]> 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 300467ec7d12dc67d2cc560d5cc54721429a8aab..18b503b549848d8499472978f0926f642443d563 100644 (file)
 \use_package cancel 0
 \use_package esint 1
 \use_package mathdots 1
-\use_package mathtools 1
+\use_package mathtools 2
 \use_package mhchem 1
 \use_package stackrel 0
 \use_package stmaryrd 0
@@ -2262,10 +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
@@ -3461,8 +3465,6 @@ status collapsed
 
 \begin_layout Plain Layout
 can be found in the submenu of the toolbar button 
-\family sans
-
 \begin_inset Info
 type  "icon"
 arg   "math-insert \\space"
@@ -6926,7 +6928,7 @@ A+B
 \begin_inset space \textvisiblespace{}
 \end_inset
 
-^v3
+^3
 \begin_inset ERT
 status collapsed
 
@@ -7113,12 +7115,561 @@ underbrace
  is inserted at first.
 \end_layout
 
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+If you 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
+, you have access to square backets:
+\end_layout
+
+\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 only used as spacer.
+\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
+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
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+raisebox{2.3mm}{
+\end_layout
+
+\end_inset
+
+
+\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
+\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
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Commands ! O ! 
+\backslash
+overbracket
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbracket{A+B}^{3}$
+\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
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+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
+{A+B
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_5
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+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
+
+
+\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 $\underbracket{A+B}_{5}$
+\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
+overbracket{
+\backslash
+underbracket{A+B_w
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+_7
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+^
+\begin_inset space \textvisiblespace{}
+\end_inset
+
+C
+\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 $\overbracket{\underbracket{A+B_{w}}_{7}}^{C}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+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="3" 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 only used as spacer.
+\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
+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
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+raisebox{2.3mm}{
+\end_layout
+
+\end_inset
+
+
+\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
+\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
+
+^3
+\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" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $\overbracket[3pt]{A+B}^{3}$
+\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
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+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 are needed that overlap each other, multiline formulas, as
described in 
+When brackets should overlap each other, multiline formulas, as described
+ in 
 \begin_inset CommandInset ref
 LatexCommand ref
 reference "sec:Multiline-Formulas"
@@ -7246,8 +7797,8 @@ hphantom{bbqq+dddd}
 \end_layout
 
 \begin_layout Standard
-It gets more complicated when brackets overlap each other, like in the following
- example:
+It gets more complicated when brackets overlap each other above and under
the formula, like in the following example:
 \begin_inset ERT
 status collapsed
 
@@ -7291,7 +7842,7 @@ The first formula row is the same as the second row of the previous example,
  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
+ This is not easily possible due to a bug in LyX.
 \begin_inset Foot
 status collapsed
 
@@ -7308,7 +7859,6 @@ target "http://www.lyx.org/trac/ticket/1505"
 
 \end_inset
 
-.
  As a solution for the problem, the global formula row separation 
 \series bold
 
@@ -8291,7 +8841,7 @@ F(x)
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\raisebox{5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
+\begin_inset Formula $\raisebox{5.5mm}{}F(a)\xleftarrow[x>0]{x=a}F(x)\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8328,7 +8878,7 @@ 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 $\raisebox{5.5mm}{}F(x)\xrightarrow[x>0]{x=a}F(a)\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8344,32 +8894,57 @@ F(a)
 
 \end_layout
 
-\begin_layout Subsection
-Vertical and diagonal Arrows
-\begin_inset Index idx
-status collapsed
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
 
-\begin_layout Plain Layout
-Arrows ! diagonal
 \end_layout
 
+\begin_layout Standard
+If you 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
-Arrows ! vertical
+Packages ! mathtools
 \end_layout
 
 \end_inset
 
+ the option 
+\family sans
+Load
+\begin_inset space ~
+\end_inset
 
+always
+\family default
+, you have access to the following labeled arrows:
 \end_layout
 
 \begin_layout Standard
-\begin_inset space \hfill{}
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\align center
+\begin_inset space \hspace*{\fill}
 \end_inset
 
 
@@ -8392,7 +8967,23 @@ 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
@@ -8404,8 +8995,20 @@ 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
-uparrow
+xleftrightarrow
 \end_layout
 
 \end_inset
@@ -8414,7 +9017,7 @@ uparrow
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\uparrow$
+\begin_inset Formula $\raisebox{6mm}{}\xleftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8429,8 +9032,20 @@ uparrow
 
 \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
-Uparrow
+xLeftarrow
 \end_layout
 
 \end_inset
@@ -8439,7 +9054,7 @@ Uparrow
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\Uparrow$
+\begin_inset Formula $\raisebox{6mm}{}\xLeftarrow[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8455,7 +9070,19 @@ Uparrow
 \begin_layout Plain Layout
 
 \backslash
-updownarrow
+
+\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
@@ -8464,7 +9091,7 @@ updownarrow
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\updownarrow$
+\begin_inset Formula $\raisebox{6mm}{}\xRightarrow[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8480,7 +9107,19 @@ updownarrow
 \begin_layout Plain Layout
 
 \backslash
-Updownarrow
+
+\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
@@ -8489,7 +9128,7 @@ Updownarrow
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\Updownarrow$
+\begin_inset Formula $\raisebox{6mm}{}\xLeftrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8499,22 +9138,34 @@ Updownarrow
 </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
 
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
 \backslash
-Downarrow
+xhookleftarrow
 \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 $\Downarrow$
+\begin_inset Formula $\raisebox{6mm}{}\xhookleftarrow[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8524,22 +9175,34 @@ Downarrow
 </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
 
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\strikeout off
+\uuline off
+\uwave off
+\noun off
+\color none
+
 \backslash
-downarrow
+xhookrightarrow
 \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 $\downarrow$
+\begin_inset Formula $\raisebox{6mm}{}\xhookrightarrow[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8553,12 +9216,12 @@ downarrow
 \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">
@@ -8576,7 +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
@@ -8589,7 +9268,19 @@ Result
 \begin_layout Plain Layout
 
 \backslash
-nearrow
+
+\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
@@ -8598,7 +9289,7 @@ nearrow
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\nearrow$
+\begin_inset Formula $\raisebox{6mm}{}\xleftharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8614,7 +9305,19 @@ nearrow
 \begin_layout Plain Layout
 
 \backslash
-searrow
+
+\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
@@ -8623,7 +9326,7 @@ searrow
 \begin_inset Text
 
 \begin_layout Plain Layout
-\begin_inset Formula $\searrow$
+\begin_inset Formula $\raisebox{6mm}{}\xleftharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8633,22 +9336,34 @@ searrow
 </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
-swarrow
+
+\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
 </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 $\swarrow$
+\begin_inset Formula $\raisebox{6mm}{}\xrightharpoondown[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8658,22 +9373,34 @@ swarrow
 </cell>
 </row>
 <row>
-<cell alignment="center" valignment="top" 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
-nwarrow
+
+\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" 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 $\nwarrow$
+\begin_inset Formula $\raisebox{6mm}{}\xrightharpoonup[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
@@ -8682,173 +9409,680 @@ nwarrow
 \end_inset
 </cell>
 </row>
-</lyxtabular>
-
-\end_inset
-
-
-\begin_inset space \hfill{}
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-\begin_inset VSpace medskip
-\end_inset
-
-Vertical arrows can be used also as delimiters together with the commands
- described in 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Manual-Bracket-Size"
-
-\end_inset
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
 
- and 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Automatic-Bracket-Size"
+\begin_layout Plain Layout
 
-\end_inset
+\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 Section
-Accents
-\begin_inset CommandInset label
-LatexCommand label
-name "sec:Accents"
-
 \end_inset
-
-
-\begin_inset Index idx
-status collapsed
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
 
 \begin_layout Plain Layout
-Accents
-\end_layout
-
+\begin_inset Formula $\raisebox{6mm}{}\xleftrightharpoons[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
 \end_layout
 
-\begin_layout Standard
-Accents can be inserted via the math toolbar button 
-\begin_inset Graphics
-       filename ../images/math/hat.png
-       scale 85
-
 \end_inset
-
- or the commands listed in the following subsections.
-\end_layout
-
-\begin_layout Subsection
-Accents for one Character
-\begin_inset ERT
-status collapsed
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
 
 \begin_layout Plain Layout
 
-
 \backslash
-texorpdfstring{
-\end_layout
-
-\end_inset
-
-
-\begin_inset Foot
-status collapsed
-
-\begin_layout Plain Layout
-accents in text see 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Accents-in-Text"
-
-\end_inset
-
 
+\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
-
-
-\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
-
-}{}
-\end_layout
-
+\begin_inset Formula $\raisebox{6mm}{}\xrightleftharpoons[x=a]{x>0}\raisebox{-4mm}{}$
 \end_inset
 
 
-\begin_inset Note Note
-status collapsed
-
-\begin_layout Plain Layout
-
-\series bold
-
-\backslash
-texorpdfstring
-\series default
- is used to avoid that the footnote appears in the PDF-bookmark.
 \end_layout
 
-\begin_layout Plain Layout
-More about 
-\series bold
-
-\backslash
-texorpdfstring
-\series default
- is in section 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "sub:Formulas-in-Section"
-
 \end_inset
-
-.
-\end_layout
+</cell>
+</row>
+</lyxtabular>
 
 \end_inset
 
 
-\begin_inset CommandInset label
-LatexCommand label
-name "sub:Accents-for-one"
-
+\begin_inset space \hspace*{\fill}
 \end_inset
 
 
-\begin_inset Index idx
-status collapsed
-
-\begin_layout Plain Layout
-Accents ! for one character
 \end_layout
 
-\end_inset
-
-
+\begin_layout Standard
+The command scheme is for all these arrows:
 \end_layout
 
 \begin_layout Standard
-\begin_inset space \hfill{}
-\end_inset
-
-
+\align center
 \begin_inset Tabular
-<lyxtabular version="3" rows="8" 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">
+<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
+\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
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+F(a)
+\backslash
+xleftrightarrow[x=a]
+\backslash
+{x>0
+\begin_inset Formula $\to$
+\end_inset
+
+F(x)
+\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 $\raisebox{6mm}{}F(a)\xleftrightarrow[x=a]{x>0}F(x)\raisebox{-4mm}{}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vertical and diagonal Arrows
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Arrows ! diagonal
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Arrows ! vertical
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset space \hfill{}
+\end_inset
+
+
+\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" 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
+uparrow
+\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 $\uparrow$
+\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
+Uparrow
+\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 $\Uparrow$
+\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
+updownarrow
+\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 $\updownarrow$
+\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
+Updownarrow
+\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 $\Updownarrow$
+\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
+Downarrow
+\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 $\Downarrow$
+\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
+downarrow
+\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 $\downarrow$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\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
+nearrow
+\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 $\nearrow$
+\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
+searrow
+\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 $\searrow$
+\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
+swarrow
+\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 $\swarrow$
+\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
+nwarrow
+\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 $\nwarrow$
+\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
+
+Vertical arrows can be used also as delimiters together with the commands
+ described in 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Manual-Bracket-Size"
+
+\end_inset
+
+ and 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Automatic-Bracket-Size"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Section
+Accents
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Accents"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Accents
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Accents can be inserted via the math toolbar button 
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\hat"
+\end_inset
+
+ or the commands listed in the following subsections.
+\end_layout
+
+\begin_layout Subsection
+Accents for one Character
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+texorpdfstring{
+\end_layout
+
+\end_inset
+
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+accents in text see 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Accents-in-Text"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+}{}
+\end_layout
+
+\end_inset
+
+
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ is used to avoid that the footnote appears in the PDF-bookmark.
+\end_layout
+
+\begin_layout Plain Layout
+More about 
+\series bold
+
+\backslash
+texorpdfstring
+\series default
+ is in section 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Formulas-in-Section"
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Accents-for-one"
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Accents ! for one character
+\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">
@@ -9694,6 +10928,13 @@ fi
 \end_inset
 
 
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
 \end_layout
 
 \begin_layout Subsection
@@ -10124,13 +11365,6 @@ A=B
 \end_inset
 
 
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
 \end_layout
 
 \begin_layout Section
@@ -10206,10 +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.
@@ -11994,13 +13227,6 @@ fbox
 .
 \end_layout
 
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
 \begin_layout Standard
 \align center
 \begin_inset Tabular
@@ -13077,10 +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 
@@ -13539,10 +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
 
 .
@@ -14804,10 +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
 
 .
@@ -15182,13 +16405,6 @@ dotsint
 \end_inset
 
 
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
 \end_layout
 
 \begin_layout Subsection
@@ -15565,22 +16781,59 @@ reference "eq:substack"
 \series bold
 
 \backslash
-mathclap
+smashoperator
 \series default
 
 \begin_inset Index idx
 status collapsed
 
 \begin_layout Plain Layout
-Commands ! M ! 
+Commands ! S ! 
 \backslash
-mathclap
+smashoperator
 \end_layout
 
 \end_inset
 
  can be used.
- It sets the width of its content to 0
+ 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
+smashoperator
+\series default
+ sets the space besides the operator to 0
 \begin_inset space \thinspace{}
 \end_inset
 
@@ -15603,27 +16856,69 @@ reference "eq:substack"
 \series bold
 
 \backslash
-sum_
-\backslash
-mathclap
-\backslash
-substack
-\begin_inset space \textvisiblespace{}
-\end_inset
-
-0<k<1000 Ctrl+Return
+smashoperator{
 \end_layout
 
 \begin_layout Standard
-to create the lower limit.
The summand is now directly behind the summation operator:
+and inserts the operator with its limits into the braces.
Behind the brace one continues the formula:
 \begin_inset Formula 
 \[
-\sum_{\mathclap{\substack{0<k<1000\\
+\smashoperator{\sum_{\begin{subarray}{c}
+0<k<1000\\
 \\
 k\,\in\,\mathbb{N}
-}
-}}^{n}k^{-2}
+\end{subarray}}^{n}}k^{-2}
+\]
+
+\end_inset
+
+
+\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.
+ 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
@@ -17043,10 +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
 
 .
@@ -18040,10 +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.
@@ -18461,7 +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
@@ -18795,10 +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
 
 .
@@ -20390,17 +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
 
 .
@@ -22478,10 +23775,9 @@ status collapsed
 
 \begin_layout Standard
 All following relations can also be inserted via the toolbar button 
-\begin_inset Graphics
-       filename ../images/math/leq.png
-       scale 85
-
+\begin_inset Info
+type  "icon"
+arg   "math-insert \\leq"
 \end_inset
 
 .
@@ -23821,6 +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
 
 \end_layout
 
-\begin_layout Standard
-\begin_inset VSpace bigskip
-\end_inset
-
-
-\end_layout
-
-\begin_layout Standard
-LyX supports also many special relations.
- Use the toolbar button 
-\begin_inset Graphics
-       filename ../images/math/leq.png
-       scale 85
-
-\end_inset
-
- to see a list of possible relations.
-\end_layout
-
 \begin_layout Section
 Functions
 \end_layout
@@ -24546,10 +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
 
 .
@@ -25160,6 +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
@@ -25661,10 +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
 
 .
@@ -26919,15 +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
@@ -26981,17 +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 
@@ -27647,6 +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
@@ -27862,17 +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 
@@ -28673,6 +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
@@ -28830,10 +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
 
 .
@@ -28892,10 +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
 
 .
@@ -30232,6 +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
@@ -30422,13 +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
@@ -31527,13 +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
@@ -32322,10 +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
 
 .
@@ -32685,10 +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
 
 
@@ -32720,10 +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
 
 
@@ -32755,10 +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
 
 
@@ -32779,7 +34337,7 @@ Macro
 \end_inset
 
 Definition\SpecialChar \menuseparator
-Make First Non-Optional into
+Transform First Non-Optional to
 \begin_inset Newline newline
 \end_inset
 
@@ -32813,10 +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
 
 
@@ -32837,7 +34394,7 @@ Macro
 \end_inset
 
 Definition\SpecialChar \menuseparator
-Make Last Optional into
+Transform Last Optional to
 \begin_inset Newline newline
 \end_inset
 
@@ -32871,10 +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
 
 
@@ -32906,10 +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
 
 
@@ -32941,10 +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
 
 
@@ -32999,10 +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
 
 
@@ -33057,10 +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
 
 
@@ -33256,7 +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
 
@@ -35633,6 +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
@@ -36755,49 +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