 3\InsetSpace \thinspace{}
pt.
 To create 3\InsetSpace \thinspace{}
mm additional line separation as in the previous example, the
 command
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{
\backslash
jot}{3mm+3pt}
\end_layout

\begin_layout Standard
is inserted in TeX-mode before the formula.
 This requires that the LaTeX-package 
\series bold
calc
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold
calc
\series default
 is part of every LaTeX standard installation.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Packages ! calc"

\end_inset

 was loaded in LaTeX-preamble with the line
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{calc}
\end_layout

\begin_layout Standard
One gets: 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
setlength{
\backslash
jot}{3mm+3pt}
\end_layout

\end_inset


\begin_inset Formula \begin{eqnarray*}
B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
setlength{
\backslash
jot}{3pt}
\end_layout

\end_inset

 To get back to the predefined distance, 
\series bold

\backslash
jot
\series default
 is set to the value 3\InsetSpace \thinspace{}
pt.
\end_layout

\begin_layout Subsubsection
Column Separation
\begin_inset LatexCommand label
name "sub:Column-Separation"

\end_inset


\begin_inset LatexCommand index
name "Formula ! multiline ! Column separation"

\end_inset


\end_layout

\begin_layout Standard
Multiline formulas form a matrix.
 A formula in the eqnarray environment is for example a matrix with three
 columns.
 By changing the column separation in this environment, the space beside
 the relation sign can be changed.
\end_layout

\begin_layout Standard
The column separation is specified with the length 
\series bold

\backslash
arraycolsep
\series default

\begin_inset LatexCommand index
name "Commands ! A ! \\textbackslash arraycolsep"

\end_inset

 according to:
\newline
column separation = 2\InsetSpace \thinspace{}

\series bold

\backslash
arraycolsep
\series default

\newline
Thus, the command
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{
\backslash
arraycolsep}{1cm}
\end_layout

\begin_layout Standard
inserted in TeX-mode, sets for all following formulas a column separation
 of 2\InsetSpace \thinspace{}
cm.
 To get back to the predefined distance, 
\series bold

\backslash
arraycolsep
\series default
 is set to 5\InsetSpace \thinspace{}
pt.
\end_layout

\begin_layout Standard
A formula with 2\InsetSpace \thinspace{}
cm column separation:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
setlength{
\backslash
arraycolsep}{1cm}
\end_layout

\end_inset


\begin_inset Formula \begin{eqnarray*}
A & = & B\\
C & \ne & A\end{eqnarray*}

\end_inset

A formula with the predefined column separation for matrices of 10\InsetSpace \thinspace{}
pt:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
setlength{
\backslash
arraycolsep}{5pt}
\end_layout

\end_inset


\begin_inset Formula \begin{eqnarray*}
A & = & B\\
C & \ne & A\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Subsubsection
Long Formulas
\begin_inset LatexCommand index
name "Formula ! long"

\end_inset


\end_layout

\begin_layout Standard
Long formulas can be typeset using these methods:
\end_layout

\begin_layout Itemize
When one side of the equation is much shorther than the line width, this
 one is chosen for the left side and the right side is typeset over two
 lines:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
medskip
\end_layout

\end_inset

 
\begin_inset Formula \begin{eqnarray}
H & = & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\nonumber \\
 &  & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:kurzlang}\end{eqnarray}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
smallskip
\end_layout

\end_inset


\newline
The minus sign at the beginning of the second line does normally not appear
 as operator because it is the first character of the line.
 Thus it would not be surrounded by space and could not be distinguished
 from the fraction bar.
 To avoid this, space was inserted behind the minus sign with the command
 
\series bold

\backslash
hspace{3pt}
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard
more about 
\series bold

\backslash
hspace
\series default
 see 
\begin_inset LatexCommand ref
reference "sub:Variable-Space"

\end_inset


\end_layout

\end_inset


\begin_inset LatexCommand index
name "Commands ! H ! \\textbackslash hspace"

\end_inset

.
\end_layout

\begin_layout Itemize
When both sides of the equation are too long, the command 
\series bold

\backslash
lefteqn
\series default

\begin_inset LatexCommand index
name "Commands ! L ! \\textbackslash lefteqn"

\end_inset

 is used.
 It is inserted to the first column of the first line and effects that all
 further insertions overwrite the following columns:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
medskip
\end_layout

\end_inset


\begin_inset Formula \begin{eqnarray}
\lefteqn{4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}}\nonumber \\
 &  & -\hspace{3pt}B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\nonumber \\
 &  & =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\label{eq:lefteqn}\end{eqnarray}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
smallskip
\end_layout

\end_inset


\newline
After the insertion of 
\series bold

\backslash
lefteqn
\series default
, the cursor is in a purple box that is a bit shifted to the left from the
 blue one.
 In this the formula is inserted.
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
medskip
\end_layout

\end_inset


\newline
The content of the further lines is inserted to the second or another formula
 column.
 The greater the column number where it was inserted, the larger the indentation.
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
medskip
\end_layout

\end_inset


\newline

\begin_inset Note Greyedout
status open

\begin_layout Standard
Note the following when using 
\series bold

\backslash
lefteqn
\series default
:
\end_layout

\begin_layout Itemize
The formula doesn't use the full page width.
 When e.\InsetSpace \thinspace{}
g.\InsetSpace ~
the term 
\begin_inset Formula $-B^{2}$
\end_inset

 is added to the first line in the above example, it would have been outside
 the page margin.
 To better use the width, negative space can be inserted at the beginning
 of the first line.
\end_layout

\begin_layout Itemize
Due to a bug in LyX the cursor cannot be set with the mouse into the first
 line.
\begin_inset Foot
status collapsed

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=1429}{
\end_layout

\end_inset

LyX-bug #1429
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\end_layout

\end_inset

 One can only set the cursor at the beginning of the line and move it with
 the arrow keys.
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Other methods to set long formulas are offered by the environments described
 in 
\begin_inset LatexCommand ref
reference "sub:Multline-Environment"

\end_inset

 and 
\begin_inset LatexCommand ref
reference "sub:Multiline-Formula-Parts"

\end_inset

.
\end_layout

\begin_layout Subsubsection
Multiline Brackets
\begin_inset LatexCommand label
name "sub:Multiline-Brackets"

\end_inset


\begin_inset LatexCommand index
name "Brackets ! for multiline expressions"

\end_inset


\end_layout

\begin_layout Standard
For brackets spanning multiple lines the following problem occurs:
\begin_inset Formula \begin{eqnarray*}
A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
 &  & \left.\cdots+B-D\right]\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Standard
The closing bracket is smaller than the opening bracket because brackets
 with variable size may not span multiple lines.
\end_layout

\begin_layout Standard
To set the bracket size for the second line correctly, the first line is
 ended with 
\series bold

\backslash
right.
\series default

\begin_inset LatexCommand index
name "Commands ! R ! \\textbackslash right"

\end_inset

 and the second line with 
\series bold

\backslash
left.
\begin_inset Foot
status collapsed

\begin_layout Standard
for more about 
\series bold

\backslash
left
\series default
 and 
\series bold

\backslash
right
\series default
 see 
\begin_inset LatexCommand ref
reference "sub:Automatic-Bracket-Size"

\end_inset


\end_layout

\end_inset


\series default

\begin_inset LatexCommand index
name "Commands ! L ! \\textbackslash left"

\end_inset

.
 After 
\series bold

\backslash
left.

\series default
 the command 
\series bold

\backslash
vphantom
\series default

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series bold

\backslash
prod
\series default
^
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series bold

\backslash
infty
\series default

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\series bold

\begin_inset Formula $\downarrow$
\end_inset

_R=1}
\series default

\begin_inset LatexCommand index
name "Commands ! V ! \\textbackslash vphantom"

\end_inset

 is inserted, because the multiplication operator with its limits is the
 largest symbol in the first line and this should be the size for the bracket
 in the second line.
\end_layout

\begin_layout Standard
The result is this:
\begin_inset Formula \begin{eqnarray*}
A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
 &  & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Subsection
Align Environments
\end_layout

\begin_layout Standard
Align environments can be used for every kind of multiline formulas.
 They are specially useful to set several formulas side by side.
\end_layout

\begin_layout Standard
Align environments consist of columns.
 The odd columns are right aligned, the even ones left aligned.
 Every line in an Align environment can be numbered.
\end_layout

\begin_layout Standard
Align environments are created via the menu 
\family sans
Insert\SpecialChar \menuseparator
Math
\family default
.
 With the menu 
\family sans
Edit\SpecialChar \menuseparator
Math\SpecialChar \menuseparator
Change Formula Type
\family default
 already existing existing formulas can be converted to Align environments.
\end_layout

\begin_layout Standard
To add or delete columns, the math toolbar buttons 
\begin_inset Graphics
        filename ../images/tabular-feature_append-column.png
        scale 85

\end_inset

 or 
\begin_inset Graphics
        filename ../images/tabular-feature_delete-column.png
        scale 85

\end_inset

, respectively, or the menu 
\family sans
Edit\SpecialChar \menuseparator
Rows & Columns
\family default
 can be used.
\end_layout

\begin_layout Subsubsection
Standard align Environment
\begin_inset LatexCommand label
name "sub:Standard-align-Environment"

\end_inset


\begin_inset LatexCommand index
name "Formula ! multiline ! align environment"

\end_inset


\end_layout

\begin_layout Standard
This Align environment is created by presssing 
\family sans
Ctrl-Return
\family default
 in a formula or by the menu 
\family sans
Insert\SpecialChar \menuseparator
Math\SpecialChar \menuseparator
AMS align Environment
\family default
.
\end_layout

\begin_layout Standard
An example for two formulas set side by side, that are created with a four
 column align environment:
\begin_inset Formula \begin{align*}
A & =\sin(B) & C & =D\\
C & \ne A & B & \ne D\end{align*}

\end_inset

As it can be seen, the formulas in this environment are placed so as if
 there would be a 
\series bold

\backslash
hfill
\begin_inset Foot
status collapsed

\begin_layout Standard
more about 
\series bold

\backslash
hfill
\series default
 see 
\begin_inset LatexCommand ref
reference "sub:Variable-Space"

\end_inset


\end_layout

\end_inset


\series default
 before the first and after every even column.
 When the formula style 
\series bold
Indented
\begin_inset Foot
status collapsed

\begin_layout Standard
formula styles see 
\begin_inset LatexCommand ref
reference "sec:Formula-Styles"

\end_inset


\end_layout

\end_inset


\series default
 is used, the formula is set without the 
\series bold

\backslash
hfill
\series default
 before the first column.
\end_layout

\begin_layout Subsubsection
Alignat Environment
\begin_inset LatexCommand index
name "Formula ! multiline ! alignat environment"

\end_inset


\end_layout

\begin_layout Standard
The alignat environment has no predefined column separation.
 It can be inserted manually with the spaces that are described 
\begin_inset LatexCommand ref
reference "sub:Space"

\end_inset

.
\end_layout

\begin_layout Standard
The above example in the alignat environment where 1\InsetSpace \thinspace{}
cm space was inserted
 at the beginning of the second formula:
\begin_inset Formula \begin{alignat*}{2}
A & =\sin(B) & \hspace{1cm}C & =D\\
C & \ne A & B & \ne D\end{alignat*}

\end_inset

Because the column separation can be set separately for every column, this
 environment is especially suitable to set three and more formulas side
 by side.
\end_layout

\begin_layout Subsubsection
Flalign Environment
\begin_inset LatexCommand label
name "sub:Flalign-Environment"

\end_inset


\begin_inset LatexCommand index
name "Formula ! multiline ! flalign environment"

\end_inset


\end_layout

\begin_layout Standard
In this environment the first two columns are always set as much as possible
 to the left and the last two ones to the right.
 An example:
\begin_inset Formula \begin{flalign*}
A & =1 & B & =2 & C & =3\\
X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4\end{flalign*}

\end_inset


\end_layout

\begin_layout Standard
By creating a flalign environment with an odd number of columns where an
 empty TeX-brace is inserted to the last column, several formulas in a document
 can be set to the left, although the formula style 
\series bold
Centered
\series default
 is used.
 As example the indented formula 
\begin_inset LatexCommand eqref
reference "eq:VolInt"

\end_inset

:
\begin_inset Formula \begin{flalign}
\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}

\end_inset

The first two columns contain the formula.
 To indent it as with the formula style 
\series bold
Indented
\series default
, 30\InsetSpace \thinspace{}
pt space was inserted at the beginning of the first column.
\end_layout

\begin_layout Subsection
Eqnarray Environment
\begin_inset LatexCommand index
name "Formula ! multiline ! eqnarray environment"

\end_inset


\end_layout

\begin_layout Standard
When this environment has been created, three blue boxes appear.
 The content of the first box is right aligned, the content of the last
 one left aligned.
 The content of the middle box appears centered and a bit smaller, because
 it is designed to insert there only relation characters.
\begin_inset Formula \begin{eqnarray*}
\frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
AB & AB & AB\\
A & = & A\end{eqnarray*}

\end_inset


\end_layout

\begin_layout Subsection
Gather Environment
\begin_inset LatexCommand index
name "Formula ! multiline ! gather environment"

\end_inset


\end_layout

\begin_layout Standard
This environment consists of only one centered column.
 Every line can be numbered.
\begin_inset Formula \begin{gather}
A=1\\
X=\textrm{-}1\end{gather}

\end_inset


\end_layout

\begin_layout Subsection
Multline Environment
\begin_inset LatexCommand label
name "sub:Multline-Environment"

\end_inset


\begin_inset LatexCommand index
name "Formula ! multiline ! multline environment"

\end_inset


\end_layout

\begin_layout Standard
The multline environment consists, like the gather environment, of only
 one column.
 But the first line is left aligned, the last one right aligned.
 All other lines are centered.
 Therefore this environment is suitable for long formulas.
 As example formula 
\begin_inset LatexCommand eqref
reference "eq:lefteqn"

\end_inset

 in the multline environment:
\begin_inset Formula \begin{multline}
4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\\
=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\end{multline}

\end_inset


\end_layout

\begin_layout Standard
In the output only the the last (first) line of a multline environment appears
 numbered when the document numbering is right (left).
\begin_inset Foot
status collapsed

\begin_layout Standard
numbering styles see 
\begin_inset LatexCommand ref
reference "sec:Formula-Styles"

\end_inset


\end_layout

\end_inset

 This is also the case when there is a formula number displayed after every
 line in LyX.
\begin_inset Foot
status collapsed

\begin_layout Standard
This is 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=518}{
\end_layout

\end_inset

LyX-bug #518
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
With the commands 
\series bold

\backslash
shoveright
\begin_inset LatexCommand index
name "Commands ! S ! \\textbackslash shoveright"

\end_inset


\series default
 and 
\series bold

\backslash
shoveleft
\begin_inset LatexCommand index
name "Commands ! S ! \\textbackslash shoveleft"

\end_inset


\series default
 a centered line can be right or left aligned, respectively.
 The commands are used as follows:
\end_layout

\begin_layout Standard

\series bold

\backslash
shoveright{line content}
\series default
 and 
\series bold

\backslash
shoveleft{line content}
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

The length 
\series bold

\backslash
multlinegap
\begin_inset LatexCommand index
name "Commands ! M ! \\textbackslash multlinegap"

\end_inset


\series default
 specifies the distance of the first line from the left page margin.
 Predefined is the length 0\InsetSpace \thinspace{}
pt.
\end_layout

\begin_layout Standard
As example the above formula where the command
\end_layout

\begin_layout Standard

\series bold

\backslash
setlength{
\backslash
multlinegap}{2cm}
\end_layout

\begin_layout Standard
was inserted in TeX-mode before:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
setlength{
\backslash
multlinegap}{2cm}
\end_layout

\end_inset


\begin_inset Formula \begin{multline}
4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
\shoveleft{-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}\\
=B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\end{multline}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
setlength{
\backslash
multlinegap}{0pt}
\end_layout

\end_inset

The second line was left aligned using 
\series bold

\backslash
shoveleft
\series default
.
\end_layout

\begin_layout Subsection
Multiline Formula Parts
\begin_inset LatexCommand label
name "sub:Multiline-Formula-Parts"

\end_inset


\begin_inset LatexCommand index
name "Formula ! multiline ! formula parts"

\end_inset


\end_layout

\begin_layout Standard
To display only parts of a formula with multiple lines, one of the following
 environments are used: 
\series bold
aligned
\series default
, 
\series bold
alignedat
\series default
, 
\series bold
gathered
\series default
 or 
\series bold
split
\series default
.
 They can be inserted via the menu 
\family sans
Insert\SpecialChar \menuseparator
Math
\family default
 or by using the commands described in this section.
\end_layout

\begin_layout Standard
The first three have the same properties as the corresponding multiline
 formula environments, but it is possible to set further formula parts beside
 them.
 An example:
\begin_inset Formula \[
\left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
\Delta E\Delta t & \ge\frac{\hbar}{2}\end{aligned}
\right\} \textrm{Uncertainty relations}\]

\end_inset


\end_layout

\begin_layout Standard
To get this formula, a displayed formula is created where the command 
\series bold

\backslash
aligned
\begin_inset LatexCommand index
name "Commands ! A ! \\textbackslash aligned"

\end_inset


\series default
 is inserted.
 A purple box appears around the blue formula box where now columns and
 lines can be added.
 Outside the multiline environment other formula parts can be set, like
 the brace.
\end_layout

\begin_layout Standard
The aligned environment is also suitable for long formulas whose lines are
 horizontally aligned.
 Using aligned in a displayed formula has the advantage that the formula
 number is vertically centered behind the lines.
 As example formula 
\begin_inset LatexCommand eqref
reference "eq:kurzlang"

\end_inset

 in the aligned environment:
\begin_inset Formula \begin{equation}
\begin{aligned}H=\; & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\\
 & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\end{aligned}
\end{equation}

\end_inset


\end_layout

\begin_layout Standard
To use the environments 
\series bold
alignedat
\series default
, 
\series bold
gathered
\series default
, or 
\series bold
split
\series default
, the command 
\series bold

\backslash
alignedat
\series default
,
\begin_inset LatexCommand index
name "Commands ! A ! \\textbackslash alignedat"

\end_inset

 
\series bold

\backslash
gathered
\series default

\begin_inset LatexCommand index
name "Commands ! G ! \\textbackslash gathered"

\end_inset

, or 
\series bold

\backslash
split
\series default

\begin_inset LatexCommand index
name "Commands ! S ! \\textbackslash split"

\end_inset

 are inserted, respectively.
 The split environment has the same properties as the aligned environment
 but it can only have two columns.
\end_layout

\begin_layout Subsection
Text in multiline Formulas
\begin_inset LatexCommand label
name "sub:Text-in-multiline"

\end_inset


\begin_inset LatexCommand index
name "Text ! in formulas"

\end_inset


\begin_inset LatexCommand index
name "Formula ! multiline ! text"

\end_inset


\end_layout

\begin_layout Standard
In the Align environments, and the multline and gather environment, text
 can be inserted that will appear in a separate line and doesn't affect
 the column alignment.
 To do this, the command 
\series bold

\backslash
intertext
\begin_inset LatexCommand index
name "Commands ! I ! \\textbackslash intertext"

\end_inset


\series default
 is used in the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
intertext{text}
\end_layout

\begin_layout Standard
The text should not be longer than a line because it cannot be hyphenated.
 As LyX doesn't yet support 
\series bold

\backslash
intertext
\series default
 directly, the text is written as mathematical text.
 
\series bold

\backslash
intertext
\series default
 must hereby be at the beginning of a line and appears in the output above
 this line.
 An example where the text was inserted at the beginning of the second line:
\begin_inset Formula \begin{align}
I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
\intertext{\text{integrand is symmetric to $\phi=\pi$, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\end{align}

\end_inset


\end_layout

\begin_layout Section
Formula Numbering
\begin_inset LatexCommand index
name "Formula numbering"

\end_inset


\begin_inset LatexCommand index
name "Formula ! numbering|see{Formula numbering}"

\end_inset


\end_layout

\begin_layout Subsection
General
\end_layout

\begin_layout Standard
Numbered formulas can be created with the menu 
\family sans
Insert\SpecialChar \menuseparator
Math\SpecialChar \menuseparator
Numbered\InsetSpace ~
Formula
\family default
 (shortcut 
\family sans
Ctrl-Alt\InsetSpace ~
n
\family default
).
 Existing formulas can be numbered with the menu 
\family sans
Edit\SpecialChar \menuseparator
Math\SpecialChar \menuseparator
Toggle\InsetSpace ~
Numbering
\family default
 (shortcut 
\family sans
Alt-m\InsetSpace ~
n
\family default
).
 The formula number is displayed in LyX behind the formula as number sign
 in parentheses.
 The number sign is replaced in the output by the formula number.
\end_layout

\begin_layout Standard
When numbering is turned on in multiline formulas, all lines will be numbered.
 But the numbering can be controlled with the menu 
\family sans
Edit\SpecialChar \menuseparator
Math\SpecialChar \menuseparator
Toggle\InsetSpace ~
Numbering\InsetSpace ~
of\InsetSpace ~
Line
\family default
 (shortcut 
\family sans
Alt-m\InsetSpace ~
N
\family default
) for every line.
\end_layout

\begin_layout Standard
Except of inline formulas, all formulas can be numbered with two different
 styles, see 
\begin_inset LatexCommand ref
reference "sec:Formula-Styles"

\end_inset

.
\end_layout

\begin_layout Subsection
Cross-References
\begin_inset LatexCommand label
name "sub:Cross-References"

\end_inset


\begin_inset LatexCommand index
name "Cross-references ! to formulas"

\end_inset


\end_layout

\begin_layout Standard
All labeled formulas can be cross-referenced.
 A label is added by the menu 
\family sans
Insert\SpecialChar \menuseparator
Label
\family default
 or the toolbar button 
\begin_inset Graphics
        filename ../images/label-insert.png
        scale 85

\end_inset

.
 The cursor must hereby be inside a displayed formula.
 A dialog pops up displaying the prefix 
\series bold
eq:
\series default
 in a text field.
 The label is inserted there behind the prefix.
 The predefined prefix means 
\begin_inset Quotes eld
\end_inset

equation
\begin_inset Quotes erd
\end_inset

 and makes it easier to find labels in large documents because it marks
 it as formula label to divide it from e.\InsetSpace \thinspace{}
g.\InsetSpace ~
section labels.
 To change a label, the menu 
\family sans
Insert\SpecialChar \menuseparator
Label
\family default
 is used again.
\end_layout

\begin_layout Standard
The name of the label is displayed in LyX within two parentheses behind
 formula.
 A formula with a label is always numbered.
 The label is deleted when the numbering is turned off.
 This is at the moment the only way to delete a label, see 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{http://bugzilla.lyx.org/show_bug.cgi?id=2556}{
\end_layout

\end_inset

LyX-bug #2556
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

.
\end_layout

\begin_layout Standard
Cross-references are inserted via the menu 
\family sans
Insert\SpecialChar \menuseparator
Cross-Reference
\family default
 or with the toolbar button 
\begin_inset Graphics
        filename ../images/dialog-show-new-inset_ref.png
        scale 85

\end_inset

.
 A formula cross-reference appears in the output as formula number.
 When in the cross-reference dialog window the format 
\series bold
(<reference>)
\series default
 is chosen, the cross-reference appears in the output as formula number
 in parentheses.
\newline
By right-clicking on a cross-reference in LyX, one jumps
 to the formula that is referenced.
\end_layout

\begin_layout Standard
Here are as examples cross-references to formulas of the following subsections:
\begin_inset Note Note
status open

\begin_layout Standard
Note the different cross-reference types.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
The equations 
\begin_inset LatexCommand eqref
reference "eq:tag"

\end_inset

 and 
\begin_inset LatexCommand eqref
reference "eq:c"

\end_inset

 are equivalent.
 In (
\begin_inset LatexCommand ref
reference "eq:Lat"

\end_inset

) big Latin letters are used for the numbering in contrary to (
\begin_inset LatexCommand ref
reference "eq:Rom"

\end_inset

).
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

When the argument of 
\series bold

\backslash
tag
\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold

\backslash
tag
\series default
 is described in 
\begin_inset LatexCommand ref
reference "sub:User-defined-Numbering"

\end_inset

.
\end_layout

\end_inset


\series default
 contains a box like in 
\begin_inset LatexCommand ref
reference "sub:Paragraph-Boxes"

\end_inset

, the formula cannot be referenced.
\end_layout

\begin_layout Subsection
Subnumbering
\begin_inset LatexCommand index
name "Formula numbering ! subnumbering"

\end_inset


\end_layout

\begin_layout Standard
With the help of the commands 
\series bold

\backslash
begin{subequations}
\series default
 and 
\series bold

\backslash
end{subequations}
\series default
 formulas can be subnumbered.
 Both commands are inserted in TeX-mode.
\end_layout

\begin_layout Standard
An example:
\begin_inset Formula \begin{equation}
A=C-B\label{eq:a}\end{equation}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
addtocounter{equation}{-1}
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
begin{subequations}
\end_layout

\end_inset


\begin_inset VSpace -5mm
\end_inset


\begin_inset Formula \begin{equation}
B=C-A\label{eq:b}\end{equation}

\end_inset


\begin_inset Formula \begin{equation}
C=A+B\label{eq:c}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
end{subequations}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
To create the example, the following is done:
\end_layout

\begin_layout Enumerate
first formula is inserted
\end_layout

\begin_layout Enumerate

\series bold

\backslash
addtocounter{equation}{-1} 
\backslash
begin{subequations}
\begin_inset LatexCommand index
name "Commands ! A ! \\textbackslash addtocounter"

\end_inset


\newline

\series default
is inserted after the first formula
\end_layout

\begin_layout Enumerate
second formula is inserted
\end_layout

\begin_layout Enumerate
third formula is inserted
\end_layout

\begin_layout Enumerate

\series bold

\backslash
end{subequations}
\series default
 is inserted after the third formula
\end_layout

\begin_layout Standard
Every formula between the commands 
\series bold

\backslash
begin
\series default
 and 
\series bold

\backslash
end
\series default
 is subnumbered as a, b, 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
linebreak 
\end_layout

\end_inset

c, \SpecialChar \ldots{}
 For multiline formulas every line will be subnumbered.
 All subnumbered formulas are treated as 
\emph on
one
\emph default
 numbered formula.
 But as every numbered formula increases the counter 
\series bold
equation
\series default
 by one, the command 
\series bold

\backslash
addtocounter
\series default
 is needed to decrease it.
 Otherwise the formulas 
\begin_inset LatexCommand eqref
reference "eq:a"

\end_inset

, 
\begin_inset LatexCommand eqref
reference "eq:b"

\end_inset

, 
\begin_inset LatexCommand eqref
reference "eq:c"

\end_inset

 would be numbered as 
\begin_inset LatexCommand eqref
reference "eq:a"

\end_inset

, 
\begin_inset LatexCommand eqref
reference "eq:d"

\end_inset

, 
\begin_inset LatexCommand eqref
reference "eq:f"

\end_inset

.
\end_layout

\begin_layout Standard
By inserting the commands in TeX-mode, a space is created between the first
 two formulas.
 To revert this -5\InsetSpace \thinspace{}
mm vertical space is inserted after the command 
\series bold

\backslash
begin{subequations}
\series default
.
 When the formula style 
\series bold
Indented
\begin_inset Foot
status collapsed

\begin_layout Standard
formula styles see 
\begin_inset LatexCommand ref
reference "sec:Formula-Styles"

\end_inset


\end_layout

\end_inset


\series default
 is used, -7\InsetSpace \thinspace{}
mm space is inserted instead.
\end_layout

\begin_layout Standard
Here is an example for a multiline formula where the numbering was turned
 off for the second line:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
begin{subequations}
\end_layout

\end_inset


\begin_inset Formula \begin{eqnarray}
A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
 & = & B^{2}-ZB-BZ+Z^{²}\nonumber \\
 & = & B^{2}-2BZ+Z^{2}\label{eq:f}\end{eqnarray}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
end{subequations}
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
User-defined Numbering
\begin_inset LatexCommand label
name "sub:User-defined-Numbering"

\end_inset


\begin_inset LatexCommand index
name "Formula numbering ! user-defined"

\end_inset


\end_layout

\begin_layout Standard
\begin_inset LatexCommand index
name "Formula numbering ! self-defined delimiters"

\end_inset

With the standard numbering parentheses are set around the formula number.
 To replace the parentheses for example by vertical bars, the following
 line is added to the LaTeX-preamble:
\end_layout

\begin_layout Standard

\series bold

\backslash
def
\backslash
tagform@#1{
\backslash
maketag@@@{|#1|}}
\series default

\begin_inset Note Note
status collapsed

\begin_layout Standard
This macro is already declared in the LaTeX-preamble for testing.
 To activate it, remove the percent sign at the beginning.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
To use other characters, the vertical bars besides the 
\series bold
#1
\series default
 are replaced by one ore more characters.
 To get only the formula number the vertical bars are omitted.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

When there should be an expression of your choice instead of the consecutive
 formula number in parentheses behind the formula, the command 
\series bold

\backslash
tag{expression}
\series default

\begin_inset LatexCommand index
name "Commands ! T ! \\textbackslash tag"

\end_inset

 is used:
\begin_inset Formula \begin{equation}
A+B=C\tag{something}\label{eq:tag}\end{equation}

\end_inset

In this example the command 
\series bold

\backslash
tag
\backslash
{something
\series default
 was inserted to the formula.
\end_layout

\begin_layout Standard
When the command 
\series bold

\backslash
tag*
\backslash
{something
\series default
 is inserted instead, the star prevents the parentheses around the expression:
\begin_inset Formula \[
A+B=C\tag*{something}\]

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

To restart the formula numbering with new document parts or sections, the
 following command is used:
\end_layout

\begin_layout Standard

\series bold

\backslash
@addtoreset{equation}{part}
\series default

\begin_inset LatexCommand index
name "Commands ! \"@\" ! \\textbackslash \"@\"addtoreset"

\end_inset


\newline
resp.
\newline

\series bold

\backslash
@addtoreset{equation}{section}
\end_layout

\begin_layout Standard
To be able to use these commands in TeX-mode, the 
\begin_inset Quotes eld
\end_inset

@
\begin_inset Quotes erd
\end_inset

 character has to be made 
\begin_inset Quotes eld
\end_inset

active
\begin_inset Quotes erd
\end_inset

 for LaTeX using the command 
\series bold

\backslash
makeatletter.

\series default
 The command 
\series bold

\backslash
makeatother
\series default
 reverts this.
 So the command sequence in TeX-mode is:
\end_layout

\begin_layout Standard

\series bold

\backslash
makeatletter
\newline

\backslash
@addtoreset{equation}{section}
\newline

\backslash
makeatother
\end_layout

\begin_layout Standard
In the LaTeX-preamble 
\series bold

\backslash
makeatletter
\series default
 and 
\series bold

\backslash
makeatother
\series default
 can be omitted as they are automatically internally inserted by LyX.
\end_layout

\begin_layout Standard
To revert 
\series bold

\backslash
@addtoreset
\series default
, the file 
\series bold
remreset.sty
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold
remreset
\series default
 is part of the LaTeX-package 
\series bold
carlisle
\series default

\begin_inset LatexCommand index
name "Packages ! carlisle"

\end_inset

 that is part of every LaTeX standard installation.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Packages ! remreset"

\end_inset

 has to be loaded in the LaTeX-preamble with the line
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{remreset}
\end_layout

\begin_layout Standard
Then the command 
\series bold

\backslash
@removefromreset
\series default

\begin_inset LatexCommand index
name "Commands ! \"@\" ! \\textbackslash \"@\"removefromreset"

\end_inset

 can be used with the same scheme as 
\series bold

\backslash
@addtoreset
\series default
.
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset

Sometimes formulas should be numbered in the following form:
\end_layout

\begin_layout Standard

\family typewriter
(section number.formula number)
\end_layout

\begin_layout Standard
The formula number should start with every section with 
\begin_inset Quotes eld
\end_inset

1
\begin_inset Quotes erd
\end_inset

.
\end_layout

\begin_layout Standard
For this case there is the command 
\series bold

\backslash
numberwithin
\series default

\begin_inset LatexCommand index
name "Commands ! N ! \\textbackslash numberwithin"

\end_inset

, which is used with the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
numberwithin{counter}{sectioning}
\end_layout

\begin_layout Standard
Counter denotes what kind of numbering is affected, sectioning denotes what
 number is before the dot.
\end_layout

\begin_layout Standard
Thus in our case the following LaTeX-preamble or ERT line is used:
\end_layout

\begin_layout Standard

\series bold

\backslash
numberwithin{equation}{section}
\end_layout

\begin_layout Standard
This is the result:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
numberwithin{equation}{section}
\end_layout

\end_inset


\begin_inset Formula \begin{equation}
A+B=C\end{equation}

\end_inset


\end_layout

\begin_layout Standard
To number e.\InsetSpace \thinspace{}
g.\InsetSpace ~
tables so that the number of the part is the sectioning,
\newline

\series bold

\backslash
numberwithin{table}{part}
\series default
 is used.
\end_layout

\begin_layout Standard
To go back to the standard numbering or to prevent this kind of numbering
 when it is defined by the document class, the following command is inserted
 as ERT or to the LaTeX-preamble:
\end_layout

\begin_layout Standard

\series bold

\backslash
renewcommand{
\backslash
theequation}{
\backslash
arabic{equation}}
\begin_inset LatexCommand index
name "Commands ! A ! \\textbackslash arabic"

\end_inset


\series default

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
renewcommand{
\backslash
theequation}{
\backslash
arabic{equation}}
\end_layout

\end_inset


\series bold

\newline

\series default
or
\series bold

\newline

\backslash
renewcommand{
\backslash
thetable}{
\backslash
arabic{table}}
\end_layout

\begin_layout Standard

\series bold

\backslash
numberwithin
\series default
 uses internally the command 
\series bold

\backslash
@addtoreset
\series default
, described above, that also needs to be reverted.
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
makeatletter
\end_layout

\begin_layout Standard


\backslash
@removefromreset{equation}{section}
\end_layout

\begin_layout Standard


\backslash
makeatother
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Numbering with Roman Numbers and Letters
\begin_inset LatexCommand label
name "sub:Numbering-with-Roman"

\end_inset


\begin_inset LatexCommand index
name "Formula numbering ! with letters"

\end_inset


\begin_inset LatexCommand index
name "Formula numbering ! with Roman numbers"

\end_inset


\end_layout

\begin_layout Standard
Formulas can also be numbered with Roman numbers and Latin letters.
 To number for example with small Roman numbers, the command
\end_layout

\begin_layout Standard

\series bold

\backslash
renewcommand{
\backslash
theequation}{
\backslash
roman{equation}}
\end_layout

\begin_layout Standard
is inserted before the formula in TeX-mode.
 
\series bold

\backslash
renewcommand
\series default

\begin_inset LatexCommand index
name "Commands ! R ! \\textbackslash renewcommand"

\end_inset

 redefines the predefined command 
\series bold

\backslash
theequation
\series default
 to the command 
\series bold

\backslash
roman{equation}
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard
The command 
\series bold

\backslash
renewcommand
\series default
 has the same scheme like the command 
\series bold

\backslash
newcommand
\series default
 that is described in 
\begin_inset LatexCommand ref
reference "sec:User-defined-commands"

\end_inset

.
\end_layout

\end_inset

.
 
\series bold
equation
\series default
 is the formula counter.
 When the command 
\series bold

\backslash
the
\series default
 is used as prefix for a counter, the value of the counter is output as
 Arabic number.
 When a formula is numbered, LaTeX sets internally the command 
\series bold

\backslash
theequation
\series default
 behind the formula.
 
\series bold

\backslash
roman{equation}
\begin_inset LatexCommand index
name "Commands ! R ! \\textbackslash roman"

\end_inset


\series default
 outputs the counter as small Roman number.
\end_layout

\begin_layout Standard
All formulas behind the command 
\series bold

\backslash
renew
\series default
c
\series bold
ommand
\series default
 are now numbered Roman.
 To switch to numbering with big Roman numbers, the command is inserted
 again, but 
\series bold

\backslash
roman
\series default
 is replaced by 
\series bold

\backslash
Roman
\series default

\begin_inset LatexCommand index
name "Commands ! R ! \\textbackslash roman@\\textbackslash Roman"

\end_inset

.
 To 
\begin_inset Quotes eld
\end_inset

number
\begin_inset Quotes erd
\end_inset

 with small Latin letters there is the command 
\series bold

\backslash
alph
\series default

\begin_inset LatexCommand index
name "Commands ! A ! \\textbackslash alph"

\end_inset

, for big ones there is the command 
\series bold

\backslash
Alph
\series default

\begin_inset LatexCommand index
name "Commands ! A ! \\textbackslash alph@\\textbackslash Alph"

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Standard

\series bold
Note:
\series default
 Only maximal 26 formulas can be numbered with Latin letters in one document.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
renewcommand{
\backslash
theequation}{
\backslash
roman{equation}}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Formula \begin{equation}
A=\textrm{small roman}\label{eq:rom}\end{equation}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
renewcommand{
\backslash
theequation}{
\backslash
Roman{equation}}
\end_layout

\end_inset


\begin_inset Formula \begin{equation}
B=\textrm{big Roman}\label{eq:Rom}\end{equation}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
renewcommand{
\backslash
theequation}{
\backslash
alph{equation}}
\end_layout

\end_inset


\begin_inset Formula \begin{equation}
C=\textrm{small Latin}\label{eq:lat}\end{equation}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
renewcommand{
\backslash
theequation}{
\backslash
Alph{equation}}
\end_layout

\end_inset


\begin_inset Formula \begin{equation}
D=\textrm{big Latin}\label{eq:Lat}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
To switch back to the default numbering, insert the command:
\end_layout

\begin_layout Standard

\series bold

\backslash
renewcommand{
\backslash
theequation}{
\backslash
arabic{equation}}
\begin_inset LatexCommand index
name "Commands ! A ! \\textbackslash arabic"

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
renewcommand{
\backslash
theequation}{
\backslash
arabic{equation}}
\end_layout

\end_inset


\begin_inset Formula \begin{equation}
E=\textrm{Arabic}\label{eq:arab}\end{equation}

\end_inset


\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

As you see, formulas are numbered serially independent from the numbering
 style.
 When then numbering should start with 
\begin_inset Quotes eld
\end_inset

1
\begin_inset Quotes erd
\end_inset

 when the style is changed, new equation counters have to be defined.
 A description about this can be found in the file 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
href{Formula-numbering.pdf}{
\end_layout

\end_inset

Formula-numbering.pdf
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

.
\begin_inset Note Note
status collapsed

\begin_layout Standard
More about the command 
\series bold

\backslash
href
\series default
, see section 
\begin_inset LatexCommand ref
reference "sub:Links-in-DVI-"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
User-defined commands
\begin_inset LatexCommand label
name "sec:User-defined-commands"

\end_inset


\begin_inset LatexCommand index
name "User-defined commands"

\end_inset


\end_layout

\begin_layout Standard
Many LaTeX-commands are too long to be used frequently.
 But it is possible to define with the command 
\series bold

\backslash
newcommand
\series default

\begin_inset LatexCommand index
name "Commands ! N ! \\textbackslash newcommand"

\end_inset

 new shorter commands.
\end_layout

\begin_layout Standard
The command scheme of 
\series bold

\backslash
newcommand
\series default
 is:
\end_layout

\begin_layout Standard

\series bold

\backslash
newcommand{new command name}[number of arguments][optional
\series default
 
\series bold
value]
\newline

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
phantom{
\end_layout

\end_inset


\backslash
newcommand
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

{command definition}
\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Standard

\series bold
Note:
\series default
 Assure that the name of the new command is not already used in your document
 or by LaTeX-packages that you use.
 When you for example define the command 
\series bold

\backslash
le
\series default
 for 
\series bold

\backslash
Leftarrow
\series default
, you get an error message because 
\series bold

\backslash
le
\series default
 is already defined as command for 
\begin_inset Quotes eld
\end_inset


\begin_inset Formula $\le$
\end_inset


\begin_inset Quotes erd
\end_inset

.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Standard

\series bold
Note:
\series default
 The names of user-defined commands may only consist of Latin letters.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
The number of arguments is an integer in the range 0\InsetSpace \thinspace{}
-\InsetSpace \thinspace{}
9 and specifies how
 many arguments the new command should have.
 With the optional value a value for an optional argument can be predefined.
 When this is done, the 
\emph on
first
\emph default
 
\emph on
a
\emph default
rgument of the new command is automatically an optional one.
\end_layout

\begin_layout Standard
Here are some examples:
\end_layout

\begin_layout Itemize
To define the command 
\series bold

\backslash
gr
\series default
 for 
\series bold

\backslash
Longrightarrow
\series default
, the LaTeX-preamble line is:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
medskip
\end_layout

\end_inset


\series bold

\newline

\backslash
newcommand{
\backslash
gr}{
\backslash
Longrightarrow}
\end_layout

\begin_layout Itemize
To define the command 
\series bold

\backslash
us
\series default
 for 
\series bold

\backslash
underline
\series default
, the argument (that should be underlined) must be taken into account.
 For this the preamble line is:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
medskip
\end_layout

\end_inset


\series bold

\newline

\backslash
newcommand{
\backslash
us}[1]{
\backslash
underline{#1}}
\series default

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
medskip
\end_layout

\end_inset


\series bold

\newline

\series default
The character 
\series bold
#
\series default
 acts as argument placeholder, the 
\series bold
1
\series default
 behind it denotes that it is the placeholder for the first argument.
\end_layout

\begin_layout Itemize
For 
\series bold

\backslash
framebox
\series default
 one can e.\InsetSpace \thinspace{}
g.\InsetSpace ~
define the command 
\series bold

\backslash
fb
\series default
:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
medskip
\end_layout

\end_inset


\series bold

\newline

\backslash
newcommand{
\backslash
fb}[3]{
\backslash
framebox#1#2{$#3$}}
\series default

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
medskip
\end_layout

\end_inset


\series bold

\newline

\series default
The two Dollar signs creates the extra formula needed for 
\series bold

\backslash
framebox
\series default
, see 
\begin_inset LatexCommand ref
reference "sub:Boxes-with-Frame"

\end_inset

.
\end_layout

\begin_layout Itemize
To create a new command for 
\series bold

\backslash
fcolorbox
\series default
 where the color for the box needn't to be specified, the argument for the
 color is defined optional:
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
medskip
\end_layout

\end_inset


\series bold

\newline

\backslash
newcommand{
\backslash
cb}[3][white]{
\backslash
fcolorbox{#2}{#1}{$#3$}}
\series default

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
medskip
\end_layout

\end_inset


\newline
When the color is not specified when using 
\series bold

\backslash
cb
\series default
, the predefined color 
\series bold
white
\series default
 will be used.
\end_layout

\begin_layout Standard
A test of the new defined commands:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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
spce 
\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
spce 
\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
spce 
\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
Diagrams
\begin_inset LatexCommand index
name "Diagrams"

\end_inset


\end_layout

\begin_layout Standard
To create diagrams, the LaTeX-package 
\series bold
amscd
\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold
amscd
\series default
 is part of every LaTeX standard installation.
\end_layout

\end_inset


\series default

\begin_inset LatexCommand index
name "Packages ! amscd"

\end_inset

 is needed.
 It is loaded in the LaTeX-preamble with the line
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{amscd}
\end_layout

\begin_layout Standard
Diagrams visualize relations and look like this:
\begin_inset Formula \[
\begin{CD}A@>>>B@>>>C\\
@AAA@.@VVV\\
F@<<<E@<<<D\end{CD}\]

\end_inset


\end_layout

\begin_layout Standard
To get them, the command 
\series bold

\backslash
CD
\begin_inset LatexCommand index
name "Commands ! C ! \\textbackslash CD"

\end_inset


\series default
 is inserted to a formula.
 A blue box appears with two dashed lines where further commands can be
 inserted.
 With 
\family sans
Ctrl-Return
\family default
 a new line is created.
 Horizontal relations are inserted in odd, vertical in even formula lines.
\end_layout

\begin_layout Standard
To create the relations there are the following commands:
\end_layout

\begin_layout Itemize

\series bold
@<<<
\series default
 creates a left arrow, 
\series bold
@>>>
\series default
 a right arrow, and 
\series bold
@=
\series default
 a long equal sign
\end_layout

\begin_layout Itemize

\series bold
@AAA
\series default
 creates an up arrow, 
\series bold
@VVV
\series default
 an down arrow, and 
\series bold
@|
\series default
 a vertical equal sign
\end_layout

\begin_layout Itemize

\series bold
@.

\series default
 is a placeholder for non-existent relations
\end_layout

\begin_layout Standard
All arrows can be labeled as follows:
\end_layout

\begin_layout Itemize
Is text inserted between the first and second < or >, resp., it is placed
 above the arrow.
 When it is inserted between the second and third one, it appears under
 the arrow.
\end_layout

\begin_layout Itemize
When text for vertical arrows is inserted between the first and second A
 or V, resp., it is placed left beside the arrow.
 When it is inserted between the second and third one, it appears right
 beside the arrow.
 If the text contains an A or V, these letters must be set into a TeX-brace.
\end_layout

\begin_layout Standard
As example a diagram with all possible relations:
\end_layout

\begin_layout Standard
\begin_inset Formula \[
\begin{CD}A@>j>>B@>>k>C@=F\\
@AmAA@.@VV{V}V@|\\
D@<<j<E@>k>>F@=C\end{CD}\]

\end_inset


\end_layout

\begin_layout Standard
The command for this is:
\newline

\series bold

\backslash
CD
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset

A@>j>>B@>>k>C@=F Ctrl-Enter
\newline

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
hphantom{
\end_layout

\end_inset


\backslash
CD
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

@AmAA@.@VV
\backslash
{V
\series default

\begin_inset Formula $\to$
\end_inset


\series bold
V@| Ctrl-Enter
\newline

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
hphantom{
\end_layout

\end_inset


\backslash
CD
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
spce 
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

D@<<j<E@>k>>F@=C
\end_layout

\begin_layout Standard

\newpage

\end_layout

\begin_layout Section
Tips
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
texorpdfstring{
\end_layout

\end_inset


\begin_inset Foot
status collapsed

\begin_layout Standard
Other useful math tips can be found in 
\begin_inset LatexCommand cite
key "Voss"

\end_inset

.
\end_layout

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard

}{}
\end_layout

\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Standard

\backslash
texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
\end_layout

\begin_layout Standard
More about 
\backslash
texorpdfstring is in section 
\begin_inset LatexCommand ref
reference "sub:Formulas-in-Section"

\end_inset

.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Tips"

\end_inset


\begin_inset LatexCommand index
name "Ions|see{Chemical characters}"

\end_inset


\end_layout

\begin_layout Subsection
Chemical Symbols and Equations
\begin_inset LatexCommand label
name "sub:Chemical-Symbols-and"

\end_inset


\begin_inset LatexCommand index
name "Chemical characters ! Symbols"

\end_inset


\begin_inset LatexCommand index
name "Chemical equations"

\end_inset


\begin_inset LatexCommand index
name "Symbols ! chemical"

\end_inset


\end_layout

\begin_layout Standard
An example text from chemistry:
\end_layout

\begin_layout Quote
The 
\begin_inset Formula $\mathrm{SO_{4}^{2-}}$
\end_inset

-ion reacts with two 
\begin_inset Formula $\mathrm{Na^{+}}$
\end_inset

-ions to sodium sulfate 
\begin_inset Formula $\left(\mathrm{Na_{2}SO_{4}}\right)$
\end_inset

.
 The chemical equation for this is:
\begin_inset Formula \[
\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\]

\end_inset


\end_layout

\begin_layout Standard
This chemical equation can directly be created as formula.
 To avoid that the symbols appear italic, everything is highlighted and
 changed by the shortcut 
\family sans
Alt-c\InsetSpace ~
r
\family default
 to the upright font style.
\begin_inset Foot
status collapsed

\begin_layout Standard
font styles
\series bold
 
\series default
see 
\begin_inset LatexCommand ref
reference "sub:Font-Styles"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Negative Numbers
\begin_inset LatexCommand index
name "Numbers ! negative"

\end_inset


\end_layout

\begin_layout Standard
Negative numbers often look ugly in formulas because the minus sign before
 the number is set with the same length as the minus operator sign.
 When writing the negative number in normal text, the minus sign appears
 correctly.
\end_layout

\begin_layout Standard
Thus, the problem disappears when converting the minus sign to mathematical
 text.
\end_layout

\begin_layout Standard
An example to visualize the problem:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
normal 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
formula:
\end_layout

\end_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
solution:
\end_layout

\end_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
Comma as Decimal Separator
\begin_inset LatexCommand index
name "Comma"

\end_inset


\end_layout

\begin_layout Standard
In LaTeX a comma inside a formula is used, according to the English convention,
 as number group separator.
 So there will be space added behind all commas in formulas.
\end_layout

\begin_layout Standard
To avoid this, the comma is highlighted and changed to mathematical text
 (shortcut 
\family sans
Alt-m\InsetSpace ~
m
\family default
).
\end_layout

\begin_layout Standard
To use all formula commas in the document as decimal separator, the file
 
\series bold
icomma.sty
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold
icomma
\series default
 is part of the LaTeX-package 
\series bold
was
\series default

\begin_inset LatexCommand index
name "Packages ! was\\vspace{4mm}"

\end_inset

.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Packages ! icomma"

\end_inset

 is loaded with the LaTeX-preamble line
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{icomma}
\end_layout

\begin_layout Subsection
Physical Vectors
\begin_inset LatexCommand label
name "sub:Physical-Vectors"

\end_inset


\begin_inset LatexCommand index
name "Vectors ! physical"

\end_inset


\end_layout

\begin_layout Standard
Predefined vectors are offered by the LaTeX-package 
\series bold
braket
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold
braket
\series default
 should be part of every LaTeX standard installation.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Packages ! braket"

\end_inset

 that is loaded with the LaTeX-preamble line
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{braket}
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
ifbraket 
\end_layout

\end_inset


\begin_inset Note Note
status open

\begin_layout Standard
The following table will only be displayed when the LaTeX-package 
\series bold
braket
\series default
 is installed.
\end_layout

\end_inset

The following commands are defined:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\end_layout

\end_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
The command 
\series bold

\backslash
Braket
\series default
 assures that all vertical bars are set in the size of the surrounding brackets:
\begin_inset Formula \[
\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
else 
\end_layout

\end_inset


\begin_inset Note Note
status open

\begin_layout Standard
The following will be displayed when the LaTeX-package 
\series bold
braket
\series default
 is not installed:
\end_layout

\end_inset


\end_layout

\begin_layout Standard
You need to install the LaTeX-package 
\series bold
braket
\series default
 to see the rest of this subsection in the output.
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
fi 
\end_layout

\end_inset


\end_layout

\begin_layout Standard
The effect of 
\series bold

\backslash
Braket
\series default
 can also be achieved using the command 
\series bold

\backslash
middle
\series default
, that is described in 
\begin_inset LatexCommand ref
reference "sub:Automatic-Bracket-Size"

\end_inset

.
\end_layout

\begin_layout Subsection
Self-defined Fractions
\begin_inset LatexCommand label
name "sub:Self-defined-Fractions"

\end_inset


\begin_inset LatexCommand index
name "Fractions ! self-defined"

\end_inset


\end_layout

\begin_layout Standard
To define custom commands for fractions, the command 
\series bold

\backslash
genfrac
\series default

\begin_inset LatexCommand index
name "Commands ! G ! \\textbackslash genfrac"

\end_inset

 is used in the following scheme:
\end_layout

\begin_layout Standard

\series bold

\backslash
genfrac{left
\series default
 
\series bold
bracket}{right
\series default
 
\series bold
bracket}{fraction bar thickness}{style}
\newline

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
phantom{
\end_layout

\end_inset


\backslash
genfrac
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

{numerator}{denominator}
\end_layout

\begin_layout Standard
The style is a number in the range of 0\InsetSpace \thinspace{}
-\InsetSpace \thinspace{}
3.
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Number
\end_layout

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

\begin_layout Standard
Style (Size)
\end_layout

\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
display style formula
\end_layout

\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
inline formula
\end_layout

\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
small
\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
tiny
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
When no style is given, the size is adjusted to the surrounding environment
 like for the command 
\series bold

\backslash
frac
\series default
.
\end_layout

\begin_layout Standard
When no fraction bar thickness is given, the predefined value of 0.4\InsetSpace \thinspace{}
pt will
 be used.
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

For example, the commands 
\series bold

\backslash
dfrac
\series default
 and 
\series bold

\backslash
tbinom
\series default
 from 
\begin_inset LatexCommand ref
reference "sub:Fractions"

\end_inset

 are defined with the commands
\end_layout

\begin_layout Standard

\series bold

\backslash
newcommand{
\backslash
dfrac}[2]{
\backslash
genfrac{}{}{}{0}{#1}{#2}}
\end_layout

\begin_layout Standard
and
\end_layout

\begin_layout Standard

\series bold

\backslash
newcommand{
\backslash
tbinom}[2]{
\backslash
genfrac{(}{)}{0pt}{1}{#1}{#2}}
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

To define a fraction where the fraction bar thickness can be given as optional
 argument, the following line is inserted to the LaTeX-preamble:
\end_layout

\begin_layout Standard

\series bold

\backslash
newcommand{
\backslash
fracS}[3][]{
\backslash
genfrac{}{}{#1}{}{#2}{#3}}
\end_layout

\begin_layout Standard
A test:
\begin_inset Formula \begin{align*}
\text{Command} &  & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} &  & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
\text{Result} &  & \fracS[1mm]{A}{B} &  & \fracS[5mm]{A}{B}\end{align*}

\end_inset

As one can see, the distance of the numerator and the denominator to the
 fraction bar is round about three times the bar thickness.
\end_layout

\begin_layout Subsection
Canceled Formulas
\begin_inset LatexCommand label
name "sub:Canceled-Formulas"

\end_inset


\begin_inset LatexCommand index
name "Formula ! canceled"

\end_inset


\end_layout

\begin_layout Standard
To cancel formulas or formula parts, the LaTeX-package 
\series bold
cancel
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold
cancel
\series default
 is part of every LaTeX standard installation.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Packages ! cancel"

\end_inset

 has to be loaded with the LaTeX-preamble line
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage[samesize]{cancel}
\end_layout

\begin_layout Standard
There are four ways to cancel formulas:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
Result
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
hspace
\series default
 and
\series bold
 
\backslash
raisebox
\series default
 are used here as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
spce 
\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
spce 
\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
spce 
\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
spce 
\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
 is especially suitable to visualize the reduction of fractions within formulas:
\begin_inset Formula \[
\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]

\end_inset


\end_layout

\begin_layout Subsection
Formulas in Section Headings
\begin_inset LatexCommand label
name "sub:Formulas-in-Section"

\end_inset


\begin_inset LatexCommand index
name "Formula ! in section headings"

\end_inset


\end_layout

\begin_layout Standard
When formulas are used in section headings, the following has to be taken
 into account:
\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Standard
When the LaTeX-package 
\series bold
hyperref
\series default

\begin_inset LatexCommand index
name "Packages ! hyperref"

\end_inset

 is used, PDF-bookmarks are automatically created for every section heading
 in the table of contents.
 If a section heading contains formulas, they are incorrectly displayed
 in the bookmark text, because formulas in bookmarks infringe the PDF convention
s.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Both problems can be solved by inserting at the end of the section heading
 a short title with the menu 
\family sans
Insert\SpecialChar \menuseparator
Short\InsetSpace ~
Title
\family default
.
 Short titles are used as alternative for multiline section headings to
 keep the table of contents clearly arranged.
 Only the short title appears in the table of contents and therefore also
 in the PDF-bookmark.
\end_layout

\begin_layout Standard
When formulas should be used in the table of contents but 
\series bold
hyperref
\series default
 is used, one can use the following command in TeX-mode:
\end_layout

\begin_layout Standard

\series bold

\backslash
texorpdfstring{part}{alternative}
\begin_inset LatexCommand index
name "Commands ! T ! \\textbackslash texorpdfstring"

\end_inset


\end_layout

\begin_layout Standard
Part is the part of the heading that shouldn't appear in the PDF-bookmark.
 This can be characters, formulas, footnotes, but also cross-references.
 The alternative is used instead of the part for the bookmark.
\end_layout

\begin_layout Standard
Here are two example headings:
\begin_inset VSpace -3mm
\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
boldmath 
\end_layout

\end_inset


\end_layout

\begin_layout Subsubsection
Heading without formula in table of contents 
\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
\end_inset


\begin_inset OptArg
status collapsed

\begin_layout Standard
Heading without formula in table of contents
\end_layout

\end_inset


\end_layout

\begin_layout Subsubsection
Heading with formula in table of contents
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
texorpdfstring{
\end_layout

\end_inset

 
\begin_inset Formula $\sqrt{-1}=\mathrm{i}$
\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard

}{}
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
unboldmath 
\end_layout

\end_inset

In the first heading a short title was used, in the second one 
\series bold

\backslash
texorpdfstring
\series default
.
\end_layout

\begin_layout Standard
To get the same formatting as for the other headings, the complete heading
 was set into a 
\series bold
boldmath environment
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard
see 
\begin_inset LatexCommand ref
reference "sub:Bold-Formulas"

\end_inset


\end_layout

\end_inset

.
\end_layout

\begin_layout Subsection
Formulas in multi-column Text
\begin_inset LatexCommand index
name "Formula ! in multi-column text"

\end_inset


\end_layout

\begin_layout Standard
Formulas in multi-column text are often too wide to fit into a column and
 thus need to be set over the whole page width.
 This is done by using the LaTeX-package 
\series bold
multicol
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold
multicol
\series default
 is part of every LaTeX standard installation.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Packages ! multicol"

\end_inset

, that is loaded with the LaTeX-preamble line
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{multicol}
\end_layout

\begin_layout Standard
\begin_inset Note Greyedout
status open

\begin_layout Standard
Note herby that the setting 
\family sans
Two-column\InsetSpace ~
document
\family default
 in the menu 
\family sans
Document\SpecialChar \menuseparator
Settings
\family default
 under 
\family sans
Text\InsetSpace ~
Layout
\family default
\emph on
 
\emph default
must 
\emph on
not
\emph default
 be selected.
\end_layout

\end_inset


\end_layout

\begin_layout Standard
Before the multi-column text the command
\end_layout

\begin_layout Standard

\series bold

\backslash
begin{multicols}{column number}
\end_layout

\begin_layout Standard
is written in TeX-mode.
 The column number is a number in the range of 2\InsetSpace \thinspace{}
-\InsetSpace \thinspace{}
10.
 Before the formula the multi-column text is ended by inserting the command
\end_layout

\begin_layout Standard

\series bold

\backslash
end{multicols}
\end_layout

\begin_layout Standard
in TeX-mode.
\end_layout

\begin_layout Standard
Due to the command some space is automatically added before the formula.
 To revert this, -6\InsetSpace \thinspace{}
mm vertical space is inserted before the formula.
 When the formula style 
\series bold
Indented
\begin_inset Foot
status collapsed

\begin_layout Standard
formula styles see 
\begin_inset LatexCommand ref
reference "sec:Formula-Styles"

\end_inset


\end_layout

\end_inset


\series default
 is used, -9\InsetSpace \thinspace{}
mm space is inserted instead.
\end_layout

\begin_layout Standard
As example a multi-column text with a displayed formula:
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
begin{multicols}{2}
\end_layout

\end_inset

Das Spektrum wird fouriertransformiert.
 the Fouriertransformation wird verwendet, um the überlagerten Signale (Netzwerk
, Lösungsmittel) zu trennen.
 Nachdem wir the Phasenverschiebung bestimmen konnten, interessiert uns
 nun das Aussehen des Ausgangssignals.
 Im Experiment haben wir es with sehr vielen Teilchen zu tun, so that man
 über alle Phasen integrieren muss.
 Sei nun 
\begin_inset Formula $S$
\end_inset

 unser normiertes Ausgangssignal and 
\begin_inset Formula $P$
\end_inset

 the Phasenverteilungsfunktion, so ergibt sich the Beziehung
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
end{multicols}
\end_layout

\end_inset


\begin_inset VSpace -6mm
\end_inset


\begin_inset Formula \begin{equation}
S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\label{eq:fouriertrafo}\end{equation}

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
begin{multicols}{2}
\end_layout

\end_inset

wobei 
\begin_inset Formula $S_{0}$
\end_inset

 das Signal ohne Gradient ist and the Normierungsbedingung 
\begin_inset Formula $\int_{-\infty}^{\infty}P(\phi,t)\,\mathrm{d}\phi=1$
\end_inset

 gilt.
 Nun dürfen wir aber nicht the Relaxationsprozess außer Acht lassen.
 Direkt nach the 
\begin_inset Formula $\nicefrac{\pi}{2}$
\end_inset

\InsetSpace \thinspace{}
-rf-Puls beginnt sich the Magnetisierung zu entfokussieren, wodurch sich
 das Signal zusätzlich abschwächt.
 Diese Abschwächung verläuft exponentiell in Abhängigkeit the so genannten
 
\begin_inset Formula $T_{2}$
\end_inset

-Zeit.
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
end{multicols}
\end_layout

\end_inset

 
\end_layout

\begin_layout Subsection
Formulas with Description of Variables
\begin_inset LatexCommand index
name "Formula ! with description of variables"

\end_inset


\end_layout

\begin_layout Standard
To describe variables within a formula, like in formula 
\begin_inset LatexCommand eqref
reference "eq:within"

\end_inset

, a 2
\series bold
×
\series default

\begin_inset Formula $n$
\end_inset

\InsetSpace ~
matrix is used with left aligned columns for the 
\begin_inset Formula $n$
\end_inset

 used variables.
\begin_inset Foot
status collapsed

\begin_layout Standard
matrices see 
\begin_inset LatexCommand ref
reference "sec:Matrices"

\end_inset


\end_layout

\end_inset

 To set the description in a smaller size, before the matrix e.\InsetSpace \thinspace{}
g.\InsetSpace ~
the command
 
\series bold

\backslash
footnotesize
\series default
 is inserted.
\begin_inset Foot
status collapsed

\begin_layout Standard
font sizes see 
\begin_inset LatexCommand ref
reference "sub:Font-Sizes"

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
When the formula style 
\series bold
Indented
\begin_inset Foot
status collapsed

\begin_layout Standard
formula styles see 
\begin_inset LatexCommand ref
reference "sec:Formula-Styles"

\end_inset


\end_layout

\end_inset


\series default
 is used, a 
\series bold

\backslash
hfill
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold

\backslash
hfill
\series default
 only works in formulas with the style 
\series bold
Indented
\series default
, see 
\begin_inset LatexCommand ref
reference "sub:Variable-Space"

\end_inset

.
\end_layout

\end_inset

 is inserted before and after the matrix to have the same separation of
 the matrix from the equation and the side margin.
\end_layout

\begin_layout Standard
When the formula style 
\series bold
Centered
\series default
 is used, the method described in 
\begin_inset LatexCommand ref
reference "sub:Flalign-Environment"

\end_inset

 is used to indent formulas.
 Formula 
\begin_inset LatexCommand eqref
reference "eq:within"

\end_inset

 consists of five columns whereas in the first two columns contain the equation,
 the third the matrix, and the last one an empty TeX-brace.
\begin_inset Formula \begin{flalign}
\hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
\rho & \textrm{density}\\
V & \textrm{volume}\\
g & \textrm{gravitational acceleration}\end{array} &  & {}\label{eq:within}\end{flalign}

\end_inset


\end_layout

\begin_layout Subsection
Upright small Greek Letters
\begin_inset LatexCommand label
name "sub:Upright-small-Greek"

\end_inset


\begin_inset LatexCommand index
name "Greek letters ! upright"

\end_inset


\end_layout

\begin_layout Standard
Most of the math fonts only provide italic small Greek letters.
 But for symbols of elementary particles like pions and neutrinos, upright
 Greek letters are needed.
 The file 
\series bold
upgreek.sty
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard

\series bold
upgreek
\series default
 is part of the LaTeX-package 
\series bold
was
\series default

\begin_inset LatexCommand index
name "Packages ! was\\vspace{4mm}"

\end_inset

.
\end_layout

\end_inset


\begin_inset LatexCommand index
name "Packages ! upgreek"

\end_inset

 that is loaded with the LaTeX-preamble line
\end_layout

\begin_layout Standard

\series bold

\backslash
usepackage{upgreek}
\end_layout

\begin_layout Standard
provides them.
 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
ifupgreek 
\end_layout

\end_inset


\begin_inset Note Note
status open

\begin_layout Standard
The following table will only be displayed when the LaTeX-package 
\series bold
upgreek
\series default
 is installed.
\end_layout

\end_inset

 They are created when the command for a small Greek letters is started
 with 
\series bold
up
\series default
.
 For example the command 
\series bold

\backslash
uptau
\series default
 creates this: 
\begin_inset Formula $\uptau$
\end_inset


\end_layout

\begin_layout Standard
With these commands reactions of elementary particles can be typeset:
\begin_inset Formula \[
\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]

\end_inset


\end_layout

\begin_layout Standard
The upright letters are more bold and wider than the italic ones.
 They should therefore not be used for units like 
\begin_inset Quotes eld
\end_inset

µm
\begin_inset Quotes erd
\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
else 
\end_layout

\end_inset


\begin_inset Note Note
status open

\begin_layout Standard
The following will be displayed when the LaTeX-package 
\series bold
upgreek
\series default
 is not installed:
\end_layout

\end_inset


\end_layout

\begin_layout Standard
You need to install the LaTeX-package 
\series bold
upgreek
\series default
 to see the rest of this subsection in the output.
\end_layout

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
fi 
\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Text Characters in Formulas
\begin_inset LatexCommand label
name "sub:Text-Characters-in"

\end_inset


\begin_inset LatexCommand index
name "Text ! in formulas"

\end_inset


\end_layout

\begin_layout Standard
In some cases you might want to insert text characters directly into formulas.
 When for example the centered dot · is often used in formulas like 
\begin_inset Formula $\nu=5·10^{5}\,\mathrm{Hz}$
\end_inset

, one would have to insert the command 
\series bold

\backslash
cdot
\series default

\begin_inset Foot
status collapsed

\begin_layout Standard
see 
\begin_inset LatexCommand ref
reference "sub:Binary-Operators"

\end_inset


\end_layout

\end_inset

 all the time, because this character is defined in all encodings as text
 character.
 But the encoding can be changed by this LaTeX-preamble line:
\end_layout

\begin_layout Standard

\series bold

\backslash
Declare Inputtext{183}{
\backslash
ifmmode
\backslash
cdot
\backslash
else
\backslash
textperiodcentered
\backslash
f\SpecialChar \textcompwordmark{}
i}
\end_layout

\begin_layout Standard
The character encoding (menu 
\family sans
Document\SpecialChar \menuseparator
Settings\SpecialChar \menuseparator
Language
\family default
) specifies what character appears when a keyboard key is pressed.
 When the key for the character '·' is pressed, internally the command 
\series bold

\backslash
textperiodcentered
\series default
 is used.
 But this command is not available in a formula so that you would get LaTeX-erro
rs.
 With the changed encoding the right command is chosen automatically, depending
 on if the character was inserted into a formula or not.
\end_layout

\begin_layout Standard
The encoding of several characters is saved in definition files.
 Fore example the encoding 
\series bold
latin9
\series default
 is defined in the file 
\series bold
latin9.def
\series default
 that is in the installation folder of LaTeX.
 Encodings should only be changed via the LaTeX-preamble and not in the
 definition files.
 Otherwise own documents could not be edited by other LyX users working
 on other computers.
\end_layout

\begin_layout Standard
\begin_inset VSpace medskip
\end_inset

Besides the centered dot, in this document the degree sign ° is defined
 with the following LaTeX-preamble line so that it can directly be inserted
 to a formula:
\end_layout

\begin_layout Standard

\series bold

\backslash
DeclareInputtext{176}{
\backslash
ifmmode^
\backslash
circ
\backslash
else
\backslash
textdegree
\backslash
f\SpecialChar \textcompwordmark{}
i}
\end_layout

\begin_layout Standard

\newpage

\end_layout

\begin_layout Section
\start_of_appendix
Typographic Advises
\begin_inset LatexCommand index
name "Typographic Advises"

\end_inset


\end_layout

\begin_layout Standard
This section is a summary of the most important typographic rules, listed
 in ISO norms.
\begin_inset Foot
status collapsed

\begin_layout Standard
This collection was partly taken from the German semi-official dictionary
 called 
\begin_inset Quotes eld
\end_inset

Duden
\begin_inset Quotes erd
\end_inset

 
\begin_inset LatexCommand cite
key "Duden"

\end_inset

 that lists some of the ISO rules.
\end_layout

\end_inset


\end_layout

\begin_layout Itemize
Physical units are 
\emph on
always
\emph default
 set upright
\begin_inset Foot
status collapsed

\begin_layout Standard
done with font styles, see 
\begin_inset LatexCommand ref
reference "sub:Font-Styles"

\end_inset


\end_layout

\end_inset

: 30\InsetSpace \thinspace{}
km/h
\newline
Between the value and the unit is the smallest space, see 
\begin_inset LatexCommand ref
reference "sub:Predefined-Space"

\end_inset

.
\end_layout

\begin_layout Itemize
Percent and perthousand signs are set like physical units:
\newline
1,2\InsetSpace \thinspace{}

\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
textperthousand 
\end_layout

\end_inset

\InsetSpace ~
alcohol in blood
\end_layout

\begin_layout Itemize
The degree sign follows directly on the value: 15°, but not when it is used
 in units: 15\InsetSpace \thinspace{}
°C
\end_layout

\begin_layout Itemize
In numbers with more than four digits the smallest space is inserted before
 every third digit to group them: 
\family roman
\series medium
\shape up
\size normal
\emph off
\bar no
\noun off
\color none
18\InsetSpace \thinspace{}
473\InsetSpace \thinspace{}
588
\end_layout

\begin_layout Itemize
For dimensionings like 120×90×40\InsetSpace \thinspace{}
cm the multiplication sign 
\begin_inset Quotes eld
\end_inset

×
\begin_inset Quotes erd
\end_inset

 is used.
 It is available with the LaTeX-command 
\series bold

\backslash
texttimes
\series default
, but can also directly be inserted with some keyboard definitions.
\end_layout

\begin_layout Itemize
Functions with names consisting of several letters are set upright to avoid
 confusions, see 
\begin_inset LatexCommand ref
reference "sub:Predefined-Functions"

\end_inset

.
\end_layout

\begin_layout Itemize
Indices consisting of several letters, are set upright: 
\begin_inset Formula $E_{\mathrm{kin}}$
\end_inset


\newline
Components of matrices are set italic: 
\begin_inset Formula $\hat{H}_{kl}$
\end_inset


\end_layout

\begin_layout Itemize
The differentiation/integration operator 'd', the Euler's number 'e', and
 the imaginary unit 'i' should be set upright, to avoid mixing them up with
 other variables.
\end_layout

\begin_layout Standard

\newpage

\end_layout

\begin_layout Section
Synonyms
\begin_inset LatexCommand index
name "Synonyms"

\end_inset


\end_layout

\begin_layout Standard
Some characters and symbols can be created with several commands.
 Here is a list of the synonym commands:
\end_layout

\begin_layout Standard
\begin_inset VSpace bigskip
\end_inset


\hfill

\begin_inset Tabular
<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
Command
\end_layout

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

\begin_layout Standard
equivalent to
\begin_inset Note Note
status collapsed

\begin_layout Standard

\series bold

\backslash
raisebox
\series default
 is only used as spacer.
\end_layout

\end_inset


\end_layout

\end_inset
</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
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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
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
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\end_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>
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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
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
Command
\end_layout

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

\begin_layout Standard
equivalent 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
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

Description
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

 of LaTeX's math abilities
\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "Voss"

\end_inset

LaTeX tips and tricks-
\begin_inset ERT
status collapsed

\begin_layout Standard


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

\end_inset

page
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "AMS"

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


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

\end_inset

Description
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

 of 
\begin_inset ERT
status collapsed

\begin_layout Standard


\backslash
AmS
\end_layout

\end_inset

-LaTeX
\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "Symbole"

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


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

\end_inset

List
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

 of all symbols available with LaTeX-packages
\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "hyperref"

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


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

\end_inset

Documentation
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

 of the LaTeX-package 
\series bold
hyperref
\series default

\begin_inset LatexCommand index
name "Packages ! hyperref"

\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "Mathclap"

\end_inset


\begin_inset ERT
status collapsed

\begin_layout Standard


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

\end_inset

Description
\begin_inset ERT
status collapsed

\begin_layout Standard

}
\end_layout

\end_inset

 of the command 
\series bold

\backslash
mathclap
\series default
, described in 
\begin_inset LatexCommand ref
reference "sub:Operator-Limits"

\end_inset


\begin_inset LatexCommand index
name "Commands ! M ! \\textbackslash mathclap"

\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset LatexCommand bibitem
key "Duden"

\end_inset


\emph on
Duden Band 1
\emph default
.
 22.
 Auflage, Duden 2001
\end_layout

\begin_layout Subsubsection*
\begin_inset LatexCommand printindex

\end_inset


\end_layout

\end_body
\end_document