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User’s Guide for the amsmath Package
(Version 2.0)
American Mathematical Society
1999/12/13
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ii
CONTENTS
Contents
1 Introduction 1
2 Options for the amsmath
package 2
3 Displayed equations 3
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.2 Single equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.3 Split equations without alignment . . . . . . . . . . . . . . . . . 5
3.4 Split equations with alignment . . . . . . . . . . . . . . . . . . . 5
3.5 Equation groups without alignment . . . . . . . . . . . . . . . . . 6
3.6 Equation groups with mutual alignment . . . . . . . . . . . . . . 6
3.7 Alignment building blocks . . . . . . . . . . . . . . . . . . . . . . 7
3.8 Adjusting tag placement . . . . . . . . . . . . . . . . . . . . . . . 8
3.9 Vertical spacing and page breaks in multiline displays . . . . . . 8
3.10 Interrupting a display . . . . . . . . . . . . . . . . . . . . . . . . 9
3.11 Equation numbering . . . . . . . . . . . . . . . . . . . . . . . . . 9
4 Miscellaneous mathematical features 10
4.1 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.2 Math spacing commands . . . . . . . . . . . . . . . . . . . . . . . 11
4.3 Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.4 Nonbreaking dashes . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.5 Accents in math . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.6 Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.7 Boxed formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.8 Over and under arrows . . . . . . . . . . . . . . . . . . . . . . . . 13
4.9 Extensible arrows . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.10 Affixing symbols to other symbols . . . . . . . . . . . . . . . . . 13
4.11 Fractions and related constructions . . . . . . . . . . . . . . . . . 14
4.12 Continued fractions . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.13 Smash options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.14 Delimiters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5 Operator names 17
5.1 Defining new operator names . . . . . . . . . . . . . . . . . . . . 17
5.2
\mod
and its relatives . . . . . . . . . . . . . . . . . . . . . . . . . 18
6 The
\text command 18
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CONTENTS
iii
7 Integrals and sums 19
7.1 Multiline subscripts and superscripts . . . . . . . . . . . . . . . . 19
7.2 The
\sideset
command . . . . . . . . . . . . . . . . . . . . . . . 19
7.3 Placement of subscripts and limits . . . . . . . . . . . . . . . . . 20
7.4 Multiple integral signs . . . . . . . . . . . . . . . . . . . . . . . . 20
8 Commutative diagrams 20
9 Using math fonts 21
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
9.2 Recommended use of math font commands . . . . . . . . . . . . 21
9.3 Bold math symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 22
9.4 Italic Greek letters . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10 Error messages and output problems 23
10.1 General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10.2 Error messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10.3 Warning messages . . . . . . . . . . . . . . . . . . . . . . . . . . 29
10.4 Wrong output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
11 Additional information 30
11.1 Converting existing documents . . . . . . . . . . . . . . . . . . . 30
11.2 Technical notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
11.3 Getting help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
11.4 Of possible interest . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Bibliography 31
Index 33
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iv
CONTENTS
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1
—1—
Introduction
The amsmath
package is a L
A
T
E
X package that provides miscellaneous enhance-
ments for improving the information structure and printed output of documents
that contain mathematical formulas. Readers unfamiliar with L
A
T
E
X should refer
to [7]. If you have an up-to-date version of L
A
T
E
X, the amsmath package is nor-
mally provided along with it. Upgrading when a newer version of the
amsmath
package is released can be done via
http://www.ams.org/tex/amsmath.html
or
ftp://ftp.ams.org/pub/tex/
.
This documentation describes the features of the amsmath package and dis-
cusses how they are intended to be used. It also covers some ancillary packages:
amsbsy amstext
amscd amsxtra
amsopn
These all have something to do with the contents of math formulas. For infor-
mation on extra math symbols and math fonts, see [1] and http://www.ams.
org/tex/amsfonts.html
. For documentation of the amsthm
package or AMS
document classes (amsart
,
amsbook
, etc.) see [3] or [2] and
http://www.ams.
org/tex/author-info.html.
If you are a long-time L
A
T
E
X user and have lots of mathematics in what you
write, then you may recognize solutions for some familiar problems in this list
of amsmath
features:
•
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- or 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 overprinting
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
or product symb ols.
•
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.
The
amsmath
package is distributed together with some small auxiliary pack-
ages:
amsmath Primary package, provides various features for displayed equations and
other mathematical constructs.
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