\font_osf false
\font_sf_scale 100
\font_tt_scale 100
+
\graphics default
\default_output_format default
\output_sync 0
\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"
+\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
\tracking_changes false
\output_changes false
\html_math_output 0
+\html_css_as_file 0
\html_be_strict false
\end_header
\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*}
frac
\series default
:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\cfrac{A}{B+\cfrac{C+\frac{E}{F}}{D}}
\]
dots
\series default
:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\left(\begin{array}{cccc}
A & B & C & D\\
\hdotsfor[2]{4}\\
)
\series default
creates
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\ln(\frac{A}{C})
\]
right)
\series default
creates
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\ln\left(\frac{A}{C}\right)
\]
creates:
\series bold
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\left.\frac{A}{B}\right\}
\]
\end_inset
needed for physical vectors:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\left\langle \phi\:\middle|\: J=\frac{3}{2}\,,\, M_{J}\right\rangle
\]
\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*}
\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*}
n
\series default
produces:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\sideset{}{'}\sum_{k=1}^{n}
\]
a
\series default
produces:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\overset{a}{\maltese}
\]
\series default
will only be set in the output with a length of three characters, as shown
in the following example:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\widetilde{A+B=C-D}
\]
***
\series default
creates:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\underset{***}{A=B}
\]
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\boxed{A+B=C}
\]
\begin_layout Standard
\color red
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\int A=B\label{eq:red}
\end{equation}
\color green
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\textcolor{red}{\int A=B}\label{eq:redgreen}
\end{equation}
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\fcolorbox{cyan}{magenta}{A=B}
\]
yellow
\series default
:
-\begin_inset Formula \begin{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
-\begin_inset Formula \begin{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
using the mathematical textmode:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
5x-7b=3b\textrm{This is a description. It is not separated from the formula ...}
\]
\begin_layout Standard
The default limits type is this:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\sum_{x=0}^{\infty}\frac{1}{x^{2}}
\]
\family default
\series default
:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\sum\nolimits _{x=0}^{\infty}\frac{1}{x^{2}}
\]
Display
\series default
and so set below the integrals:
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\iiint\limits _{V}X\,\mathrm{d}V=U\label{eq:VolInt}
\end{equation}
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\\
\\
\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}
\end_inset
:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\Lozenge_{n=1}^{\infty}
\]
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\mathop{\sum\negmedspace\sum}_{i,j=1}^{N}
\]
\begin_layout Standard
The style commands work also for letters in mathematical constructs:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\mathfrak{A=\frac{b}{C}}
\]
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\mathbf{\int_{n}^{2}f(\theta)=\Gamma}\qquad\textrm{equation with \textbackslash mathbf}
\]
boldsymbol
\series default
is used:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\boldsymbol{\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation with \textbackslash boldsymbol}}
\]
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\int_{n}^{2}f(\theta)=\Gamma\qquad\textrm{equation in a boldmath environment}
\]
\family default
dialog.
Here is a formula in magenta:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
{\color{magenta}\int A\,\mathrm{d}x=\frac{\sqrt[5]{B}}{\ln\left(\frac{1}{3}\right)}}
\]
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\int A\,\mathrm{d}x=\frac{{\color{red}\sqrt[5]{B}}}{\ln\left(\frac{1}{3}\right)}
\]
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
A=\frac{B}{c}\cdot\maltese
\]
\end_inset
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\maltese A\textrm{\Large\maltese\textit{A}}\textrm{\tiny\maltese\textit{A}}
\]
\begin_layout Standard
In a displayed formula the limit is set below the formula, as usual:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\lim_{x\to A}x=B
\]
\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\\
\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*}
\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*}
\end_inset
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
A & = & B\\
C & \ne & A
\end{eqnarray*}
\end_inset
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
A & = & B\\
C & \ne & A
\end{eqnarray*}
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}
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}
\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*}
\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*}
\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*}
\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*}
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*}
\end_inset
:
-\begin_inset Formula \begin{flalign}
+\begin_inset Formula
+\begin{flalign}
\hspace{30pt}\iiint\limits _{V}X\,\mathrm{d}V & =U & {}
\end{flalign}
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
\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}
\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}}
\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}}
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}
\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}
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}
\begin_layout Standard
An example:
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
A=C-B\label{eq:a}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
B=C-A\label{eq:b}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
C=A+B\label{eq:c}
\end{equation}
\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}
\end_inset
is used:
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
A+B=C\tag{something}\label{eq:tag}
\end{equation}
something
\series default
is inserted instead, the star prevents the parentheses around the expression:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
A+B=C\tag*{something}
\]
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
A+B=C
\end{equation}
\end_layout
\begin_layout Standard
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
A=\textrm{small roman}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
B=\textrm{big Roman}\label{eq:Rom}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
C=\textrm{small Latin}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
D=\textrm{big Latin}\label{eq:Lat}
\end{equation}
\end_inset
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
E=\textrm{Arabic}
\end{equation}
.
The chemical equation for this is:
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\mathrm{2\, Na^{+}+SO_{4}^{2-}\longrightarrow Na_{2}SO_{4}}\label{eq:chem-reaction}
\end{equation}
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}
\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_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
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 \[
+\begin_inset Formula
+\[
0=\lambda^{2}+p\lambda+q
\]
\end_inset
The general form of the solution is
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\lambda_{1,2}=-\frac{p}{2}\pm\sqrt{\frac{p²}{4}-q}
\]
\end_layout
\begin_layout Standard
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\qG x{\ln(x)}B
\]
Braket
\series default
assures that all vertical bars are set in the size of the surrounding brackets:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\Braket{\phi|J=\frac{3}{2}\,,\, M_{J}}
\]
\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*}
cancelto
\series default
is especially suitable to visualize the reduction of fractions within formulas:
-\begin_inset Formula \[
+\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
-\begin_inset Formula \begin{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}
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}\\
\begin_layout Standard
With these commands reactions of elementary particles can be typeset:
-\begin_inset Formula \[
+\begin_inset Formula
+\[
\uppi^{+}\to\upmu^{+}+\upnu_{\upmu}
\]
projects / features.git / commitdiff