From: gmaltby@unpcs1.cs.unp.ac.za (Gavin Maltby)
Newsgroups: comp.text.tex
Subject: latex notes: 4 of 4
Summary: part 4 of 4
Keywords: latex notes
Date: 27 Jan 93 06:55:29 GMT
Organization: University of Natal, Pietermaritzburg, South Africa
NNTP-Posting-Host: pc038.cc.unp.ac.za

% part 4 of 4
Now let's see how to set a sub- or superscript that consists of more than
just one character.  This is no more difficult than before if we remember
the following rule: {\em \verb@_@ and \verb@^@ set the group that
follows them as a sub- and superscripts to the group that precedes
the sub- and superscript symbols.}  We see now now that our initial examples worked by considering a single
character to be a group by itself.  Here are some examples:

\begin{mathegs}
\verb@$a^2b^3$@ & $a^2b^3$\\
\verb@$2^{21}$@ & $2^{21}$\\
\verb@$2^21$@ & $2^21$\\
\verb@$a^{x+1}$@ & $a^{x+1}$\\
\verb@$a^{x^2+1}$@ & $a^{x^2+1}$\\
\verb@$(x+1)^3$@ & $(x+1)^3$\\
\verb@$\Gamma_{\alpha\beta\gamma}$@ & $\Gamma_{\alpha\beta\gamma}$\\
\verb@${}_1A_2$@ & ${}_1A_2$\\
\end{mathegs}

In the very last example we see a case of setting a subscript to 
an empty group, which
resulted in a kind of ``pre-subscript''.  With some imagination this
can be put to all sorts of uses.

In all of the above examples the sub- and superscripts were set
to single-character groups.  Nowhere did we group an expression 
before sub- or superscripting it.  Even in setting the expression
$(x+1)^3$, the superscript ${}^3$ was really only set to the
character $)$.  If we had wanted to group the $(x+1)$ before
setting the superscript, we would have typed \verb@${(x+1)}^3$@ which
gives ${(x+1)}^3$, with the superscript slightly raised.  One has
to go to this trouble because, to most people, something like
$(x^a)^b$ is just as acceptable and as readable as ${(x^a)}^b$.
It also has the advantage of aligning the base lines in expressions
such as 
$$
(ab)^{-2} = [(ab)^{-1}]^2 = [b^{-1}a^{-1}]^2 = b^{-1}a^{-1}b^{-1}a^{-1}
$$
which looks more pleasing than if we use additional grouping to force
$$
{(ab)}^{-2} = {[{(ab)}^{-1}]}^2 = {[b^{-1}a^{-1}]}^2 = b^{-1}a^{-1}b^{-1}a^{-1}\quad,
$$
and the latter has rather more braces in it that require balancing.

Here are some more examples, showing how \LaTeX\ will set things just as we
want without any further work on our part:

\begin{mathegs}
\verb@$x^{y^z}$@ & $x^{y^z}$\\
\verb@$2^{(2^2)}$@ & $2^{(2^2)}$\\
\verb@$2^{2^{2^{\aleph_0}}}$@ & $2^{2^{2^{\aleph_0}}}$\\
\verb@$\Gamma^{z_c^d}$@ & $\Gamma^{z_c^d}$
\end{mathegs}

We can also make use of empty groups in order to stagger sub- and
superscripts to an expression, as in

\moveright0.1\textwidth\vbox{
\footnotesize\begin{verbatim}
$\Gamma_{\alpha\beta}{}^{\gamma}{}_\delta$
\end{verbatim}
}
\noindent which will yield

\result{%
$\Gamma_{\alpha\beta}{}^{\gamma}{}_\delta$
}

One can specify the sub- and superscripts to a group in any order,
but it is best to be consistent.  The most natural order seems to 
be to have subscripts first, but you may think otherwise.
It is also a good idea to always include your sub- and superscripts
in braces (i.e.\ make them a group), whether they consist of just
a single character or not.  This enhances readability and also helps
avoid the unfortunate case where you believe that a particular control
word gives a single symbol yet it really is defined in terms of several.

\subsection{Primes}
\LaTeX\ provides the control word \verb@\prime@ ($\prime$) for
priming symbols.  Note that it is not automatically at the superscript
height, so that to get $f^\prime$ you would have to type

\moveright0.1\textwidth\vbox{
\footnotesize\begin{verbatim}
$f^\prime$ .
\end{verbatim}
}
\noindent  To make lighter work of this, \LaTeX\ will interpret
a right-quote character as a prime if used in maths mode.
Thus we can type

\moveright0.1\textwidth\vbox{
\footnotesize\begin{verbatim}
$f'(g(x)) g'(x) h''(x)$
\end{verbatim}
}
\noindent in order to get

\noindent

\result{%
$f'(g(x)) g'(x) h''(x)\quad.$
}

\subsection{Fractions}
\LaTeX\ provides the \verb@\frac@ command that accepts two
arguments: the numerator and the denominator (in that order).
Before we look at examples of its use, let us just note that many simple
in-text fractions are often better written in the form 
$\mbox{\it num} / \!\mbox{\it den}$, as with $3/8$ which can be typed
as \verb@$3/8$@.  This is also often the better form for 
a fraction that occurs {\em within\/} some expression.

\begin{mathegs}
\verb@$\frac{x+1}{x+2}$@ & $\displaystyle\frac{x+1}{x+2}$\\
\verb@$\frac{1}{x^2+1}$@ & $\displaystyle\frac{1}{x^2+1}$\\
\verb@$\frac{1+x^2}{x^2+y^2} + x^2 y$@ & $\displaystyle\frac{1+x^2}{x^2+y^2} + x^2 y$\\
\verb@$\frac{1}{1 + \frac{x}{2}}$@ & $\displaystyle\frac{1}{1 + \frac{x}{2}}$\\
\verb@$\frac{1}{1+x/2}$@ & $\displaystyle\frac{1}{1+x/2}$
\end{mathegs}

\subsection{Roots}
The \verb@\sqrt@ command accepts two arguments.  The first, 
and optional, argument specifies what order of root you desire
if it is anything other than the square root.  The second, and
mandatory, argument specifies the expression that the root sign
should enclose:

{\renewcommand{\arraystretch}{1.6}
\begin{mathegs}
\verb@$\sqrt{a+b}$@ & $\displaystyle\sqrt{a+b}$\\
\verb@$\sqrt[5]{a+b}$@ & $\displaystyle\sqrt[5]{a+b}$\\
\verb@$\sqrt[n]{\frac{1+x}{1+x^2}}$@ & $\displaystyle\sqrt[n]{\frac{1+x}{1+x^2}}$\\
\verb@$\frac{\sqrt{x+1}} {\sqrt[3]{x^3+1}}$@ & $\displaystyle\frac{\sqrt{x+1}} {\sqrt[3]{x^3+1}}$
\end{mathegs}
}

\subsection{Ellipsis}
Simply typing three periods in a row will not give the correct
spacing of the periods if it is an ellipsis that is desired.  So
\LaTeX\ provides the commands \verb@\ldots@ and \verb@\cdots@.
Centered ellipsis should be used between symbols like
$+$, $-$, $*$, $\times$, and $=$.  Here are some examples:

\begin{mathegs}
\verb@$a_1+ \cdots + a_n$@ & $a_1+ \cdots + a_n$\\
\verb@$x_1 \times x_2 \times \cdots \times x_n$@ & $x_1 \times x_2 \times \cdots \times x_n$\\
\verb@$v_1 = v_2 = \cdots = v_n = 0$@ & $v_1 = v_2 = \cdots = v_n = 0$\\
\verb@$f(x_1,\ldots,x_n) = 0$@ & $f(x_1,\ldots,x_n) = 0$
\end{mathegs}

\subsection{Text within an expression}\label{sec:mathtext}
One can use the \verb@\mbox@ command to insert normal text into
an expression.  This command forces \LaTeX\ temporarily out of
maths mode, so that its argument will be treated as normal text.
It's use is simple, but we must be wary on one count: remember that
\LaTeX\ ignores all space characters when in maths mode; so to 
surround words in an expression that were placed by an
\verb@\mbox@ command by space you must include the space 
in the \verb@\mbox@ argument.

\begin{mathegs}
\verb@$f_i(x) \leq 0 \mbox{ for } x \in I$@ & $f_i(x) \leq 0 \mbox{ for } x \in I$\\
\verb@$\Gamma(n)=(n-1)! \mbox{ when $n$ is an integer}$@ & $\Gamma(n)=(n-1)! \mbox{ when $n$ is an integer}$
\end{mathegs}

In section~\ref{sec:mathspace} we'll learn of some special spacing commands
that can be used in math mode.  These are often very useful in positioning
text within an expression, enhancing readability and logical layout.

\subsection{Log-like functions}
There are a number of function names and operation symbols that should
be set in normal (roman) type in an expression, such as in
$$
f(\theta) = \sin\theta + \log(\theta+1) - \sinh(\theta^2+1)
$$
and
$$
\lim_{h \rightarrow 0} \frac{\sin h}{h} = 1\quad.
$$

We know that simply typing \verb@$log\theta$@ would produce the
incorrect result
$$
log\theta
$$
and that using \verb@$\mbox{log}\theta$@ would leave us having to insert
a little extra space between the log and the $\theta$
$$
\mbox{log}\theta\quad.
$$
So \LaTeX\ provides a collection of ``log-like functions'' defined
as control sequences.  Table~\ref{tab:loglike} shows those that are
available.  Here are some examples of their use:

\begin{table}[tbp]
{\centering\footnotesize\tt
\begin{tabular}{llllllll}
\bs arccos & \bs cos & \bs csc &\bs exp & \bs ker & \bs limsup & \bs min & \bs sinh\\
\bs arcsin & \bs cosh & \bs deg & \bs gcd & \bs lg & \bs ln & \bs Pr & \bs sup\\
\bs arctan & \bs cot & \bs det & \bs hom & \bs lim & \bs log & \bs sec & \bs tan\\
\bs arg & \bs coth & \bs dim & \bs inf & \bs liminf & \bs max & \bs sin & \bs tanh
\end{tabular}}
\caption{\rm Log-like functions}
\label{tab:loglike}
\end{table}

\begin{mathegs}
\verb@$f(x)=\sin x + \log(x^2)$@ & $f(x)=\sin x + \log(x^2)$\\
\verb@$\delta = \min \{ \delta_1, \delta_2 \}$@ & $\delta = \min \{ \delta_1, \delta_2 \}$\\
\verb@$\chi(X) = \sup_{x\in X} \chi(x)$@ & $\chi(X) = \sup_{x\in X} \chi(x)$\\
\verb@$\lim_{n \rightarrow \infty} S_n = \gamma$@ & $\lim_{n \rightarrow \infty} S_n = \gamma$
\end{mathegs}

Notice how \LaTeX\ does more than just set an operation like
sup in roman type.  It also knew where a subscript to that operator
should go.

\subsection{Over- and Underlining and bracing}
The \verb@\underline@ command will place an unbroken line
under its argument, and the \verb@\overline@ command will place
an unbroken line over its argument.  These two commands can also
be used in normal paragraphing mode (but be careful: \LaTeX\ will
not break the line within an under- or overlined phrase, so don't
go operating on large phrases).

You can place horizontal braces above or below an expression
by making that expression the argument of \verb@\overbrace@
or \verb@\underbrace@.  You can place a label on an overbrace
(resp.\ underbrace) by superscripting (resp.\ subscripting the
group defined by the bracing command.

\begin{mathegs}
\verb@$\overline{a+bi} = a- bi$@ & $\overline{a+bi} = a- bi$\\
\verb@$\overline{\overline{a+bi}} = a+bi$@ & $\overline{\overline{a+bi}} = a+bi$\\
\end{mathegs}

And some examples of horizontal bracing:

\moveright0.1\textwidth\vbox{
\footnotesize\begin{verbatim}
$A^n=\overbrace{A \times A \times \ldots \times A}^{\mbox{$n$ terms}}$

$\forall x \underbrace{\exists y (y \succ x)}_{\mbox{scope of $\forall$}}$
\end{verbatim}
}
\noindent will produce
$$A^n=\overbrace{A \times A \times \ldots \times A}^{\mbox{$n$ terms}}$$
and
$$\forall x \underbrace{\exists y (y \succ x)}_{\mbox{scope of $\forall$}}$$

\subsection{Stacking symbols}
\LaTeX\ allows you to set one symbol above another through the
\verb@\stackrel@ command.  This command accepts two arguments, 
and sets the first centrally above the second.

\begin{mathegs}
\verb@$X \stackrel{f^*}{\rightarrow}Y$@ & $X \stackrel{f^*}{\rightarrow}Y$\\
\verb@$f(x) \stackrel{\triangle}{=} x^2 + 1$@ & $f(x) \stackrel{\triangle}{=} x^2 + 1$
\end{mathegs}

\subsection{Operators;  Sums, Integrals, etc.}
Each of the operation symbols in table~\ref{tab:bigops} can occur
with limits.  They are specified as sub- and superscripts to the
operator, and \LaTeX\ will position them appropriately.  In an in-text
formula they will appear in more-or-less the usual scripting positions;
but in a displayed formula they will be set below and above the 
symbol (which will also be a little larger).  The following should
give you an idea of how to use them:

\begin{mathegs}
\verb@$\sum_{i=1}^{N} a_i$@ & $\sum_{i=1}^{N} a_i$\\
\verb@$\int_a^b f$@ & $\int_a^b f$\\
\verb@$\oint_{\cal C}f(x)\,dx$@ & $\oint_{\cal C}f(x)\,dx$\\
\verb@$\prod_{\alpha \in A} X_\alpha$@ & $\prod_{\alpha \in A} X_\alpha$\\
\verb@$\lim_{N\rightarrow\infty}\sum_{i=1}^{N}f(x_i)\Delta x_i$@ & $\lim_{N\rightarrow\infty}\sum_{i=1}^{N}f(x_i)\Delta x_i$
\end{mathegs}

We'll have more to say about the use of \verb@\,@ in section~\ref{sec:mathspace}.
Let's have a look at each of those expressions when displayed:

$$
\sum_{i=1}^{N} a_i\quad,\quad
\int_a^b f\quad,\quad
\oint_{\cal C}f(x)\,dx\quad,\quad
\prod_{\alpha \in A} X_\alpha\quad,\quad
\lim_{N\rightarrow\infty}\sum_{i=1}^{N}f(x_i)\Delta x_i
$$

\subsection{Arrays}\label{sec:arrays}

The \verb@array@ environment is provided for typesetting arrays
and array-like material.  It accepts two arguments, one optional
and one mandatory.  The optional argument specifies the vertical
alignment of the array---use \verb@t@, \verb@b@, or \verb@c@ to align
the top, bottom, or centre of the array with the centreline of the
line it occurs on (the default being \verb@c@).  The second argument
is as for the \verb@tabular@ environment:  a series of \verb@l@,
\verb@r@, and \verb@c@'s that specify the number of columns and the
justification of these columns.  The body of the \verb@array@ environment
uses the same syntax as the \verb@tabular@ environment to specify
the individual entries of the array.

For instance the input

\moveright0.1\textwidth\vbox{
\footnotesize\begin{verbatim}
... let $A = \begin{array}{rrr}
12 & 3 & 4\\
-2 & 1 & 0\\
3 & 7 & 9
\end{array}$ ...
\end{verbatim}
}
\noindent will produce the output

\result{%
let $A = \left[\begin{array}{rrr}
12 & 3 & 4\\
-2 & 1 & 0\\
3 & 7 & 9
\end{array}\right] 
$}

Note that we had to choose and supply the enclosing brackets
ourselves (they are not placed for us so that we can use the
\verb@array@ environment for array-like material; also,
we get to choose what type of brackets we want this way).
As in the \verb@tabular@ environment, the scope of a  command
given inside a matrix entry is restricted to that entry.

We can use ellipsis within arrays as in the following example:

\moveright0.1\textwidth\vbox{
\footnotesize\begin{verbatim}
\det A = \left| \begin{array}{cccc}
a_{11} & a_{12} & \cdots & a_{1n}\\
a_{21} & a_{22} & \cdots & a_{2n}\\
\vdots & \vdots & \ddots & \vdots\\
a_{m1} & a_{m2} & \cdots & a_{mn}
\end{array} \right|
\end{verbatim}
}
\noindent which produces

\result{%
$\det A = \left| \begin{array}{cccc}
a_{11} & a_{12} & \cdots & a_{1n}\\
a_{21} & a_{22} & \cdots & a_{2n}\\
\vdots & \vdots & \ddots & \vdots\\
a_{m1} & a_{m2} & \cdots & a_{mn}
\end{array} \right|$
}


The \verb@array@ environment is often used to typeset material that
is not, strictly speaking, an array:

\moveright0.1\textwidth\vbox{
\footnotesize\begin{verbatim}
f(x) = \left\{ \begin{array}{ll}
   x & \mbox{for $x<1$}\\
 x^2 & \mbox{for $x \geq 1$}  
\end{array} \right.
\end{verbatim}
}
\noindent which will yield

\result{%
$f(x) = \left\{ \begin{array}{ll}
   x & \mbox{for $x<1$}\\
 x^2 & \mbox{for $x \geq 1$}  
\end{array} \right.$
}

\subsection{Changes to spacing}\label{sec:mathspace}
Sometimes \LaTeX\ needs a little help in spacing an expression,
or perhaps you think that the default spacing needs adjusting.
For these purposes we have the following spacing commands:\medskip

\begin{tabular}{lllll}
\verb@\,@ & thin space & & \verb@\:@ & medium space\\
\verb@\!@ & negative thin space && \verb@\;@ & thick space\\
\verb@\quad@ & a quad of space && \verb@\qquad@ & two quads of space
\end{tabular}\medskip

The spacing commands \verb@\,@, \verb@\quad@, and \verb@\qquad@ can
be used in paragraphing mode, too.  Here are some examples of these
spacing commands used to make subtle modifications to some expressions.

\begin{mathegs}
\verb@$\sqrt{2} \, x$@ & $\sqrt{2} \, x$\\
\verb@$\int_a^b f(x)\,dx$@ & $\int_a^b f(x)\,dx$\\
\verb@$\Gamma_{\!2}$@ & $\Gamma_{\!2}$\\
\verb@$\int_a^b \! \int_c^d f(x,y)\,dx\,dy$@ & $\int_a^b \! \int_c^d f(x,y)\,dx\,dy$\\
\verb@$x / \! \sin x$@ & $x / \! \sin x$\\
\verb@$\sqrt{\,\sin x}$@ & $\sqrt{\,\sin x}$
\end{mathegs}

\section{Alignment}
Recall that the \verb@$equation$@
environment can be used to display and automatically number a single-\
line equation\footnote{See section \ref{sec:display}}.
The \verb@eqnarray@ environment is used for displaying
and automatically numbering either a single expression that spreads
over several lines or multiple expressions, while taking care of 
alignment for us.  The syntax is similar to that of the
\verb@tabular@ and \verb@array@ environments, except that no argument
is necessary to declare the number and justification of columns.  The
\verb@eqnarray*@ environment does this without numbering any equations.

\moveright0.1\textwidth\vbox{
\footnotesize\begin{verbatim}
\begin{eqnarray}
(a+b)(a+b) & = & a^2 + 2ab + b^2\\
(a+b)(a-b) & = & a^2 - b^2
\end{eqnarray}
\end{verbatim}
}
\noindent will give

\begin{eqnarray}
(a+b)(a+b) & = & a^2 + 2ab + b^2\\
(a+b)(a-b) & = & a^2 - b^2
\end{eqnarray}

See how we identify the columns so as to line the $=$ signs up.
We can also leave entries empty, to obtain effect like the
following:

\vbox{
\footnotesize\begin{verbatim}
\begin{eqnarray*}
\frac{d}{dx} \sin x & = & \lim_{h\rightarrow0}\frac{\sin(x+h)-\sin x}{h}\\
 & = & \lim_{h\rightarrow0}\frac{\sin x\cos h + \cos x\sinh - \sin x}{h}\\ 
 & = & \lim_{h\rightarrow0}\frac{\sin x(\cos h-1)}{h} + \cos x\frac{\sin h}{h}\\
 & = & \cos x
\end{eqnarray*}
\end{verbatim}
}
\noindent which produces

\begin{eqnarray*}
\frac{d}{dx} \sin x & = & \lim_{h\rightarrow0}\frac{\sin(x+h)-\sin x}{h}\\
 & = & \lim_{h\rightarrow0}\frac{\sin x\cos h + \cos x\sinh - \sin x}{h}\\ 
 & = & \lim_{h\rightarrow0}\left\{\frac{\sin x(\cos h-1)}{h} + \cos x\frac{\sin h}{h}\right\}\\
 & = & \cos x
\end{eqnarray*}

\section{Theorems, Propositions, Lemmas, $\ldots$}
Suppose you document contains four kinds of theorem-like structures:
``theorems'', ``propositions'', ``conjectures'', and ``wild guesses''.
Then near the beginning of the document you should have something
like the following:

\moveright0.1\textwidth\vbox{
\footnotesize\begin{verbatim} 
\newtheorem{thm}{Theorem}
\newtheorem{prop}{Proposition}
\newtheorm{conjec}{Conjecture}
\newtheorem{wildshot}{Hypothesis} % make it sound good!
\end{verbatim}
}

\newtheorem{thm}{Theorem}
\newtheorem{prop}{Proposition}
\newtheorem{conjec}{Conjecture}
\newtheorem{wildshot}{Hypothesis}

The first argument to \verb@\newtheorem@ defines a new
theorem-like environment name of your own choosing.  The second argument
contains the text that you want inserted when your theorem is
proclaimed:

\moveright0.1\textwidth\vbox{
\footnotesize\begin{verbatim}
\begin{thm} $X$ is normal if, and only if, each pair of disjoint
closed sets in $X$ is completely separated.
\end{thm}

\begin{wildshot} % remember, we chose the name 'wildshot'
The property of Moore extends to all objects of the class $\Sigma$.
\end{wildshot}
\end{verbatim}
}
\noindent which will produce the following:

\begin{thm} $X$ is normal if, and only if, each pair of disjoint
closed sets in $X$ is completely separated.
\end{thm}

\begin{wildshot}
The property of Moore extends to all objects of the class $\Sigma$.
\end{wildshot}

Notice that \LaTeX\ italicises the theorem statement, and that you
still have to shift in to maths mode when you want to set symbols
and expression.  Typically, it is the style file that determines
what a theorem will appear like---so don't go changing this if
you are preparing for submission for publication (because the journal
staff want to substitute their production style for your document style
choice, and not be over-ridden by other commands).

\section{Where to from here?}
We have covered a good deal of \LaTeX's mathematical abilities, 
albeit rather superficial coverage here and there.  There is
much that has been impressive, but there is clearly a lot more
to {\TeX}nical typesetting than we have covered here---it is
not difficult to think of an expression that we don't yet know
how to typeset.  Also, there are places where \LaTeX\ is a
little weak and it leaves us to do somewhat more work than
the spirit of \TeX\ would suggest.

Of course, we cannot criticise \LaTeX\ until we know its full
capability.  So the first place to go from here is the
{\em\LaTeX\ User's Guide \& Reference Manual}.  Particularly, the
command reference guide in Appendix C of that book is an
invaluable source of \LaTeX\ information that few can afford to 
do without.  With good knowledge of the \LaTeX\ environments and their
options (and we've left out many here) one can accomplish a good
deal of most typesetting problems.  A little imagination (say
putting an environment to a slightly non-standard use) can often
solve more difficult problems.  Lastly, of course, much of
raw \TeX\ still sits underneath \LaTeX\ and so it is true to say that
you can do {\em anything\/} with \LaTeX---but you may need some
divine inspiration from time to time (ask your local \TeX\ guru).

In the next chapter we will look, very briefly, at a number of
\LaTeX\ commands that we have not yet considered.  Nothing
exciting on the mathematical front, but there is some other
important material (e.g.\ cross-referencing and page-sizing).
For now, let's look at the ``way forward'' with respect to 
mathematical typesetting.

\section{\AmSLaTeX}
Back in the introduction we said that \AmSLaTeX\ was just a big
macro package, the result of a marriage of \LaTeX\ and \AmSTeX\
designed to endow the powerful general-purpose \LaTeX\ package with the
mathematical prowess of \AmSTeX\ without compromising the \LaTeX\ syntax.
Most of that is true, except that \AmSLaTeX\ is really just 
a document-style option (like \verb@12pt@) that can be used within
a ``tweaked \LaTeX''.  The most visible part of this tweak is the
{\em new font selection scheme of Mittelbach and Sch\"{o}pf}, 
discussed more fully in the next chapter.  Almost every
\LaTeX\ command and environment survived the transition to \AmSLaTeX, the
exceptions being those that were considered redundant or under-used (space
is at a premium with such a big package).
The tweaked \LaTeX\ package is therefore able to deal with practically
every existing \LaTeX\ document, giving just a few (often pleasant)
surprises.

With the \verb@amstex@ style option, one can just start a \LaTeX\
document with

\moveright0.1\textwidth\vbox{
\footnotesize\begin{verbatim}
\documentstyle[amstex]{article} % or report, book, etc
\end{verbatim}
}
\noindent to gain access to the {\TeX}nical excellence of the
AMS technical staff.  It is not necessary to have read
{\em The Joy of \TeX} (the \AmSTeX\ reference guide) to
be able to use the \verb@amstex@ option, for \AmSLaTeX\
comes with its own reference guide.  Even so, 
{\em The Joy of TeX\/} is still highly recommended reading.
The syntax of \AmSTeX\ has been changed to that of \LaTeX, 
but one can perform that transformation as you read ``{\em Joy\/}''
and still learn much of the art of technical typesetting.  Nowhere
else will you find so comprehensive a coverage of the conventions
and pitfalls of mathematical typesetting.  In addition, {\em Joy\/}
lists all the extra symbols that are available through the
\verb@amstex@ option (if you thought \LaTeX\ had a fair selection
of esoteric symbols, just wait 'til you see those!) and provides
in-depth accounts where the \AmSLaTeX\ documentation is brief.

Just as \AmSTeX\ comes with the AMS preprint style
(\verb@amsppt@), \AmSLaTeX\ comes with a specialist style file for
preparation of articles with \AmSLaTeX\ for submission to journals:
\verb@amsart@.  The \AmSLaTeX\ User's Guide is quite short and very
terse in its explanations (assuming you to be competent in \LaTeX),
but is supplemented by a large body of examples and a comprehensive
sample article that is a showcase of the abilities of the \verb@amsart@
style.  You must read both these documents to really
learn \AmSLaTeX.  The AMS also distributes a guide to authors
who wish to submit using \AmSLaTeX, and this is a must-read once
you are familiar with some of \AmSLaTeX. 

\end{document}

--
Gavin Maltby, University of Natal, Pietermaritzburg, South Africa
gmaltby@unpcs1.cs.unp.ac.za, maltby@unpsun1.cc.unp.ac.za
Any opinion expressed is mine and mine alone.
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