# Copyright: (c) 2007 The Open University, Milton Keynes, UK.
# License: GPL version 2 or (at your option) any later version.
# Author: Jonathan Fine <jfine@pytex.org>, <J.Fine@open.ac.uk>
# $Source: /cvsroot/mathtran/website/txt/examples.txt,v $
# $Revision: 1.3 $ $Date: 2007/04/23 10:08:44 $

# Examples are separated by '\n=====\n'.
=====
math=Math basics
Use \$\dots\$ for math in running text, and \$\$\dots\$\$
for display math.  Use \^{}  and \_ for superscripts and
subscripts.  Use $\{$ and $\}$ for compound scripts.  
Greek letters are accessed using their name.

Some examples: $\alpha_2^{n+1}$, $\Gamma(2)$, $\zeta(3)$ and
$$a^2 + b^2 = c^2$$
=====
roots=Square roots, cube roots, etc
$\sqrt{2}$, $\root 3\of{x+1}$.
$$
\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1}}}}
$$
=====
binop=Binary operators
Don't use `x', use times: $2 \times 2 = 4$.

There are lots of other binary operators: $ a \le b \le c$.

And some more: $A_i \otimes A_j \subseteq A_{i+j}$.
=====
frac=Fractions
Plain \TeX\ uses an `over' command, while La\TeX\ has
a 'frac' command.  Just for now, we provide both.
$${1\over3} + \frac{1}{6} = \frac{1}{2}$$
=====
contfrac=Continued fractions
A good part of the trick here is to use `displaystyle'.
$$ a + \frac{1}{\displaystyle b + 
\frac{1}{\displaystyle c + \frac{1}{d}}}$$

Here's what it looks like without the `displaystyle'.
$$ a + \frac{1}{b + \frac{1}{c + \frac{1}{d}}}$$
=====
para=Setting paragraphs
Use blank lines to separate paragraphs. 
Use blank lines to separate paragraphs. 
Use blank lines to separate paragraphs. 
Use blank lines to separate paragraphs. 

Use blank lines to separate paragraphs. 
Use blank lines to separate paragraphs. 
Use blank lines to separate paragraphs. 
Use blank lines to separate paragraphs. 
=====
cases=Displaying several cases
Depending on the value of $d = b^2 -4ac$, a
the number $n$ of roots is:
$$n = \cases{2&if $d >0$ (two real roots)\cr
    1&if $d = 0$ (one double root)\cr
    0&if $d <0$ (no real roots)\cr
}$$
=====
matrices=Matrices
$$A = \pmatrix{a&b&c\cr d&e&f\cr g&h&i\cr}$$
=====
delim=Delimiters that grow
Compare 
$$(q - \frac{1}{p})^n \quad{\rm with}\quad
\left(q - \frac{1}{p}\right)^n$$.

Compare
$$\left\lfloor \sum_{k=1}^n \frac{1}{k} \right\rfloor
\quad{\rm with}\quad
\lfloor \sum_{k=1}^n \frac{1}{k} \rfloor
$$
=====
eqalign=Aligned equations
$$\eqalign{
 (a+b)(a-b) &= a^2 -ab + ba - b^2\cr
  &= a^2 - b^2\cr
}$$
=====
greek=Greek letters
Well there's $\alpha$, $\beta$, $\gamma$ and $\delta$.

And $\epsilon$, $\zeta$, $\eta$ and $\theta$.

And $\iota$, $\kappa$, $\lambda$ and $\mu$.

And quite a few more.  A table would be nice.