X-Git-Url: https://git.lyx.org/gitweb/?a=blobdiff_plain;f=lib%2Fdoc%2FMath.lyx;h=064438495e4c7d744e06b45e99e3a4f7ed7fb040;hb=5fd5b8be71515fcf56fca05ec2be6ef68cd1647d;hp=ddb2abd4b2d2fb130bd217406095fde0e4d14693;hpb=121ded490b0ecdc6a818107bb0b2f57c05a32158;p=lyx.git

diff --git a/lib/doc/Math.lyx b/lib/doc/Math.lyx
index ddb2abd4b2..064438495e 100644
--- a/lib/doc/Math.lyx
+++ b/lib/doc/Math.lyx
@@ -1,5 +1,5 @@
-#LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
-\lyxformat 401
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
 \begin_document
 \begin_header
 \textclass scrartcl
@@ -41,11 +41,13 @@
 \AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}
 \newlength{\abc}
 \settowidth{\abc}{\space}
+\AtBeginDocument{%
 \addto\extrasenglish{
  \renewcommand{\equationautorefname}{\hspace{-\abc}}
  \renewcommand{\sectionautorefname}{sec.\negthinspace}
  \renewcommand{\subsectionautorefname}{sec.\negthinspace}
  \renewcommand{\subsubsectionautorefname}{sec.\negthinspace}}
+}
 
 % don't load packages twice
 % see first footnote in sec. 9.3
@@ -69,14 +71,13 @@
 % provides caption formatting
 \setkomafont{captionlabel}{\bfseries}
 
-% used in Kap. 22.6
+% used in sec. 23.6
 \usepackage[samesize]{cancel}
 
-% enables calculation of values,
+% enables calculation of values
 \usepackage{calc}
 
-% for multiple table row and column cells
-\usepackage{multirow}
+% for multiple columns used in sec. 23.7
 \usepackage{multicol}
 
 % needed in sec. 19.4
@@ -85,9 +86,6 @@
 % for the Fourier transformation symbol
 \usepackage{mathrsfs}
 
-% center multirows (e.g. in sec. 13.3)
-\renewcommand{\multirowsetup}{\centering}
-
 % define a color, used in sec.9.3
 \definecolor{darkgreen}{cmyk}{0.5, 0, 1, 0.5}
 
@@ -112,9 +110,6 @@
 \def\mathclap {\mathpalette \mathclapinternal}
 \def\mathclapinternal #1#2{\clap{$\mathsurround =0pt #1{#2}$}}
 
-% redefine the greyed out note
-\renewenvironment{lyxgreyedout}
- {\textcolor{blue}\bgroup}{\egroup}
 
 % ------------------------------------
 % used to check for needed LaTeX packages
@@ -150,17 +145,18 @@
   \setboolean{upgreek}{true}}
  {\setboolean{upgreek}{false}}
 \end_preamble
-\options bibtotoc,idxtotoc,BCOR7.5mm,titlepage,tablecaptionabove
+\options bibliography=totoc,index=totoc,BCOR7.5mm,titlepage,captions=tableheading
 \use_default_options false
 \maintain_unincluded_children false
 \language english
+\language_package default
 \inputencoding auto
 \fontencoding global
 \font_roman default
 \font_sans default
 \font_typewriter default
 \font_default_family default
-\use_xetex false
+\use_non_tex_fonts false
 \font_sc false
 \font_osf false
 \font_sf_scale 100
@@ -187,7 +183,7 @@
 \pdf_colorlinks true
 \pdf_backref false
 \pdf_pdfusetitle false
-\pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue,  pdfpagelayout=OneColumn, pdfnewwindow=true,  pdfstartview=XYZ, plainpages=false, pdfpagelabels"
+\pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue, pdfpagelayout=OneColumn, pdfnewwindow=true, pdfstartview=XYZ, plainpages=false"
 \papersize a4paper
 \use_geometry false
 \use_amsmath 2
@@ -199,6 +195,8 @@
 \use_indices false
 \paperorientation portrait
 \suppress_date false
+\use_refstyle 0
+\notefontcolor #0000ff
 \index Index
 \shortcut idx
 \color #008000
@@ -217,6 +215,7 @@
 \tracking_changes false
 \output_changes false
 \html_math_output 0
+\html_css_as_file 0
 \html_be_strict false
 \end_header
 
@@ -293,7 +292,7 @@ braket, cancel, eurosym,
 \series default
  
 \series bold
-mhchem, multirow
+mhchem
 \series default
  and 
 \series bold
@@ -2074,7 +2073,8 @@ cfrac
 \end_layout
 
 \begin_layout Standard
-\begin_inset Formula \begin{align*}
+\begin_inset Formula 
+\begin{align*}
 \textrm{created with \textbf{\textbackslash frac}} &  & \textrm{created with \textbf{\textbackslash cfrac}}\\
 \frac{A}{B+\frac{C+\frac{E}{F}}{D}} &  & \cfrac{A}{B+\cfrac{C+\cfrac{E}{F}}{D}}
 \end{align*}
@@ -2262,8 +2262,10 @@ cfrac
 frac
 \series default
 :
-\begin_inset Formula \[
-\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
+\begin_inset Formula 
+\[
+\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
+\]
 
 \end_inset
 
@@ -4587,7 +4589,7 @@ dots
 \begin_layout Standard
 \align center
 \begin_inset Tabular
-<lyxtabular version="3" rows="8" columns="2">
+<lyxtabular version="3" rows="9" columns="2">
 <features tabularvalignment="middle">
 <column alignment="center" valignment="top" width="0pt">
 <column alignment="center" valignment="top" width="0pt">
@@ -4841,7 +4843,7 @@ vdots
 </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
@@ -4852,7 +4854,7 @@ ddots
 
 \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
@@ -4860,6 +4862,31 @@ ddots
 \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
+iddots
+\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 $\iddots$
+\end_inset
+
+
 \end_layout
 
 \end_inset
@@ -4926,6 +4953,40 @@ ldots
 \begin_inset VSpace medskip
 \end_inset
 
+To use 
+\series bold
+
+\backslash
+iddots
+\series default
+, one of the options 
+\family sans
+Use mathdots package (automatically)
+\family default
+ must be set in the document settings under 
+\family sans
+Math
+\begin_inset space ~
+\end_inset
+
+Options
+\family default
+.
+\begin_inset Newline newline
+\end_inset
+
+Using the option 
+\family sans
+Use mathdots package
+\family default
+ will improve the appearance of all dots in the documents if their font
+ style or size is not the default.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
 Specially for matrices there are ellipses that span over several columns.
  They are created with the command 
 \series bold
@@ -4976,12 +5037,14 @@ hdotsfor[2]{4}
 dots
 \series default
 :
-\begin_inset Formula \[
+\begin_inset Formula 
+\[
 \left(\begin{array}{cccc}
 A & B & C & D\\
 \hdotsfor[2]{4}\\
 q & w & e & r
-\end{array}\right)\]
+\end{array}\right)
+\]
 
 \end_inset
 
@@ -5764,6 +5827,44 @@ vmatrix
 Note that decorated matrices ignore the vertical alignment.
 \end_layout
 
+\begin_layout Standard
+\begin_inset Note Greyedout
+status open
+
+\begin_layout Plain Layout
+
+\series bold
+Note:
+\series default
+ LaTeX limits the number of matrix columns with decorations to 10.
+ If you need more than 10
+\begin_inset space \thinspace{}
+\end_inset
+
+columns, you have to add this line to the document preamble:
+\end_layout
+
+\begin_layout Plain Layout
+
+\series bold
+
+\backslash
+setcounter{MaxMatrixCols}{number}
+\end_layout
+
+\begin_layout Plain Layout
+where 
+\emph on
+number
+\emph default
+ is the number of columns between 11 and 99.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 \begin_inset VSpace bigskip
 \end_inset
@@ -7156,8 +7257,10 @@ spce
 )
 \series default
  creates
-\begin_inset Formula \[
-\ln(\frac{A}{C})\]
+\begin_inset Formula 
+\[
+\ln(\frac{A}{C})
+\]
 
 \end_inset
 
@@ -7209,8 +7312,10 @@ spce
 right)
 \series default
  creates
-\begin_inset Formula \[
-\ln\left(\frac{A}{C}\right)\]
+\begin_inset Formula 
+\[
+\ln\left(\frac{A}{C}\right)
+\]
 
 \end_inset
 
@@ -7319,8 +7424,10 @@ right}
  creates:
 \series bold
 
-\begin_inset Formula \[
-\left.\frac{A}{B}\right\} \]
+\begin_inset Formula 
+\[
+\left.\frac{A}{B}\right\} 
+\]
 
 \end_inset
 
@@ -7376,8 +7483,10 @@ g.
 \end_inset
 
 needed for physical vectors:
-\begin_inset Formula \[
-\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
+\begin_inset Formula 
+\[
+\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle 
+\]
 
 \end_inset
 
@@ -7787,7 +7896,8 @@ reference "sec:Multiline-Formulas"
 \end_inset
 
 , must be used:
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula 
+\begin{eqnarray*}
 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd\\
  &  & \hphantom{gggg+\:}\underbrace{\hphantom{bbqq+dddd}}_{s}
 \end{eqnarray*}
@@ -7923,7 +8033,8 @@ jot}{-6pt}
 \end_inset
 
 
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula 
+\begin{eqnarray*}
  &  & \hphantom{gggg+\:}\overbrace{\hphantom{bbqq+dddd}}^{s}\\
 A & = & \underbrace{gggg+bbqq}_{r}+\: dddd
 \end{eqnarray*}
@@ -8045,13 +8156,6 @@ Arrows can be inserted via the math toolbar button
  or the commands listed in the following subsections.
 \end_layout
 
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
 \begin_layout Subsection
 Horizontal Arrows
 \begin_inset Index idx
@@ -9400,13 +9504,6 @@ reference "sub:Automatic-Bracket-Size"
 .
 \end_layout
 
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
 \begin_layout Section
 Accents
 \begin_inset CommandInset label
@@ -9487,14 +9584,22 @@ status collapsed
 
 \begin_layout Plain Layout
 
+\series bold
+
 \backslash
-texorpdfstring is used to avoid that the footnote appears in the PDF-bookmark.
+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 is in section 
+texorpdfstring
+\series default
+ is in section 
 \begin_inset CommandInset ref
 LatexCommand ref
 reference "sub:Formulas-in-Section"
@@ -10485,8 +10590,10 @@ spce
 n
 \series default
  produces:
-\begin_inset Formula \[
-\sideset{}{'}\sum_{k=1}^{n}\]
+\begin_inset Formula 
+\[
+\sideset{}{'}\sum_{k=1}^{n}
+\]
 
 \end_inset
 
@@ -10537,8 +10644,10 @@ spce
 a
 \series default
  produces:
-\begin_inset Formula \[
-\overset{a}{\maltese}\]
+\begin_inset Formula 
+\[
+\overset{a}{\maltese}
+\]
 
 \end_inset
 
@@ -10991,8 +11100,10 @@ widehat
 \series default
  will only be set in the output with a length of three characters, as shown
  in the following example:
-\begin_inset Formula \[
-\widetilde{A+B=C-D}\]
+\begin_inset Formula 
+\[
+\widetilde{A+B=C-D}
+\]
 
 \end_inset
 
@@ -11062,8 +11173,10 @@ A=B
 ***
 \series default
  creates:
-\begin_inset Formula \[
-\underset{***}{A=B}\]
+\begin_inset Formula 
+\[
+\underset{***}{A=B}
+\]
 
 \end_inset
 
@@ -13095,8 +13208,10 @@ fboxsep 3mm
 \end_inset
 
 
-\begin_inset Formula \[
-\boxed{A+B=C}\]
+\begin_inset Formula 
+\[
+\boxed{A+B=C}
+\]
 
 \end_inset
 
@@ -13952,16 +14067,20 @@ An example:
 \begin_layout Standard
 
 \color red
-\begin_inset Formula \begin{equation}
-\int A=B\label{eq:red}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+\int A=B\label{eq:red}
+\end{equation}
 
 \end_inset
 
 
 \color green
 
-\begin_inset Formula \begin{equation}
-\textcolor{red}{\int A=B}\label{eq:redgreen}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+\textcolor{red}{\int A=B}\label{eq:redgreen}
+\end{equation}
 
 \end_inset
 
@@ -14073,8 +14192,10 @@ fboxsep 1mm
 \end_inset
 
 
-\begin_inset Formula \[
-\fcolorbox{cyan}{magenta}{A=B}\]
+\begin_inset Formula 
+\[
+\fcolorbox{cyan}{magenta}{A=B}
+\]
 
 \end_inset
 
@@ -14256,8 +14377,10 @@ darkgreen
 yellow
 \series default
 :
-\begin_inset Formula \begin{equation}
-\colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+\colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
+\end{equation}
 
 \end_inset
 
@@ -14678,8 +14801,10 @@ fboxrule}{
 \end_inset
 
 
-\begin_inset Formula \begin{equation}
-\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
+\end{equation}
 
 \end_inset
 
@@ -14914,8 +15039,10 @@ commented
 \end_inset
 
  using the mathematical textmode:
-\begin_inset Formula \[
-5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
+\begin_inset Formula 
+\[
+5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
+\]
 
 \end_inset
 
@@ -16145,8 +16272,10 @@ arg   "math-limits"
 
 \begin_layout Standard
 The default limits type is this:
-\begin_inset Formula \[
-\sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
+\begin_inset Formula 
+\[
+\sum_{x=0}^{\infty}\frac{1}{x^{2}}
+\]
 
 \end_inset
 
@@ -16157,8 +16286,10 @@ Inline
 \family default
 \series default
 :
-\begin_inset Formula \[
-\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
+\begin_inset Formula 
+\[
+\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
+\]
 
 \end_inset
 
@@ -16185,8 +16316,10 @@ ointop
 Display
 \series default
  and so set below the integrals:
-\begin_inset Formula \begin{equation}
-\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
+\end{equation}
 
 \end_inset
 
@@ -16235,12 +16368,14 @@ substack
 
  are used.
  To create for example this expression 
-\begin_inset Formula \begin{equation}
+\begin_inset Formula 
+\begin{equation}
 \sum_{\begin{subarray}{c}
 0<k<1000\\
 \\
 k\,\in\,\mathbb{N}
-\end{subarray}}^{n}k^{-2}\label{eq:substack}\end{equation}
+\end{subarray}}^{n}k^{-2}\label{eq:substack}
+\end{equation}
 
 \end_inset
 
@@ -16511,12 +16646,14 @@ spce
 \begin_layout Standard
 to create the lower limit.
  The summand is now directly behind the summation operator:
-\begin_inset Formula \[
+\begin_inset Formula 
+\[
 \sum_{\mathclap{\substack{0<k<1000\\
 \\
 k\,\in\,\mathbb{N}
 }
-}}^{n}k^{-2}\]
+}}^{n}k^{-2}
+\]
 
 \end_inset
 
@@ -16537,6 +16674,13 @@ reference "sub:Self-defined-Operators"
 .
 \end_layout
 
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
 \begin_layout Subsection
 Binary Operators
 \begin_inset CommandInset label
@@ -17768,8 +17912,10 @@ reference "sub:Miscellaneous-Symbols"
 \end_inset
 
 :
-\begin_inset Formula \[
-\Lozenge_{n=1}^{\infty}\]
+\begin_inset Formula 
+\[
+\Lozenge_{n=1}^{\infty}
+\]
 
 \end_inset
 
@@ -17883,8 +18029,10 @@ be used to use one limit for several operators:
 \end_layout
 
 \begin_layout Standard
-\begin_inset Formula \[
-\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
+\begin_inset Formula 
+\[
+\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
+\]
 
 \end_inset
 
@@ -18664,8 +18812,10 @@ mathnormal
 
 \begin_layout Standard
 The style commands work also for letters in mathematical constructs:
-\begin_inset Formula \[
-\mathfrak{A=\frac{b}{C}}\]
+\begin_inset Formula 
+\[
+\mathfrak{A=\frac{b}{C}}
+\]
 
 \end_inset
 
@@ -18754,8 +18904,10 @@ mathbf
 \end_layout
 
 \begin_layout Standard
-\begin_inset Formula \[
-\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
+\begin_inset Formula 
+\[
+\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
+\]
 
 \end_inset
 
@@ -18770,8 +18922,10 @@ To display the formula correctly, the command
 boldsymbol
 \series default
  is used:
-\begin_inset Formula \[
-\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
+\begin_inset Formula 
+\[
+\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
+\]
 
 \end_inset
 
@@ -18831,8 +18985,10 @@ boldmath
 \end_inset
 
 
-\begin_inset Formula \[
-\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
+\begin_inset Formula 
+\[
+\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
+\]
 
 \end_inset
 
@@ -18874,8 +19030,10 @@ Text Style
 \family default
  dialog.
  Here is a formula in magenta:
-\begin_inset Formula \[
-{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
+\begin_inset Formula 
+\[
+{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
+\]
 
 \end_inset
 
@@ -18938,8 +19096,10 @@ textcolor{darkgreen}{
 \end_inset
 
 
-\begin_inset Formula \[
-\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
+\begin_inset Formula 
+\[
+\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
+\]
 
 \end_inset
 
@@ -19120,13 +19280,6 @@ normalsize
  is inserted behind the formula in TeX-mode.
 \end_layout
 
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
 \begin_layout Standard
 Within a formula the size can be changed using the following size commands:
 \end_layout
@@ -19327,14 +19480,18 @@ huge
 \end_inset
 
 
-\begin_inset Formula \[
-A=\frac{B}{c}\cdot\maltese\]
+\begin_inset Formula 
+\[
+A=\frac{B}{c}\cdot\maltese
+\]
 
 \end_inset
 
 
-\begin_inset Formula \[
-\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
+\begin_inset Formula 
+\[
+\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
+\]
 
 \end_inset
 
@@ -19505,13 +19662,6 @@ If a symbol cannot be displayed in different sizes, it will always be displayed
  in the default size.
 \end_layout
 
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
 \begin_layout Section
 Greek Letters
 \begin_inset Index idx
@@ -19527,7 +19677,7 @@ Greek letters
 \end_layout
 
 \begin_layout Standard
-All Greek letters can also be inserted via the toolbar button 
+Greek letters can also be inserted via the toolbar button 
 \begin_inset Graphics
 	filename ../images/math/alpha.png
 	scale 85
@@ -19535,6 +19685,10 @@ All Greek letters can also be inserted via the toolbar button
 \end_inset
 
 .
+ All international typesetting norms purport that Greek letters in math
+ have to be typeset italic/slanted.
+ In some languages, like French or Russian, they are nevertheless sometimes
+ typeset upright.
 \end_layout
 
 \begin_layout Subsection
@@ -20441,7 +20595,7 @@ omega
 \end_layout
 
 \begin_layout Standard
-How to create upright Greek letters is explained in 
+How to create special upright Greek letters is explained in 
 \begin_inset CommandInset ref
 LatexCommand ref
 reference "sub:Upright-small-Greek"
@@ -20832,11 +20986,79 @@ var
 \backslash
 varGamma
 \series default
- produces: 
+ produces 
 \begin_inset Formula $\varGamma$
 \end_inset
 
+.
+ Another way is to load the package 
+\series bold
+fixmath
+\series default
+
+\begin_inset Foot
+status collapsed
+
+\begin_layout Plain Layout
+
+\series bold
+fixmath
+\series default
+ is part of the LaTeX-package 
+\series bold
+was
+\series default
 
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! was
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+vspace{4mm}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\begin_inset Index idx
+status collapsed
+
+\begin_layout Plain Layout
+Packages ! fixmath
+\end_layout
+
+\end_inset
+
+ with the LaTeX-preamble line
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+
+\backslash
+usepackage{fixmath}
+\end_layout
+
+\begin_layout Standard
+Then all big Greek letters in a document will automatically be typeset italic.
 \end_layout
 
 \begin_layout Subsection
@@ -20966,6 +21188,13 @@ theta
 \end_inset
 
 
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
 \end_layout
 
 \begin_layout Section
@@ -25774,8 +26003,10 @@ x=B
 
 \begin_layout Standard
 In a displayed formula the limit is set below the formula, as usual:
-\begin_inset Formula \[
-\lim_{x\to A}x=B\]
+\begin_inset Formula 
+\[
+\lim_{x\to A}x=B
+\]
 
 \end_inset
 
@@ -25802,7 +26033,8 @@ The modulo-function is special, because it exists in four variants.
 
 \begin_layout Standard
 The variants in a displayed formula:
-\begin_inset Formula \begin{align*}
+\begin_inset Formula 
+\begin{align*}
 \underline{\textrm{Command}\raisebox{-0.9mm}{}} &  & \underline{\textrm{Result}}\\
 \mathrm{a\backslash mod\textrm{\spce}b} &  & a\mod b\\
 \mathrm{a\backslash pmod\textrm{\spce}b} &  & a\pmod b\\
@@ -27715,6 +27947,13 @@ textdegree
 fi}
 \end_layout
 
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Formula Styles
 \begin_inset CommandInset label
@@ -28005,7 +28244,8 @@ Formula ! multiline ! Line separation
 
 \begin_layout Standard
 There is sometimes not enough space in multiline formulas between the lines:
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula 
+\begin{eqnarray*}
 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
 4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0
 \end{eqnarray*}
@@ -28212,7 +28452,8 @@ jot}{3mm+3pt}
 \end_inset
 
 
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula 
+\begin{eqnarray*}
 B^{2}(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2})+4x_{0}^{2}x^{2}+4x_{0}xD & = & \textrm{-}4x^{2}B^{2}+4x_{0}xB^{2}\\
 4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right) & = & 0
 \end{eqnarray*}
@@ -28370,7 +28611,8 @@ arraycolsep}{1cm}
 \end_inset
 
 
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula 
+\begin{eqnarray*}
 A & = & B\\
 C & \ne & A
 \end{eqnarray*}
@@ -28397,7 +28639,8 @@ arraycolsep}{5pt}
 \end_inset
 
 
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula 
+\begin{eqnarray*}
 A & = & B\\
 C & \ne & A
 \end{eqnarray*}
@@ -28429,7 +28672,8 @@ Long formulas can be typeset using these methods:
 When one side of the equation is much shorther than the line width, this
  one is chosen for the left side and the right side is typeset over two
  lines:
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula 
+\begin{eqnarray}
 H & = & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\nonumber \\
  &  & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}\label{eq:shortlong}
 \end{eqnarray}
@@ -28510,7 +28754,8 @@ lefteqn
  is used.
  It is inserted to the first column of the first line and effects that all
  further insertions overwrite the following columns:
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula 
+\begin{eqnarray}
 \lefteqn{4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}}\nonumber \\
  &  & -\hspace{3pt}B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\nonumber \\
  &  & =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}\label{eq:lefteqn}
@@ -28644,7 +28889,8 @@ Brackets ! for multiline expressions
 
 \begin_layout Standard
 For brackets spanning multiple lines the following problem occurs:
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula 
+\begin{eqnarray*}
 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
  &  & \left.\cdots+B-D\right]
 \end{eqnarray*}
@@ -28818,7 +29064,8 @@ vphantom
 
 \begin_layout Standard
 The result is this:
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula 
+\begin{eqnarray*}
 A & = & \sin(x)\left[\prod_{R=1}^{\infty}\frac{1}{R}+\cdots\right.\\
  &  & \left.\vphantom{\prod_{R=1}^{\infty}}\cdots+B-D\right]
 \end{eqnarray*}
@@ -28922,7 +29169,8 @@ AMS align Environment
 \begin_layout Standard
 An example for two formulas set side by side, that are created with a four
  column align environment:
-\begin_inset Formula \begin{align*}
+\begin_inset Formula 
+\begin{align*}
 A & =\sin(B) & C & =D\\
 C & \ne A & B & \ne D
 \end{align*}
@@ -29022,7 +29270,8 @@ The above example in the alignat environment where 1
 \end_inset
 
 cm space was inserted at the beginning of the second formula:
-\begin_inset Formula \begin{alignat*}{2}
+\begin_inset Formula 
+\begin{alignat*}{2}
 A & =\sin(B) & \hspace{1cm}C & =D\\
 C & \ne A & B & \ne D
 \end{alignat*}
@@ -29059,7 +29308,8 @@ Formula ! multiline ! flalign environment
 In this environment the first two columns are always set as much as possible
  to the left and the last two ones to the right.
  An example:
-\begin_inset Formula \begin{flalign*}
+\begin_inset Formula 
+\begin{flalign*}
 A & =1 & B & =2 & C & =3\\
 X & =\textrm{-}1 & Y & =\textrm{-}2 & Z & =4
 \end{flalign*}
@@ -29085,8 +29335,10 @@ reference "eq:VolInt"
 \end_inset
 
 :
-\begin_inset Formula \begin{flalign}
-\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
+\begin_inset Formula 
+\begin{flalign}
+\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
+\end{flalign}
 
 \end_inset
 
@@ -29129,7 +29381,8 @@ When this environment has been created, three blue boxes appear.
  one left aligned.
  The content of the middle box appears centered and a bit smaller, because
  it is designed to insert there only relation characters.
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula 
+\begin{eqnarray*}
 \frac{ABC}{D} & \frac{ABC}{D} & \frac{ABC}{D}\\
 AB & AB & AB\\
 A & = & A
@@ -29157,7 +29410,8 @@ Formula ! multiline ! gather environment
 \begin_layout Standard
 This environment consists of only one centered column.
  Every line can be numbered.
-\begin_inset Formula \begin{gather}
+\begin_inset Formula 
+\begin{gather}
 A=1\\
 X=\textrm{-}1
 \end{gather}
@@ -29202,7 +29456,8 @@ reference "eq:lefteqn"
 \end_inset
 
  in the multline environment:
-\begin_inset Formula \begin{multline}
+\begin_inset Formula 
+\begin{multline}
 4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
 -B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}\\
 =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}
@@ -29351,7 +29606,8 @@ multlinegap}{2cm}
 \end_inset
 
 
-\begin_inset Formula \begin{multline}
+\begin_inset Formula 
+\begin{multline}
 4x^{2}\left(B^{2}+x_{0}^{2}\right)+4x_{0}x\left(D-B^{2}\right)+B^{2}\left(B^{2}-2r_{g}^{2}+2x_{0}^{2}-2r_{k}^{2}\right)+D^{2}\\
 \shoveleft{-B^{2}-2B\sqrt{r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}+r_{g}^{2}-x^{2}+2x_{0}x-x_{0}^{2}}\\
 =B^{2}+2\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)+\frac{\left(r_{g}^{2}+2x_{0}x-x_{0}^{2}-r_{k}^{2}\right)^{2}}{B^{2}}
@@ -29436,11 +29692,13 @@ The first three have the same properties as the corresponding multiline
  formula environments, but it is possible to set further formula parts beside
  them.
  An example:
-\begin_inset Formula \[
+\begin_inset Formula 
+\[
 \left.\begin{aligned}\Delta x\Delta p & \ge\frac{\hbar}{2}\\
 \Delta E\Delta t & \ge\frac{\hbar}{2}
 \end{aligned}
-\right\} \textrm{Uncertainty relations}\]
+\right\} \textrm{Uncertainty relations}
+\]
 
 \end_inset
 
@@ -29486,7 +29744,8 @@ reference "eq:shortlong"
 \end_inset
 
  in the aligned environment:
-\begin_inset Formula \begin{equation}
+\begin_inset Formula 
+\begin{equation}
 \begin{aligned}H=\; & W_{SB}+W_{mv}+W_{D}-\frac{\hbar^{2}}{2m_{0}}\Delta-\frac{\hbar^{2}}{2m_{1}}\Delta_{1}-\frac{\hbar^{2}}{2m_{2}}\Delta_{2}-\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{1}|}\\
  & -\hspace{3pt}\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{r}-\mathbf{R}_{2}|}+\frac{e^{2}}{4\pi\varepsilon_{0}|\mathbf{R}_{1}-\mathbf{R}_{2}|}
 \end{aligned}
@@ -29651,7 +29910,8 @@ intertext
  must hereby be at the beginning of a line and appears in the output above
  this line.
  An example where the text was inserted at the beginning of the second line:
-\begin_inset Formula \begin{align}
+\begin_inset Formula 
+\begin{align}
 I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
 \intertext{\text{integrand is symmetric to \ensuremath{\phi=\pi}, therefore}} & =2a\sqrt{2}\int_{0}^{\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi
 \end{align}
@@ -29659,6 +29919,13 @@ I & =a\sqrt{2}\int_{0}^{2\pi}\sqrt{1+\cos(\phi)}\;\mathrm{d}\phi\\
 \end_inset
 
 
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
 \end_layout
 
 \begin_layout Section
@@ -30013,8 +30280,10 @@ end{subequations}
 
 \begin_layout Standard
 An example:
-\begin_inset Formula \begin{equation}
-A=C-B\label{eq:a}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+A=C-B\label{eq:a}
+\end{equation}
 
 \end_inset
 
@@ -30049,14 +30318,18 @@ begin{subequations}
 \end_inset
 
 
-\begin_inset Formula \begin{equation}
-B=C-A\label{eq:b}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+B=C-A\label{eq:b}
+\end{equation}
 
 \end_inset
 
 
-\begin_inset Formula \begin{equation}
-C=A+B\label{eq:c}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+C=A+B\label{eq:c}
+\end{equation}
 
 \end_inset
 
@@ -30271,7 +30544,8 @@ begin{subequations}
 \end_inset
 
 
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula 
+\begin{eqnarray}
 A & = & (B-Z)^{2}=(B-Z)(B-Z)\label{eq:d}\\
  & = & B^{2}-ZB-BZ+Z^{2}\nonumber \\
  & = & B^{2}-2BZ+Z^{2}\label{eq:f}
@@ -30389,8 +30663,10 @@ tag
 \end_inset
 
  is used:
-\begin_inset Formula \begin{equation}
-A+B=C\tag{something}\label{eq:tag}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+A+B=C\tag{something}\label{eq:tag}
+\end{equation}
 
 \end_inset
 
@@ -30437,8 +30713,10 @@ spce
 something
 \series default
  is inserted instead, the star prevents the parentheses around the expression:
-\begin_inset Formula \[
-A+B=C\tag*{something}\]
+\begin_inset Formula 
+\[
+A+B=C\tag*{something}
+\]
 
 \end_inset
 
@@ -30820,8 +31098,10 @@ numberwithin{equation}{section}
 \end_inset
 
 
-\begin_inset Formula \begin{equation}
-A+B=C\end{equation}
+\begin_inset Formula 
+\begin{equation}
+A+B=C
+\end{equation}
 
 \end_inset
 
@@ -31232,8 +31512,10 @@ roman{equation}}
 \end_layout
 
 \begin_layout Standard
-\begin_inset Formula \begin{equation}
-A=\textrm{small roman}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+A=\textrm{small roman}
+\end{equation}
 
 \end_inset
 
@@ -31255,8 +31537,10 @@ Roman{equation}}
 \end_inset
 
 
-\begin_inset Formula \begin{equation}
-B=\textrm{big Roman}\label{eq:Rom}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+B=\textrm{big Roman}\label{eq:Rom}
+\end{equation}
 
 \end_inset
 
@@ -31278,8 +31562,10 @@ alph{equation}}
 \end_inset
 
 
-\begin_inset Formula \begin{equation}
-C=\textrm{small Latin}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+C=\textrm{small Latin}
+\end{equation}
 
 \end_inset
 
@@ -31301,8 +31587,10 @@ Alph{equation}}
 \end_inset
 
 
-\begin_inset Formula \begin{equation}
-D=\textrm{big Latin}\label{eq:Lat}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+D=\textrm{big Latin}\label{eq:Lat}
+\end{equation}
 
 \end_inset
 
@@ -31355,8 +31643,10 @@ arabic{equation}}
 \end_inset
 
 
-\begin_inset Formula \begin{equation}
-E=\textrm{Arabic}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+E=\textrm{Arabic}
+\end{equation}
 
 \end_inset
 
@@ -31449,8 +31739,10 @@ The
 
 .
  The chemical equation for this is:
-\begin_inset Formula \begin{equation}
-\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}\end{equation}
+\begin_inset Formula 
+\begin{equation}
+\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
+\end{equation}
 
 \end_inset
 
@@ -32226,7 +32518,8 @@ reference "eq:TEOS-reaction-2"
 
  are an example of a multi-stage chemical reaction where every equation
  has its own number.
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula 
+\begin{eqnarray}
 \ce{TEOS + 4O} & \ce{->} & \ce{Si(OH)4 + 4C2H4O}\label{eq:TEOS-reaction-1}\\
 \ce{Si(OH)4} & \ce{->} & \ce{SiO2 + 2H2O}\label{eq:TEOS-reaction-2}
 \end{eqnarray}
@@ -32286,13 +32579,6 @@ key "mhchem"
 .
 \end_layout
 
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
-\end_layout
-
 \begin_layout Section
 Diagrams
 \end_layout
@@ -32326,11 +32612,13 @@ Diagrams ! amscd
 \begin_layout Standard
 Diagrams of this type visualize relations by vertical and horizontal lines
  or arrows:
-\begin_inset Formula \[
+\begin_inset Formula 
+\[
 \begin{CD}A@>>>B@>>>C\\
 @AAA@.@VVV\\
 F@<<<E@<<<D
-\end{CD}\]
+\end{CD}
+\]
 
 \end_inset
 
@@ -32438,11 +32726,13 @@ As example a diagram with all possible relations:
 \end_layout
 
 \begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula 
+\[
 \begin{CD}A@>j>>B@>>k>C@=F\\
 @AmAA@.@VV{V}V@|\\
 D@<<j<E@>k>>F@=C
-\end{CD}\]
+\end{CD}
+\]
 
 \end_inset
 
@@ -33355,14 +33645,18 @@ User-defined commands are especially convenient for complex expressions.
  When you are for example dealing in a document with quadratic equations,
  the same solution type occurs several times.
  The general form of a quadratic equation is
-\begin_inset Formula \[
-0=\lambda^{2}+p\lambda+q\]
+\begin_inset Formula 
+\[
+0=\lambda^{2}+p\lambda+q
+\]
 
 \end_inset
 
 The general form of the solution is
-\begin_inset Formula \[
-\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
+\begin_inset Formula 
+\[
+\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
+\]
 
 \end_inset
 
@@ -33691,8 +33985,10 @@ Here is our macro example with the arguments
 \end_layout
 
 \begin_layout Standard
-\begin_inset Formula \[
-\qG x{\ln(x)}B\]
+\begin_inset Formula 
+\[
+\qG x{\ln(x)}B
+\]
 
 \end_inset
 
@@ -33854,7 +34150,6 @@ The macro toolbar contains from left to right the following buttons:
 \begin_layout Plain Layout
 \begin_inset Graphics
 	filename ../images/math-macro-remove-param.png
-	BoundingBox 0bp 5bp 20bp 25bp
 	rotateOrigin center
 
 \end_inset
@@ -33890,7 +34185,6 @@ Remove Last Argument
 \begin_layout Plain Layout
 \begin_inset Graphics
 	filename ../images/math-macro-add-param.png
-	BoundingBox 0bp 5bp 20bp 25bp
 	rotateOrigin center
 
 \end_inset
@@ -33926,7 +34220,6 @@ Append Argument
 \begin_layout Plain Layout
 \begin_inset Graphics
 	filename ../images/math-macro-make-optional.png
-	BoundingBox 0bp 5bp 20bp 25bp
 	rotateOrigin center
 
 \end_inset
@@ -33985,7 +34278,6 @@ Optional Argument
 \begin_layout Plain Layout
 \begin_inset Graphics
 	filename ../images/math-macro-make-nonoptional.png
-	BoundingBox 0bp 5bp 20bp 25bp
 	rotateOrigin center
 
 \end_inset
@@ -34044,7 +34336,6 @@ Non-Optional Argument
 \begin_layout Plain Layout
 \begin_inset Graphics
 	filename ../images/math-macro-remove-optional-param.png
-	BoundingBox 0bp 5bp 20bp 25bp
 	rotateOrigin center
 
 \end_inset
@@ -34080,7 +34371,6 @@ Remove Optional Argument
 \begin_layout Plain Layout
 \begin_inset Graphics
 	filename ../images/math-macro-add-optional-param.png
-	BoundingBox 0bp 5bp 20bp 25bp
 	rotateOrigin center
 
 \end_inset
@@ -34116,7 +34406,6 @@ Insert Optional Argument
 \begin_layout Plain Layout
 \begin_inset Graphics
 	filename ../images/math-macro-remove-greedy-param.png
-	BoundingBox 0bp 5bp 20bp 25bp
 	rotateOrigin center
 
 \end_inset
@@ -34175,7 +34464,6 @@ Spitting Out To The Right
 \begin_layout Plain Layout
 \begin_inset Graphics
 	filename ../images/math-macro-append-greedy-param.png
-	BoundingBox 0bp 5bp 20bp 25bp
 	rotateOrigin center
 
 \end_inset
@@ -34234,7 +34522,6 @@ Eating From The Right
 \begin_layout Plain Layout
 \begin_inset Graphics
 	filename ../images/math-macro-add-greedy-optional-param.png
-	BoundingBox 0bp 5bp 20bp 25bp
 	rotateOrigin center
 
 \end_inset
@@ -34293,6 +34580,148 @@ Eating From The Right
 
 \end_layout
 
+\begin_layout Section
+Computer Algebra Systems
+\end_layout
+
+\begin_layout Standard
+LyX offers the exchange between mathematical expressions written in LyX's
+ math editor and external applications or user defined scripts.
+ Currently supported applications are 
+\family sans
+Maple
+\family default
+, 
+\family sans
+Mathematica
+\family default
+, 
+\family sans
+Maxima
+\family default
+ and 
+\family sans
+Octave
+\family default
+.
+ Note that the set of supported mathematical constructs is limited only
+ to very simple cases.
+\end_layout
+
+\begin_layout Subsection
+Usage
+\end_layout
+
+\begin_layout Standard
+Write some expression in a formula, go to the 
+\family sans
+Edit\SpecialChar \menuseparator
+Math\SpecialChar \menuseparator
+Use Computer Algebra System
+\family default
+ menu and choose the application you have installed on the computer.
+ After that the result of computation should show on the right side of the
+ expression together with the 
+\begin_inset Quotes eld
+\end_inset
+
+=
+\begin_inset Quotes erd
+\end_inset
+
+ operator.
+\end_layout
+
+\begin_layout Standard
+Here are few simple examples (with results from 
+\family typewriter
+Maxima
+\family default
+) to show what kind of computations can be performed:
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\frac{37}{3}*2-\sum_{i=1}^{3}i^{i}=-\frac{22}{3}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\frac{37.0}{3}=12.33333333333333$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\int_{1}^{2}\sin(x)dx=\cos1-\cos2$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\det\left[\begin{array}{ccc}
+1 & 6 & 7\\
+2 & 5 & 8\\
+3 & 4 & 17
+\end{array}\right]=-56$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $\lim_{x\rightarrow0}\left(\frac{\sin(x)}{x}\right)=1$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Keyboard shortcut
+\end_layout
+
+\begin_layout Standard
+Currently there is no keyboard shortcut for calling the algebra applications.
+ One can easily bind a shortcut to the 
+\family sans
+math-extern
+\family default
+ LyX function (see the 
+\family sans
+\emph on
+LyX Functions
+\family default
+\emph default
+ manual).
+ One could e.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
+\begin_inset space ~
+\end_inset
+
+bind the 
+\family sans
+Return
+\family default
+ key inside the math editor.
+ To bind it to 
+\family typewriter
+Maxima
+\family default
+ one would use this shortcut definition command:
+\end_layout
+
+\begin_layout Standard
+
+\series bold
+command-alternatives break-paragraph;math-extern maxima
+\end_layout
+
 \begin_layout Standard
 \begin_inset Newpage newpage
 \end_inset
@@ -34729,8 +35158,10 @@ The command
 Braket
 \series default
  assures that all vertical bars are set in the size of the surrounding brackets:
-\begin_inset Formula \[
-\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
+\begin_inset Formula 
+\[
+\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
+\]
 
 \end_inset
 
@@ -35109,7 +35540,8 @@ genfrac{}{}{#1}{}{#2}{#3}}
 
 \begin_layout Standard
 A test:
-\begin_inset Formula \begin{align*}
+\begin_inset Formula 
+\begin{align*}
 \text{Command} &  & \mathrm{\backslash fracS[1mm]\backslash\{A\to\backslash\{B} &  & \mathrm{\backslash fracS[5mm]\backslash\{A\to\backslash\{B}\\
 \text{Result} &  & \fracS[1mm]{A}{B} &  & \fracS[5mm]{A}{B}
 \end{align*}
@@ -35418,8 +35850,10 @@ A=B
 cancelto
 \series default
  is especially suitable to visualize the reduction of fractions within formulas:
-\begin_inset Formula \[
-\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
+\begin_inset Formula 
+\[
+\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}
+\]
 
 \end_inset
 
@@ -35937,8 +36371,10 @@ end{multicols}
 \end_inset
 
 
-\begin_inset Formula \begin{equation}
-S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi\end{equation}
+\begin_inset Formula 
+\begin{equation}
+S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
+\end{equation}
 
 \end_inset
 
@@ -36171,12 +36607,14 @@ reference "eq:within"
 
  consists of five columns whereas in the first two columns contain the equation,
  the third the matrix and the last one an empty TeX-brace.
-\begin_inset Formula \begin{flalign}
+\begin_inset Formula 
+\begin{flalign}
 \hspace{30pt}F_{A} & =\rho·V·g & \footnotesize\begin{array}{ll}
 \rho & \textrm{density}\\
 V & \textrm{volume}\\
 g & \textrm{gravitational acceleration}
-\end{array} &  & {}\label{eq:within}\end{flalign}
+\end{array} &  & {}\label{eq:within}
+\end{flalign}
 
 \end_inset
 
@@ -36324,8 +36762,10 @@ uptau
 
 \begin_layout Standard
 With these commands reactions of elementary particles can be typeset:
-\begin_inset Formula \[
-\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
+\begin_inset Formula 
+\[
+\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
+\]
 
 \end_inset