User's Guide for the amsmath Package (Version 2.0)
Contents
1. and give horizontal and vertical double lines A null arrow command can be used instead of a visible arrow to fill out an array where needed 9 Using math fonts 9 1 Introduction For more comprehensive information on font use in ATEX see the ATEX font guide fntguide tex or The ATEX Companion 4 The basic set of math font commands in TEX includes mathbf mathrm mathcal mathsf mathtt mathit Additional math alphabet commands such as mathbb for black board bold mathfrak for Fraktur and mathscr for Euler script are available through the packages amsfonts and euscript distributed separately 9 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 Of course there is nothing to keep you from providing such abbreviations for yourself by suitable newcommand statements But for ATEX to provide shorter names would actually be a disservice to authors as that would obscure a 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 22 9 USING MATH FONTS newcomma2. begin split 24 10 ERROR MESSAGES AND OUTPUT PROBLEMS h Did you forget a preceding begin equation If not perhaps the aligned environment is what you want 3 Explanation The split environment does not construct a stand alone displayed equation it needs to be used within some other environment such as equation or gather L Extra amp on this line Example Package amsmath Error Extra amp on this line See the amsmath package documentation for explanation Type H lt return gt for immediate help 1 9 end alignat h An extra amp here is so disastrous that you should probably exit and fix things up Explanation In an alignat structure the number of alignment points per line is dictated by the numeric argument given after begin alignat If you use more alignment points in a line it is assumed that you accidentally left out a newline command and the above error is issued L Improper argument for math accent Example Package amsmath Error Improper argument for math accent amsmath Extra braces must be added to amsmath prevent wrong output See the amsmath package documentation for explanation Type H lt return gt for immediate help 1 415 tilde k_ lambda_j P_ tilde mathcal M Explanation Non simple arguments for any ATEX command should be enclosed in braces In this example extra braces are needed as follows P_ tilde mathcal M Le Font OMX cmex
3. s guide Amer Math Soc Providence RI 1994 distributed with the AMSFonts package 32 BIBLIOGRAPHY 2 Instructions for preparation of papers and monographs AMS ATEX Amer Math Soc Providence RI 1996 1999 3 Using the amsthm Package Amer Math Soc Providence RI 1999 4 Michel Goossens Frank Mittelbach and Alexander Samarin The ATpX companion Addison Wesley Reading MA 1994 Note The 1994 edition is not a reliable guide for the amsmath package unless you refer to the errata for Chapter 8 file compan err distributed with ATRX 5 G Gratzer Math into ATX An Introduction to ATpxX and AMS BT pX http www ams org cgi bin bookstore bookpromo fn 91k argl bookvideo amp itmc MLTEX Birkhauser Boston 1995 6 Donald E Knuth The TpXbook Addison Wesley Reading MA 1984 7 Leslie Lamport ATRX A document preparation system 2nd revised ed Addison Wesley Reading MA 1994 8 Frank Mittelbach and Rainer Schopf The new font family selection user interface to standard ATEX TUGboat 11 no 2 June 1990 pp 297 305 9 Michael Spivak The joy of TX 2nd revised ed Amer Math Soc Provi dence RI 1990 Index Sioa Need 11 3 11 3 5 8 9 24 26 Mx 9 l 16 above 14 29 abovewithdelims 14 accentedsymbol 2 accents package 12 addtocounter 10 addtolength 5 align environment 3 5 7 28 30 alignat environment 7 24 26 29 aligned environm
4. 6 1 Fiz _1 0 is monotonic 1 c 1 7 2 THE SIDESET COMMAND 19 f_ x_ i 1 x_i text is monotonic quad i 1 1dots c 1 7 Integrals and sums 7 1 Multiline subscripts and superscripts The substack command can be used to produce a multiline subscript or su perscript for example sum_ substack ys P i j O le i le m 0 lt i lt m 0 lt j lt n ees P i j A slightly more generalized form is the subarray environment which allows you to specify that each line should be left aligned instead of centered as here sum_ begin subarray 1 y P i j i in Lambda 0 lt j lt n ic A end subarray vont P i j 7 2 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 Note this command is not designed to be applied to anything other than sum class symbols 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 7 1 ye If however you want not only the prime but also something below or above the sum symbol it s not so easy indeed without sideset it would be downright difficult With sideset you can write 1 sideset XO nEn sum_ n lt k text n odd nE_n n lt k n odd The extra pair of empty braces
5. 7Ag Aco TAO If you want to use only the boldsymbol command without loading the whole amsmath package the bm package is recommended this is a standard TAT X package not an AMS package you probably have it already if you have a 1997 or newer version of TAT X 9 4 Italic Greek letters For italic versions of the capital Greek letters the following commands are provided varGamma I varSigma X varDelta A varUpsilon Y varTheta O varPhi 09 varLambda lt A XvarPsi Y XvarXi varOmega 2 varPi II Error messages and output problems 10 1 General remarks This is a supplement to Chapter 8 of the TEX manual 7 first edition Chap ter 6 For the reader s convenience the set of error messages discussed here overlaps somewhat with the set in that chapter but please be aware that we don t provide exhaustive coverage here The error messages are arranged in alphabetical order disregarding unimportant text such as LaTeX Error at the beginning and nonalphabetical characters such as Where examples are given we show also the help messages that appear on screen when you respond to an error message prompt by entering h There is also a section discussing some output errors i e instances where the printed document has something wrong but there was no TpX error during typesetting 10 2 Error messages L begin split won t work here Example Package amsmath Error begin split won t work here 1 8
6. command and thus need not be repeated in the option list of the usepackage amsmath statement 3 2 SINGLE EQUATIONS 3 leqno Place equation numbers on the left reqno Place equation numbers on the right fleqn Position equations at a fixed indent from the left margin rather than centered in the text column 3 Displayed equations 3 1 Introduction The amsmath package provides a number of additional displayed equation struc tures beyond the ones provided in basic ATEX The augmented set includes equation equation align align gather gather flalign flalign multiline multline alignat alignat 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 ATRX 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 within the unnumbered versions of all the amsmath alignment structures Some examples of the use of tag may be found in the sample files testmath tex and subeqn tex
7. environment alignat allows the horizontal space between equations to be explicitly specified This environment takes one argument the number of equation columns count the maximum number of amp s in any row add 1 and divide by 2 3 18 T Yy Ya Yyas Ys yg by 3 21 3 19 y o y by 4 1 3 20 y 0 y by Axiom 1 begin alignat 2 x amp y_1 y_2 y_3 y_5 y_8 dots amp quad amp text by eqreffeq C I amp y circ y amp amp text by eqreffeq D y 0 y amp amp text by Axiom 1 end alignat 3 7 Alignment building blocks Like equation the multi equation environments gather align and alignat are designed to produce a structure whose width is the full line width This means for example that one cannot readily add parentheses around the entire structure But variants gathered aligned and alignedat are provided whose total width is the actual width of the contents thus they can be used as a component in a containing expression E g B 9xE Maxwell s equations ae begin equation left begin aligned B amp partial times E E amp partial times B 4 pi j end aligned right qquad text Maxwell s equations end equation 8 3 DISPLAYED EQUATIONS Like the array environment these ed variants also take an optional t or b argument to specify vertical positioning Cases constructions like the following are common in mathem
8. in a matrix spanning the given number of columns For example a bcd begin matrix a amp b amp c amp a EN a e amp hdotsfor 3 end matrix 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 Dit ajato OS Qintn t Dot ee t 4 1 a2101 2 02nUn An1iti An2ta Dnt begin pmatrix D_1t amp a_ 12 t_2 amp dots amp a_ 1n t_n a_ 21 t_1 amp D_2t amp dots amp a_ 2n t_n hdotsfor 2 4 a_ ni t_1 amp a_ n2 t_2 amp dotsxD_nt end pmatrix 4 2 Math spacing commands The amsmath package slightly extends the set of math spacing commands as shown below Both the spelled out and abbreviated forms of these commands are robust and they can also be used outside of math Abbrev Spelled out Example Abbrev Spelled out Example no space gt no space gt thinspace gt lt negthinspace lt medspace gt lt negmedspace As thickspace gt lt negthickspace quad gt lt qquad gt lt 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 3 Dots 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 o
9. m n 7 cmex7 not loadable Example 10 2 ERROR MESSAGES 25 Font OMX cmex m n 7 cmex7 not loadable Metric TFM file not found lt to be read again gt relax 1 8 a btb 2 h I wasn t able to read the size data for this font so I will ignore the font specification Wizards can fix TFM files using TFtoPL PLtoTF You might try inserting a different font spec e g type I font lt same font id gt lt substitute font name gt Explanation Certain extra sizes of some Computer Modern fonts that were formerly available mainly through the AMSFonts distribution are considered part of standard TFX as of June 1994 cmex7 9 cmmib5 9 and cmbsy5 9 If these extra sizes are missing on your system you should try first to get them from the source where you obtained TEX If that fails you could try getting the fonts from CTAN e g in the form of Metafont source files directory tex archive fonts latex mf or in PostScript Type 1 format directory tex archive fonts cm ps type1 bakoma If the font name begins with cmex there is a special option cmex10 for the amsmath package that provides a temporary workaround I e change the usepackage to usepackage cmex10 amsmath This will force the use of the 10 point size of the cmex font in all cases Depend ing on the contents of your document this may be adequate L Math formula deleted Insufficient extension fonts Example Math formula deleted Insufficient
10. new ones come up all the time in mathematical papers so the amsmath package provides a general mechanism for defining new operator names To define a math function xxx to work like sin you write DeclareMathOperator xxx xxx whereupon ensuing uses of xxx will produce xxx in the proper font and au tomatically add proper spacing on either side when necessary so that you get Axxx B instead of AxxxB In the second argument of DeclareMathOperator the name text a pseudo text mode prevails the hyphen character will print as a text hyphen rather than a minus sign and an asterisk will print as a raised text asterisk instead of a centered math star Compare a b c and a b x c But otherwise the name text is printed in math mode so that you can use e g subscripts and superscripts there If the new operator should have subscripts and superscripts placed in limits position above and below as with lim sup or max use the form of the DeclareMathOperator command DeclareMathOperator Lim Lim See also the discussion of subscript placement in Section 7 3 The following operator names are predefined 18 6 THE TEXT COMMAND Narccos arccos deg deg Mg lg Xprojlim projlim arcsin arcsin det det lin lim sec sec arctan arctan dim dim liminf liminf sin sin arg arg exp exp limsup lim sup sinh sinh cos cos gcd gcd ln In sup sup cosh cosh hom hom log log tan tan cot cot inf inf max max tan
11. par 1 100 h I suspect you ve forgotten a causing me to apply this control sequence to too much text How can we recover My plan is to forget the whole thing and hope for the best Explanation This might be produced by a misspelling in the end multline command e g begin multline end multiline or by using abbreviations for certain environments such as bal and eal for begin align and end align bal eal 28 10 ERROR MESSAGES AND OUTPUT PROBLEMS For technical reasons that kind of abbreviation does not work with the more complex displayed equation environments of the amsmath package gather align split etc cf technote tex L Runaway argument See the discussion for the error message Paragraph ended before xxx was complete L Unknown option xxx for package yyy Example LaTeX Error Unknown option intlim for package amsmath h The option intlim was not declared in package amsmath perhaps you misspelled its name Try typing lt return gt to proceed gt Explanation This means that you misspelled the option name or the package simply does not have an option that you expected it to have Consult the documentation for the given package L Old form pmatrix should be begin pmatrix Example Package amsmath Error Old form pmatrix should be begin pmatrix See the amsmath package documentation for explanation Ty
12. L Missing right inserted Example Missing right inserted lt inserted text gt right 1 10 end multline h I ve inserted something that you may have forgotten See the lt inserted text gt above With luck this will get me unwedged But if you really didn t forget anything try typing 2 now then my insertion and my current dilemma will both disappear 10 2 ERROR MESSAGES 27 Explanation This error typically arises when you try to insert a linebreak inside a left right pair of delimiters in a multline or split environment begin multline AAA Left BBB CCC right end multline There are two possible solutions 1 instead of using left and right use big delimiters of fixed size bigl bigr biggl biggr see 4 14 1 or 2 use null delimiters to break up the left right pair into parts for each line AAA left BBB right left CCC right The latter solution may result in mismatched delimiter sizes ensuring that they match requires using vphantom in the line that has the smaller delimiter or possibly smash in the line that has the larger delimiter In the argument of vphantom put a copy of the tallest element that occurs in the other line e g xxx left int_t yyy right left vphantom int_t zzz right L Paragraph ended before xxx was complete Example Runaway argument Paragraph ended before multline was complete lt to be read again gt
13. Qi gt Tij versus Qi gt Tij F a P 1 1 j 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 en compassed material but what you really want is to make some of the delimiters slightly larger to make the nesting easier to see a1b1 a2b2 a2b1 a1b3 versus a1b1 a2b2 a2b1 a1b2 Meft a_1 b_1 a_2 b_2 right Meft a_2 b_1 a_1 b_2 right quad text versus quad bigl a_1 b_1 a_2 b_2 bigr bigl a_2 b_1 a_1 b_2 bigr The third kind of situation is a slightly oversize object in running text such as a 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 that are slightly larger than the base size but still able to fit within the normal line spacing 5 In ordinary ATEX big bigg Big and Bigg delimiters aren t scaled properly over the full range of ATEX font sizes With the amsmath package they are 4 14 2 Vertical bar notations The amsmath package provides commands lvert rvert MlVert rVert compare langle rangle to address the problem of overloading for the vert bar character This character is currently used in TEX documents to represent a wide variety of mathematical objects the divides relation in a number theory expression like p q or the absolute
14. User s Guide for the amsmath Package Version 2 0 American Mathematical Society 1999 12 13 ii CONTENTS Contents 1 Introduction 1 2 Options for the amsmath package 2 3 Displayed equations 3 IL Introductions rs 04 A AA ta ayes 3 3 2 Single equations sasaaa 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 0 o oo 7 3 8 Adjusting tag placement 2 20040 8 3 9 Vertical spacing and page breaks in multiline displays 8 3 10 Interrupting a display o 9 3 11 Equation numbering 0 000000 9 4 Miscellaneous mathematical features 10 AOL Matrices aca dig Soe Bee we BAM a A 10 4 2 Math spacing commands a oa 11 AS Dot 5 fe ele a es ele Ge ek Bed ae ee amp eee 11 4 4 Nonbreaking dashes 0 000000 12 4 5 Accents in math 02200000002 ee ee 12 ALO a ROOTS o A be Behe ow a e 13 47 Boxed tormulas siaaa ee Re a e 13 4 8 Over and under arrows e 13 4 9 Extensible arrows 0 0 e ee eee eee 13 4 10 Affixing symbols to other symbols 13 4 11 Fractions and related constructions 14 4 12 Continued fractions 0 0 000000 ee ee 15 4 13 Smas
15. atics 0 if r j is odd O20 Pr ADA fp js r 1 if r j is even and in the amsmath package there is a cases environment to make them easy to write P_ r j begin cases 0 text if r j is odd r 1 r j 2 amp text if r j is even end cases Notice the use of text cf 6 and the nested math formulas 3 8 Adjusting tag placement Placing equation numbers can be a rather complex problem in multiline displays The environments of the amsmath 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 Difficulties in accurately calculating the profile of an equation can occasionally result in number movement that doesn t look right There is a raisetag command provided to adjust the vertical position of the current equation number if it has been shifted away from its normal position To move a particular number up by six points write raisetag 6pt This kind of adjustment is fine tuning like line breaks and page breaks and should therefore be left undone until your document is nearly finalized or you may end up redoing the fine tuning several times to keep up with changing document contents 3 9 Vertical spacing and page breaks in multiline displays You can use the dimension command to get extra vertical space between lines in all the amsmath displayed equation environments as is usual in IAT X When the a
16. c dfrac and tfrac commands The frac command which is in the basic command set of ATX takes two arguments numerator and denominator and typesets them in normal fraction form The amsmath package provides also dfrac and tfrac as convenient abbreviations for displaystyle frac and textstyle frac 14 Flogse f Flogs zlosaclf 1 7 loss clf begin equation frac i k log_2 c tfrac 1 k log_2 c f sqrt frac i k log_2 c sqrt dfrac i k log_2 c f end equation 4 11 2 The binom dbinom and tbinom commands n k 4 5 2 G ay Oe 27k binom k 1 27 k 1 binom k 2 27 k 2 For binomial expressions such as amsmath has binom dbinom and Xtbinom 4 11 3 The genfrac command The capabilities of frac binom and their variants are subsumed by a general ized fraction command genfrac with six arguments The last two correspond to frac s numerator and denominator the first two are optional delimiters as seen in binom the third is a line thickness override binom uses this to set the fraction line thickness to 0 i e invisible and the fourth argument is a mathstyle override integer values 0 3 select respectively displaystyle textstyle scriptstyle and scriptscriptstyle If the third argument is left empty the line thickness defaults to normal genfrac left delim right delim thickness mathstyle numerator denominator To illustrate here is
17. d 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 first 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 affects other symbols of the same type J 9 and so forth but 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 command e g usepackage intlimits amsmath The amsmath package also recognizes the following options which are nor mally selected implicitly or explicitly through the documentclass
18. dotsc 12 dotsi 12 dotsm 12 dotso 12 e math ams org 31 ellipsis dots in matrices 11 eqnarray environment 1 3 26 30 eqref 10 equation environment 1 3 5 7 24 30 equation numbers cross references 10 hierarchy 9 left or right placement 3 overriding 3 subordinate numbering 10 vertical placement 2 equation environment 3 equations see displayed equations euscript package 21 exp 18 fbox 13 fleqn option 3 5 fntguide tex 21 frac 14 15 fractions 14 fracwithdelims 2 INDEX function names see operator names gather environment 5 7 24 28 30 gathered environment 7 9 Ngcd 18 genfrac 14 hat 12 hdotsfor 11 hom 18 horizontal space around operator names 17 in math mode 11 idotsint 20 iiiint 20 iiint 20 iint 20 inf 18 injlim 18 integrals multiple 20 placement of limits 2 intertext 9 intlimits option 2 20 ker 18 kuvio package 20 label 6 10 langle 16 ldots 12 Meft 15 16 27 Meftroot 13 leqno option 3 5 Mg 18 Xlim 1 2 17 18 liminf 18 limits see subscripts and superscripts limits 20 limsup 18 Man 18 log 17 18 lVert 16 lvert 16 math fonts 21 INDEX math symbols see math fonts mathbb 21 22 mathbf 21 22 mathcal 21 mathfrak 21 mathit 21 mathrm 21 mathscr 21 mathsf 21 mathtt 21 matrices 10 ellipsis dots 11 matrix 28 matrix environment 10 max 18
19. e last one takes precedence 7 4 Multiple integral signs iint iiint and iiiint give multiple integral signs with the spacing be tween 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 7 2 f x y dx dy JII f a y z de dy dz A A 7 3 LL Kov dwadedy dz fof tent A A 8 Commutative diagrams Some commutative diagram commands like the ones in AMS T X are available as a separate package amscd For complex commutative diagrams authors will need to turn to more comprehensive packages like kuvio or XY pic but for simple diagrams without diagonal arrows the amscd commands may be more 9 2 RECOMMENDED USE OF MATH FONT COMMANDS 21 convenient Here is one example Mor T pna p S T I Z T J begin CD S mathcal W _ Lambda otimes T gt j gt gt TAM VVV VV End P V S otimes T I Z otimes T J end CD In the CD environment the commands gt gt gt lt lt lt VVV and AAA give respec tively right left down and up arrows For the horizontal arrows material between the first and second gt or lt symbols will be typeset as a superscript and material between the second and third will be typeset as a subscript Sim ilarly material between the first and second or second and third As or Vs of vertical arrows will be typeset as left or right sidescripts The commands
20. ed formulas The command boxed puts a box around its argument like fbox except that the contents are in math mode 4 2 n lt C d n Am 0 boxed eta Meg C delta eta Lambda_M 0 delta 4 8 Over and under arrows Basic ATEX provides overrightarrowand overleftarrow commands Some additional over and under arrow commands are provided by the amsmath package to extend the set overleftarrow underleftarrow overrightarrow underrightarrow overleftrightarrow underleftrightarrow 4 9 Extensible arrows xleftarrow and xrightarrow produce arrows that extend automatically to accommodate unusually wide subscripts or superscripts These commands take one optional argument the subscript and one mandatory argument the su perscript possibly empty 4 3 Age op a C xleftarrow n mu 1 quad xrightarrow T n pm i 1 4 10 Affixing symbols to other symbols I4TeX provides stackrel for placing a superscript above a binary relation In the amsmath 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 87 2 14 4 MISCELLANEOUS MATHEMATICAL FEATURES 4 11 Fractions and related constructions 4 11 1 The fra
21. ent 7 9 alignedat environment 7 9 allowdisplaybreaks 8 9 amsart class 1 amsbook class 1 amsbsy package 1 2 amscd package 1 2 20 amsfonts package 21 AMSFonts collection 25 amsmath package i 1 3 5 8 18 22 23 25 26 28 32 amsopn package 1 2 amssymb package 22 amstext package 1 2 amsthm package 1 32 amsxtra package 1 2 12 arccos 18 arcsin 18 arctan 18 arg 18 array environment 8 10 26 arrows extensible 13 in commutative diagrams 20 atop 14 29 atopwithdelims 14 33 BaKoMa fonts 25 big Big bigg 16 biggl 27 biggr 27 bigl 27 bigr 27 binom 14 binomials 14 bm package 2 23 Bmatrix environment 10 bmatrix environment 10 bmod 18 boldsymbol 22 23 boxed 13 bslash 6 delimiters C 22 cases 28 cases environment 8 CD environment 2 21 cdots 12 centertags option 2 cfrac 15 cmbsy5 25 cmex 25 cmex10 25 cmex7 25 cmmib5 25 comp text tex 31 compan err 32 continued fractions 15 cos 18 cosh 18 cot 18 coth 18 csc 18 dbinom 14 ddddot 12 dddot 12 ddot 12 DeclareMathOperator 2 17 18 34 deg 18 det 18 dfrac 14 diffs m txt 30 dim 18 displaybreak 8 9 displayed equations 3 displayed equations centering 3 displaylimits 20 displaymath environment 3 displaystyle 14 documentclass 2 dot 12 dots see ellipsis dots dotsb 12
22. entequation romanfequation 4 Miscellaneous mathematical features 4 1 Matrices The amsmath package provides some environments for matrices beyond the basic array environment of TEX The pmatrix bmatrix 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 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 IAT X s setcounter or addtocounter commands 4 3 DOTS 11 To produce a small matrix suitable for use in text there is a smallmatrix environment e g 7 that comes closer to fitting 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 begin smallmatrix akb c amp d end smallmatrix bigr hdotsfor number produces a row of dots
23. ewcommand Ndash nobreakdash for pages 1 Ndash 9 For n dimensional n dimensional newcommand n 1 n nobreakdash hspace Opt The last example shows how to prohibit a linebreak after the hyphen but allow normal hyphenation in the following word It suffices to add a zero width space after the hyphen 4 5 Accents in math In ordinary TFX the placement of the second accent in doubled math accents is often poor With the amsmath package you will get improved placement of the second accent A 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 avail able in TEX To get a superscripted hat or tilde character load the amsxtra package and use sphat or sptilde Usage is A sphat note the absence of the character To place an arbitrary symbol in math accent position or to get under accents see the accents package by Javier Bezos 4 10 AFFIXING SYMBOLS TO OTHER SYMBOLS 13 4 6 Roots In ordinary IAT FX the placement of root indices is sometimes not so good k sqrt beta k In the amsmath 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 Wk The negative argument used with leftroot moves the 8 to the right The units are a small amount that is a useful size for such adjustments 4 7 Box
24. extension fonts 1 8 ab b 2 Explanation This usually follows a previous error Font not loadable see the discussion of that error above for solutions L Missing number treated as zero Example Missing number treated as zero lt to be read again gt a 1 100 end alignat h A number should have been here I inserted 0 26 10 ERROR MESSAGES AND OUTPUT PROBLEMS If you can t figure out why I needed to see a number look up weird error in the index to The TeXbook Explanation There are many possibilities that can lead to this error However one possibility that is relevant for the amsmath package is that you forgot to give the number argument of an alignat environment as in begin falignat ag bk c amp d ark b amp ok d end alignat where the first line should read instead begin falignat 2 Another possibility is that you have a left bracket character following a linebreak command in a multiline construction such as array tabular or eqnarray This will be interpreted by IXT X as the beginning of an additional vertical space request 7 C 1 6 even if it occurs on the following line and is intended to be part of the contents For example beginfarray a b f g m n end array To prevent the error message in such a case you can add braces as discussed in the ATEX manual 7 C 1 1 beginfarray a b f g I m n end array
25. f taste By using the semantically oriented commands 12 4 MISCELLANEOUS MATHEMATICAL FEATURES e dotsc for dots with commas e dotsb for dots with binary operators relations e dotsm for multiplication dots e dotsi for dots with integrals e dotso for other dots none of the above instead of ldots and cdots you make it possible for your document to be adapted to different conventions on the fly in case for example you have to submit it to a publisher who insists on following house tradition in this respect The default treatment for the various kinds follows American Mathematical Society conventions Then we have the series A_1 A_2 Then we have the series Aj Ao 7 dotsc the regional sum A_1 the regional sum A A2 the A_2 dotsb the orthogonal orthogonal product A A2 and product A_1 A_2 dotsm and the infinite integral the infinite integral int_ A_1 int_ A_2 dotsi f f peer Ar JAz 4 4 Nonbreaking dashes A command nobreakdash is provided to suppress the possibility of a linebreak after the following hyphen or dash For example if you write pages 1 9 as pages 1 nobreakdash 9 then a linebreak will never occur between the dash and the 9 You can also use nobreakdash to prevent undesirable hyphen ations in combinations like p adic For frequent use it s advisable to make abbreviations e g newcommand p p nobreakdash for p adic n
26. h options sa srp 66 bk a a a ee a 15 AMA De limiters cede lolo tg shes otal e s Sy A ala Bok aoe wh ceed ie de wes 15 5 Operator names 17 5 1 Defining new operator names e 17 5 2 mod and its relatives 2 2 2 2 0 e e 18 6 The text command 18 CONTENTS 7 Integrals and sums 7 1 Multiline subscripts and superscripts 7 2 The sideset command 000 4 7 3 Placement of subscripts and limits 7 4 Multiple integral signs 0 0 0 8 Commutative diagrams 9 Using math fonts 9 10 ntroduction 60 4 a ee 1 eR ey ees 9 2 Recommended use of math font commands 9 3 Bold math symbols o o e e 9 4 Italic Greek letters o 10 Error messages and output problems 10 1 General remarks o 10 2 Error messages doo led eis e a da td ee ea 10 3 Warning Messages e 10 4 Wrong output e ia ae ee RRA A A g ew S 11 Additional information 11 1 Converting existing documents 0 11 2 Technical notes ee ee a 113 Getting helps cc ius a Be Se Ale at tee ts eens 11 4 Of possible interest 2 2 2 ee ee ee Bibliography Index 111 19 19 19 20 20 20 21 21 21 22 23 23 23 29 29 30 30 30 30 31 31 33 iv CONTENTS Introduction The amsmath package is a ATEX package that p
27. h tanh coth coth injlim injlim Amin min esc csc ker ker Pr Pr varlimsup lim varinjlim lim varliminf lim varprojlim lim There is also a command operatorname such that using operatornamef abc in a math formula is equivalent to a use of abc defined by DeclareMathOper ator This may be occasionally useful for constructing more complex notation or other purposes Use the variant operatorname to get limits 5 2 mod and its relatives Commands mod bmod pmod pod are provided to deal with the special spacing conventions of mod notation bmod and pmod are available in ATRX but with the amsmath 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 5 1 ged n mmodn x y modb rx y mode r y d gcd n m bmod n quad x equiv y pmod b quad x equiv y mod c quad x equiv y pod d 6 The text command The main use of the command text is for words or phrases in a display It is very similar to the BTEX 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 equivalent _ mbox scriptsize word or phrase The other advantage is the more descriptive name
28. how frac tfrac and binom might be defined newcommand frac 2 genfrac 1 2 newcommand tfrac 2 genfrac F 1 1 2 newcommand binom 2 genfrac Opt 1 2 If you find yourself repeatedly using genfrac throughout a document for a particular notation you will do yourself a favor and your publisher if you define a meaningfully named abbreviation for that notation along the lines of frac and binom The primitive generalized fraction commands over overwithdelims atop atopwithdelims above abovewithdelims produce warning messages if used with the amsmath package for reasons discussed in technote tex 4 14 DELIMITERS 15 4 12 Continued fractions The continued fraction 4 6 V2 ae can be obtained by typing cfrac i sqrt 2 cfrac i sqrt 2 cfrac 1 sqrt 2 dotsb FH This produces better looking results than straightforward use of frac Left or right placement of any of the numerators is accomplished by using cfrac 1 or cfrac r instead of cfrac 4 13 Smash options The command smash is used to typeset a subformula with an effective height and depth of zero which is sometimes useful in adjusting the subformula s position with respect to adjacent symbols With the amsmath package smash has optional arguments t and b because occasionally it is advantageous to be able to smash only the top or only the bottom of something while retaini
29. if applicable and the version numbers of the document class and option files being used 11 4 Of possible interest Information about obtaining AMSFonts or other TpX related software from the AMS Internet archive e math ams org can be obtained by sending a request through electronic mail to webmaster ams org Information about obtaining the amsmath distribution 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 ams org The TFX Users Group is a nonprofit organization that publishes a journal TUGboat holds meetings and serves as a clearing house of general informa tion about TEX and T X related software TEX Users Group PO Box 2311 Portland OR 97208 2311 USA Phone 1 503 223 9994 Email office tug org Membership in the TEX Users Group is a good way to support continued de velopment of free TpX related software There are also many local T X user groups in other countries information about contacting a local user group can be gotten from the TX Users Group There is a Usenet newsgroup called comp text tex that is a fairly good source of information about 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 2 user
30. 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 TL 20 8 COMMUTATIVE DIAGRAMS 7 3 Placement of subscripts and limits The default positioning for subscripts depends on the base symbol involved The default for sum class symbols is displaylimits positioning When a sum class symbol appears in a displayed formula subscript and superscript are placed in limits position above and below but in an inline formula they are placed to the side to avoid unsightly and wasteful spreading of the surrounding text lines The default for integral class symbols is to have sub and superscripts always to the side even in displayed formulas See the discussion of the intlimits and related options in Section 2 Operator names such as sin or lim may have either displaylimits or limits positioning depending on how they were defined The standard operator names are defined according to normal mathematical usage The commands limits and nolimits can be used to override the normal behavior of a base symbol eS I limpo A To define a command whose subscripts follow the same displaylimits behavior as sum put displaylimits at the tail end of the definition When multiple instances of limits nolimits or displaylimits occur consecutively th
31. lign a_ 11 amp b_ 11 amp a_ 12 amp b_ 12 8 au bu a big a_ 21 amp b_ 21 amp a_ 22 amp b_ 22 c_ 22 end align begin flalign a_ 11 amp b_ 11 amp a_ 12 amp b_ 12 a_ 21 amp b_ 21 amp a_ 22 amp b_ 22 c_ 22 end flalign 9 a21 b21 a22 b22 C22 a11 b11 a12 b12 a21 b21 a22 b22 C22 3 4 SPLIT EQUATIONS WITH ALIGNMENT 5 3 3 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 Any additional lines in between will be centered independently within the display width unless the fleqn option is in effect Like equation multline has only a single equation number thus none of the individual lines should be marked with notag The equation number is placed on the last line reqno option or first line leqno option vertical centering as for split is not supported by multline It s 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 final for example 810 begin multline framebox 65 columnwidth A framebox 5 columnwidth B shoveright framebox 55 col
32. mbox 18 medspace 11 Metafont source files 25 nin 18 Xmod 18 mspace 11 multline environment 3 5 27 30 multlinegap 5 namelimits option 2 negmedspace 11 negthickspace 11 negthinspace 11 newcommand 21 nobreakdash 12 nointlimits option 2 nolimits 19 20 nonamelimits option 2 nosumlimits option 2 notag 3 5 numberwithin 9 29 30 operator names 17 operatorname 18 operatorname 18 over 14 29 overleftarrow 13 overleftrightarrow 13 overrightarrow 13 overset 13 overwithdelims 14 35 page breaks 8 pagebreak 8 pmatrix 28 pmatrix environment 10 pmb 22 pmod 18 pod 18 PostScript fonts 25 Pr 18 projlim 18 qquad 11 quad 11 R 22 raisetag 8 rangle 16 ref 10 reqno option 3 5 right 15 16 27 rVert 16 rvert 16 scriptscriptstyle 14 scriptstyle 14 sec 18 setcounter 9 10 setlength 5 shoveleft 5 shoveright 5 sideset 13 19 sin 1 2 17 18 sinh 18 smallmatrix environment 11 smash 15 27 sphat 12 split environment 3 5 6 9 24 27 30 sptilde 12 stackrel 13 subarray environment 19 subeqn tex 3 subequations environment 10 subscripts and superscripts 13 multi line 19 on sums 19 36 placement 2 substack 19 sum 20 22 sumlimits option 2 sup 18 superscripts see subscripts and su perscripts tabular environment 26 tag 3 tag 3 tan 18 tanh 18 tbi
33. msmath package is in use page breaks between equation lines are normally disallowed the philosophy is that page breaks in such material should receive individual attention from the author To get an individual page break inside a particular displayed equation a displaybreak command is provided displaybreak is best placed immediately before the where it is to take effect Like ATRX 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 display break with no optional argument is the same as displaybreak 4 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 allowdisplaybreaks 1 in the preamble of your document An optional argument 1 4 can be used for 3 11 EQUATION NUMBERING 9 finer 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 effect on them These include split aligned gathered and alignedat 3 10 Interr
34. nd vect 1 mathbf 1 you can write vect a vect b to produce a b 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 vect 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 indeed an instance of a vector It can also be useful 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 blackboard bold 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 usepackage amsfonts to get the mathbb alphabet newcommand field 1 mathbb 1 newcommand C field C newcommand R field R 9 3 Bold math symbols The mathbf command is commonly used to obtain bold Latin letters in math but for most other kind
35. ng 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 Vit y vVz and z y Vz where the latter was produced by sqrt x sqrt smash b y sqrt z 4 14 Delimiters 4 14 1 Delimiter sizes The automatic delimiter sizing done by left and right has two limitations First it is applied mechanically to produce delimiters large enough to encompass the largest contained item and second the range of sizes is not even approxi mately continuous but has fairly large quantum jumps This means that a math fragment that is infinitesimally too large for a given delimiter 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 text left bigl Bigl biggl Biggl size size right bigr MBigr biggr Biggr res 109 06 00 00 06 o 16 4 MISCELLANEOUS MATHEMATICAL FEATURES 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 the Big or bigg sizes instead gives better results j 1 p biggl sum_i a_i Bigl lvert sum_j x_ ij Bigr rvert p biggr 1 p 1 p P gt
36. nom 14 tbtags option 2 technote tex 14 28 30 testmath tex 3 TEX Users Group 31 text 2 7 9 18 text fragments inside math 9 18 textstyle 14 tfrac 14 theequation 9 10 thickspace 11 thinspace 11 TUGboat 31 underleftarrow 13 underleftrightarrow 13 underrightarrow 13 underset 13 uproot 13 usepackage 2 25 value 10 varDelta 23 varGamma 23 varinjlim 18 varLambda 23 varliminf 18 varlimsup 18 varOmega 23 varPhi 23 varPi 23 varprojlim 18 varPsi 23 INDEX varSigma 23 varTheta 23 varUpsilon 23 varXi 23 Vmatrix environment 10 vmatrix environment 10 vphantom 27 xleftarrow 13 xrightarrow 13
37. o write e Equation numbers automatically adjust up or down to avoid overprinting on the equation contents unlike eqnarray e Spacing around equals signs matches the normal spacing in the equation environment unlike eqnarray e A way to produce multiline subscripts as are often used with summation or product symbols e An easy way to substitute a variant equation number for a given equation instead of the automatically supplied number e 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 2 2 OPTIONS FOR THE AMSMATH PACKAGE amstext Provides a text command for typesetting a fragment of text inside a display amsopn Provides DeclareMathOperator for defining 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 IXAT X 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 an
38. pe H lt return gt for immediate help pmatrix gt left matrix check pmatrix env matrix 1 16 pmatrix akb cr ck amp d cr h pmatrix is old Plain TeX syntax whose use is ill advised in LaTeX Explanation When the amsmath package is used the old forms of pmatrix matrix and cases cannot be used any longer because of naming conflicts Their syntax did not conform with standard TEX syntax in any case L Erroneous nesting of equation structures Example Package amsmath Error Erroneous nesting of equation structures amsmath trying to recover with aligned See the amsmath package documentation for explanation 10 4 WRONG OUTPUT 29 Type H lt return gt for immediate help 1 260 end alignat endfequation Explanation The structures align alignat etc are designed for top level use and for the most part cannot be nested inside some other displayed equation structure The chief exception is that align and most of its variants can be used inside the gather environment 10 3 Warning messages Li Foreign command over or atop or above Example Package amsmath Warning Foreign command over frac or genfrac amsmath should be used instead Explanation The primitive generalized fraction commands of TEX A over atop above are deprecated when the amsmath package is used because their syn tax is foreign to ATRX and amsmath provides native TeX equivalents See technote tex for f
39. 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 amp before them but not after unlike eqnarray Putting the amp after the relation symbol will interfere with the normal spacing it has to go before 3 2 Single 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 1Basic IATRX doesn t provide an equation environment but rather a functionally equiv alent environment named displaymath 4 3 DISPLAYED EQUATIONS Table 3 1 Comparison of displayed equation environments vertical lines in dicating nominal margins Xbeginfequation a b a b end equation begin fequation _ a a b end equation begin equation label xx begin split ag bt c d eae ad amp quad e f 2 amp gth gth amp i end split end equation i begin multline atbtctdtetf 3 atb c d e f itj ktl mtn Hi j k l m n end multline begin gather a_1 b_1 c_1 4 a b c a_2 b_2 c_2 d_2 e_2 5 as bg c2 d2 e2 end gather begin align a_1 amp b_1 c_1 6 ay b c a_2 amp b_2 c_2 d_2 e_2 7 as b2 c2 d e2 end align begin a
40. rovides miscellaneous enhance ments for improving the information structure and printed output of documents that contain mathematical formulas Readers unfamiliar with ATEX should refer to 7 If you have an up to date version of TAT 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 BT 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 e 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 e Multiple substitutes for the eqnarray environment to make various kinds of equation arrangements easier t
41. s of math symbols it has no effect or its effects depend unreliably on the set of math fonts that are in use For example writing Delta mathbf Delta mathbf delta mathbf delta produces AA 66 the mathbf has no effect on the plus sign or the small delta The amsmath package therefore provides two additional commands bold symbol and pmb that can be applied to other kinds of math symbols bold symbol can be used for a math symbol that remains unaffected by mathbf if and only if your current math font set includes a bold version of that symbol pmb can be used as a last resort for any math symbols that do not have a true bold version provided by your set of math fonts pmb stands for poor man s bold and the command works by typesetting multiple copies of the symbol with slight offsets The quality of the output is inferior especially for symbols that contain any hairline strokes When the standard default set of ATEX math fonts are in use Computer Modern the only symbols that are likely to require pmb are large operator symbols like sum extended delimiter symbols or the extra math symbols provided by the amssymb package 1 The following formula shows some of the results that are possible A_ infty Api A_O sim mathbf A _ boldsymbol infty boldsymbol 10 2 ERROR MESSAGES 23 boldsymbol pi mathbf A _ boldsymbo1 0 sim pmb A _ pmb infty pmb pmb pi pmb A _ pmb 0 Ax TA0 Aco
42. ses page breaks inside multiple line displayed equation structures such as eqnarray align and gather To continue allowing page breaks inside eqnarray after switching to amsmath you will need to add the following line in your document preamble allowdisplaybreaks 1 To ensure normal spacing around relation symbols you might also want to change eqnarray to align multline or equation split as appropriate Most of the other differences in amsmath usage can be considered optional refinements e g using DeclareMathOperator Hom Hom instead of newcommand Hom mbox Hom 11 1 2 Converting from Ay S KT pX 1 1 See diffs m txt 11 2 Technical notes The file technote tex contains some remarks on miscellaneous technical ques tions that are less likely to be of general interest 11 3 Getting help Questions or comments regarding amsmath and related packages should be sent to American Mathematical Society Technical Support Electronic Products and Services P O Box 6248 Providence RI 02940 Phone 800 321 4AMS 321 4267 or 401 455 4080 Internet tech supportOams org BIBLIOGRAPHY 31 If you are reporting a problem you should include the following information to make proper investigation possible 1 The source file where the problem occurred preferably reduced to mini mum size by removing any material that can be removed without affecting the observed problem 2 A TAT X log file showing the error message
43. tic reset of the equation counter write numberwithin fequation section As its name implies the numberwithin command can be applied to any counter not just the equation counter 10 4 MISCELLANEOUS MATHEMATICAL FEATURES 3 11 2 Cross 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 L e if ref abc produces 3 2 then eqref abc produces 3 2 3 11 3 Subordinate 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 begin subequations end subequations 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 Nlabel command immediately after begin subequations 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 ATRX methods for changing numbering style 7 6 3 C 8 4 For example redefining theequation as follows will produce roman numerals begin subequations renewcommand theequation thepar
44. umnwidth C I framebox 65 columnwidth D end multline The value of multlinegap can be changed with the usual ATEX commands setlength or addtolength 3 4 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 amp to mark alignment points Unlike the other amsmath 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 n 1 p 2 z Ni He AA E IC 1 0 lit lp li 1 NM A 3 11 M Il m m 1 ni ha t n a Gis 1 I 6 3 DISPLAYED EQUATIONS begin equation label e barwq begin split H_ck amp frac 1 2n sum n_ 1 0 1 113 a 1 p 2 Xsum_11 _1 dots 1 _p 1 prod p_ i 1 Mbinomtn_iH1 _i amp quad cdot n 1 n_i 1 _i n_i 1 _i cdot Bigl 1 2 sum p_ j 1 m_i 1 _i 2 Bigr end split end equation The split structure should constitute the entire body of the enclosing struc ture apart from commands like label that produce no visible material 3 5 Equation groups without alignment The gather environment is used for a group of consecutive equations
45. upting 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 3 22 Aj No A 0 A Q 3 23 Az A Q 900 and 3 24 As N A w begin align A_1 amp N_0 lambda Omega phi lambda Omega A_2 amp phi lambda Omega phi lambda Omega MM intertext and A_3 amp mathcal N lambda omega end align 3 11 Equation numbering 3 11 1 Numbering hierarchy In IXT X 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 could redefine theequation as suggested in the ATX manual 7 86 3 C 8 4 renewcommand theequation thesection arabic equation This works pretty well 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 ansmath package pro vides a command numberwithin To have equation numbering tied to section numbering with automa
46. urther information L Cannot use split here Example Package amsmath Warning Cannot use split here amsmath trying to recover with aligned Explanation The split environment is designed to serve as the entire body of an equation or an entire line of an align or gather environment There cannot be any printed material before or after it within the same enclosing structure begin fequation left lt Not allowed begin split end split right lt Not allowed end equation 10 4 Wrong output 10 4 1 Section numbers 0 1 5 1 8 1 instead of 1 2 3 This most likely means that you have the arguments for numberwithin in reverse order numberwithin section equation That means print the section number as equation number section number and reset to 1 every time an equation occurs when what you probably wanted was the inverse numberwithin fequation section 30 11 ADDITIONAL INFORMATION 10 4 2 The numberwithin command had no effect on equation num bers Are you looking at the first section in your document Check the section num bers elsewhere to see if the problem is the one described in 10 4 1 Additional information 11 1 Converting existing documents 11 1 1 Converting from plain ATRxX A I8TRX document will typically continue to work the same in most respects if usepackagefamsmath is added in the document preamble By default how ever the amsmath package suppres
47. value operation z or the such that condition in set notation or the evaluated at notation fe t a The multiplicity of uses in itself is not so bad what is bad however is that fact that not all of the uses take the same typographical treatment and that the complex discriminatory powers of a knowledgeable reader cannot be replicated in computer processing of mathematical documents It is recommended there fore that there should be a one to one correspondence in any given document between the vert bar character and a selected mathematical notation and similarly for the double bar command This immediately rules out the use of and for delimiters because left and right delimiters are distinct usages 5 1 DEFINING NEW OPERATOR NAMES 17 that do not relate in the same way to adjacent symbols recommended prac tice is therefore to define suitable commands in the document preamble for any paired delimiter use of vert bar symbols providecommand abs 1 lvert 1 rvert providecommand norm 1 1Vert 1 rVert whereupon the document would contain abs z to produce z and norm v to produce w 5 Operator names 5 1 Defining new operator names Math functions such as log sin and lim are traditionally typeset in roman type to make them visually more distinct from one letter math variables which are set in math italic The more common ones have predefined names log sin lim and so forth but
48. when there is no alignment desired among them 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 begin split end split structure for example begin gather first equation begin split second amp equation amp on two lines end split third equation end gather 3 6 Equation groups with mutual alignment The align environment is used for two or more equations when vertical align ment is desired 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 3 12 z Y X Y a b c 3 13 al y x ey a b 3 14 ata yty X X Y Y a b c b begin align x amp y amp X amp Y ak btc x kay amp KPY amp a amp b xt x amp yty X X amp Y Y amp a bk amp c b end align Line by line annotations on an equation can be done by judicious application of 3 7 ALIGNMENT BUILDING BLOCKS 7 text inside an align environment 3 15 z yi yo2tys Yystys by 3 21 3 16 y o y by 4 1 3 17 y 0 y by Axiom 1 begin align x amp y_1 y_2 y_3 y_5 y_8 dots amp amp text by eqreffeq C H I amp y circ y amp amp text by eqreffeq D amp y 0 y amp amp text by Axiom 1 end align A variant
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