AMS-L^{A}TEX Version 1.2

User’s Guide

American Mathematical Society October 1994 Contents

1 How to use AMS-L^{A}TEX 1 1.1 Using an AMS package with a L^{A}TEX document . . . . . . . . . . 1

2 Displayed equations (amstex package) 2 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Single equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.3 Equation groups without alignment . . . . . . . . . . . . . . . . . 3 2.4 Equation groups with mutual alignment . . . . . . . . . . . . . . 3 2.5 Multiple alignment points in an equation group . . . . . . . . . . 3 2.6 Split equations without alignment . . . . . . . . . . . . . . . . . 4 2.7 Split equations with alignment . . . . . . . . . . . . . . . . . . . 5 2.8 Alignment environments that don’t constitute an entire display . 5 2.9 Adjusting tag placement . . . . . . . . . . . . . . . . . . . . . . . 6 2.10 Vertical spacing and page breaks within multiline displays …. 6 2.11 Textual interjections within a display . . . . . . . . . . . . . . . . 6 2.12 Equation numbering . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Miscellaneous mathematics features (amstex package) 7 3.1 Multicase equations . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 Math spacing commands . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 Over and under arrows . . . . . . . . . . . . . . . . . . . . . . . . 9 3.5 Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.6 Accents in math . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.7 Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.8 Boxed formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.9 Extensible arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.10 Affixing symbols to other symbols . . . . . . . . . . . . . . . . . 11 3.11 Operator names . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.12 \mod and its relatives . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.13 Fractions and related constructions . . . . . . . . . . . . . . . . . 12 3.14 Continued fractions . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.15 Smash options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.16 Delimiter sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 The \text command (amstext, amstex packages) 14

5 The \boldsymbol command (amsbsy, amstex packages) 15 6 Integrals and sums (amstex, amsintsm packages) 15

6.1 Multiple integral signs . . . . . . . . . . . . . . . . . . . . . . . . 15 6.2 Multiline subscripts and superscripts . . . . . . . . . . . . . . . . 15 6.3 The \sideset command . . . . . . . . . . . . . . . . . . . . . . . 16 6.4 The amsintsm package . . . . . . . . . . . . . . . . . . . . . . . . 16

7 Commutative diagrams (amscd package) 16

8 Using math fonts 17 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 8.2 Recommended use of math font commands . . . . . . . . . . . . 18

9 Theorems and similar structures (amsthm package) 19 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 9.2 The \newtheorem command . . . . . . . . . . . . . . . . . . . . . 19 9.3 Numbering modifications . . . . . . . . . . . . . . . . . . . . . . 20 9.4 Changing styles for theorem-like environments . . . . . . . . . . . 21 9.5 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

A Installation instructions 22 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 A.2 Putting files in a suitable place on your system . . . . . . . . . . 22 A.3 Running L^{A}TEX on the installation script amslatex.ins . . . . . 23 A.4 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 A.5 Extra math fonts . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 A.6 Memory requirements . . . . . . . . . . . . . . . . . . . . . . . . 23 A.7 Files included in this distribution . . . . . . . . . . . . . . . . . . 23

B Error messages 24

C Where to find other information 24

C.1 Differences between AMS-L^{A}TEX version 1.1 and AMS-L^{A}TEX ver-

sion 1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 C.2 Differences between AMS-TEX and AMS-L^{A}TEX . . . . . . . . . . 24 C.3 Technical notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

D Getting help 24 D.1 Further information . . . . . . . . . . . . . . . . . . . . . . . . . 25

iv WHAT IS ‘AMS-L^{A}TEX’?

What is ‘AMS-L^{A}TEX’, and why would anyone want to use it?

What is ‘AMS-L^{A}TEX’?

The name AMS-L^{A}TEX is used for convenience to describe a set of loosely related files that are distributed together by the American Mathematical Society. Basically they may be described as miscellaneous enhancements to L^{A}TEX for superior information structure of mathematical documents and superior printed output. As AMS-L^{A}TEX is an extension for L^{A}TEX, and L^{A}TEX in turn is a ‘macro package’ for the TEX typesetting program, it follows that in order to use any of the pieces of AMS-L^{A}TEX you need to have TEX and L^{A}TEX installed first.

L^{A}TEX by itself does a rather good job of typesetting mathematics, compared to non-TEX-based software; but it doesn’t add much to the basic set of mathematical capabilities that it adopted from the Plain TEX macro package.

At the same time that L^{A}TEX was being developed by Leslie Lamport (roughly 1982–1986), the American Mathematical Society was throwing its resources into the development of a different macro package known as AMS-TEX, written by Michael Spivak. Eventually (by 1987 or so) it became evident that AMS-TEX and L^{A}TEX had complementary feature sets: AMS-TEX focused on the typesetting of math formulas and on fine-tuning typically done by publishers, and was relatively weak in other areas (for example no automatic numbering or cross-reference facilities); L^{A}TEX focused on document structure and logical markup of text, and had a comparatively limited set of features for dealing with math formula contents. This situation led to dissatisfaction among both AMS-TEX and L^{A}TEX users who saw desirable features tantalizingly just out of reach in the other macro package. So the American Mathematical Society looked into the question of producing some sort of combination of the two macro packages that would better serve mathematicians in their writing tasks. The decision that was eventually taken was to graft the mathematical capabilities of AMS-TEX onto the base stock of L^{A}TEX through an extension package: AMS-L^{A}TEX. The lion’s share of the programming work was done by Frank Mittelbach and Rainer Schöpf in 1989–1990 and version 1.0 of AMS-L^{A}TEX was released in mid-1990.

Why would a L^{A}TEX user want to bother with AMS-L^{A}TEX?

If you are just starting out as a L^{A}TEX user, you’ll probably have to take our word for this (or the word of friends and colleagues), but:

If your writing contains a significant proportion of mathematics, and you care about the quality of the printed results, then sooner or later you’ll find shortcomings in standard L^{A}TEX and want to remedy them. Chances are that at least the first few of the shortcomings you encounter will be ones that are already addressed by an AMS-L^{A}TEX package. If you want to have maximum mathematical typesetting power ready at hand, rather than stop to cast about

WHY BOTHER WITH AMS-L^{A}TEX? v

for a solution whenever you run into some unusual demand in your writing, then AMS-L^{A}TEX will go a long way toward meeting your needs.

If you are a long-time L^{A}TEX user and have lots of mathematics in what you write, then how do these features sound:

• Easy access to extra math symbols as found in the AMSFonts font package, including blackboard bold and fraktur letters. And they change size properly through all the range of L^{A}TEX font sizes, including sub/superscript sizes.

• A convenient way to define new ‘operator name’ commands analogous to \sin and \lim, including proper side spacing and automatic selection of the correct font style and size (even when used in sub/superscripts).

• Multiple substitutes for the eqnarray environment to make various kinds of equation arrangements easier to write.

• Equation numbers automatically adjust up or down to avoid over-printing on the equation contents (unlike eqnarray).

• Spacing around equals signs matches the normal spacing in the equation environment (unlike eqnarray).

• A way to produce multiline subscripts as are often used with summation symbols.

• An easy way to substitute a variant equation number for a given equation instead of the automatically supplied number.

• An easy way to produce subordinate equation numbers of the form (1.3a) (1.3b) (1.3c) for selected groups of equations.

• Horizontal arrows that automatically expand to encompass wide subscripts or superscripts

• A \boldsymbol command for printing bold versions of individual symbols, including things like ∞ and lowercase Greek letters.

• A cases environment to make it easy to produce a typical case statement with large left brace, as in

(0.1) P_{r−j} = \begin{cases}0 & if r − j is odd, \\ r! (−1)^{(r−j)/2} & if r − j is even. \end{cases}

Chapter 1

How to use AMS-L^{A}TEX

1.1 Using an AMS package with a L^{A}TEX document

A ‘package’ in L^{A}TEX terminology is an extension written in such a form that it can be used via the \usepackage command. Many of the principal features of AMS-L^{A}TEX are provided in separate packages so that they can be used individually on demand. The amstex package is perhaps the single most noteworthy package, as it subsumes the amsfonts, amstext, and amsbsy packages, and provides a number of other enhancements for mathematical typesetting. Table 1.1 gives the current list of packages.

The amstex package has the following options:

intlimits Place the subscripts and superscripts of integral symbols above and below rather than to the side (in displayed equations only).

nointlimits (default) Always place the subscripts and superscripts of integral symbols to the side.

sumlimits (default) Like intlimits, but for sums and similar symbols (∏, ∐, ⨂, ⨁, and so forth).

nosumlimits Opposite of sumlimits.

namelimits Like intlimits, but for ‘operator names’ such as det, inf, lim, max, min and so forth.

nonamelimits Opposite of namelimits.

tbtags ‘Top-or-bottom tags’: For a split equation, place equation numbers level with the last (resp. first) line, if numbers are on the right (resp. left).

Table 1.1. Packages

amstex Defines extra environments for multiline displayed equations, as well as a number of other enhancements for math

amstext Provides a \text command for proper typesetting of a

fragment of text inside a display

     amsbsy  Defines \boldsymbol and \pmb commands

amsintsm Provides more logical command syntax for \int, \sum

amscd Provides a CD environment for simple commutative diagrams (no support for diagonal arrows) amsthm Provides a proof environment and extensions for the

               \newtheorem command

centertags (default) For a split equation, place equation numbers vertically centered on the total height of the equation.

The amstex package also recognizes the following options which are usually given in the options list of the \documentclass command:

fleqn Position equations at a fixed indent from the left margin rather than centered in the text column. This option is typically inherited from the documentclass declaration, and so doesn’t need to be specified explicitly in the \usepackage command.

reqno Place equation numbers on the right.

leqno Place equation numbers on the left. This option and the reqno option are typically inherited from the documentclass declaration, so there is no default to speak of.

Example: \usepackage[intlimits]{amstex}. In compatibility mode obsolete option names intlim, nosumlim, nonamelm, righttag are recognized as well.

Chapter 2

Displayed equations (amstex package)

2.1 Introduction

The amstex package provides several environments for multi-line displayed equations. They are similar in function to L^{A}TEX’s equation and eqnarray environments. These environments are:

 align      gather     alignat    xalignat   xxalignat
 multline   split

Each environment, except for split, has both starred and unstarred forms, where the unstarred forms have automatic numbering, using L^{A}TEX’s equation counter. You can suppress the number on any particular line by putting \notag before the \\; you can also override it with a tag of your own using \tag{⟨label⟩}, where ⟨label⟩ means arbitrary text such as $*$ or ii used to “number” the equation. There is also a \tag* command that causes the text you supply to be typeset literally, without adding parentheses around it. \tag and \tag* can also be used in the starred versions of all the amstex alignment structures. See testmath.tex for examples of the use of \tag.

2.2 Single equations

The equation environment is for a single equation with an automatically generated number. The equation* environment is the same except for omitting the number.^{1} 2.3 Equation groups without alignment

1Basic L^{A}TEX doesn’t provide an equation* environment, but rather a functionally equivalent environment named displaymath.

The gather environment is used for a group of consecutive equations when there is no alignment desired among them; each one is centered separately within the text width. For example:

(2.1) ix(Ω, β, [a, b]) = ∑_{λ>0} nul(Ω + λΛ, β, [a, b]),

∑_{a<t<b} nul(Ω, γ ⊕ ∞, [a, t]), (2.2)

[α(λ) : Γ_{β}]_{ϵ≤λ≤λ^{+}} (2.3)

\begin{gather}
\ix(\Omega,\beta,[a,b])
  = \sum_{\lambda>0} \nul(\Omega +\lambda\Lambda,\beta,[a,b]),\\
\sum_{a<t<b} \nul(\Omega,\gamma \oplus\infty, [a,t]),\\
[\alpha(\lambda):\Gamma_\beta]_{\epsilon\leq\lambda\leq\lambda^+}
\end{gather}

2.4 Equation groups with mutual alignment

The align environment is used for two or more equations when vertical alignment is desired (usually binary relations such as equal signs are aligned). For example:

(2.4)  Λ(ω) = ix(Ω, β_{ω}, [0, 1])
(2.5)  N(ω) = nul(Ω, β_{ω}, [0, 1]).

\begin{align}
\Lambda(\omega) &= \operatorname{ix}(\Omega,\beta_{\omega},[0,1])\\
N(\omega) &= \operatorname{nul}(\Omega,\beta_{\omega},[0,1]).
\end{align}

2.5 Multiple alignment points in an equation group

The align environment takes up the whole width of a display. If you want to have several “align”-type structures side by side, there is an alignat environment you can use. There is one required argument, to specify the number of “align” structures.^{2} The xalignat and xxalignat environments are forms of the alignat environment with expanded spacing between the component align structures. If we consider each align structure to be a column, xalignat has equal spacing between columns and at the margins; xxalignat has equal spacing between columns and zero spacing at the margins. Here is an example of

2For an argument of n, the number of &’s per line is 2n − 1 (one ampersand for alignment within each align structure, and ampersands to separate the align structures from one another).

alignat:

(2.6) V_{i} = v_{i} − q_{i}v_{j},  X_{i} = x_{i} − q_{i}x_{j},  U_{i} = u_{i},  for i ≠ j;
(2.7) V_{j} = v_{j},  X_{j} = x_{j},  U_{j} = u_{j} + ∑_{i≠j} q_{i}u_{i}.

\begin{alignat}{3}
V_i & =v_i - q_i v_j, & \qquad X_i & = x_i - q_i x_j,
 & \qquad U_i & = u_i,
 \qquad \text{for $i\ne j$;}\\
V_j & = v_j, & \qquad X_j & = x_j,
  & \qquad U_j & u_j | \sum_{i\ne j} q_i u_i.
\end{alignat}

The xalignat is sometimes used to add annotations on each line, as in the following example.

(2.8)  x = y  by (2.6)
(2.9)  x′ = y′  by (2.7)
(2.10)  x + x′ = y + y′  by Axiom 1.

\begin{xalignat}{2}
x& =y && \text {by (\ref{eq:C})}\\
x'& = y' && \text {by (\ref{eq:D})}\\
x+x' & = y+y' && \text {by Axiom 1.}
\end{xalignat}

2.6 Split equations without alignment

The multline environment is a variation of the equation environment used for equations that don’t fit on a single line. The first line of a multline will be at the left margin and the last line at the right margin, except for an indention on both sides in the amount of \multlinegap. For example:

∑_{t_{0}≤t≤t_{1}} nul(Ω, ∞ ⊕ γ_{1}, [t, b]) − ∑_{t_{0}≤t≤t_{1}} nul(Ω, ∞ ⊕ γ_{2}, [t, b])

≤ dim(E^{ν}) − dim(γ_{1} ∩ γ_{2}).

\begin{multline*}
\textstyle
\sum_{t_0\leq t\leq t_1} \nul(\Omega,\infty\oplus\gamma_1,[t,b])
-\sum_{t_0\leq t\leq t_1} \nul(\Omega, \infty \oplus\gamma_2, [t,b])\\
\leq \dim(E^\nu) -\dim(\gamma_1 \cap \gamma_2).
\end{multline*}

or

(2.11) (∑_{i∈n} a_{l_{i}}x_{i}) det K(t = 1, x_{1}, …, x_{n}; l|l)

= (∏_{i∈n} x̂_{i}) ∑_{I⊆n−\{l\}}(−1)^{|I|}A^{(λ)}(I|I) det A^{(λ)}(\overline{I} ∪ \{l\}|\overline{I} ∪ \{l\}).

\begin{multline}
\biggl(\sum_{\,i\in\mathbf{n}}a_{l _i}x_i\biggr)
\det\mathbf{K}(t=1,x_1,\dots,x_n;l \vertl )\\
=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)
\sum_{I\subseteq\mathbf{n}-\{l \}}
(-1)^{\lvert I\rvert}\mathbf{A}^{(\lambda)}(I\vert I)
\det\mathbf{A}^{(\lambda)}
(\overline I\cup\{l \}\vert\overline I\cup\{l \}).
\label{sum-ali}
\end{multline}

The value of \multlinegap can be changed using L^{A}TEX’s \setlength and \addtolength commands. If the multline contains more than two lines, any lines other than the first and last will be centered individually between the margins (except when the fleqn option is in effect).

2.7 Split equations with alignment

Like multline, the split environment is for single equations that are too long to fit on one line and hence must be split into multiple lines. Unlike multline, however, the split environment provides for alignment among the split lines, using & to mark alignment points, as usual. In addition, unlike the other amstex equation structures, the split environment provides no numbering, because it is intended to be used only inside some other displayed equation structure, usually an equation, align, or gather environment, which provides the numbering. For example:

(2.12)  \begin{aligned}H_{c} & = \frac{1}{2n} ∑_{l=0}^{n}(−1)^{l}(n − l)^{p−2} ∑_{l_{1}+···+l_{p}=l} ∏_{i=1}^{p} \binom{n_{i}}{l_{i}} \\ & · [(n − l) − (n_{i} − l_{i})]^{n_{i}−l_{i}} · [(n − l)^{2} − ∑_{j=1}^{p}(n_{i} − l_{i})^{2}]. \end{aligned}

\begin{equation}\label{e:barwq}
\begin{split}
H_c&=\frac{1}{2n}
\sum^n_{l=0}(-1)^{l}(n-{l})^{p-2}
\sum_{l _1+\dots+l _p=l}\prod^p_{i=1}
\binom{n_i}{l _i}\\
&\quad\cdot[(n-l )-(n_i-l _i)]^{n_i-l _i}\cdot
\biggl[(n-l )^2-\sum^p_{j=1}(n_i-l _i)^2\biggr].\end{split}
\end{equation}

2.8 Alignment environments that don’t constitute an entire display

In addition to the split environment, there are some other equation alignment environments that do not constitute an entire display. They are self-contained units that can be used inside of other formulas, or set side-by-side. The environment names are aligned, gathered, and alignedat. These environments take an optional argument to specify their vertical positioning with respect to the material on either side. The default is [c]. A gathered environment with the first line level with the material on either side would be done like this.

\begin{gathered}[t]
...\\
...
\end{gathered}

2.9 Adjusting tag placement

Placing equation numbers can be a very complex problem in multiline displays. The environments of the amstex package try hard to avoid overprinting an equation number on the equation contents, if necessary moving the number down or up to a separate line. But even so, the placement can’t be guaranteed to always be ideal. There is an \adjusttag command provided to adjust the vertical position of the next upcoming equation number. To move a particular number up by 6pt, you would write \adjusttag{-6pt}.

2.10 Vertical spacing and page breaks within multiline displays

You can use the \\[⟨dimension⟩] command to get extra vertical space between lines in all the amstex displayed equation environments, as is usual in L^{A}TEX. Unlike eqnarray, the amstex environments don’t allow page breaks

between lines, unless \displaybreak or \allowdisplaybreaks is used. The

philosophy is that page breaks in such situations should receive individual attention from the author. \displaybreak must go before the \\ where it is supposed to take effect. Like L^{A}TEX’s \pagebreak, \displaybreak takes an optional argument between 0 and 4 denoting the desirability of the pagebreak. \displaybreak[0] means “it is permissible to break here” without encouraging a break; \displaybreak with no optional argument is the same as

\displaybreak[4] and forces a break.
   There is also an optional argument for \allowdisplaybreaks. \allowdisplaybreaks

obeys the usual L^{A}TEX scoping rules; the normal way of limiting its scope would be to put {\allowdisplaybreaks at the beginning and } at the end of the desired range. Within the scope of an \allowdisplaybreaks command, the \\* command can be used to prohibit a pagebreak, as usual.

2.11 Textual interjections within a display

The command \intertext is used for a short interjection of one or two lines of text in the middle of a display alignment. Its salient feature is preservation of the alignment, which would not be possible if you simply ended the display and then started it up again afterwards. \intertext may only appear right after a \\ or \\* command. An example of its use follows.

\begin{align}

A_1&=N_0(\lambda;\Omega')-\phi(\lambda;\Omega'),\\
A_2&=\phi(\lambda;\Omega')-\phi(\lambda;\Omega),\\
\intertext{and}
A_3&=\mathcal{N}(\lambda;\omega).
\end{align}

To produce

(2.13)  A_{1} = N_{0}(λ; Ω′) − ϕ(λ; Ω′),
(2.14)  A_{2} = ϕ(λ; Ω′) − ϕ(λ; Ω),

and

(2.15)  A_{3} = N (λ; ω).

Notice the word “and” would fall outside the display, at the left margin.

2.12 Equation numbering

In L^{A}TEX if you wanted to have equations numbered within sections—that is, have equation numbers (1.1), (1.2), …, (2.1), (2.2), …, in sections 1, 2, and so forth—you would probably redefine \theequation:

\renewcommand{\theequation}{\thesection.\arabic{equation}}

This works fine except that the equation counter won’t be reset to zero at the beginning of a new section or chapter, unless you do it yourself using \setcounter. To make this a little more convenient, the amstex package provides a command \numberwithin. To have equation numbering tied to section numbering, with automatic reset of the equation counter, the command would be

\numberwithin{equation}{section}

As the name implies, \numberwithin can be applied to other counters besides the equation counter, but the results are not guaranteed because of potential complications. Normal L^{A}TEX methods should be used where available, e.g., in

\newtheorem.

To make cross-references to equations easier, an \eqref command is provided. This automatically supplies the parentheses around the equation number, and adds an italic correction if necessary. To refer to an equation that was labeled with the label e:baset, the usage would be \eqref{e:baset}.

Chapter 3

Miscellaneous mathematics features (amstex package)

3.1 Multicase equations

“Cases” constructions like the following are common in mathematics:

(3.1) P_{r−j} = \{ \begin{matrix}0 & if r − j is odd, \\ r! (−1)^{(r−j)/2} & if r − j is even. \end{matrix}

and in the amstex package there is a cases environment:

\begin{equation} P_{r-j}=
  \begin{cases}
    0&  \text{if $r-j$ is odd},\\
    r!\,(-1)^{(r-j)/2}&  \text{if $r-j$ is even}.
  \end{cases}
\end{equation}

Notice the use of \text and the embedded math.

3.2 Matrices

The amstex package provides some environments for matrices beyond the basic

array environment of L^{A}TEX. The pmatrix, bmatrix, vmatrix and Vmatrix

have (respectively) (), [], ||, and ∥∥ delimiters built in. For naming consistency there is a matrix environment sans delimiters. This is not entirely redundant with the array environment; the matrix environments all use more economical horizontal spacing than the rather prodigal spacing of the array environment. Also, unlike the array environment, you don’t have to give column specifications for any of the matrix environments; by default you can have up to 10 centered columns. And the maximum number of columns is determined by the counter MaxMatrixCols, which you can change if necessary using L^{A}TEX’s \setcounter or \addtocounter commands. I.e., suppose you have a big matrix with 19 or 20 columns. Then you’d write something like this:

\begin{equation}
\setcounter{MaxMatrixCols}{20}
A=\begin{pmatrix}
...&...&...&...&...&...&...&...&...&...&...&...&  ... \\
  ...  \\
  ...
\end{pmatrix}
\end{equation}

To produce a small matrix suitable for use in text, there is a smallmatrix environment (e.g., ( \begin{matrix}a & b \\ c & d \end{matrix} )) that comes closer to fitting within a single text line than a normal matrix. Delimiters must be provided; there are no p,b,v,V versions

of smallmatrix.

\begin{math}
  \bigl( \begin{smallmatrix}
      a&b\\ c&d
    \end{smallmatrix} \bigr)
\end{math}

\hdotsfor{⟨number⟩} produces a row of dots in a matrix spanning the given number of columns.

\begin{matrix} a&b&c&d\\
e&\hdotsfor{3} \end{matrix}

would give dots spanning the last three columns in the second row. The spacing of the dots can be varied through use of a square-bracket option, for example, \hdotsfor[1.5]{3}. The number in square brackets will be used as a multiplier (i.e., the normal value is 1.0).

3.3 Math spacing commands

Both the spelled-out and abbreviated forms of these commands are robust, and in addition they can also be used outside of math. The primary math spacing commands are:

Abbrev. Spelled out  Abbrev.  Spelled out

      \,       \thinspace      \!            \negthinspace
      \:       \medspace                     \negmedspace
      \;       \thickspace                   \negthickspace
      @,                       @!

               \quad
               \qquad

@, and @! give one-tenth the space of \, and \! respectively, for extra fine tuning where necessary.

3.4 Over and under arrows

There are some additional over and under arrow operations provided in the amstex package:

    \underleftarrow        \underrightarrow
    \overleftrightarrow    \underleftrightarrow

All over and under operations, including the previously available ones ( \overrightarrow, \overleftarrow), have been modified to scale properly in subscript sizes. (After you have installed AMS-L^{A}TEX, you can process and print the sample file testmath.tex to see examples of the arrows.)

3.5 Dots

In the amstex package, ellipsis dots should almost always be typed as \dots. Placement (on the baseline or centered) is selected according to whatever follows the \dots. If the next thing is a plus sign, the dots will be centered; if it’s a comma, they will be on the baseline. These default dot placements provided by the amstex package can be changed by the documentstyle if different conventions are wanted.

If the dots fall at the end of a math formula, the next thing is something like \end or \) or $, which does not give any information about how to place the dots. Then you must help by using \dotsc for “dots with commas,” or \dotsb for “dots with binary operators/relations,” or \dotsm for “multiplication dots,” or \dotsi for “dots with integrals.” For example, the input

Then we have the series $A_1,A_2,\dotsc$,
the regional sum $A_1+A_2+\dotsb$,
the orthogonal product $A_1A_2\dotsm$,
and the infinite integral
\[\int_{A_1}\int_{A_2}\dotsi\].

will produce low dots in the first instance and centered dots in the others, with the spacing on either side of the dots nicely adjusted.

Then we have the series A_{1}, A_{2}, …, the regional sum A_{1} + A_{2} + ⋯, the orthogonal product A_{1}A_{2} ⋯, and the infinite integral

∫_{A_{1}} ∫_{A_{2}} · · · .

Specifying dots this way, in terms of their meaning rather than in terms of their visual placement, is in keeping with the general philosophy of L^{A}TEX and makes documents more portable between places where different conventions prevail. The control sequences \ldots and \cdots are still available, however, for compatibility.

3.6 Accents in math

The following accent commands automatically give good positioning of double accents:

 \Hat    \Check  \Tilde  \Acute  \Grave  \Dot    \Ddot
 \Breve  \Bar    \Vec

In ordinary L^{A}TEX the second accent will usually be askew: ˆ Â (\hat{\hat{A}}). In the amstex package, if you type \Hat{\Hat{A}} (using the capitalized form

for both accents) the second accent will be properly positioned: ˆ Â.

This double accent operation is complicated and tends to slow down the processing of a TEX file. If your document contains many double accents, you can use the amsxtra package, which provides an \accentedsymbol command.

\accentedsymbol is used like \newcommand, in the preamble of your document, to store the result of the double accent command in a ‘box register’ for quick retrieval.

\accentedsymbol{\Ahathat}{\Hat{\Hat A}}

The commands \dddot and \ddddot are available to produce triple and quadruple dot accents in addition to the \dot and \ddot accents already available in L^{A}TEX.

3.7 Roots

In ordinary L^{A}TEX the placement of root indices is sometimes not so good: \sqrt[β]{k}

(\sqrt[\beta]{k}). In the amstex package \leftroot and \uproot allow you

to adjust the position of the root:

\sqrt[\leftroot{-2}\uproot{2}\beta]{k}

will move the beta up and to the right: \sqrt[β]{k}. The negative argument used with \leftroot moves the β to the right. The units are a small amount that is a useful size for such adjustments.

3.8 Boxed formulas

The command \boxed puts a box around its argument, like \fbox except that the contents are in math mode.

3.9 Extensible arrows

@>>> and @<<< produce arrows that extend automatically to accommodate unusually wide subscripts or superscripts. The text of a superscript is typed in between the first and second > or < symbols, and for a subscript, it’s typed between the second and third symbols. For example, @>\xi F_k\Gamma_k\alpha>> would have a superscript ξF_{k}Γ_{k}α placed above the arrow. These arrows were originally developed for use in commutative diagrams but can be used elsewhere also. (See section 7 for more information about the amscd package.)

3.10 Affixing symbols to other symbols

L^{A}TEX provides \stackrel for placing a superscript above a binary relation. In the amstex package there are somewhat more general commands, \overset and \underset, that can be used to place one symbol above or below another symbol, whether it’s a relation or something else. The input \overset{*}{X}

will place a superscript-size ∗ above the X: X^{∗}; \underset is the analog for adding a symbol underneath.

See also the description of \sideset in §6.3.

3.11 Operator names

Math functions such as log, sin, and lim are traditionally typeset in roman type to help avoid confusion with single math variables, set in math italic. The more common ones have predefined names, \log, \sin, \lim, and so forth, but new ones come up all the time in mathematical papers, so amstex provide’s a general mechanism for producing such names: \operatorname{xxx} produces xxx in the proper font and automatically adds proper spacing on either side when necessary, so that you get A xxx B instead of AxxxB.

Since \operatorname takes rather a lot of typing, you would usually put some definitions in the preamble of the form

\newcommand{\xxx}{\operatorname{xxx}}
\newcommand{\yyy}{\operatorname{yyy}}

for any operator names you’re going to use frequently.

Some of the operator names, such as \lim, have actually been defined using \operatorname* rather than \operatorname, because in displayed formulas if there is a subscript on \lim it is conventionally placed underneath, like the limits on sums:

C_{+}f(x) = lim_{t→0} C(f)(x + it) (3.2)

You can use \operatorname* just like \operatorname; the only difference is the placement of subscripts and superscripts. A few special operator names with limits are defined for you in the amstex package: \varinjlim, \varprojlim, \varliminf, and \varlimsup; there are some examples in the sample file testmath.tex.

3.12 \mod and its relatives

Commands \mod, \bmod, \pmod, \pod are provided to deal with the rather special spacing conventions of “mod” notation. \bmod and \pmod are available in L^{A}TEX, but in the amstex package the spacing of \pmod will adjust to a smaller value if it’s used in a non-display-mode formula. \mod and \pod are variants of \pmod preferred by some authors; \mod omits the parentheses, whereas \pod omits the “mod” and retains the parentheses.

3.13 Fractions and related constructions

In addition to \frac (which was already available in L^{A}TEX), amstex provides

\dfrac and \tfrac as convenient abbreviations for {\displaystyle\frac ...

} and {\textstyle\frac ... }. Furthermore, the thickness of the fraction line can be varied, using an optional argument of the \frac command. \frac [⟨dimension⟩]{...}{...} makes a fraction where the thickness of the horizontal rule is determined by the given dimension. The sample file testmath.tex shows an example using a thickness of 1.5pt.

For binomial expressions such as ({n \atop k}) amstex has \binom, \dbinom and

\tbinom.

3.14 Continued fractions

The continued fraction

\frac{1}{\sqrt{2} + \frac{1}{\sqrt{2} + \frac{1}{\sqrt{2} + ⋯}}} (3.3)

can be obtained by typing

\cfrac{1}{\sqrt{2}+
 \cfrac{1}{\sqrt{2}+
  \cfrac{1}{\sqrt{2}+\dotsb
}}}

Left or right placement of any of the numerators is accomplished by using

\cfrac[l] or \cfrac[r] instead of \cfrac.

3.15 Smash options

The plain TEX command \smash is used to typeset a subformula and give it an effective height and depth of zero, which is sometimes useful in adjusting the subformula’s position with respect to adjacent symbols. In the amstex package \smash has optional arguments t and b, because sometimes it is advantageous to be able to “smash” only the top or only the bottom of something while retaining the natural depth or height. For example, when adjacent radical symbols are unevenly sized or positioned because of differences in the height and depth of their contents, \smash can be employed to make them more consistent. Compare \sqrt{x} + \sqrt{y} and \sqrt{x} + \sqrt{y}, where the latter was produced by $\sqrt\{x\}

+ \sqrt{\smash[b]{y}}$.

3.16 Delimiter sizes

A subject that escapes mention in the L^{A}TEX book is how to control the size of large delimiters if the automatic sizing done by \left and \right produces unpleasing results. The automatic sizing has two limitations: First, it is applied mechanically to produce delimiters large enough to encompass the largest contained items, and second, the range of sizes is not even approximately continuous but has fairly large quantum jumps. This means that a math fragment that is infinitesimally too large for a given size will get the next larger size, a jump of 3pt or so in normal-sized text. There are two or three situations where the delimiter size is commonly adjusted, using a set of commands that have ‘big’ in their names.

Delimiter size  Result
normal size  (b)(\frac{c}{d})

                     \left, \right (b) (\frac{c}{d})
                     \bigl, \bigr  (b)(\frac{c}{d})
                     \Bigl, \Bigr  (b)(\frac{c}{d})
                     \biggl, \biggr (b)(\frac{c}{d})

                     \Biggl, \Biggr (b)(\frac{c}{d})

The first kind of situation is a cumulative operator with limits above and below. With \left and \right the delimiters usually turn out larger than necessary, and using \biggl and \biggr instead gives better results:

[∑_{i} a_{i} |∑_{j} x_{ij}|^{p}]^{1/p} versus [∑_{i} a_{i}|∑_{j} x_{ij}|^{p}]^{1/p}

The second kind of situation is clustered pairs of delimiters where \left and \right make them all the same size (because that is adequate to cover the encompassed material) but what you really want is to make some of the delimiters slightly larger to make the nesting easier to see.

((a_{1}b_{1}) − (a_{2}b_{2})) ((a_{2}b_{1}) + (a_{1}b_{2})) versus ((a_{1}b_{1}) − (a_{2}b_{2}))((a_{2}b_{1}) + (a_{1}b_{2}))

The third kind of situation is a slightly oversize object in running text, such as |\frac{b′}{d′} | where the delimiters produced by \left and \right cause too much line spreading. In that case \bigl and \bigr can be used to produce delimiters slightly larger than the base size but still able to fit within the normal line spacing: |\frac{b′}{d′} |.

In ordinary L^{A}TEX \big, \bigg, \Big, and \Bigg delimiters aren’t scaled properly over the full range of L^{A}TEX font sizes. With the amstex package they are.

Chapter 4

The \text command (amstext, amstex packages)

The \text command is defined by the amstex package through a subordinate package amstext (which can also be used independently if desired). The main use of the command \text is for words or phrases in a display. It is very similar to the L^{A}TEX command \mbox in its effects, but has a couple of advantages. If you want a word or phrase of text in a subscript, you can type ..._{\text{word or phrase}}, which is slightly easier than the \mbox equiv-

alent: ..._{\mbox{\scriptsize word or phrase}}. The other advantage is

the more descriptive name.

Chapter 5

The \boldsymbol command (amsbsy, amstex packages)

The \boldsymbol and \pmb commands are defined by the amstex package through a subordinate package amsbsy (which can also be used independently if desired). The \boldsymbol command is used to obtain bold numbers and other nonalphabetic symbols, as well as bold Greek letters, which cannot be made bold via the \mathbf command. It can also be used to obtain bold math italic letters; compare the results of M, \mathbf{M} and \boldsymbol{M}: MMM.

The availability of bold symbols varies on different systems depending on whether or not suitable fonts are installed. The \boldsymbol command should usually work fine for the common math symbols at 10pt size or larger, but if you find that it is not having the desired effect for a particular symbol, you could either (a) verify that the necessary fonts are available and properly installed; or (b) use \pmb: “poor man’s bold,” which works by printing multiple copies of the same symbol with slight offsets.

Chapter 6

Integrals and sums (amstex, amsintsm packages)

6.1 Multiple integral signs

\iint, \iiint, and \iiiint give multiple integral signs with the spacing between them nicely adjusted, in both text and display style. \idotsint is an extension of the same idea that gives two integral signs with dots between them.

6.2 Multiline subscripts and superscripts

The Sb and Sp environments can be used to typeset several lines as a subscript or superscript: for example

\begin{equation}
  \sum\begin{Sb}
        0\le i\le m\\ 0<j<n
      \end{Sb}
    P(i,j)
\end{equation}

produces a two-line subscript underneath the sum:

∑_{{0≤i≤m \atop 0<j<n}} P (i, j) (6.1)

Sb and Sp can be used anywhere that an ordinary subscript or superscript can be used.

6.3 The \sideset command

There’s also a command called \sideset, for a rather special purpose: putting symbols at the subscript and superscript corners of a large operator symbol such as ∑ or ∏. The prime example is the case when you want to put a prime on a sum symbol. If there are no limits above or below the sum, you could just use

\nolimits: here’s \sum\nolimits' E_n in display mode:

∑′ E_{n}. (6.2)

But if you want not only the prime but also something below or above the sum symbol, it’s not so easy. If you have

∑_{n<k, n odd} nE_{n} (6.3)

and you want to add a prime on the sum symbol, use \sideset like this:

\sideset{}{'}\sum_{...}nE_n

The extra pair of empty braces is explained by the fact that \sideset has the capability of putting an extra symbol or symbols at each corner of a large operator; to put an asterisk at each corner of a product symbol, you would type

\sideset{_*^*}{_*^*}\prod

producing

_{∗}^{∗}∏_{∗}^{∗} (6.4)

6.4 The amsintsm package

The amsintsm package, which is not automatically included with the amstex package, is an experimental package that changes the \int and \sum commands to better mark the boundaries of the quantity being summed or integrated. For example,

\int[t,a,b]{(\Omega[x] -\lambda x^2)}

means ‘the integral with respect to t, from a to b, over the following quantity’: ∫_{a}^{b}(Ω[x] − λx^{2}) dt. For more details, run L^{A}TEX on the file amsintsm.dtx.

Chapter 7

Commutative diagrams (amscd package)

Some commutative diagram commands like the ones in AMS-TEX are available as a separate package, amscd. For complex commutative diagrams authors will need to turn to more comprehensive packages like XY-pic, but for simple diagrams without diagonal arrows the amscd commands may be more convenient.

The commutative diagram

\begin{matrix}S^{W_{Λ}} ⊗ T & ⟶^{j} & T \\ ↓ & & ↓^{End P} \\ (S ⊗ T)/I & = & (Z ⊗ T)/J \end{matrix} (7.1)

can be produced in ordinary L^{A}TEX by

\begin{array}{ccc}
S^{{\mathcal{W}}_\Lambda}\otimes T&
    \stackrel{j}{\longrightarrow}&  T\\
\Big\downarrow&
        &\Big\downarrow\vcenter{%
          \rlap{$\scriptstyle\mathrm{End}\,P$}}\\
(S\otimes T)/I& =&  (Z\otimes T)/J
\end{array}

When the amscd package is used you would type instead

\begin{CD}
S^{{\mathcal{W}}_\Lambda}\otimes T   @>j>>   T\\
@VVV                                    @VV{\End P}V\\
(S\otimes T)/I                  @=      (Z\otimes T)/J
\end{CD}

(with \End defined as \operatorname{End}; see §3.11). This would give longer horizontal arrows than in (7.1) and improved spacing between elements of the diagram:

S^{W_{Λ}} ⊗ T ⟶^{j}  T
↓  ↓^{End P}
(S ⊗ T)/I  (Z ⊗ T)/J

In the CD environment the commands @>>>, @<<<, @VVV, and @AAA give respectively right, left, down, and up arrows. For the horizontal arrows, material between the first and second > or < symbols will be typeset as a superscript, and material between the second and third will be typeset as a subscript. Similarly, material between the first and second or second and third As or Vs of vertical arrows will be typeset as left or right “sidescripts”.

Chapter 8

Using math fonts

8.1 Introduction

For full details on font use in L^{A}TEX, see the L^{A}TEX documentation (fntguide.tex) and [3]. Math font commands in L^{A}TEX include \mathbf, \mathrm, \mathcal, \mathsf, \mathtt, \mathit. Certain other math alphabet commands are available through the packages amsfonts, eufrak, and euscript, if the requisite extra math fonts (from a font set called ‘AMSFonts’) are installed on your system (see the installation instructions, Appendix A).

8.2 Recommended use of math font commands

If you find yourself employing math font commands frequently in your document, you might wish that they had shorter names, such as \mb instead of \mathbf. However, for L^{A}TEX to provide shorter names would actually be a disservice to authors, in light of the much better alternative: defining custom command names derived from the names of the underlying mathematical objects, rather than from the names of the fonts used to distinguish the objects. For example, if you are using bold to indicate vectors, then you will be better served in the long run if you define a ‘vector’ command instead of a ‘math-bold’ command:

\newcommand{\vec}[1]{\mathbf{#1}}

whereupon you can write \vec{a} + \vec{b} to produce a+b. ^{1} If you decide several months down the road that you want to use the bold font for some other purpose, and mark vectors by a small over-arrow instead, then you can put the change into effect merely by changing the definition of \vec; otherwise you would have to replace all occurrences of \mathbf throughout your document, perhaps even needing to inspect each one to see whether it is an instance of a vector, if you’re not absolutely sure that you used \mathbf only for vectors and nothing else.

It might also be appropriate in some circumstances to assign distinct command names for different letters of a particular font:

\DeclareSymbolFont{AMSb}{U}{msb}{m}{n}% or use amsfonts package
\DeclareMathSymbol{\C}{\mathalpha}{AMSb}{"43}
\DeclareMathSymbol{\R}{\mathalpha}{AMSb}{"52}

These statements would define the commands \C and \R to produce blackboardbold letters from the ‘AMSb’ math symbols font. If you refer often to the complex numbers or real numbers in your document, you might find this method more convenient than (let’s say) defining a \field command and writing \field{C}, \field{R}. But for maximum flexibility and control, define such a \field command and then define \C and \R in terms of that command:

1If you actually tried this example you would discover that the command \vec is already defined. Looking up the command \vec, you would find that it produces a different sort of notation for vectors: a small over-arrow x⃗. The solution is to use \renewcommand (if you expect that you will never need the over-arrow version of the notation) or to choose a different name for your new vector command.

\usepackage{amsfonts}% to get the \mathbb alphabet
\newcommand{\field}[1]{\mathbb{#1}}
\newcommand{\C}{\field{C}}
\newcommand{\R}{\field{R}}

Chapter 9

Theorems and similar structures (amsthm package)

9.1 Introduction

The amsthm package provides an enhanced version of the L^{A}TEX command \newtheorem for defining theorem-like environments. The amsthm version of the \newtheorem command recognizes a \theoremstyle specification (as in Mittelbach’s theorem package) and has a * form for defining unnumbered environments. The amsthm package also defines a proof environment that automatically adds a ‘Q.E.D’ symbol at the end. The amsart and amsbook document classes automatically load the amsthm package, so everything described here applies to them as well.

9.2 The \newtheorem command

In mathematical research articles and books, there are many theorem-like elements serving authors’ goal of stating theorems and proofs: lemmas, propositions, axioms, theorems (of course), corollaries, conjectures, definitions, remarks, proofs, cases, steps, and so forth. As these elements form a slice of the text stream with well-defined boundaries, they are naturally handled in L^{A}TEX as environments. But L^{A}TEX document classes normally do not provide predefined environments for theorem-like elements because (a) that would make it difficult for authors to exercise the necessary control over the automatic numbering and (b) the variety of such elements is so wide that it’s just not possible for a document class to provide every one that will ever be needed. Instead there is a command \newtheorem, similar to \newenvironment in effect, that makes it easy for authors to define environments for the elements required for a particular document.

The \newtheorem command has two mandatory arguments; the first one is the environment name that the author would like to use for this element; the second one is the heading text. For example,

\newtheorem{lem}{Lemma}

means that instances in the document of

\begin{lem} Text text ... \end{lem}

will produce

Lemma 1. Text text …

where the heading consists of the specified text ‘Lemma’ and an automatically generated number and punctuation.

If \newtheorem* is used instead of \newtheorem in the above example, there will not be any automatic numbers generated for any of the lemmas in the document. This form of the command can be useful if you have only one lemma and don’t want it to be numbered; more often, though, it is used to produce a special named variant of one of the common theorem types. For example, if you have a lemma whose name should be ‘Klein’s Lemma’ instead of ‘Lemma’ + number, then the statement

\newtheorem*{KL}{Klein's Lemma}

would allow you to write

\begin{KL} Text text ... \end{KL}

and get the desired output.

9.3 Numbering modifications

In addition to the two mandatory arguments, \newtheorem has two (mutually exclusive) optional arguments. These affect the sequencing and hierarchy of the numbering.

By default each theorem-like environment is numbered independently. Thus if you have three lemmas and two theorems interspersed, they will be numbered something like this: Lemma 1, Lemma 2, Theorem 1, Lemma 3, Theorem 2. If you want lemmas and theorems to share the same numbering sequence—Lemma 1, Lemma 2, Theorem 3, Lemma 4, Theorem 5—then you should indicate the desired relationship as follows:

\newtheorem{thm}{Theorem}
\newtheorem{lem}[thm]{Lemma}

The optional argument [thm] in the second statement means that the lem environment should share the thm numbering sequence instead of having its own independent sequence.

To have a theorem-like environment numbered subordinately within a sectional unit—e.g., to get propositions numbered Proposition 2.1, Proposition 2.2, and so on in section 2—put the name of the parent unit in square brackets in final position:

\newtheorem{prop}{Proposition}[section]

The optional argument [section] means that the prop counter will be reset to 0 whenever the parent counter section is incremented.

9.4 Changing styles for theorem-like environments

The amsthm package supports the notion of a current theorem style, which determines what will be produced by a given \newtheorem command. The three theorem styles provided—plain [default], definition, and remark—receive different typographical treatment that gives them visual emphasis corresponding to their relative importance. The details of this typographical treatment may vary depending on the document class but, for example, the plain style, used for normally produces italic body text, while the other two styles produce roman body text.

To create new theorem-like environments in the different styles, divide your \newtheorem commands into groups and preface each group with the appropriate \theoremstyle. If no \theoremstyle command is given, the style used will be plain. Some examples:

\theoremstyle{plain}% default
\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}[thm]{Lemma}
\newtheorem{prop}[thm]{Proposition}
\newtheorem*{cor}{Corollary}
\newtheorem*{KL}{Klein's Lemma}
\theoremstyle{definition}
\newtheorem{defn}{Definition}[section]
\newtheorem{conj}{Conjecture}[section]
\newtheorem{exmp}{Example}[section]
\theoremstyle{remark}
\newtheorem*{rem}{Remark}
\newtheorem*{note}{Note}
\newtheorem{case}{Case}

9.5 Proofs

A predefined proof environment is provided for proofs, and produces the heading “Proof” with appropriate spacing and punctuation. The proof environment is primarily intended for short proofs, no more than a page or so in length; longer proofs should probably be done as a separate section or subsection in your document.

A “Q.E.D.” symbol, , is automatically appended at the end of a proof. To substitute a different end-of-proof symbol, use \renewcommand to redefine the command \qedsymbol. For a long proof done as a subsection or section, you can obtain the symbol and the usual amount of preceding space by using \qed.

Placement of the Q.E.D. symbol can be problematic if the last part of a proof environment is a displayed equation or list environment or something of that nature. Adequate results can sometimes be obtained by using \qed at the appropriate spot and then undefining \qed just before the end of the proof.

(The effect will be automatically localized to the current proof by normal L^{A}TEX scoping rules.) For example:

\begin{proof}
...
\begin{equation}
G(t)=L\gamma!\,t^{-\gamma}+t^{-\delta}\eta(t) \qed
\end{equation}
\renewcommand{\qed}{}\end{proof}

An optional argument of the proof environment allows you to substitute a different name for the standard “Proof”. If you want the proof heading to be, say, “Proof (sufficiency)”, then write

\begin{proof}[Proof (sufficiency)]

Appendix A

Installation instructions

A.1 Introduction

To use version 1.2 of AMS-L^{A}TEX it is necessary for you to have a recent version of L^{A}TEX (June 1994 or later, ‘L^{A}TEX 2ε’). If you’re not sure about the version, look at the startup message that is printed on screen and in the TEX log when you run L^{A}TEX. It should mention the L^{A}TEX version number and date somewhere in the first ten lines. If your version of L^{A}TEX is older than June 1994, we suggest getting the latest version from the Comprehensive TEX Archive Network (CTAN), directory tex-archive/macros/latex, ftp addresses ftp.shsu.edu (US), ftp.dante.de (Germany), or ftp.tex.ac.uk (UK). If ftp file transfer is not an option for you, contact the source from which you originally obtained L^{A}TEX.

A.2 Putting files in a suitable place on your system

See also the READ.ME file for late-breaking news about installation procedures.

There are two ‘areas’ (directories or folders) on your system that are involved in installing AMS-L^{A}TEX: an AMS-L^{A}TEX source files area, and a L^{A}TEX input files area. The basic procedure is to put all the files in the AMS-L^{A}TEX distribution into the AMS-L^{A}TEX source files area, then run L^{A}TEX on an installation file amslatex.ins, and then move the resulting files to the L^{A}TEX input area.

Typical area names

AMS-L^{A}TEX source files area  L^{A}TEX input area

 DOS c:\emtex\latex\packages\amslatex    c:\emtex\latex\inputs
 Unix /tex/latex/packages/amslatex        /tex/latex/inputs
 Mac OzTeX:latex:packages:amslatex       OzTeX:latex:inputs
 VMS tex_disk:[latex.packages.amslatex]  tex_disk:[latex.inputs]

In the following suggested installation process, we use PC/DOS directory and file name conventions for concreteness; for other systems, it should be obvious how to adapt the names.

The destination directory for the AMS-L^{A}TEX files should be

  xxx\latex\packages\amslatex

where xxx depends on the type of computer system and TEX directory structure the user has. Let’s say it is emTEX, then xxx will normally be c:\emtex.

So you would put the above files into the directory

  c:\emtex\latex\packages\amslatex

A.3 Running L^{A}TEX on the installation script amslatex.ins

Next run L^{A}TEX on the installation file amslatex.ins. This will create the stripped files amstex.sty, amssymb.sty, amsart.cls, etc., that are actually used for processing documents. All these files should then be moved to an input directory, e.g.,

  c:\emtex\latex\inputs

(this directory should be added to your TEX search path, if it isn’t there already).

A.4 Testing

For a quick test of the installation, try printing the test file subeqn.tex. For more detailed and comprehensive information about using AMS-L^{A}TEX, print the AMS-L^{A}TEX user’s guide (amsldoc.tex).

A.5 Extra math fonts

There are L^{A}TEX packages called amsfonts and amssymb that are designed to exploit the extra math fonts provided by the AMSFonts font set. If you don’t have this set already on your system, and would like to use some of the symbols in it, it can be obtained by anonymous FTP from CTAN and from the AMS archive at e-math.ams.org. It can also be ordered on disk from the AMS catalog.

A.6 Memory requirements

Incomplete.

A.7 Files included in this distribution

[Incomplete] See the READ.ME file for details on the contents of the individual files.

READ.ME
amslatex.ins
amslatex.chg
amslatex.bug
amsbsy.dtx
amscd.dtx
amsgen.dtx
amsintsm.dtx
amstex.dtx
amstext.dtx
amsxtra.dtx

               amsldoc.dtx
               subeqn.tex
               testmath.tex
               dif11-12.tex

Appendix B

Error messages

Incomplete.

Appendix C

Where to find other information

C.1 Differences between AMS-L^{A}TEX version 1.1 and AMS-L^{A}TEX version 1.2

These are described in the document dif11-12.tex (incomplete).

C.2 Differences between AMS-TEX and AMS-L^{A}TEX

These are described in the document amstexdf.tex (incomplete).

C.3 Technical notes

These are found in technote.tex (incomplete).

Appendix D

Getting help

Comments or questions regarding the AMS-L^{A}TEX package should be sent to:

American Mathematical Society

Technical Support P. O. Box 6248 Providence, RI 02940 Phone: 800-321-4AMS (321-4267) or 401-455-4080

         Internet: tech-support@math.ams.org

If you are reporting a problem you should include the following information:

1. the source file where the problem occurred, preferably reduced to minimum size by removing any material that can be removed without affecting the observed problem.

2. a L^{A}TEX log file showing the error message (if applicable) and the version numbers of the document class and option files being used.

D.1 Further information

Information about obtaining AMSFonts or other TEX-related software from the AMS Internet archive e-math.ams.org can be obtained by sending a request through electronic mail to:

                       e-math@math.ams.org

Information about obtaining AMS-L^{A}TEX on diskette from the AMS is available from:

American Mathematical Society

Customer Services P. O. Box 6248 Providence, RI 02940 Phone: 800-321-4AMS (321-4267) or 401-455-4000

          Internet: cust-serv@math.ams.org

The TEX Users Group is a nonprofit organization that publishes a journal (TUGboat), holds meetings, and serves as a clearing-house of general information about TEX and TEX-related software.

TEX Users Group P. O. Box 869 Santa Barbara, CA 93102-0869 Phone: (805) 963-1338

          Internet: tug@tug.org

Membership in the TEX Users Group is a good way to support continued development of TEX-related public-domain software.

There are also many TEX user groups in other countries; information about contacting a local user group can be gotten from the TEX Users Group.

There is a Usenet newsgroup called comp.text.tex that is a fairly good source of information about L^{A}TEX and TEX in general. If you don’t know about reading newsgroups, check with your local system administrator to see if newsgroup service is available at your site.

Bibliography

[1] AMSFonts version 2.1—user’s guide, American Mathematical Society, Providence, R.I., 1991; distributed with the AMSFonts package.

[2] Instructions for preparing electronic manuscripts—AMS-L^{A}TEX, American Mathematical Society, Providence, R.I., 1990.

[3] Michel Goossens, Frank Mittelbach, and Alexander Samarin, The L^{A}TEX Companion, Addison-Wesley, 1993.

[4] Donald Knuth, The TEXbook, Addison-Wesley, 1984.

[5] Leslie Lamport, L^{A}TEX: A document preparation system, Addison-Wesley, 2nd edition, 1994.

[6] Frank Mittelbach and Rainer Schöpf, The new font family selection—user interface to standard L^{A}TEX, TUGboat 11, no. 2 (June 1990), pp. 297–305.

[7] Michael Spivak, The joy of TEX, 2nd ed., American Mathematical Society, Providence, R.I., 1990.

Index

\!, 9
\,, 9
\:, 9
\;, 9
@!, 9
@,, 9

\\, 2, 6

\\*, 6
\accentedsymbol, 10, 11
\addtocounter, 8
\addtolength, 5
\adjusttag, 6

align environment, 3, 5 alignat environment, 3, 4 aligned environment, 6 alignedat environment, 6

\allowdisplaybreaks, 6
amsart.cls, 20

amsbsy package, 1, 15 amscd package, 1, 11, 17 amsfonts package, 1, 20 amsintsm package, 1, 15, 16

amsintsm.dtx, 16
amslatex.ins, 19, 20
amsldoc.tex, 20

amssymb package, 20

amssymb.sty, 20

amstex package, 1, 2, 5–16

amstex.sty, 20
amstexdf.tex, 21

amstext package, 1, 14 amsxtra package, 10 array environment, 8

\Big, 14
\big, 14
\Bigg, 14
\bigg, 14
\Biggl, 14
\biggl, 14
\Biggr, 14
\biggr, 14

                                    \Bigl, 14
                                    \bigl, 14
                                    \Bigr, 14
                                    \bigr, 14
                                    \binom, 12

bmatrix environment, 8

                                    \bmod, 12
                                    \boldsymbol, v, 1, 15
                                    \boxed, 11

\C, 18

cases environment, v, 8 CD environment, 1, 17

                                    \cdots, 10
                                    centertags option, 1
                                    \cfrac, 13
                                    comp.text.tex, 22
                                    \dbinom, 12
                                    \ddddot, 11
                                    \dddot, 11
                                    \ddot, 11
                                    \dfrac, 12
                                    dif11-12.tex, 21

dimension, 12

                                    \displaybreak, 6

displaymath environment, 2

                                    \documentclass, 2
                                    \dot, 11
                                    \dots, 10
                                    \dotsb, 10
                                    \dotsc, 10
                                    \dotsi, 10
                                    \dotsm, 10
                                    e-math.ams.org, 20, 21
                                    \End, 17
                                    \end, 10

eqnarray environment, v, 2, 6

                                    \eqref, 7

equation environment, v, 2, 4, 5 equation* environment, 2

\fbox, 11
\field, 18

fleqn option, 2, 5

fntguide.tex, 18
\frac, 12

gather environment, 3, 5 gathered environment, 6

\Hat, 10
\hat, 10
\hdotsfor, 9
\idotsint, 15
\iiiint, 15
\iiint, 15
\iint, 15

\int, 1, 16

\intertext, 6

intlim option, 2

intlimits option, 1
\ldots, 10

\left, 13, 14

\leftroot, 11

leqno option, 2 \lim, v, 11, 12

\log, 11
\mathbb, 18
\mathbf, 15, 18
\mathcal, 18
\mathfrak, 18
\mathit, 18
\mathrm, 18
\mathsf, 18
\mathtt, 18

matrix environment, 8

\mb, 18
\mbox, 15
\medspace, 9
\mod, 12

multline environment, 4, 5

\multlinegap, 4, 5
namelimits option, 1
\negmedspace, 9

\negthickspace, 9
\negthinspace, 9
\newcommand, 11
\newtheorem, 7
nointlimits option, 1
\nolimits, 16
nonamelimits option, 1
nonamelm option, 2
nosumlim option, 2
nosumlimits option, 1
\notag, 2
\numberwithin, 7
\operatorname, 12, 17
\operatorname*, 12
\overleftarrow, 9
\overleftrightarrow, 9
\overrightarrow, 9
\overset, 11
\pagebreak, 6

pmatrix environment, 8 \pmb, 1, 15

\pmod, 12
\pod, 12
\qquad, 9
\quad, 9

\R, 18

READ.ME, 20
\renewcommand, 18

reqno option, 2

\right, 13, 14
righttag option, 2

Sb environment, 15, 16

\setcounter, 7, 8
\setlength, 5
\sideset, 11, 16

\sin, v, 11 smallmatrix environment, 8

\smash, 13

Sp environment, 15, 16 split environment, 2, 5

\stackrel, 11
subeqn.tex, 20

\sum, 1, 16

sumlimits option, 1
\tag, 2
\tag*, 2
\tbinom, 12

tbtags option, 1

technote.tex, 21
testmath.tex, 2, 9, 12

\text, 1, 8, 14

\tfrac, 12
\theequation, 7
\thickspace, 9
\thinspace, 9
\underleftarrow, 9
\underleftrightarrow, 9
\underrightarrow, 9
\underset, 11
\uproot, 11
\usepackage, 1, 2
\varinjlim, 12
\varliminf, 12
\varlimsup, 12
\varprojlim, 12
\vec, 18

Vmatrix environment, 8 vmatrix environment, 8

xalignat environment, 3, 4 xxalignat environment, 3