Matt's Latex Playground Page

This page may turn into a tutorial

A latex example:

<latex> 
\frac{1+\frac{1}{x}}{3x + 2}

\dbinom{9}{3}
</latex>

=====Pictures=====
<latex>

\setlength{\unitlength}{0.8cm}
\begin{picture}(6,4)(-3,-2)
\put(-2.5,0){\vector(1,0){5}}
\put(2.7,-0.1){$\chi$}
\put(0,-1.5){\vector(0,1){3}}
\put(0.2,1.4){$\beta=v/c=\tanh\chi$}

\qbezier(0,0)(0.8853,0.8853)(2,0.9640)

\qbezier(0,0)(-0.8853,-0.8853)(-2,-0.9640)

\end{picture}

</latex>
\\
\\
<latex>
\setlength{\unitlength}{0.8cm}
\begin{picture}(6,5)
\thicklines
\put(1,0.5){\line(2,1){3}}
\put(4,2){\line(-2,1){2}}
\put(2,3){\line(-2,-5){1}}
\put(0.7,0.3){$A$}
\put(4.05,1.9){$B$}
\put(1.7,2.95){$C$}
\put(3.1,2.5){$a$}
\put(1.3,1.7){$b$}
\put(2.5,1.05){$c$}
\put(0.3,4){$F=
\sqrt{s(s-a)(s-b)(s-c)}$}
\put(3.5,0.4){$\displaystyle
s:=\frac{a+b+c}{2}$}
\end{picture}
\\
\\
\setlength{\unitlength}{0.8cm}
\begin{picture}(6,4)(-3,-2)
\put(-2.5,0){\vector(1,0){5}}
\put(2.7,-0.1){$\chi$}
\put(0,-1.5){\vector(0,1){3}}
\multiput(-2.5,1)(0.4,0){13}
{\line(1,0){0.2}}
\multiput(-2.5,-1)(0.4,0){13}
{\line(1,0){0.2}}
\put(0.2,1.4)
{$\beta=v/c=\tanh\chi$}
\qbezier(0,0)(0.8853,0.8853)
(2,0.9640)
\qbezier(0,0)(-0.8853,-0.8853)
(-2,-0.9640)
\put(-3,-2){\circle*{0.2}}
\end{picture}

</latex>

=====Matrices=====
<latex>
The characteristic polynomial $f(\lambda)$ of the
$3 \times 3$ matrix
\[
\left(
\begin{array}{ccc}
a & b & c \\
d & e & f \\
g & h & i \end{array}
\right)\]
is given by the equation
\[ f(\lambda)
= \left|
\begin{array}{ccc}
\lambda - a & -b & -c \\
-d & \lambda - e & -f \\
-g & -h & \lambda - i \end{array}
\right|.\]
</latex>
====shorthand matrices=====
<latex>
The characteristic polynomial $f(\lambda)$ of the
$3 \times 3$ matrix
\[
\begin{pmatrix}
a & b & c \\
d & e & f \\
g & h & i
\end{pmatrix} \]
is given by the equation
\[ f(\lambda)
= \begin{vmatrix}
\lambda - a & -b & -c \\
-d & \lambda - e & -f \\
-g & -h & \lambda - i
\end{vmatrix}.\]
</latex>

=====An equation I hope to display in a block====
<latex>
\begin{array}{2}
-1(3x +  y  - 3z = 11)\\
\underline{+3x - 3y + 2z = 11}\\
.\end{array} \\
\theta
</latex>

<latex>
    (3x - 3y + 2z = 11)+(-1(3x +  y  - 3z = 11))=> -4y + 5z = 0
\cdots
\ddots
</latex>

=====One more=====

<latex>
    \frac{3}{4 \pi}   \sqrt{4 \cdot x^2   12}\\
    \lim_{n \to \infty}
    \sum_{k=1}^n \frac{1}{k^2} = \frac{\pi^2}{6}\\
    \it{f}(x) = \frac{1}{\sqrt{x} x^2}\\
    e^{i \pi} + 1 = 0\;
</latex>

=====Other math I'm not familiar with=====

<latex>
 $ \begin{align*}
\int x^2 dx & = \frac{1}{3}x^3\\ 
\therefore\quad\int_0^1 x^2 dx &= \frac{1}{3}
\end{align*}
$ 
</latex>

And some more:

<latex>
\begin{tabular}{|l|l|p{9cm}|}
\hline
option & variants & explanation \\
\hline
id & unique string & Identifies the user uniquely.\\
\hline
logmask & ALL & Log everything \\
\cline{2-3}
& DBG & Log only debug \\
\cline{2-3}
& WARN & Log only warning messages \\
\hline
printTID & flag & Print Thread ID or not.\\
\hline
prefix & any string & With this will be prefixed all messages of this user.\\
\hline
p & p & p \\
\hline
p & p & p \\
\hline
p & p & p \\
\hline
p & p & p \\
\hline
\end{tabular}
</latex>


\\
=====More ...=====
\\
\\
<latex>

\setlength{\unitlength}{0.8cm}
\begin{picture}(6,4)(-3,-2)
\put(-2.5,0){\vector(1,0){5}}
\put(2.7,-0.1){$\chi$}
\put(0,-1.5){\vector(0,1){3}}
\put(0.2,1.4){$\beta=v/c=\tanh\chi$}

\qbezier(0,0)(0.8853,0.8853)(2,0.9640)

\qbezier(0,0)(-0.8853,-0.8853)(-2,-0.9640)

\end{picture}

</latex>
=====yet more=====
<latex>
\documentclass[14pt]{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{eurosym}
\usepackage{ucs}
\usepackage[utf8x]{inputenc}
\usepackage{amssymb}
\pagestyle{empty}
\begin{document}
$a^2+b^2=c^2$
\Latex2e\ ist nett!
\end{document}
</latex>