#LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
-\lyxformat 401
+\lyxformat 410
\begin_document
\begin_header
\textclass scrartcl
\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
% 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
% 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}
\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
\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
\use_indices false
\paperorientation portrait
\suppress_date false
+\use_refstyle 0
+\notefontcolor #0000ff
\index Index
\shortcut idx
\color #008000
\series default
\series bold
-mhchem, multirow
+mhchem
\series default
and
\series bold
\series default
:
\begin_inset Formula \[
-\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}\]
+\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
+\]
\end_inset
\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">
</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
\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
\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
\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
A & B & C & D\\
\hdotsfor[2]{4}\\
q & w & e & r
-\end{array}\right)\]
+\end{array}\right)
+\]
\end_inset
\series default
creates
\begin_inset Formula \[
-\ln(\frac{A}{C})\]
+\ln(\frac{A}{C})
+\]
\end_inset
\series default
creates
\begin_inset Formula \[
-\ln\left(\frac{A}{C}\right)\]
+\ln\left(\frac{A}{C}\right)
+\]
\end_inset
\series bold
\begin_inset Formula \[
-\left.\frac{A}{B}\right\} \]
+\left.\frac{A}{B}\right\}
+\]
\end_inset
needed for physical vectors:
\begin_inset Formula \[
-\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle \]
+\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
+\]
\end_inset
\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"
\series default
produces:
\begin_inset Formula \[
-\sideset{}{'}\sum_{k=1}^{n}\]
+\sideset{}{'}\sum_{k=1}^{n}
+\]
\end_inset
\series default
produces:
\begin_inset Formula \[
-\overset{a}{\maltese}\]
+\overset{a}{\maltese}
+\]
\end_inset
will only be set in the output with a length of three characters, as shown
in the following example:
\begin_inset Formula \[
-\widetilde{A+B=C-D}\]
+\widetilde{A+B=C-D}
+\]
\end_inset
\series default
creates:
\begin_inset Formula \[
-\underset{***}{A=B}\]
+\underset{***}{A=B}
+\]
\end_inset
\begin_inset Formula \[
-\boxed{A+B=C}\]
+\boxed{A+B=C}
+\]
\end_inset
\color red
\begin_inset Formula \begin{equation}
-\int A=B\label{eq:red}\end{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}
+\textcolor{red}{\int A=B}\label{eq:redgreen}
+\end{equation}
\end_inset
\begin_inset Formula \[
-\fcolorbox{cyan}{magenta}{A=B}\]
+\fcolorbox{cyan}{magenta}{A=B}
+\]
\end_inset
\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}
+\colorbox{darkgreen}{\color{yellow}\boxed{\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}}
+\end{equation}
\end_inset
\begin_inset Formula \begin{equation}
-\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}\end{equation}
+\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}
+\end{equation}
\end_inset
using the mathematical textmode:
\begin_inset Formula \[
-5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}\]
+5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
+\]
\end_inset
\begin_layout Standard
The default limits type is this:
\begin_inset Formula \[
-\sum_{x=0}^{\infty}\frac{1}{x^{2}}\]
+\sum_{x=0}^{\infty}\frac{1}{x^{2}}
+\]
\end_inset
\series default
:
\begin_inset Formula \[
-\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}\]
+\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
+\]
\end_inset
\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}
+\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
+\end{equation}
\end_inset
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
\\
k\,\in\,\mathbb{N}
}
-}}^{n}k^{-2}\]
+}}^{n}k^{-2}
+\]
\end_inset
:
\begin_inset Formula \[
-\Lozenge_{n=1}^{\infty}\]
+\Lozenge_{n=1}^{\infty}
+\]
\end_inset
\begin_layout Standard
\begin_inset Formula \[
-\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}\]
+\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
+\]
\end_inset
\begin_layout Standard
The style commands work also for letters in mathematical constructs:
\begin_inset Formula \[
-\mathfrak{A=\frac{b}{C}}\]
+\mathfrak{A=\frac{b}{C}}
+\]
\end_inset
\begin_layout Standard
\begin_inset Formula \[
-\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}\]
+\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
+\]
\end_inset
\series default
is used:
\begin_inset Formula \[
-\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}\]
+\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
+\]
\end_inset
\begin_inset Formula \[
-\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}\]
+\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
+\]
\end_inset
dialog.
Here is a formula in magenta:
\begin_inset Formula \[
-{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}\]
+{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
+\]
\end_inset
\begin_inset Formula \[
-\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}\]
+\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
+\]
\end_inset
\begin_inset Formula \[
-A=\frac{B}{c}\cdot\maltese\]
+A=\frac{B}{c}\cdot\maltese
+\]
\end_inset
\begin_inset Formula \[
-\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}\]
+\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
+\]
\end_inset
\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
\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
\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"
\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
\begin_layout Standard
In a displayed formula the limit is set below the formula, as usual:
\begin_inset Formula \[
-\lim_{x\to A}x=B\]
+\lim_{x\to A}x=B
+\]
\end_inset
:
\begin_inset Formula \begin{flalign}
-\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}\end{flalign}
+\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
+\end{flalign}
\end_inset
\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
\begin_layout Standard
An example:
\begin_inset Formula \begin{equation}
-A=C-B\label{eq:a}\end{equation}
+A=C-B\label{eq:a}
+\end{equation}
\end_inset
\begin_inset Formula \begin{equation}
-B=C-A\label{eq:b}\end{equation}
+B=C-A\label{eq:b}
+\end{equation}
\end_inset
\begin_inset Formula \begin{equation}
-C=A+B\label{eq:c}\end{equation}
+C=A+B\label{eq:c}
+\end{equation}
\end_inset
is used:
\begin_inset Formula \begin{equation}
-A+B=C\tag{something}\label{eq:tag}\end{equation}
+A+B=C\tag{something}\label{eq:tag}
+\end{equation}
\end_inset
\series default
is inserted instead, the star prevents the parentheses around the expression:
\begin_inset Formula \[
-A+B=C\tag*{something}\]
+A+B=C\tag*{something}
+\]
\end_inset
\begin_inset Formula \begin{equation}
-A+B=C\end{equation}
+A+B=C
+\end{equation}
\end_inset
\begin_layout Standard
\begin_inset Formula \begin{equation}
-A=\textrm{small roman}\end{equation}
+A=\textrm{small roman}
+\end{equation}
\end_inset
\begin_inset Formula \begin{equation}
-B=\textrm{big Roman}\label{eq:Rom}\end{equation}
+B=\textrm{big Roman}\label{eq:Rom}
+\end{equation}
\end_inset
\begin_inset Formula \begin{equation}
-C=\textrm{small Latin}\end{equation}
+C=\textrm{small Latin}
+\end{equation}
\end_inset
\begin_inset Formula \begin{equation}
-D=\textrm{big Latin}\label{eq:Lat}\end{equation}
+D=\textrm{big Latin}\label{eq:Lat}
+\end{equation}
\end_inset
\begin_inset Formula \begin{equation}
-E=\textrm{Arabic}\end{equation}
+E=\textrm{Arabic}
+\end{equation}
\end_inset
.
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}
+\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
+\end{equation}
\end_inset
\begin{CD}A@>>>B@>>>C\\
@AAA@.@VVV\\
F@<<<E@<<<D
-\end{CD}\]
+\end{CD}
+\]
\end_inset
\begin{CD}A@>j>>B@>>k>C@=F\\
@AmAA@.@VV{V}V@|\\
D@<<j<E@>k>>F@=C
-\end{CD}\]
+\end{CD}
+\]
\end_inset
the same solution type occurs several times.
The general form of a quadratic equation is
\begin_inset Formula \[
-0=\lambda^{2}+p\lambda+q\]
+0=\lambda^{2}+p\lambda+q
+\]
\end_inset
The general form of the solution is
\begin_inset Formula \[
-\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}\]
+\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
+\]
\end_inset
\begin_layout Standard
\begin_inset Formula \[
-\qG x{\ln(x)}B\]
+\qG x{\ln(x)}B
+\]
\end_inset
\begin_layout Plain Layout
\begin_inset Graphics
filename ../images/math-macro-remove-param.png
- BoundingBox 0bp 5bp 20bp 25bp
rotateOrigin center
\end_inset
\begin_layout Plain Layout
\begin_inset Graphics
filename ../images/math-macro-add-param.png
- BoundingBox 0bp 5bp 20bp 25bp
rotateOrigin center
\end_inset
\begin_layout Plain Layout
\begin_inset Graphics
filename ../images/math-macro-make-optional.png
- BoundingBox 0bp 5bp 20bp 25bp
rotateOrigin center
\end_inset
\begin_layout Plain Layout
\begin_inset Graphics
filename ../images/math-macro-make-nonoptional.png
- BoundingBox 0bp 5bp 20bp 25bp
rotateOrigin center
\end_inset
\begin_layout Plain Layout
\begin_inset Graphics
filename ../images/math-macro-remove-optional-param.png
- BoundingBox 0bp 5bp 20bp 25bp
rotateOrigin center
\end_inset
\begin_layout Plain Layout
\begin_inset Graphics
filename ../images/math-macro-add-optional-param.png
- BoundingBox 0bp 5bp 20bp 25bp
rotateOrigin center
\end_inset
\begin_layout Plain Layout
\begin_inset Graphics
filename ../images/math-macro-remove-greedy-param.png
- BoundingBox 0bp 5bp 20bp 25bp
rotateOrigin center
\end_inset
\begin_layout Plain Layout
\begin_inset Graphics
filename ../images/math-macro-append-greedy-param.png
- BoundingBox 0bp 5bp 20bp 25bp
rotateOrigin center
\end_inset
\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
\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
\series default
assures that all vertical bars are set in the size of the surrounding brackets:
\begin_inset Formula \[
-\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}\]
+\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
+\]
\end_inset
\series default
is especially suitable to visualize the reduction of fractions within formulas:
\begin_inset Formula \[
-\frac{\left(x_{0}+bB\right)^{2}}{\left(1+b^{2}\right)^{\cancelto{2}{3}}}=\frac{x_{0}^{2}+B^{2}-r_{g}^{2}}{\cancel{1+b^{2}}}\]
+\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
\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}
+S(t)=S_{0}(t)\int_{-\infty}^{\infty}P(\phi,t)\mathrm{e}^{\mathrm{i}\phi}\,\mathrm{d}\phi
+\end{equation}
\end_inset
\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
\begin_layout Standard
With these commands reactions of elementary particles can be typeset:
\begin_inset Formula \[
-\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}\]
+\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
+\]
\end_inset
projects / lyx.git / blobdiff