latex学习-必备的amsmath包的介绍

Users Guide for the amsmath Package (Version 2.0) American Mathematical Society 1999/12/13 iiCONTENTS Contents 1Introduction1 2Options for the amsmath package2 3Displayed equations3 3.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 3.2Single equations. . . . . . . . . . . . . . . . . . . . . . . . . . .3 3.3Split equations without alignment. . . . . . . . . . . . . . . . .5 3.4Split equations with alignment. . . . . . . . . . . . . . . . . . .5 3.5Equation groups without alignment . . . . . . . . . . . . . . . . .6 3.6Equation groups with mutual alignment . . . . . . . . . . . . . .6 3.7Alignment building blocks . . . . . . . . . . . . . . . . . . . . . .7 3.8Adjusting tag placement . . . . . . . . . . . . . . . . . . . . . . .8 3.9Vertical spacing and page breaks in multiline displays. . . . . .8 3.10 Interrupting a display. . . . . . . . . . . . . . . . . . . . . . . .9 3.11 Equation numbering . . . . . . . . . . . . . . . . . . . . . . . . .9 4Miscellaneous mathematical features10 4.1Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 4.2Math spacing commands . . . . . . . . . . . . . . . . . . . . . . .11 4.3Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 4.4Nonbreaking dashes. . . . . . . . . . . . . . . . . . . . . . . . .12 4.5Accents in math. . . . . . . . . . . . . . . . . . . . . . . . . . .12 4.6Roots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 4.7Boxed formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 4.8Over and under arrows . . . . . . . . . . . . . . . . . . . . . . . .13 4.9Extensible arrows . . . . . . . . . . . . . . . . . . . . . . . . . . .13 4.10 Affi xing 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 5Operator names17 5.1 Defi ning new operator names . . . . . . . . . . . . . . . . . . . .17 5.2mod and its relatives . . . . . . . . . . . . . . . . . . . . . . . . .18 6The text command18 CONTENTSiii 7Integrals and sums19 7.1Multiline subscripts and superscripts . . . . . . . . . . . . . . . .19 7.2The sideset command . . . . . . . . . . . . . . . . . . . . . . .19 7.3Placement of subscripts and limits . . . . . . . . . . . . . . . . .20 7.4Multiple integral signs . . . . . . . . . . . . . . . . . . . . . . . .20 8Commutative diagrams20 9Using math fonts21 9.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21 9.2Recommended use of math font commands. . . . . . . . . . . .21 9.3Bold math symbols . . . . . . . . . . . . . . . . . . . . . . . . . .22 9.4Italic Greek letters . . . . . . . . . . . . . . . . . . . . . . . . . .23 10 Error messages and output problems23 10.1 General remarks. . . . . . . . . . . . . . . . . . . . . . . . . . .23 10.2 Error messages . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 10.3 Warning messages. . . . . . . . . . . . . . . . . . . . . . . . . .29 10.4 Wrong output . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 11 Additional information30 11.1 Converting existing documents. . . . . . . . . . . . . . . . . . .30 11.2 Technical notes . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 11.3 Getting help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 11.4 Of possible interest . . . . . . . . . . . . . . . . . . . . . . . . . .31 Bibliography31 Index33 ivCONTENTS 1 1 Introduction The amsmath package is a L ATEX package that provides miscellaneous enhance- ments for improving the information structure and printed output of documents that contain mathematical formulas. Readers unfamiliar with L ATEX should refer to 7. If you have an up-to-date version of L ATEX, 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 /tex/amsmath.html or /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: amsbsyamstext amscdamsxtra 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 ATEX 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 defi ne 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 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. 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. 22.OPTIONS FOR THE AMSMATH PACKAGE amstext Provides a text command for typesetting a fragment of text inside a display. amsopn Provides DeclareMathOperator for defi ning new operator names like sin and lim. amsbsy For backward compatibility this package continues to exist but use of the newer bm package that comes with L ATEX is recommended instead. amscd Provides a CD environment for simple commutative diagrams (no support for diagonal arrows). amsxtra Provides certain odds and ends such as fracwithdelims and ac- centedsymbol, for compatibility with documents created using version 1.1. The amsmath package incorporates amstext, amsopn, and amsbsy. The fea- tures of amscd and amsxtra, however, are available only by invoking those packages separately. 2 Options for the amsmath package The amsmath package has the following options: centertags (default) For a split equation, place equation numbers vertically centered on the total height of the equation. tbtags Top-or-bottom tags: For a split equation, place equation numbers level with the last (resp. fi rst) line, if numbers are on the right (resp. left). sumlimits (default) Place the subscripts and superscripts of summation sym- bols above and below, in displayed equations. This option also aff ects other symbols of the same typeQ, ,N,L, and so forthbut exclud- ing integrals (see below). nosumlimits Always place the subscripts and superscripts of summation-type symbols to the side, even in displayed equations. intlimits Like sumlimits, but for integral symbols. nointlimits (default) Opposite of intlimits. namelimits (default) Like sumlimits, but for certain operator names such as det, inf, lim, max, min, that traditionally have subscripts placed under- neath when they occur in a displayed equation. nonamelimits Opposite of namelimits. To use one of these package options, put the option name in the optional ar- gument of the usepackage commande.g., usepackageintlimitsamsmath. The amsmath package also recognizes the following options which are nor- mally selected (implicitly or explicitly) through the documentclass command, and thus need not be repeated in the option list of the usepackageamsmath statement. 3.2.SINGLE EQUATIONS3 leqno Place equation numbers on the left. reqno Place equation numbers on the right. fleqn Position equations at a fi xed indent from the left margin rather than centered in the text column. 3 Displayed equations 3.1Introduction The amsmath package provides a number of additional displayed equation struc- tures beyond the ones provided in basic L ATEX. The augmented set includes: equationequation*alignalign* gathergather*flalignflalign* multlinemultline*alignatalignat* split (Although the standard eqnarray environment remains available, it is better to use align or equation+split instead.) Except for split, each environment has both starred and unstarred forms, where the unstarred forms have automatic numbering using L ATEXs 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 taghlabeli, where hlabeli 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 within the unnumbered versions of all the amsmath alignment structures. Some examples of the use of tag may be found in the sample fi les testmath.tex and subeqn.tex provided with the amsmath package. The split environment is a special subordinate form that is used only inside one of the others. It cannot be used inside multline, however. In the structures that do alignment (split, align and variants), relation symbols have an it has to go before. 3.2Single equations The equation environment is for a single equation with an automatically gen- erated number. The equation* environment is the same except for omitting the number.1 1Basic LATEX doesnt provide an equation* environment, but rather a functionally equiv- alent environment named displaymath. 43.DISPLAYED EQUATIONS Table 3.1. Comparison of displayed equation environments (vertical lines in- dicating nominal margins) beginequation* a=b endequation* a = b beginequation a=b endequation (1)a = b beginequationlabelxx beginsplit a vertical centering as for split is not supported by multline. Its possible to force one of the middle lines to the left or right with com- mands shoveleft, shoveright. These commands take the entire line as an argument, up to but not including the fi nal ; for example (3.10)A B C D beginmultline framebox.65columnwidthA framebox.5columnwidthB shoverightframebox.55columnwidthC framebox.65columnwidthD endmultline The value of multlinegap can be changed with the usual L ATEX commands setlength or addtolength. 3.4Split equations with alignment Like multline, the split environment is for single equations that are too long to fi t 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 each one is centered separately within the text width (see Table 3.1). Equations inside gather are separated by a bslash command. Any equation in a gather may consist of a beginsplit . endsplit structurefor example: begingather first equation beginsplit second usually binary relations such as equal signs are aligned (see Table 3.1). To have several equation columns side-by-side, use extra ampersands to sep- arate the columns: x = yX = Ya = b + c(3.12) x0= y0X0= Y 0 a0= b(3.13) x + x0= y + y0X + X0= Y + Y 0 a0b = c0b(3.14) beginalign x thus they can be used as a component in a containing expression. E.g., B0= E, E0= B 4j, ) Maxwells equations beginequation* left.beginaligned B the philosophy is that page breaks in such material should receive individual attention from the author.To get an in- dividual page break inside a particular displayed equation, a displaybreak command is provided. displaybreak is best placed immediately before the where it is to take eff ect. Like L ATEXs pagebreak, displaybreak takes an optional argument between 0 and 4 denoting the desirability of the page- break.displaybreak0 means “it is permissible to break here” without encouraging a break; displaybreak with no optional argument is the same as displaybreak4 and forces a break. If you prefer a strategy of letting page breaks fall where they may, even in the middle of a multi-line equation, then you might put allowdisplaybreaks1 in the preamble of your document. An optional argument 14 can be used for 3.11.EQUATION NUMBERING9 fi ner control: 1 means allow page breaks, but avoid them as much as possi- ble; values of 2,3,4 mean increasing permissiveness. When display breaks are enabled with allowdisplaybreaks, the * command can be used to prohibit a pagebreak after a given line, as usual. Note: Certain equation environments wrap their contents in an unbreakable box, with the consequence that neither displaybreak nor allowdisplaybreaks will have any eff ect on them. These include split, aligned, gathered, and alignedat. 3.10Interrupting a display The command intertext is used for a short interjection of one or two lines of text in the middle of a multiple-line display structure (see also the text command in 6).Its salient feature is preservation of the alignment, which would not happen if you simply ended the display and then started it up again afterwards. intertext may only appear right after a or * command. Notice the position of the word “and” in this example. A1= N0(;0) (;0),(3.22) A2= (;0) (;),(3.23) and A3= N(;).(3.24) beginalign A_1Omega)-phi(lambda;Omega), A_2Omega)-phi(lambda;Omega), intertextand A_3omega). endalign 3.11Equation numbering 3.11.1Numbering hierarchy In L ATEX if you wanted to have equations numbered within sectionsthat is, have equation numbers (1.1), (1.2), ., (2.1), (2.2), ., in sections 1, 2, and so forthyou could redefi ne theequation as suggested in the L ATEX manual 7, 6.3, C.8.4: renewcommandtheequationthesection.arabicequation This works pretty well, except that the equation counter wont 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 amsmath package pro- vides a command numberwithin. To have equation numbering tied to section numbering, with automatic reset of the equation counter, write numberwithinequationsection As its name implies, the numberwithin command can be applied to any counter, not just the equation counter. 104.MISCELLANEOUS MATHEMATICAL FEATURES 3.11.2Cross references to equation numbers To make cross-references to equations easier, an eqref command is provided. This automatically supplies the parentheses around the equation number. I.e., if refabc produces 3.2 then eqrefabc produces (3.2). 3.11.3Subordinate numbering sequences The amsmath package provides also a subequations environment to make it easy to number equations in a particular group with a subordinate numbering scheme. For example beginsubequations . endsubequations causes all numbered equations within that part of the document to be numbered (4.9a) (4.9b) (4.9c) ., if the preceding numbered equation was (4.8). A label command immediately after beginsubequations will produce a ref of the parent number 4.9, not 4.9a. The counters used by the subequations environ- ment are parentequation and equation and addtocounter, setcounter, value, etc., can be applied as usual to those counter names. To get anything other than lowercase letters for the subordinate numbers, use standard L ATEX methods for changing numbering style 7, 6.3, C.8.4. For example, redefi ning theequation as follows will produce roman numerals. beginsubequations renewcommandtheequationtheparentequation romanequation . 4 Miscellaneous mathematical features 4.1Matrices The amsmath package provides some environments for matrices beyond the basic array environment of L ATEX. The pmatrix, bmatrix, Bmatrix, vmatrix and Vmatrix have (respectively) (), , , |, and kk 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 dont have to give column specifi cations for any of the matrix environments; by default you can have up to 10 centered columns.2(If you need left or right alignment in a column or other special formats you must resort to array.) 2More precisely: The maximum number of columns in a matrix is determined by the counter MaxMatrixCols (normal value = 10), which you can change if necessary using LATEXs setcounter or addtocounter commands. 4.3.DOTS11 To produce a small matrix suitable for use in text, there is a smallmatrix environment (e.g., ? a b c d ? ) that comes closer to fi tting within a single text line than a normal matrix.Delimiters must be provided; there are no p,b,B,v,V versions of smallmatrix. The above example was produced by bigl( beginsmallmatrix athickspacenegthickspace quad qquad For the greatest possible control over math spacing, use mspace and math units. One math unit, or mu, is equal to 1/18 em. Thus to get a negative quad you could write mspace-18.0mu. 4.3Dots For preferred placement of ellipsis dots (raised or on-line) in various contexts there is no general consensus. It may therefore be considered a matter of taste. By using the semantica