\input dua0:[tex.amstex]amstex
\documentstyle{dua0:[tex.amstex]amsppt}

\comment
This file is to test out the various capabilities of AMS-TEX.
\endcomment



\topmatter
\title
A test of the \AmSTeX\ typesetting macros
\endtitle

\author
Tex Willer \\ Arizona 
\endauthor

\address{Somewhere  USA}

\date{22 October 1934}

\thanks{Many thanks must be given to no one in particular}

\keywords{Obviously irrelevant}

\subjclass{Irrelevant too}

\abstract{Yes, this test is pretty abstract, isn't it?}
\endtopmatter
\document
\heading A test of Amstex \\ amsppt style \endheading
Here is some irrelevant information.

\proclaim{Theorem 1}
You can lead a horse to water, but you can't make him drink.
\finishproclaim

\demo{Proof}
The proof 
by mathematical induction
is left as an exercise to the reader.
\finishdemo

\noindent
Of course, we can also refer \refto{10} to a nonexistent reference.



\subheading{Mathematics}
Now, lets get into some math mode stuff.  Try a few greek letters

$$ \alpha + \beta = \gamma + \delta.$$

\def\Evec{{\bf E}}
\def\Bvec{{\bf B}}
\def\Hvec{{\bf H}}
\def\Dvec{{\bf D}}
\def\Jvec{{\bf J}}

\noindent
How about Maxwell's equations?  They are, in CGS units
$$\nabla \cdot \Dvec = 4 \pi \rho ,$$
$$\nabla \cdot \Bvec = 0,$$
$$\nabla \times \Evec + {1 \over c} 
  {{\partial \Bvec} \over {\partial t}} = 0,$$
$$\nabla \times \Hvec - {1 \over c} {{\partial \Dvec} \over {\partial t}} =
  {{4 \pi} \over {c}} \Jvec.$$

There is a family of particles

$$\psi,$$
$$\psi^\prime ,$$
$$\psi^{\prime\prime},$$

and so forth.

Let's try a footnote\footnote{This footnote is obviously irrelevant}
and see how well it works.

This one is cute

$$\left.\frac {dy}{dx}\right|_{x=a};$$

\noindent
but does it work?

The math mode is actually quite smart.  One can actually imbed lots of
large symbols inline in text, and have the program do exactly the 
correct thing.  To see this let us typeset 
$\sum\limits_{i=1}^Na_i$, and see if it really leaves the correct amount
of space around the document.  It certainly does appear to do the correct
thing.

Now some subtleties.  Try

$$\sum_{\stack{\ssize 1\le i\le N}{\ssize 1\le j \le M}}a_{ij}$$

\noindent
and see if it works.

Another test is

$$\align (a+b)(a-b) &=(a+b)a - (a+b)b\\
                    &= a^2 +ab - ab - b^2\\
                    &=a^2 - b^2,
  \endalign$$

\noindent
to see whether or not alignment works.

Matrices are easy

$$\matrixp \format \c&&\;\c\\
a_{11}&a_{12}&\ldots&a_{1n}\\
a_{21}&a_{22}&\ldots&a_{2n}\\
\vdots&\vdots&\ddots&\vdots\\
a_{m1}&a_{m2}&\ldots&a_{mn}\\
\endmatrixp$$

Finally, some under braces.

$$
\underbrace{x_1+x_2+\dots+x_n}
$$   

That's all folks!
\Refs
\ref \no 9 \by S. S. Chern \pages 947--1055
\paper Integral formulas for hypersurfaces in Euclidean space and their applications
to uniqueness theorems
\yr 1959 \vol 8
\jour J. Math. Mech.
\endref
\enddocument
\bye