]> git.lyx.org Git - lyx.git/blobdiff - lib/doc/Math.lyx
UserGuide.lyx: fix 2 Typos (thanks Ignacio)
[lyx.git] / lib / doc / Math.lyx
index a0dbea6fb2536879ec40c83823ccd1a7cd0c127d..18b503b549848d8499472978f0926f642443d563 100644 (file)
 % example macro from sec. 19.4
 %\def\tagform@#1{\maketag@@@{|#1|}}
 
-% macro from sec. 10.2
-\def\clap#1{\hbox to 0pt{\hss #1\hss}}
-\def\mathclap {\mathpalette \mathclapinternal}
-\def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
-
 
 % ------------------------------------
 % used to check for needed LaTeX packages
 % used for the command \utilde
 \newboolean{undertilde}
 \IfFileExists{undertilde.sty}
- {\setboolean{undertilde}{true}}
+ {\usepackage{undertilde}
+  \setboolean{undertilde}{true}}
  {\setboolean{undertilde}{false}}
 
 % check for package eurosym
 % check for package cancel
 \newboolean{cancel}
 \IfFileExists{cancel.sty}
- {\setboolean{cancel}{true}}
+ {\usepackage{cancel}
+  \setboolean{cancel}{true}}
  {\setboolean{cancel}{false}}
 
 % check for package upgreek
 \use_geometry false
 \use_package amsmath 2
 \use_package amssymb 2
-\use_package cancel 1
+\use_package cancel 0
 \use_package esint 1
 \use_package mathdots 1
-\use_package mathtools 0
+\use_package mathtools 2
 \use_package mhchem 1
 \use_package stackrel 0
 \use_package stmaryrd 0
-\use_package undertilde 1
+\use_package undertilde 0
 \cite_engine basic
 \cite_engine_type default
 \biblio_style plain
@@ -289,7 +286,7 @@ status open
 \begin_layout Plain Layout
 To export this document to PDF, PS or DVI the LaTeX-packages 
 \series bold
-braket, cancel, eurosym, mathdots, mhchem, undertilde
+braket, cancel, eurosym, mathdots, mathtools, mhchem, undertilde
 \series default
  and 
 \series bold
@@ -494,10 +491,9 @@ arg   "math-mode"
 \end_inset
 
  or the toolbar button 
-\begin_inset Graphics
-       filename ../images/math-mode.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-mode"
 \end_inset
 
 .
@@ -647,10 +643,9 @@ T@TeX-mode
 \end_inset
 
  is invoked by pressing the toolbar button 
-\begin_inset Graphics
-       filename ../images/ert-insert.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "ert-insert"
 \end_inset
 
  or by using the menu 
@@ -1503,10 +1498,9 @@ _
 \end_inset
 
  or via the math toolbar button 
-\begin_inset Graphics
-       filename ../images/math-subscript.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-subscript"
 \end_inset
 
 , exponents with a caret 
@@ -1518,10 +1512,9 @@ _
 \end_inset
 
  or via the math toolbar button 
-\begin_inset Graphics
-       filename ../images/math-superscript.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-superscript"
 \end_inset
 
 .
@@ -1712,20 +1705,18 @@ frac
 \end_inset
 
  or via the math toolbar button 
-\begin_inset Graphics
-       filename ../images/math/frac.png
-       scale 50
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\frac"
 \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
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\frac-square"
 \end_inset
 
  you can select different fraction types.
@@ -2271,10 +2262,14 @@ reference "sub:Self-defined-Fractions"
 \end_layout
 
 \begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
+Multiline fractions are explained in 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Multiline-Fractions"
 
+\end_inset
 
+.
 \end_layout
 
 \begin_layout Subsection
@@ -2311,10 +2306,9 @@ sqrt
 \end_inset
 
  or the math toolbar button 
-\begin_inset Graphics
-       filename ../images/math/sqrt.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\sqrt"
 \end_inset
 
 , all other roots with the command 
@@ -2336,10 +2330,9 @@ root
 \end_inset
 
  or with the math toolbar button 
-\begin_inset Graphics
-       filename ../images/math/root.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\root"
 \end_inset
 
 .
@@ -2619,10 +2612,9 @@ binom
 \end_inset
 
  or with the submenu of the math toolbar button 
-\begin_inset Graphics
-       filename ../images/math/frac-square.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\frac-square"
 \end_inset
 
 .
@@ -3069,10 +3061,9 @@ After inserting
 cases
 \series default
  or pressing the math toolbar button 
-\begin_inset Graphics
-       filename ../images/math/cases.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\cases"
 \end_inset
 
  you can create new lines with the shortcut 
@@ -3082,10 +3073,9 @@ arg   "newline-insert newline"
 \end_inset
 
  or the table toolbar button 
-\begin_inset Graphics
-       filename ../images/tabular-feature_append-row.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "inset-modify tabular append-row"
 \end_inset
 
 .
@@ -3475,10 +3465,9 @@ status collapsed
 
 \begin_layout Plain Layout
 can be found in the submenu of the toolbar button 
-\begin_inset Graphics
-       filename ../images/math/space.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\space"
 \end_inset
 
 
@@ -4188,10 +4177,9 @@ status collapsed
 
 \begin_layout Plain Layout
 In the math toolbar in the submenu of the button 
-\begin_inset Graphics
-       filename ../images/math/ldots.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\ldots"
 \end_inset
 
 
@@ -4774,10 +4762,9 @@ Matrices
 
 \begin_layout Standard
 Matrices can be inserted via the math toolbar button 
-\begin_inset Graphics
-       filename ../images/dialog-show_mathmatrix.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "dialog-show mathmatrix"
 \end_inset
 
  or the menu 
@@ -4906,17 +4893,15 @@ C & F & 10000
 \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
-
+\begin_inset Info
+type  "icon"
+arg   "inset-modify tabular append-row"
 \end_inset
 
 , 
-\begin_inset Graphics
-       filename ../images/tabular-feature_delete-row.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "inset-modify tabular delete-row"
 \end_inset
 
 , etc.
@@ -6616,10 +6601,9 @@ right
 \end_inset
 
  or via the math toolbar button 
-\begin_inset Graphics
-       filename ../images/dialog-show_mathdelimiter.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "dialog-show mathdelimiter"
 \end_inset
 
 .
@@ -6944,7 +6928,7 @@ A+B
 \begin_inset space \textvisiblespace{}
 \end_inset
 
-^v3
+^3
 \begin_inset ERT
 status collapsed
 
@@ -7132,140 +7116,182 @@ underbrace
 \end_layout
 
 \begin_layout Standard
-\begin_inset VSpace bigskip
+\begin_inset VSpace medskip
 \end_inset
 
-When brackets are needed that overlap each other, multiline formulas, as
- described in 
-\begin_inset CommandInset ref
-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_layout
 
+\begin_layout Standard
+If you set in the document settings under 
+\family sans
+Math
+\begin_inset space ~
 \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
+Options
+\family default
+ for the package 
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
 status collapsed
 
 \begin_layout Plain Layout
-Space commands are explained in 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Predefined-Space"
+Packages ! mathtools
+\end_layout
 
 \end_inset
 
-.
+ the option 
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+, you have access to square backets:
 \end_layout
 
-\end_inset
+\begin_layout Standard
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="4" columns="2">
+<features rotate="0" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
 
 \series bold
 
 \backslash
-:
+raisebox
 \series default
- is inserted before the first 
-\begin_inset Formula $d$
-\end_inset
+ is only used as spacer.
+\end_layout
 
-, because the brace that ends behind the 
-\begin_inset Formula $q$
 \end_inset
 
- prevents that the following 
-\begin_inset Quotes eld
+
+\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 Plain Layout
+Result
+\end_layout
 
-+
-\begin_inset Quotes erd
 \end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
 
- is surrounded by space.
-\begin_inset Foot
+\begin_layout Plain Layout
+\begin_inset ERT
 status collapsed
 
 \begin_layout Plain Layout
-because a bracket is not handled as a character, see 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Binary-Operators"
-
-\end_inset
 
 
+\backslash
+raisebox{2.3mm}{
 \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
-:}
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+overbracket
+\family default
 \series default
- is inserted.
-\begin_inset Foot
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+{A+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^3
+\begin_inset ERT
 status collapsed
 
 \begin_layout Plain Layout
-more about 
-\series bold
 
-\backslash
-hphantom
-\series default
- see 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Placeholders"
+}
+\end_layout
 
 \end_inset
 
 
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! O ! 
+\backslash
+overbracket
 \end_layout
 
 \end_inset
 
- This space is needed because the 
-\begin_inset Quotes eld
+
+\end_layout
+
 \end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
 
-+
-\begin_inset Quotes erd
+\begin_layout Plain Layout
+\begin_inset Formula $\overbracket{A+B}^{3}$
 \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:
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
 \begin_inset ERT
 status collapsed
 
@@ -7273,51 +7299,73 @@ status collapsed
 
 
 \backslash
-setlength{
-\backslash
-jot}{-6pt}
+raisebox{-2.2mm}{
 \end_layout
 
 \end_inset
 
 
-\begin_inset Formula 
-\begin{eqnarray*}
- &  & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
-A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
-\end{eqnarray*}
-
+\backslash
+under
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+bracket
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+{A+B
+\begin_inset space \textvisiblespace{}
 \end_inset
 
-
+_5
 \begin_inset ERT
 status collapsed
 
 \begin_layout Plain Layout
 
-
-\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 needs to be reduced.
- This is not easily possible due to a bug in LyX
-\begin_inset Foot
+
+\begin_inset Index idx
 status collapsed
 
 \begin_layout Plain Layout
-\begin_inset CommandInset href
-LatexCommand href
-name "LyX-bug #1505"
-target "http://www.lyx.org/trac/ticket/1505"
+Commands ! U ! 
+\backslash
+under
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+bracket
+\end_layout
 
 \end_inset
 
@@ -7325,106 +7373,95 @@ target "http://www.lyx.org/trac/ticket/1505"
 \end_layout
 
 \end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
 
-.
- As a solution for the problem, the global formula row separation 
-\series bold
-
-\backslash
-jot
-\series default
+\begin_layout Plain Layout
+\begin_inset Formula $\underbracket{A+B}_{5}$
+\end_inset
 
-\begin_inset Index idx
-status collapsed
 
-\begin_layout Plain Layout
-Commands ! J ! 
-\backslash
-jot
 \end_layout
 
 \end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
 
- must be changed to -6
-\begin_inset space \thinspace{}
-\end_inset
-
-pt before the formula with the command 
-\series bold
+\begin_layout Plain Layout
 
 \backslash
-setlength{
-\backslash
-jot}{-6pt}
-\series default
- in TeX-mode.
-\series bold
-
+overbracket{
 \backslash
-jot
-\series default
- is set back after the formula to the standard value of 3
-\begin_inset space \thinspace{}
+underbracket{A+B_w
+\begin_inset space \textvisiblespace{}
 \end_inset
 
-pt using the same command.
- More about the row separation in formulas is explained in 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Line-Separation"
 
+\begin_inset space \textvisiblespace{}
 \end_inset
 
-.
-\end_layout
-
-\begin_layout Section
-Arrows
-\begin_inset Index idx
-status collapsed
+_7
+\begin_inset space \textvisiblespace{}
+\end_inset
 
-\begin_layout Plain Layout
-Arrows
-\end_layout
 
+\begin_inset space \textvisiblespace{}
 \end_inset
 
+^
+\begin_inset space \textvisiblespace{}
+\end_inset
 
+C
 \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
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
 
- or the commands listed in the following subsections.
-\end_layout
+\begin_layout Plain Layout
+\begin_inset Formula $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
+\end_inset
 
-\begin_layout Subsection
-Horizontal Arrows
-\begin_inset Index idx
-status collapsed
 
-\begin_layout Plain Layout
-Arrows ! horizontal
 \end_layout
 
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
 \end_inset
 
 
 \end_layout
 
 \begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
+For 
+\series bold
 
+\backslash
+overbracket
+\series default
+ and 
+\series bold
+
+\backslash
+underbracket
+\series default
+ you can change the thickness of the bracket's stroke by specifying the
+ desired thickness in square brackets behind the command:
+\end_layout
 
+\begin_layout Standard
+\align center
 \begin_inset Tabular
-<lyxtabular version="3" rows="8" columns="2">
+<lyxtabular version="3" rows="3" columns="2">
 <features rotate="0" tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
@@ -7434,40 +7471,31 @@ Arrows ! horizontal
 
 \begin_layout Plain Layout
 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_inset Note Note
+status collapsed
 
 \begin_layout Plain Layout
-Result
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
 \end_layout
 
 \end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
 
-\begin_layout Plain Layout
 
-\backslash
-gets
 \end_layout
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\gets$
-\end_inset
-
-
+Result
 \end_layout
 
 \end_inset
@@ -7478,68 +7506,71 @@ gets
 \begin_inset Text
 
 \begin_layout Plain Layout
-
-\backslash
-Leftarrow
-\end_layout
-
-\end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
+\begin_inset ERT
+status collapsed
 
 \begin_layout Plain Layout
-\begin_inset Formula $\Leftarrow$
-\end_inset
 
 
+\backslash
+raisebox{2.3mm}{
 \end_layout
 
 \end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
 
-\begin_layout Plain Layout
 
 \backslash
-longleftarrow
-\end_layout
 
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+overbracket
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+[3pt]
+\backslash
+{A+B
+\begin_inset space \textvisiblespace{}
 \end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
 
-\begin_layout Plain Layout
-\begin_inset Formula $\longleftarrow$
-\end_inset
+^3
+\begin_inset ERT
+status collapsed
 
+\begin_layout Plain Layout
 
+}
 \end_layout
 
 \end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
 
-\begin_layout Plain Layout
 
-\backslash
-Longleftarrow
 \end_layout
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\Longleftarrow$
+\begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
 \end_inset
 
 
@@ -7549,13 +7580,513 @@ Longleftarrow
 </cell>
 </row>
 <row>
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
 
 \backslash
-leftharpoonup
+raisebox{-2.2mm}{
+\end_layout
+
+\end_inset
+
+
+\backslash
+under
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+bracket
+\family default
+\series default
+\shape default
+\size default
+\emph default
+\bar default
+\strikeout default
+\uuline default
+\uwave default
+\noun default
+\color inherit
+[1pt]
+\backslash
+{A+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_5
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\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 Plain Layout
+\begin_inset Formula $\underbracket[1pt]{A+B}_{5}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace bigskip
+\end_inset
+
+When brackets should overlap each other, multiline formulas, as described
+ in 
+\begin_inset CommandInset ref
+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 Plain Layout
+Space commands are explained in 
+\begin_inset CommandInset ref
+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 Plain Layout
+because a bracket is not handled as a character, see 
+\begin_inset CommandInset ref
+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 Plain Layout
+more about 
+\series bold
+
+\backslash
+hphantom
+\series default
+ see 
+\begin_inset CommandInset ref
+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 above and under
+ the formula, like in the following example:
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\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 Plain Layout
+
+
+\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 needs to be reduced.
+ This is not easily possible due to a bug in LyX.
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset CommandInset href
+LatexCommand href
+name "LyX-bug #1505"
+target "http://www.lyx.org/trac/ticket/1505"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ As a solution for the problem, the global formula row separation 
+\series bold
+
+\backslash
+jot
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! J ! 
+\backslash
+jot
+\end_layout
+
+\end_inset
+
+ must be changed to -6
+\begin_inset space \thinspace{}
+\end_inset
+
+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
+\begin_inset space \thinspace{}
+\end_inset
+
+pt using the same command.
+ More about the row separation in formulas is explained in 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Line-Separation"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Arrows
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Arrows
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Arrows can be inserted via the math toolbar button 
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\leftarrow"
+\end_inset
+
+ or the commands listed in the following subsections.
+\end_layout
+
+\begin_layout Subsection
+Horizontal Arrows
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Arrows ! horizontal
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features rotate="0" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+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 Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\gets$
+\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 Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\Leftarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+longleftarrow
+\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 Plain Layout
+\begin_inset Formula $\longleftarrow$
+\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 Plain Layout
+
+\backslash
+Longleftarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\Longleftarrow$
+\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 Plain Layout
+
+\backslash
+leftharpoonup
 \end_layout
 
 \end_inset
@@ -7628,12 +8159,621 @@ hookleftarrow
 \end_inset
 
 
-\begin_inset space \hfill{}
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="2">
+<features rotate="0" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+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 Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\to$
+\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 Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\Rightarrow$
+\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 Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\longrightarrow$
+\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 Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\Longrightarrow$
+\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 Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\rightharpoonup$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rightharpoondown
+\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 Plain Layout
+\begin_inset Formula $\rightharpoondown$
+\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 Plain Layout
+
+\backslash
+hookrightarrow
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\hookrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features rotate="0" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+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 Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\leftrightarrow$
+\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 Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\Leftrightarrow$
+\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 Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\longleftrightarrow$
+\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 Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\Longleftrightarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+rightleftharpoons
+\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 Plain Layout
+\begin_inset Formula $\rightleftharpoons$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hspace{}
+\length 25pt
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features rotate="0" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+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 Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\mapsto$
+\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 Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\longmapsto$
+\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 Plain Layout
+
+\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 Plain Layout
+\begin_inset Formula $\leadsto$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+dasharrow
+\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 Plain Layout
+\begin_inset Formula $\dasharrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+Arrows used as accents like e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space \space{}
+\end_inset
+
+vector arrows are listed in 
+\begin_inset CommandInset ref
+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 Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Arrows ! labeled
+\end_layout
+
+\end_inset
+
+\series bold
+
+\backslash
+xleftarrow
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! X ! 
+\backslash
+xleftarrow
+\end_layout
+
+\end_inset
+
+ and 
+\series bold
+
+\backslash
+xrightarrow
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! X ! 
+\backslash
+xrightarrow
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+vspace{4mm}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
 \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="8" columns="2">
+<lyxtabular version="3" rows="3" columns="2">
 <features rotate="0" tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
@@ -7652,29 +8792,20 @@ Command
 
 \begin_layout Plain Layout
 Result
-\end_layout
-
-\end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
+\begin_inset Note Note
+status collapsed
 
 \begin_layout Plain Layout
 
+\series bold
+
 \backslash
-to
+raisebox
+\series default
+ is only used as spacer.
 \end_layout
 
 \end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-\begin_inset Formula $\to$
-\end_inset
 
 
 \end_layout
@@ -7687,9 +8818,21 @@ to
 \begin_inset Text
 
 \begin_layout Plain Layout
-
+F(a)
 \backslash
-Rightarrow
+xleftarrow
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+x=a
+\begin_inset Formula $\downarrow$
+\end_inset
+
+x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(x)
 \end_layout
 
 \end_inset
@@ -7698,7 +8841,7 @@ Rightarrow
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\Rightarrow$
+\begin_inset Formula $\raisebox{5.5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -7708,166 +8851,176 @@ Rightarrow
 </cell>
 </row>
 <row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-
+F(x)
 \backslash
-longrightarrow
-\end_layout
-
+xrightarrow
+\begin_inset space \textvisiblespace{}
 \end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
 
-\begin_layout Plain Layout
-\begin_inset Formula $\longrightarrow$
+x=a
+\begin_inset Formula $\downarrow$
 \end_inset
 
+x>0
+\begin_inset Formula $\to$
+\end_inset
 
+F(a)
 \end_layout
 
 \end_inset
 </cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
+\begin_inset Formula $\raisebox{5.5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
+\end_inset
+
 
-\backslash
-Longrightarrow
 \end_layout
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
+</row>
+</lyxtabular>
 
-\begin_layout Plain Layout
-\begin_inset Formula $\Longrightarrow$
 \end_inset
 
 
 \end_layout
 
+\begin_layout Standard
+\begin_inset VSpace medskip
 \end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
-\begin_inset Text
 
-\begin_layout Plain Layout
 
-\backslash
-rightharpoonup
 \end_layout
 
+\begin_layout Standard
+If you set in the document settings under 
+\family sans
+Math
+\begin_inset space ~
 \end_inset
-</cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
-\begin_inset Text
 
-\begin_layout Plain Layout
-\begin_inset Formula $\rightharpoonup$
-\end_inset
+Options
+\family default
+ for the package 
+\series bold
+mathtools
+\series default
 
+\begin_inset Index idx
+status collapsed
 
+\begin_layout Plain Layout
+Packages ! mathtools
 \end_layout
 
 \end_inset
-</cell>
-</row>
-<row>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
 
-\begin_layout Plain Layout
+ the option 
+\family sans
+Load
+\begin_inset space ~
+\end_inset
 
-\backslash
-rightharpoondown
+always
+\family default
+, you have access to the following labeled arrows:
 \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 Plain Layout
-\begin_inset Formula $\rightharpoondown$
+\begin_layout Standard
+\begin_inset Newpage newpage
 \end_inset
 
 
 \end_layout
 
+\begin_layout Standard
+\align center
+\begin_inset space \hspace*{\fill}
 \end_inset
-</cell>
-</row>
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features rotate="0" tabularvalignment="middle">
+<column alignment="center" valignment="top" width="0pt">
+<column alignment="center" valignment="top" width="0pt">
 <row>
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-
-\backslash
-hookrightarrow
+Command
 \end_layout
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" bottomline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\hookrightarrow$
-\end_inset
-
-
-\end_layout
+Example
+\begin_inset Note Note
+status collapsed
 
-\end_inset
-</cell>
-</row>
-</lyxtabular>
+\begin_layout Plain Layout
 
-\end_inset
+\series bold
 
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
 
-\begin_inset space \hfill{}
 \end_inset
 
 
 \end_layout
 
-\begin_layout Standard
-\begin_inset space \hfill{}
 \end_inset
-
-
-\begin_inset Tabular
-<lyxtabular version="3" rows="6" columns="2">
-<features rotate="0" tabularvalignment="middle">
-<column alignment="center" valignment="top" width="0pt">
-<column alignment="center" valignment="top" width="0pt">
+</cell>
+</row>
 <row>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-Command
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
+\backslash
+xleftrightarrow
 \end_layout
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-Result
+\begin_inset Formula $\raisebox{6mm}{}\xleftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
+
+
 \end_layout
 
 \end_inset
@@ -7879,8 +9032,20 @@ Result
 
 \begin_layout Plain Layout
 
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
 \backslash
-leftrightarrow
+xLeftarrow
 \end_layout
 
 \end_inset
@@ -7889,7 +9054,7 @@ leftrightarrow
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\leftrightarrow$
+\begin_inset Formula $\raisebox{6mm}{}\xLeftarrow[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -7905,7 +9070,19 @@ leftrightarrow
 \begin_layout Plain Layout
 
 \backslash
-Leftrightarrow
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xRightarrow
 \end_layout
 
 \end_inset
@@ -7914,7 +9091,7 @@ Leftrightarrow
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\Leftrightarrow$
+\begin_inset Formula $\raisebox{6mm}{}\xRightarrow[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -7930,7 +9107,19 @@ Leftrightarrow
 \begin_layout Plain Layout
 
 \backslash
-longleftrightarrow
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xLeftrightarrow
 \end_layout
 
 \end_inset
@@ -7939,7 +9128,7 @@ longleftrightarrow
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\longleftrightarrow$
+\begin_inset Formula $\raisebox{6mm}{}\xLeftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -7954,8 +9143,20 @@ longleftrightarrow
 
 \begin_layout Plain Layout
 
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
 \backslash
-Longleftrightarrow
+xhookleftarrow
 \end_layout
 
 \end_inset
@@ -7964,7 +9165,7 @@ Longleftrightarrow
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\Longleftrightarrow$
+\begin_inset Formula $\raisebox{6mm}{}\xhookleftarrow[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -7979,8 +9180,20 @@ Longleftrightarrow
 
 \begin_layout Plain Layout
 
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
 \backslash
-rightleftharpoons
+xhookrightarrow
 \end_layout
 
 \end_inset
@@ -7989,7 +9202,7 @@ rightleftharpoons
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\rightleftharpoons$
+\begin_inset Formula $\raisebox{6mm}{}\xhookrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8003,17 +9216,12 @@ rightleftharpoons
 \end_inset
 
 
-\begin_inset space \hspace{}
-\length 25pt
-\end_inset
-
-
-\begin_inset space \hfill{}
+\begin_inset space \hspace*{\fill}
 \end_inset
 
 
 \begin_inset Tabular
-<lyxtabular version="3" rows="5" columns="2">
+<lyxtabular version="3" rows="7" columns="2">
 <features rotate="0" tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
@@ -8031,7 +9239,23 @@ Command
 \begin_inset Text
 
 \begin_layout Plain Layout
-Result
+Example
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+raisebox
+\series default
+ is only used as spacer.
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
 \end_inset
@@ -8044,7 +9268,19 @@ Result
 \begin_layout Plain Layout
 
 \backslash
-mapsto
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xleftharpoondown
 \end_layout
 
 \end_inset
@@ -8053,7 +9289,7 @@ mapsto
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\mapsto$
+\begin_inset Formula $\raisebox{6mm}{}\xleftharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8069,7 +9305,19 @@ mapsto
 \begin_layout Plain Layout
 
 \backslash
-longmapsto
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xleftharpoonup
 \end_layout
 
 \end_inset
@@ -8078,7 +9326,7 @@ longmapsto
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\longmapsto$
+\begin_inset Formula $\raisebox{6mm}{}\xleftharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8094,7 +9342,19 @@ longmapsto
 \begin_layout Plain Layout
 
 \backslash
-leadsto
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xrightharpoondown
 \end_layout
 
 \end_inset
@@ -8103,7 +9363,7 @@ leadsto
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\leadsto$
+\begin_inset Formula $\raisebox{6mm}{}\xrightharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8113,22 +9373,34 @@ leadsto
 </cell>
 </row>
 <row>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
 
 \backslash
-dasharrow
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xrightharpoonup
 \end_layout
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\dasharrow$
+\begin_inset Formula $\raisebox{6mm}{}\xrightharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8137,112 +9409,99 @@ dasharrow
 \end_inset
 </cell>
 </row>
-</lyxtabular>
-
-\end_inset
-
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
 
-\begin_inset space \hfill{}
-\end_inset
+\begin_layout Plain Layout
 
+\backslash
 
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xleftrightharpoons
 \end_layout
 
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-Arrows used as accents like e.
-\begin_inset space \thinspace{}
 \end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
 
-g.
-\begin_inset space \space{}
+\begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xleftrightharpoons[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
-vector arrows are listed in 
-\begin_inset CommandInset ref
-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 Index idx
-status collapsed
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
 
 \begin_layout Plain Layout
-Arrows ! labeled
-\end_layout
-
-\end_inset
-
-\series bold
 
 \backslash
-xleftarrow
-\series default
 
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! X ! 
-\backslash
-xleftarrow
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+xrightleftharpoons
 \end_layout
 
 \end_inset
-
- and 
-\series bold
-
-\backslash
-xrightarrow
-\series default
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! X ! 
-\backslash
-xrightarrow
-\begin_inset ERT
-status collapsed
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
 
 \begin_layout Plain Layout
+\begin_inset Formula $\raisebox{6mm}{}\xrightleftharpoons[x=a]{x>0}\raisebox{-4mm}{}$
+\end_inset
 
 
-\backslash
-vspace{4mm}
 \end_layout
 
 \end_inset
+</cell>
+</row>
+</lyxtabular>
 
+\end_inset
 
-\end_layout
 
+\begin_inset space \hspace*{\fill}
 \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
+The command scheme is for all these arrows:
 \end_layout
 
 \begin_layout Standard
 \align center
 \begin_inset Tabular
-<lyxtabular version="3" rows="3" columns="2">
+<lyxtabular version="3" rows="2" columns="2">
 <features rotate="0" tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
@@ -8283,62 +9542,19 @@ raisebox
 </cell>
 </row>
 <row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
 F(a)
 \backslash
-xleftarrow
-\begin_inset space \textvisiblespace{}
-\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 Plain Layout
-\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>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
-\begin_inset Text
-
-\begin_layout Plain Layout
-F(x)
+xleftrightarrow[x=a]
 \backslash
-xrightarrow
-\begin_inset space \textvisiblespace{}
-\end_inset
-
-x=a
-\begin_inset Formula $\downarrow$
-\end_inset
-
-x>0
+{x>0
 \begin_inset Formula $\to$
 \end_inset
 
-F(a)
+F(x)
 \end_layout
 
 \end_inset
@@ -8347,7 +9563,7 @@ F(a)
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
+\begin_inset Formula $\raisebox{6mm}{}F(a)\xleftrightarrow[x=a]{x>0}F(x)\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8757,10 +9973,9 @@ Accents
 
 \begin_layout Standard
 Accents can be inserted via the math toolbar button 
-\begin_inset Graphics
-       filename ../images/math/hat.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\hat"
 \end_inset
 
  or the commands listed in the following subsections.
@@ -9713,6 +10928,13 @@ fi
 \end_inset
 
 
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
 \end_layout
 
 \begin_layout Subsection
@@ -10143,13 +11365,6 @@ A=B
 \end_inset
 
 
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
 \end_layout
 
 \begin_layout Section
@@ -10225,10 +11440,9 @@ 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
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\space"
 \end_inset
 
  or special commands.
@@ -10243,22 +11457,14 @@ Space
 \begin_layout Standard
 \noindent
 \align center
-\begin_inset VSpace -5mm
-\end_inset
-
-
 \begin_inset Tabular
-<lyxtabular version="3" rows="3" columns="7">
+<lyxtabular version="3" rows="6" columns="3">
 <features rotate="0" tabularvalignment="middle">
-<column alignment="center" valignment="middle" width="6.8cm">
-<column alignment="center" valignment="top">
-<column alignment="center" valignment="top">
-<column alignment="center" valignment="top">
-<column alignment="center" valignment="top">
 <column alignment="center" valignment="top">
+<column alignment="center" valignment="top" width="15col%">
 <column alignment="center" valignment="top">
 <row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
@@ -10267,6 +11473,30 @@ Command
 
 \end_inset
 </cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Number of 
+\family sans
+Space
+\family default
+ keystrokes
+\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 Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
@@ -10281,6 +11511,29 @@ Command
 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
+\begin_layout Plain Layout
+0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\, B$
+\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 Plain Layout
 
 \backslash
@@ -10292,6 +11545,29 @@ Command
 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
+\begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\: B$
+\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 Plain Layout
 
 \backslash
@@ -10303,6 +11579,29 @@ Command
 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
+\begin_layout Plain Layout
+2
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\; B$
+\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 Plain Layout
 
 \backslash
@@ -10314,6 +11613,29 @@ quad
 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
+\begin_layout Plain Layout
+3
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\quad B$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
 \begin_layout Plain Layout
 
 \backslash
@@ -10322,20 +11644,54 @@ qquad
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
+4
+\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 Plain Layout
+\begin_inset Formula $A\qquad B$
+\end_inset
+
 
-\backslash
-!
 \end_layout
 
 \end_inset
 </cell>
 </row>
+</lyxtabular>
+
+\end_inset
+
+
+\begin_inset space \hfill{}
+\end_inset
+
+
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="3">
+<features rotate="0" tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top" width="15col%">
+<column alignment="center" valignment="top">
 <row>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Command
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
@@ -10343,25 +11699,29 @@ Number of
 \family sans
 Space
 \family default
- keystrokes after inserting the protected space
+ keystrokes
 \end_layout
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-0
+Result
 \end_layout
 
 \end_inset
 </cell>
+</row>
+<row>
 <cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-1
+
+\backslash
+hfill
 \end_layout
 
 \end_inset
@@ -10370,16 +11730,32 @@ Space
 \begin_inset Text
 
 \begin_layout Plain Layout
-2
+5
 \end_layout
 
 \end_inset
 </cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\hfill B$
+\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 Plain Layout
-3
+
+\backslash
+hspace*{1em}
 \end_layout
 
 \end_inset
@@ -10388,7 +11764,7 @@ Space
 \begin_inset Text
 
 \begin_layout Plain Layout
-4
+6
 \end_layout
 
 \end_inset
@@ -10397,39 +11773,41 @@ Space
 \begin_inset Text
 
 \begin_layout Plain Layout
-5
+\begin_inset Formula $A\hspace*{1em}B$
+\end_inset
+
+
 \end_layout
 
 \end_inset
 </cell>
 </row>
 <row>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-Result
+
+\backslash
+hspace{1em}
 \end_layout
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $A\, B$
-\end_inset
-
-
+7
 \end_layout
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $A\B$
+\begin_inset Formula $A\hspace{1em}B$
 \end_inset
 
 
@@ -10437,11 +11815,16 @@ Result
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $A\; B$
+
+\backslash
+
+\begin_inset space \textvisiblespace{}
 \end_inset
 
 
@@ -10449,11 +11832,20 @@ Result
 
 \end_inset
 </cell>
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $A\quad B$
+8
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $A\ B$
 \end_inset
 
 
@@ -10461,14 +11853,24 @@ Result
 
 \end_inset
 </cell>
+</row>
+<row>
 <cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $A\qquad B$
-\end_inset
 
+\backslash
+!
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
 
+\begin_layout Plain Layout
+9
 \end_layout
 
 \end_inset
@@ -10494,7 +11896,31 @@ Result
 \end_layout
 
 \begin_layout Standard
-The last size seem to produce no space.
+Space
+\begin_inset space ~
+\end_inset
+
+5
+\begin_inset space \thinspace{}
+\end_inset
+
+--
+\begin_inset space \thinspace{}
+\end_inset
+
+7 are variable spaces which are explained in 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Variable-Space"
+
+\end_inset
+
+.
+ Space
+\begin_inset space ~
+\end_inset
+
+9 seems 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:
@@ -10559,7 +11985,7 @@ Space
 \begin_inset Text
 
 \begin_layout Plain Layout
-6
+10
 \end_layout
 
 \end_inset
@@ -10568,7 +11994,7 @@ Space
 \begin_inset Text
 
 \begin_layout Plain Layout
-7
+11
 \end_layout
 
 \end_inset
@@ -10744,6 +12170,15 @@ f_kl
 \end_layout
 
 \begin_layout Standard
+\noindent
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\noindent
 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:
 \begin_inset VSpace bigskip
 \end_inset
 
+
+\end_layout
+
+\begin_layout Standard
 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 
@@ -11077,7 +12516,44 @@ hspace
 
 .
  The length may also be negative.
- To insert as much space as is available, the command 
+ When a space would be the first character in a line it would be omitted.
+ To force its output use the command 
+\series bold
+
+\backslash
+hspace*
+\series default
+ instead of 
+\series bold
+
+\backslash
+hspace
+\series default
+ or left-click on the 
+\begin_inset Quotes eld
+\end_inset
+
+
+\color blue
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\color inherit
+
+\begin_inset Quotes erd
+\end_inset
+
+ and check the option 
+\family sans
+Protect
+\family default
+.
+\begin_inset Newline newline
+\end_inset
+
+To insert as much space as is available, the command 
 \series bold
 
 \backslash
@@ -11145,10 +12621,6 @@ hspace
 \begin_inset space \textvisiblespace{}
 \end_inset
 
-
-\begin_inset Formula $\to$
-\end_inset
-
 A
 \backslash
 not=C (3
@@ -11184,10 +12656,6 @@ hspace
 \begin_inset space \textvisiblespace{}
 \end_inset
 
-
-\begin_inset Formula $\to$
-\end_inset
-
 A
 \backslash
 not=A (-1
@@ -11759,13 +13227,6 @@ fbox
 .
 \end_layout
 
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
 \begin_layout Standard
 \align center
 \begin_inset Tabular
@@ -12842,10 +14303,9 @@ Style
 \family default
  dialog.
  The dialog can be called with the toolbar button 
-\begin_inset Graphics
-       filename ../images/dialog-show_character.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "dialog-show character"
 \end_inset
 
  or the menu 
@@ -13304,10 +14764,9 @@ Insert\SpecialChar \menuseparator
 Box
 \family default
  or the toolbar button 
-\begin_inset Graphics
-       filename ../images/box-insert.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "box-insert"
 \end_inset
 
 .
@@ -14569,10 +16028,9 @@ biguplus
 
 \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
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\intop"
 \end_inset
 
 .
@@ -14947,13 +16405,6 @@ dotsint
 \end_inset
 
 
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
 \end_layout
 
 \begin_layout Subsection
@@ -15326,128 +16777,226 @@ reference "eq:substack"
 
  there can be too much space beside an operator, because the characters
  following the operator are set beside the limits.
-\end_layout
+ To avoid this the command 
+\series bold
 
-\begin_layout Standard
-To avoid this, the following macro can be used in the LaTeX-preamble:
+\backslash
+smashoperator
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S ! 
+\backslash
+smashoperator
 \end_layout
 
-\begin_layout Standard
+\end_inset
+
+ can be used.
+ To activate it, set in the document settings under 
+\family sans
+Math
+\begin_inset space ~
+\end_inset
 
+Options
+\family default
+ for the package 
 \series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! mathtools
+\end_layout
 
-\backslash
-def
-\backslash
-clap#1{
-\backslash
-hbox to 0pt{
-\backslash
-hss #1
-\backslash
-hss}}
-\begin_inset Newline newline
 \end_inset
 
+ the option 
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+.
+\series bold
 
 \backslash
-def
-\backslash
-mathclap {
-\backslash
-mathpalette 
-\backslash
-mathclapinternal}
+smashoperator
+\series default
+ sets the space besides the operator to 0
+\begin_inset space \thinspace{}
+\end_inset
+
+pt.
 \begin_inset Newline newline
 \end_inset
 
+Applied on formula 
+\begin_inset CommandInset ref
+LatexCommand eqref
+reference "eq:substack"
 
-\backslash
-def
-\backslash
-mathclapinternal #1#2{
-\backslash
-clap{$
-\backslash
-mathsurround =0pt #1{#2}$}}
+\end_inset
+
+, one uses the command
 \end_layout
 
 \begin_layout Standard
-This defines the command 
-\series bold
-
-\backslash
-mathclap
-\series default
 
-\begin_inset Index idx
-status collapsed
+\series bold
 
-\begin_layout Plain Layout
-Commands ! M ! 
 \backslash
-mathclap
+smashoperator{
 \end_layout
 
+\begin_layout Standard
+and inserts the operator with its limits into the braces.
+ Behind the brace one continues the formula:
+\begin_inset Formula 
+\[
+\smashoperator{\sum_{\begin{subarray}{c}
+0<k<1000\\
+\\
+k\,\in\,\mathbb{N}
+\end{subarray}}^{n}}k^{-2}
+\]
+
 \end_inset
 
- that sets the width of the limit to 0
+
+\end_layout
+
+\begin_layout Standard
+It is possible to set the space of only one side of the operator to 0
 \begin_inset space \thinspace{}
 \end_inset
 
 pt.
- The command scheme is
+ To do this write either 
+\series bold
+[l]
+\series default
+ or 
+\series bold
+[r]
+\series default
+ between 
+\series bold
+
+\backslash
+smashoperator
+\series default
+ and its brace.
+\series bold
+l
+\series default
+ stands for the left and 
+\series bold
+r
+\series default
+ for the right side of the operator.
+ Here is an example of the possible 
+\series bold
+
+\backslash
+smashoperator
+\series default
+ forms:
 \end_layout
 
 \begin_layout Standard
+\begin_inset Formula 
+\[
+Y\smashoperator{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[l]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}=Y\smashoperator[r]{\sum_{1\le i\le j\le n}^{n=3456}}X_{ij}
+\]
+
+\end_inset
 
-\series bold
 
-\backslash
-mathclap{limit}
 \end_layout
 
 \begin_layout Standard
-where the limit can consist of several conditions.
+\begin_inset VSpace bigskip
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
-Applied on formula 
-\begin_inset CommandInset ref
-LatexCommand eqref
-reference "eq:substack"
+When several consecutive operators have limits the typesetting of the limits
+ looks often imperfect in the output, see this example:
+\begin_inset Formula 
+\[
+\text{a)}\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\limsup_{n\to\infty}\max_{p\ge n}
+\]
 
 \end_inset
 
-, one uses the command
+To improve the typesetting set in the document settings under 
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ for the package 
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! mathtools
 \end_layout
 
-\begin_layout Standard
+\end_inset
+
+ the option 
+\family sans
+Load
+\begin_inset space ~
+\end_inset
 
+always
+\family default
+.
+ Then insert into your formula the command 
 \series bold
 
 \backslash
-sum_
-\backslash
-mathclap{
-\backslash
-substack
-\begin_inset space \textvisiblespace{}
-\end_inset
+adjustlimits
+\series default
 
-0<k<1000 Ctrl+Return
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! A ! 
+\backslash
+adjustlimits
 \end_layout
 
-\begin_layout Standard
-to create the lower limit.
- The summand is now directly behind the summation operator:
+\end_inset
+
+ directly before the first operator.
+ The example will then look like this:
 \begin_inset Formula 
 \[
-\sum_{\mathclap{\substack{0<k<1000\\
-\\
-k\,\in\,\mathbb{N}
-}
-}}^{n}k^{-2}
+\text{a)}\adjustlimits\lim_{n\to\infty}\max_{p\ge n}\quad\text{b)}\adjustlimits\lim_{n\to\infty}\max_{p^{2}\ge n}\quad\text{c)}\adjustlimits\lim_{n\to\infty}\sup_{p^{2}\ge nK}\quad\text{d)}\adjustlimits\limsup_{n\to\infty}\max_{p\ge n}
 \]
 
 \end_inset
@@ -15540,37 +17089,67 @@ sideset
 \end_inset
 
  characters can be set before and behind a big operator.
- The command scheme is:
 \end_layout
 
 \begin_layout Standard
+There are 4
+\begin_inset space ~
+\end_inset
 
+variants of 
 \series bold
 
 \backslash
-sideset{character
+sideset
 \series default
+:
+\end_layout
+
+\begin_layout Itemize
+
 \series bold
-before}{character
+
+\backslash
+sideset
 \series default
-\series bold
-behind}
+ is used to set characters at the corners of the operator
 \end_layout
 
-\begin_layout Standard
+\begin_layout Itemize
+
+\series bold
 
+\backslash
+sidesetn
+\series default
+ is used to set characters before and/or behind the operator (this variant
+ represents LaTeX's original 
 \series bold
 
 \backslash
 sideset
 \series default
- must always be before the operator.
- You can decorate with several characters and even with other operators
- and symbols.
- To place for example only characters behind a big operator, write nothing
- between the first braces but don't omit the braces.
+ command)
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+
+\backslash
+sidesetl
+\series default
+ is used to set characters at the left corners and/or behind the operator
+\end_layout
+
+\begin_layout Itemize
+
+\series bold
+
+\backslash
+sidesetr
+\series default
+ is used to set characters at the right corners and/or before the operator
 \end_layout
 
 \begin_layout Standard
@@ -15578,23 +17157,25 @@ For example the command
 \series bold
 
 \backslash
-sideset{
-\begin_inset Formula $\to$
+sidesetn
+\begin_inset space \textvisiblespace{}
 \end_inset
 
 
 \backslash
-{
-\series default
-'
-\series bold
+sum
+\begin_inset space \textvisiblespace{}
+\end_inset
+
 
 \begin_inset Formula $\to$
 \end_inset
 
+'
+\begin_inset Formula $\to$
+\end_inset
 
-\backslash
-sum_k=1
+_k=1
 \begin_inset space \textvisiblespace{}
 \end_inset
 
@@ -16757,10 +18338,9 @@ triangleright
 
 \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
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\pm"
 \end_inset
 
 .
@@ -17754,10 +19334,9 @@ Math\SpecialChar \menuseparator
 Text Style
 \family default
  or the toolbar button 
-\begin_inset Graphics
-       filename ../images/math/font.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\font"
 \end_inset
 
  can be used.
@@ -18175,7 +19754,14 @@ normalsize
 \end_layout
 
 \begin_layout Standard
-Within a formula the size can be changed using the following size commands:
+Within a formula the size can be changed using the following size commands
+ or the toolbar button 
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\style"
+\end_inset
+
+:
 \end_layout
 
 \begin_layout Standard
@@ -18509,10 +20095,9 @@ Greek letters
 
 \begin_layout Standard
 Greek letters can also be inserted via the toolbar button 
-\begin_inset Graphics
-       filename ../images/math/alpha.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\alpha"
 \end_inset
 
 .
@@ -20104,17 +21689,15 @@ Symbols
 \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
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\nabla"
 \end_inset
 
  and 
-\begin_inset Graphics
-       filename ../images/math/digamma.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\digamma"
 \end_inset
 
 .
@@ -22191,11 +23774,10 @@ status collapsed
 \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
-
+All following relations can also be inserted via the toolbar button 
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\leq"
 \end_inset
 
 .
@@ -23535,6 +25117,17 @@ triangleright
 , respectively.
 \end_layout
 
+\begin_layout Standard
+LyX supports also many special relations.
+ Use the toolbar button 
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\leqq"
+\end_inset
+
+ to see a list of these relations.
+\end_layout
+
 \begin_layout Standard
 Relations are, in contrary to symbols, always surrounded by space.
 \end_layout
@@ -24241,10 +25834,9 @@ gcd
 
 \begin_layout Standard
 They can also be inserted with the math toolbar button 
-\begin_inset Graphics
-       filename ../images/math/functions.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\functions"
 \end_inset
 
 .
@@ -24776,6 +26368,24 @@ In a displayed formula the limit is set below the formula, as usual:
 
 \end_layout
 
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+How to adjust the typesetting of the limits see 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Operator-Limits"
+
+\end_inset
+
+.
+\end_layout
+
 \begin_layout Subsection
 Modulo-Functions
 \begin_inset Index idx
@@ -24837,6 +26447,103 @@ Special characters
 \end_inset
 
 
+\end_layout
+
+\begin_layout Standard
+The characters ^ and _ would normally create a subscript and subscript,
+ respectively.
+ To get these characters you have to insert them with a leading 
+\backslash
+:
+\end_layout
+
+\begin_layout Standard
+\noindent
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features rotate="0" tabularvalignment="middle">
+<column alignment="block" valignment="top">
+<column alignment="block" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+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 Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+^
+\begin_inset space \textvisiblespace{}
+\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 Plain Layout
+\begin_inset Formula $\mathcircumflex$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\backslash
+_
+\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 Plain Layout
+\begin_inset Formula $\_$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Subsection
@@ -25338,10 +27045,9 @@ The characters
 \end_inset
 
  can also be inserted via the math toolbar button 
-\begin_inset Graphics
-       filename ../images/math/digamma.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\digamma"
 \end_inset
 
 .
@@ -26596,15 +28302,11 @@ General
 
 \begin_layout Standard
 In LyX multiline formulas are created by pressing 
-\series bold
-
 \begin_inset Info
 type  "shortcut"
 arg   "newline-insert newline"
 \end_inset
 
-
-\series default
  inside a formula.
  This creates either an 
 \series bold
@@ -26658,17 +28360,15 @@ arg   "newline-insert newline"
 
 .
  To add or delete lines, the math toolbar buttons 
-\begin_inset Graphics
-       filename ../images/tabular-feature_append-row.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "inset-modify tabular append-row"
 \end_inset
 
  or 
-\begin_inset Graphics
-       filename ../images/tabular-feature_delete-row.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "inset-modify tabular delete-row"
 \end_inset
 
 , respectively, or the menu 
@@ -27324,6 +29024,127 @@ reference "sub:Multiline-Formula-Parts"
 .
 \end_layout
 
+\begin_layout Subsubsection
+Multiline Fractions
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Multiline-Fractions"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Fractions ! multiline
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+There are cases where the denominator and/or the numerator of a fraction
+ is so long that the fraction does not fit into one line.
+ It is then necessary to add a line break within the fraction.
+ This can be done using the command 
+\series bold
+
+\backslash
+splitfrac
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S ! 
+\backslash
+splitfrac
+\end_layout
+
+\end_inset
+
+.
+ To activate it, set in the document settings under 
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ for the package 
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! mathtools
+\end_layout
+
+\end_inset
+
+ the option 
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+.
+\series bold
+
+\backslash
+splitfrac
+\series default
+ has the scheme
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+splitfrac{first line}{second line}
+\end_layout
+
+\begin_layout Standard
+and is used as denominator and/or numerator:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+a=\frac{\splitfrac{xy+xy+xy+xy+xy}{+wy+wy+wy+wy}}{z}\ne\frac{\splitdfrac{xy+\frac{xy}{z}+xy+xy+xy}{+xy+xy+xy+xy}}{z}
+\]
+
+\end_inset
+
+The command for the first numerator above is:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+splitfrac{xy+xy+xy+xy+xy
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\backslash
+{+wy+wy+wy+wy
+\end_layout
+
 \begin_layout Subsubsection
 Multiline Brackets
 \begin_inset CommandInset label
@@ -27539,17 +29360,15 @@ Change Formula Type
 
 \begin_layout Standard
 To add or delete columns, the math toolbar buttons 
-\begin_inset Graphics
-       filename ../images/tabular-feature_append-column.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "inset-modify tabular append-column"
 \end_inset
 
  or 
-\begin_inset Graphics
-       filename ../images/tabular-feature_delete-column.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "inset-modify tabular delete-column"
 \end_inset
 
 , respectively, or the menu 
@@ -28350,6 +30169,84 @@ I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
 \end_inset
 
 
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+intertext
+\series default
+ always creates some vertical space between the text and the formula lines.
+ To avoid this space, set in the document settings under 
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+ for the package 
+\series bold
+mathtools
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! mathtools
+\end_layout
+
+\end_inset
+
+ the option 
+\family sans
+Load
+\begin_inset space ~
+\end_inset
+
+always
+\family default
+.
+ Then you can use the command 
+\series bold
+
+\backslash
+shortintertext
+\series default
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! S ! 
+\backslash
+shortintertext
+\end_layout
+
+\end_inset
+
+ instead of 
+\series bold
+
+\backslash
+intertext
+\series default
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\begin{align}
+I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
+\shortintertext{\text{integrand is symmetric to \ensuremath{\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
@@ -28507,10 +30404,9 @@ Insert\SpecialChar \menuseparator
 Label
 \family default
  or the toolbar button 
-\begin_inset Graphics
-       filename ../images/label-insert.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "label-insert"
 \end_inset
 
 .
@@ -28569,10 +30465,9 @@ 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
-
+\begin_inset Info
+type  "icon"
+arg   "dialog-show-new-inset ref"
 \end_inset
 
 .
@@ -29909,6 +31804,13 @@ formulas can be numbered with Latin letters in one document.
 \end_inset
 
 
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
@@ -30099,13 +32001,6 @@ target "run:Formula-numbering.lyx"
 .
 \end_layout
 
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
 \begin_layout Section
 Chemical Symbols and Equations
 \begin_inset CommandInset label
@@ -31204,13 +33099,6 @@ Manuals
 .
 \end_layout
 
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
 \begin_layout Section
 User-defined Commands
 \begin_inset Index idx
@@ -31999,10 +33887,9 @@ Math\SpecialChar \menuseparator
 Macro
 \family default
  or the toolbar button 
-\begin_inset Graphics
-       filename ../images/math-macro_newmacroname_newcommand.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro newmacroname_newcommand"
 \end_inset
 
 .
 #1
 \series default
  or by using the macro toolbar button 
-\begin_inset Graphics
-       filename ../images/math-macro-add-param.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-add-param"
 \end_inset
 
 .
 
 arguments are possible.
  Optional arguments are created with the toolbar button 
-\begin_inset Graphics
-       filename ../images/math-macro-add-optional-param.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-add-optional-param"
 \end_inset
 
 .
  The first non-optional argument can be transformed to an optional one with
  the toolbar button 
-\begin_inset Graphics
-       filename ../images/math-macro-make-optional.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-make-optional"
 \end_inset
 
 .
@@ -32362,10 +34246,9 @@ The macro toolbar contains from left to right the following buttons:
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Graphics
-       filename ../images/math-macro-remove-param.png
-       rotateOrigin center
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-remove-param"
 \end_inset
 
 
@@ -32397,10 +34280,9 @@ Remove Last Argument
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Graphics
-       filename ../images/math-macro-add-param.png
-       rotateOrigin center
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-add-param"
 \end_inset
 
 
@@ -32432,10 +34314,9 @@ Append Argument
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Graphics
-       filename ../images/math-macro-make-optional.png
-       rotateOrigin center
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-make-optional"
 \end_inset
 
 
@@ -32456,7 +34337,7 @@ Macro
 \end_inset
 
 Definition\SpecialChar \menuseparator
-Make First Non-Optional into
+Transform First Non-Optional to
 \begin_inset Newline newline
 \end_inset
 
@@ -32490,10 +34371,9 @@ Optional Argument
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Graphics
-       filename ../images/math-macro-make-nonoptional.png
-       rotateOrigin center
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-make-nonoptional"
 \end_inset
 
 
@@ -32514,7 +34394,7 @@ Macro
 \end_inset
 
 Definition\SpecialChar \menuseparator
-Make Last Optional into
+Transform Last Optional to
 \begin_inset Newline newline
 \end_inset
 
@@ -32548,10 +34428,9 @@ Non-Optional Argument
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Graphics
-       filename ../images/math-macro-remove-optional-param.png
-       rotateOrigin center
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-remove-optional-param"
 \end_inset
 
 
@@ -32583,10 +34462,9 @@ Remove Optional Argument
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Graphics
-       filename ../images/math-macro-add-optional-param.png
-       rotateOrigin center
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-add-optional-param"
 \end_inset
 
 
@@ -32618,10 +34496,9 @@ Insert Optional Argument
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Graphics
-       filename ../images/math-macro-remove-greedy-param.png
-       rotateOrigin center
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-remove-greedy-param"
 \end_inset
 
 
@@ -32676,10 +34553,9 @@ Spitting Out To The Right
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Graphics
-       filename ../images/math-macro-append-greedy-param.png
-       rotateOrigin center
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-append-greedy-param"
 \end_inset
 
 
@@ -32734,10 +34610,9 @@ Eating From The Right
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Graphics
-       filename ../images/math-macro-add-greedy-optional-param.png
-       rotateOrigin center
-
+\begin_inset Info
+type  "icon"
+arg   "math-macro-add-greedy-optional-param"
 \end_inset
 
 
@@ -32933,7 +34808,7 @@ Maxima
 \begin_layout Standard
 
 \series bold
-command-alternatives break-paragraph;math-extern maxima
+command-alternatives paragraph-break;math-extern maxima
 \end_layout
 
 \begin_layout Section
 \end_inset
 
 
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
 \end_layout
 
 \begin_layout Subsection
 
 \begin_layout Subsection
 Text Characters in Formulas
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Text-Characters-in"
-
-\end_inset
-
-
 \begin_inset Index idx
 status collapsed
 
@@ -35310,6 +37171,76 @@ f\SpecialChar \textcompwordmark{}
 i}
 \end_layout
 
+\begin_layout Subsection
+LaTeX-comments in formulas
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+LaTeX-comments
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+In text you can insert a comment that will only be visible in the LaTeX
+ source code of your file with the menu 
+\family sans
+Insert\SpecialChar \menuseparator
+Note\SpecialChar \menuseparator
+Comment
+\family default
+.
+ This is not possible in a formula but you can insert LaTeX-comments with
+ the command
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+%
+\end_layout
+
+\begin_layout Standard
+This creates a box in which you can write your comment.
+ Due to a bug in LyX
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+\begin_inset CommandInset href
+LatexCommand href
+name "LyX-bug #9002"
+target "http://www.lyx.org/trac/ticket/9002"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+ you cannot write normal text into the comment, even when you use mathematical
+ text, you will see its LaTeX-commands in the LaTeX-output.
+\begin_inset Newline newline
+\end_inset
+
+This a formula with a LaTeX-comment:
+\begin_inset Formula 
+\[
+A=B%\text{This is the comment}
+\]
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 \begin_inset Newpage newpage
 \end_inset
@@ -36432,49 +38363,6 @@ Packages ! mhchem
 \end_inset
 
 
-\end_layout
-
-\begin_layout Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-key "Mathclap"
-
-\end_inset
-
-
-\begin_inset CommandInset href
-LatexCommand href
-name "Description"
-target "http://www.tug.org/TUGboat/Articles/tb22-4/tb72perlS.pdf"
-
-\end_inset
-
- of the command 
-\series bold
-
-\backslash
-mathclap
-\series default
-, described in 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Operator-Limits"
-
-\end_inset
-
-
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Commands ! M ! 
-\backslash
-mathclap
-\end_layout
-
-\end_inset
-
-
 \end_layout
 
 \begin_layout Bibliography