AMS-LATEX Version 1.2 User's Guide
Contents
1. 3 5 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 hyphenations in combinations like p adic For frequent use it s advisable to make abbreviations e g newcommand p p nobreakdash for p adic newcommand Ndash nobreakdash for pages 1 Ndash 9 For n dimensional newcommand n 1 S n nobreakdash hspace 0pt 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 3 6 Accents in math The following accent commands automatically give good positioning of double accents Hat XCheck Tilde Acute Grave Dot Ddot Breve Bar Vec With the usual non capitalized math accent commands the second accent will sometimes be askew for example A hat hat A With the amsmath package if you type Hat Hat A using the capitalized form for both accents the second accent will be better positioned A This double accent operation is complicated and tends to slow down the processing of a document If your document con tains many double accents you may wish to use the amsxt ra package which provides an accentedsymbo1 com2. 18 PostScript fonts 31 proof environment vi 1 22 25 proofs 23 pstricks package 36 ged 25 qedsymbol 25 qquad 10 quad 10 11 R 22 raisetag 7 rangle 16 READ ME 27 28 ref 1 9 29 remark theorem style 24 renewcommand 22 25 reqno option 2 right 15 16 33 rVert 16 rvert 16 savebox 12 Sch pf Rainer v scriptscriptstyle 14 scriptstyle 14 section 25 setcounter 9 10 set Length 3 shoveleft 3 shoveright 3 sideset 13 20 sin vi 1 17 smallmatrix environment 10 smash 15 33 Spivak Michael v split environment 2 5 30 33 34 square 35 stackrel 13 subarray environment 19 subeqn tex 3 27 29 subequations environment 9 subscripts and superscripts 13 multi line 19 on sums 20 placement 1 2 subsection 25 substack 19 27 sum 20 sumlimits option 1 2 sums 20 superscripts see subscripts and superscripts swapnumbers 25 syntonly package 36 tabular environment 32 tag 3 tag 3 tbinom 14 tbtags option 1 technote tex 13 29 34 37 testmath tex 3 27 29 TFX Users Group 38 Xtext 1 6 7 18 29 text fragments inside math 8 18 textstyle 14 tfrac 13 14 theequation 8 9 theorem package 22 theorems 23 numbering 23 theoremstyle 22 24 25 29 thickspace 10 thinspace 10 hmtest tex 22 25 29 TUGboat 38 ES underleftarrow 11 underleftrightarrow 11 underrightarrow 11 und
3. 31 bx 35 ex 31 ex10 31 ex7 31 mib 35 mmib5 31 comment environment 36 commutative diagrams 36 comp text tex 38 Comprehensive TEX Archive Network see CTAN continued fractions 14 CTAN 27 36 e cm cm cm cm cm cm e dbinom 14 ddddot 12 dddot 12 ddot 12 DeclareMathOperator l 17 definition theorem style 24 delimiters size adjustments 15 dfrac 13 14 diagram package 36 diff12 tex 29 37 differential notation 20 displaybreak 7 8 displayed equations 2 centering 2 displaymath environment 3 26 displaystyle 14 documentclass 2 dot 12 dots see ellipsis dots dots 11 dotsb 11 Xdotsc 11 dotsi 11 Xdotsm 11 e math ams org 35 37 ellipsis dots in matrices 10 Vena 11 eqnarray environment vi 2 7 32 eqref 9 equation environment vi 2 3 5 30 34 equation numbers cross references 9 hierarchy 9 left or right placement 2 overriding 3 subordinate numbering 9 vertical placement 1 equation environment 3 equations see displayed equations eucal package 21 V box 13 field 22 flean option 2 3 fntguide tex 21 frac 13 15 31 fractions 13 fracwithdelims 1 FTP 36 ftp dante de 27 ftp shsu edu 27 ftp tex ac uk 27 function names see operator names gather environment 5 30 34 gathered environment 6 genfrac 13 14 31 Hat 12 hat 12 hdotsfor 10 horizontal space around operator names 17 in math mod
4. C field Cc newcommand R field R Uf you actually tried this example you would discover that the command vec is already defined It produces a different sort of notation for vectors a small over arrow X 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 14 10 THEOREMS AND RELATED STRUCTURES 10 Theorems and related structures amst hm package 10 1 Introduction The amst hm package provides an enhanced version of the BIEX command newtheorem for defining theorem like en vironments 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 amst hm package also de fines a proof environment that automatically adds a Q E D symbol at the end AMS document classes automatically load the amst hm package so everything described here applies to them as well An example file thmtest tex is provided in the AMS BTEX distribution 10 2 The newtheorem command In mathematical research articles and books theorems and proofs are among the most common elements but authors also use many others that fall in the same general class lemmas propositions axioms corollaries conjectures definitions remarks cases steps and so forth As these elements form a slice of the text stream w
5. The boldsymbol command amsbsy amsmath packages The boldsymbo1 and pmb commands are defined by the amsbsy package also loaded by amsmath 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 6 1 Aso TAg Ac TAO Aco Ag A_ infty pi A0 sim mathbf A _ boldsymbol infty boldsymbol boldsymbol pi mathbf A _ boldsymbol 0 sim pmb A _ pmb infty pmb pmb pi pmb A _ pmb 0 ae EI Integrals and sums amsmath amsintx packages 7 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 Nidotsint is an extension of the same idea that gives two integral signs with do
6. an extension package AmsS BTEX Most of the programming work was done by Frank Mittelbach and Rainer Sch pf in 1989 1990 and version 1 0 of AMS BTEX was released in mid 1990 Why would a TFX user want to bother with A S LT X If you are just starting out as a WMI X 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 I4TRX 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 IBTEX package If you want to have maximum mathematical typesetting power ready at hand rather than stop to cast about for a solution whenever you run into some unusual demand in your writing then 414S 1T X will go a long way toward meeting your needs If you are a long time I4TEX user and have lots of mathematics in what you write then you may recognize solutions for some familiar problems in this list of Aj4S ATEX features e A convenient way to define new operator name commands analogous to sin and 1lim 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 wri
7. counter the command would be numberwithin equation section 2 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 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 2 11 3 Subordinate numbering sequences The amsmath package provides also a subequat ions 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 label command immediately after begin subequations will produce a ref of the parent number 4 9 not 4 9a The counters used by the subequations environment are parent equationand 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 ATEX methods for changing numbering style 5 6 3 C 8 4 For example redefining theequation as follows will produce roman numerals begin subequations renewcommand theequation theparentequation roman equation 6 3 MISCELLANEOUS MATHEMATICS FEATURES Miscellane
8. end equation begin multline atbtctdtetf i1 3 k 1 m n end multline begin gather a_l b_1 c_1 a_2 b_2 c_2 d_2 2 end gather begin align a_18 b_1l c_1 a_2 amp b_2 c_2 d_2 e_2 end align begin align a_ l1l amp b_ 11 amp a_ 12 amp b_ 12 a_ 21 amp b_ 21 8 a_ 22 amp b_ 22 c_ 22 end align begin flalign a_ l1l amp b_ 11 amp a_ 12 amp b_ 12 a_ 21 amp b_ 21 g8 a_ 22 amp b_ 22 c_ 22 end flalign a b 1 a b a b c d e f 2 Li g h i 3 a b c d e f tit j 4 a b1 c1 5 a b2 c2 d2 2 6 aj bi c 7 a b2 c2 d2 2 8 a bi a by2 9 az bz a b11 a2 b21 an b2 c2 a by2 a bn 22 18 Appendix A ERROR MESSAGES AND OUTPUT PROBLEMS Appendix A Error messages and output problems A 1 General remarks This is a supplement to Chapter 8 of the IX4IfX manual 5 first edition Chapter 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 ente
9. 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 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 9 Using math fonts 9 1 Introduction For more comprehensive information on font use in ISTRX see the BIEX font guide ntguide tex or The BIEX Com panion 3 Many users of A 4S I4TgxX also obtain an auxiliary collection of math fonts known as AMSFonts The basic set of math font commands in TEX includes mathbf mathrm mathcal mathsf mathtt mathit Additional math alphabet commands are available through the packages amsfonts and eucal if the requisite fonts are installed on your system see B 2 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 Amb instead of mathbf Of course there is nothing to keep you from providing such abbreviations for yourself by suitable newcommand statements But for IXTFX 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 usin
10. gather environment which provides the numbering For example BE P fn a 1 0 li 1 NA p D mW 0 0 Y 1 j l 2 11 begin equation label e barwq begin split H_c amp frac 1 2n sum n_ 1 0 1 1 n 1 p 2 sum_ 1 _1 dots 1 _p 1 prod p_ i 1 binom n_i 1 _i amp quad cdot n 1 n_i 1 _i n_i 1l _i cdot Bigl n 1 2 sum p_ j 1 n_i 1 _i 2 Bigr end split end equation 2 5 Equation groups without alignment 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 see Table 2 1 2 6 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 see Table 2 1 To have several equation columns side by side use extra ampersands to separate the columns 2 12 x y X Y a b c 2 13 xX y x Y a b 2 14 449 y y X X Y Y dab cb begin align x amp y amp X amp Y amp a amp bt c x amp y amp X amp Y amp a amp b xt x amp yty X X amp Y Y a b amp c b end align Line by line annotations on an equation can be done by judicious application of Ntext inside an align environment 2 15 x yi y2 y3 y5 y8 by 2 21 2 16 yoy by 3 1 2 17 y 0 y by Axio
11. symbols to other symbols BIEX provides Astackrel for placing a superscript above a binary relation In the ansmath 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 7 3 3 11 Fractions and related constructions 3 11 1 Disallowing primitive TEX fraction commands The six generalized fraction commands over overwithdelims atop atopwithdelims above abovewithdelim are expressly forbidden by the amsmath package as their syntax is decidedly out of place in IATEX use of the forms frac binom genfrac and variants is required 3 11 2 The frac dfrac and t frac commands The frac command which is in the basic command set of IEX takes two arguments numerator and denominator and typesets them in normal fraction form The amsmath package provides also dfrac and t frac as convenient abbreviations for displaystyle frac and textstyle frac 1 1 1 3 4 g Lecl log c f flossetN i log2c 1 begin equation frac 1 k log_2 c f tfrac 1l k log_2 c f sqrt frac 1 k log_2 c f sqrt dfrac 1 k log_2 c f end equation 3 11 3 The binom dbinon and tbinom commands For b
12. use any of the pieces of AMS BTEX you need to have TEX and I4TpX installed first TEX by itself does a rather good job of typesetting mathematics compared to non TpxX based software it doesn t add much however to the basic set of mathematical capabilities that it adopted from the Plain TEX macro package At the same time that IATEX 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 T X written by Michael Spivak By 1987 or so it became evident that AMS TE X and BIFX 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 IAIEX 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 4A14S TEX and IATEX users who saw desirable features tantalizingly 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 A 4S TEX onto the base stock of I4TEX through
13. 0 THEOREMS AND RELATED STRUCTURES 15 10 4 Changing styles for theorem like environments 10 4 1 The theoremstyle command 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 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 typically the plain style 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 newt heorem commands into groups and preface each group with the appropriate Atheoremstyle 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 a E an ne oe theoremstyle definition newtheorem defn Definition section newtheorem conj Conjecture section newtheorem exmp Example section Bec Spe gee theoremstyle remark newtheorem rem Remark newtheorem note Note newtheorem case Case BO BEE UA 10 4 2 Number swapping A not uncommon sty
14. AmS BT X Version 1 2 User s Guide American Mathematical Society January 1995 11 Contents What is ApyS ET EX and why would anyone want to use it Whatis A MSIE Pob E A ons A cae Why would a I4TEX user want to bother with AMS BTEX ee 1 How to use AqyS bTpx 1 1 Using an AMS package in a ATEX document 1 2 Options for the amsmath package o 2 Displayed equations amsmath package 2T introduction ss ri a a a e 2 2 Single equations tra ds a ay e a ee A 2 3 Split equations without alignment o e 2 4 Split equations with alignment o e 2 5 Equation groups without alignment o e 2 6 Equation groups with mutual alignment 2 7 Alignment building blocks aoaaa e 2 8 Adjusting tag placement L E e a a 2 9 Vertical spacing and page breaks in multiline displays 2 10 Textual interjections within a display o o 2 11 Equation numberng e 3 Miscellaneous mathematics features amsmath package Sel Matrices 2 26 a ea a A a RI odo AB 3 2 Mathspacingcommands s scs o oae a s e ane e paca g 0000000000004 33 Over and under Arrows s ieo ao i ee SA DOSE a e a AM hoe as ids a aE D A a 3 5 Nonbreaking ashes a e A a E eN 3 6 Accents math s eea D ee ITa ROOS 2 020 cs a A a a ES O Tis 3 8 Boxedformulas sre s genes mepa ee 3 9 Exten
15. 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 a1b1 a2b2 a2b1 a1b2 versus a1b1 a2b2 a2b1 a1b2 10 4 OPERATOR NAMES AMSOPN AMSMATH PACKAGES left a_1 b_1 a_2 b_2 right left a_2 b_1 a_1 b_2 right quad text versus quad bigl a_l b_1 a_2 b_2 bigr Xbigl a_2 b_1 a_1 b_2 bigr The third kind of situation is a slightly oversize object in running text such as Y where the delimiters produced by left and right cause too much line spreading In that case Abigl 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 de In ordinary BIEX big bigg Big and Bigg delimiters aren t scaled properly over the full range of I4TFX font sizes With the amsmath package they are 3 14 2 Vertical bar notations The amsmath package provides commands lvert rvert lVert rVert compare langle rangle to address the problem of overloading for the vert bar character This character is currently used in BIEX documents to represent a wide variety of mathematical objects the divides relation in a number theory expression like p q or the absolute value operatio
16. ages is amsmath Defines extra environments for multiline displayed equations as well as a number of other enhancements for math amstext Provides a text command for typesetting a fragment of text inside a display amsbsy Defines boldsymbo1 and pmb poor man s bold commands amsopn Provides DeclareMathOperator for defining new operator names like sin and lim amsthm Provides a proof environment and extensions for the newt heorem command amsintx Provides more descriptive command syntax for integrals and sums amscd Provides a CD environment for simple commutative diagrams no support for diagonal arrows amsxtra Provides certain odds and ends such as fracwithdelims and accentedsymbol upref Makes ref print cross reference numbers always in an upright roman font regardless of context 1 2 Options for the ansmath 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 symbols above and below in displayed equations This option also affects other symbols of the same type I HL Y and so forth but excluding integrals see below nosumlimits Always plac
17. al space request 5 C 1 6 even if it occurs on the following line and is intended to be part of the contents For example begin array atb 9 m n end array To prevent the error message in such a case you can add braces as discussed in the BIEX manual 5 C 1 1 begin array atb g m n end array 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 S 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 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 3 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 large
18. al 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 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 2 22 Ay MA Q A Q 2 23 Az 0 A Q H A Q and 2 24 A3 N 0 begin align A_1 amp N_0 lambda Omega phi lambda Omega A_2 amp phi lambda Omega phi lambda Omega intertext and A_3 amp mathcal N lambda omega end align 2 11 Equation numbering 2 11 1 Numbering hierarchy In XT 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 BIEX manual 5 6 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 provides a command numberwithin To have equation numbering tied to section numbering with automatic reset of the equation
19. beta beta beta beta gamma amp gamma end aligned qquad text versus qquad begin aligned t delta amp delta delta eta amp eta eta eta eta eta eta varphi varphi end aligned end equation Cases constructions like the following are common in mathematics oe ee 0 if r j is odd A rl 1 0 P 2 if r jis even and in the ansmath package there is a cases environment to make them easy to write P_ r j begin cases 08 text if r j is odd r 1 r j 2 amp text if r j is even end cases Notice the use of ttext and the embedded math 2 8 Adjusting tag placement Placing equation numbers can be a rather complex problem in multiline displays The environments of the amsmat h 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 Even so difficulties in accurately calculating the profile of an equation can occasionally result in a number placement that doesn t look right So there is a raisetag command provided to adjust the vertical position of the current equation number 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 cont
20. e 10 idotsint 19 iiiint 19 iiint 19 Viint 19 inputs 27 installation 27 instr l tex 29 int 20 integrals 20 INDEX multiple 19 placement of limits 2 intertext 8 intlimits option 2 label 9 Lamport Leslie v langle 16 left 15 16 33 leftroot 12 legno option 2 Lim vi 1 17 limits see subscripts and superscripts log 17 lVert 16 lvert 16 m math 27 math fonts 21 bold symbols 18 math symbols see math fonts mathbf 18 21 22 mathcal 21 Xmathit 21 mathrm 21 mathsf 21 Xmathtt 21 matrices 9 ellipsis dots 10 mat r ix environment 9 mbox 18 Xmedspace 10 Metafont source files 31 Mittelbach Frank v mod 18 mrabbrev bib 29 msam 35 msbm 35 mspace 11 multline environment 3 5 33 multlinegap 3 amelimits option 2 negmedspace 10 negthickspace 10 negthinspace 10 newcommand 12 21 nvironment 23 heorem vi 1 22 25 heorem 23 29 heoremstyle 25 eakdash 11 12 limits option 2 nolimits 20 onamelimits option 2 osumlimits option 2 notag 3 numberwithin 9 34 35 new new new new Gio JES oC GE GE De E AA e GN SEIS SSS NS ee ee ER ee operator names 17 over 13 INDEX overleftarrow 11 overleftrightarrow 11 overrightarrow 11 overset 13 overwithdelims 13 page breaks 7 pagebreak 8 plain theorem style 24 pmatrix environment 9 pmb 1 18 19 29 pmod 18 pod
21. e 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 underneath 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 argument of the usepackage command e g usepackage intlimits amsmath The amsmath package also recognizes the following options which are normally selected implicitly or explicitly through the document class command and thus need not be repeated in the option list of the usepackage amsmath statement 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 2 2 DISPLAYED EQUATIONS AMSMATH PACKAGE For symmetry there should perhaps be a centeregn option as well to balance with fleqn but as things currently stand there doesn t seem to be a genuine need for it A Displayed equations amsmath package 2 1 Introduction The amsmath package provides a number of additional displayed equation structures beyond the basic equation and eqnarray environments provided in basic IATEX The a
22. ent 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 instead of with the proof environment you can obtain the symbol and the usual amount of preceding space by using ged 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 IATEX scoping rules For example 16 10 THEOREMS AND RELATED STRUCTURES 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 of the Main Theorem then write begin proof Proof of the Main Theorem 10 THEOREMS AND RELATED STRUCTURES Table 2 1 Comparison of displayed equation environments vertical lines indicating nominal margins begin equation a b end equation begin equation a b end equation begin equation label xx begin split a amp btc d amp quad e f amp gth amp i end split
23. ents 2 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 XIX Unlike eqnarray the amsmath 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 is best placed immediately before the where it is to take effect Like IXIFX 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 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 in the preamble of your document An optional argument 1 4 can be used for finer control 1 means allow page breaks but avoid them as much as possible values of 2 3 4 mean increasing permissiveness When display breaks are enabled with al lowdisplaybreaks the command can be used to prohibit a pagebreak after a given line as usual The height of the cross bar in the symbol 3 MISCELLANEOUS MATHEMATICS FEATURES AMSMATH PACKAGE 5 2 10 Textu
24. erset 13 upref package upref dtx 29 uproot 12 usepackage l 2 31 value 9 varinjlim 17 varliminf 17 varlimsup 17 varprojlim 17 vec 22 vector 36 verbatim environment 36 verbatim package 36 verbatiminput 36 Vmat r 1x environment 9 vmat r ix environment 9 vphantom 33 xleftarrow 13 xrightarrow 13 Vxxx 34 xypic package 36
25. g 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 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 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 AC 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 fie1d command and then define AC and MR in terms of that command usepackage amsfonts to get the mathbb alphabet newcommand field 1 mathbb 1 newcommand
26. h perhaps you misspelled its name Try typing lt return gt to proceed Q 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 A 3 Wrong output A 3 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 numberwith 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 numberwith equation section A3 2 The numberwithin command had no effect on equation numbers Are you looking at the first section in your document Check the section numbers elsewhere to see if the problem is the one described in A 3 1 A 3 3 Double accent command failed to position the second accent properly The capitalization of the command names is important Check whether all of the accent commands are capitalized Compare A A A hat hat A quad Hat hat A quad Hat Hat A 22 Appendix C WHERE TO FIND OTHER INFORMATION A 3 4 The boldsymbol command didn t work This probably means that the font necessary to produce a bold version of the symbol in question is not available on your system or not installed in a way that I4TFX can use it For example bold versions of the AMS extra symbol fon
27. he primitive generalized fraction commands of T X are disallowed by the amsmath package because their syntax is foreign to BIEX The substitutes frac and genfrac are provided instead See 3 11 1 for further information L Math formula deleted Insufficient extension fonts Example Math formula deleted Insufficient extension fonts 1 8 Sab b 2 Explanation This usually follows a previous error Font not loadable see the discussion of that error above for solutions Li Missing number treated as zero Example Missing number treated as zero lt to be read again gt a 1 100 end alignat 2h A number should have been here I inserted 0 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 ansmath is that you forgot to give the number argument of an alignat environment as in begin alignat as b amp c amp d a amp b amp c amp d end alignat 20 Appendix A ERROR MESSAGES AND OUTPUT PROBLEMS where the first line should read instead begin alignat 2 Another possibility is that you have a left bracket character following a linebreak command in a multiline construc tion such as array tabular or eqnarray This will be interpreted by IXIFX as the beginning of an additional vertic
28. hematical 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 support math ams org 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 minimum size by removing any material that can be removed without affecting the observed problem 2 A BIEX 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 24 BIBLIOGRAPHY Information about obtaining AMS 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 T X 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 sup
29. ike environments oaaae 10 5 Proofs A l General remarks A 2 Error messages A 3 Wrong output Error messages and output problems B Other useful items for mathematical documents B 1 AMS documentclasses amsart amsbook amsproc 2 e B 2 Extra math fonts the AMSFonts collection e B 3 Syntax checking the syntonly package e B 4 Verbatim and comments the verbatim package e B 5 Commutative diagrams and other diagrams packages diagram xypic pstricks C Where to find other information C 1 Technical notes C 2 Differences between AMS BTIEX version 1 1 and AMS BTIEX version 1 2 20 0 0 ooo D Getting help D 1 Further information Bibliography Index 111 13 14 14 14 15 15 18 18 18 21 22 22 22 22 22 22 22 23 23 23 23 24 25 iv WHAT IS Aq4S I5TEX What is AmS BT X and why would anyone want to use it What is A 4S LST px The name AMS BTIEX 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 IXIFX for superior information structure of mathematical documents and superior printed output Because A S I4TgXxX is an extension for BIEX which in turn is a macro package for the TEX typesetting program it follows that in order to
30. inomial expressions such as W amsmath has binom dbinom and tbinom k k k 1 k k 2 as n Data Qe 2 k binom k 1 27 k 1 binom k 2 27 k 2 3 11 4 The genfrac command The capabilities of frac binom and their variants are subsumed by a generalized 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 1 e invisible and the fourth argument is a mathstyle override integer values 0 3 select respectively displaystyle textstyle scriptstyle and scriptscriptstyle Ifthe third argument is left empty the line thickness defaults to normal genfrac left delim right delim thickness mathstyle numerator denominator 2Not only is the unusual syntax of the primitive TEX fraction commands rather out of place in IAT X but furthermore that syntax seems to be solely responsible for one of the most significant flaws in TEX s mathematical typesetting capabilities the fact that the current mathstyle at any given point in a math formula cannot be determined until the end of the formula because of the possibility that a following generalized fraction command will change the mathstyle of the preceding material As the side effects are a bit technical in nature they are discussed in technote tex rather
31. ir 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 7 5 TL 7 4 The amsintx package The amsintx package is an experimental package that provides variants of the int and sum commands to better mark the boundaries of the quantity being summed or integrated Some commands for differential notation are also provided If you are interested in this possibility run 14TFX on the documentation file amsintx dtx to get the most up to date information on usage 8 Commutative diagrams ams cad package 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 XY pic see B 5 but for simple diagrams without diagonal arrows the ams cd commands may be more convenient Here is one example Sor gt T j S T I Z8T J 10 THEOREMS AND RELATED STRUCTURES AMSTHM PACKAGE 13 begin CD S mathcal W _ Lambda otimes T e gt 3 gt gt T 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 respectively right left down and up arrows For the horizontal arrows material between the
32. ith well defined boundaries they are naturally handled in XIEX as environments But IATEX 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 newtheoren similar to newenvironment in effect that makes it easy for authors to set up the elements required for a particular document The newt heorem 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 newt heorem 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
33. le variation for theorem heads is to have the theorem number on the left at the beginning of the heading instead of on the right As this variation is usually applied across the board regardless of individual theoremstyle changes number swapping is done by placing a swapnumbers command at the beginning of the list of newtheorem statements that should be affected For example swapnumbers theoremstyle plain newtheorem thm Theorem theoremstyle remark newtheorem rem Remark After the above declarations theorem and remark heads will be printed in the form 1 4 Theorem 9 Remark 10 4 3 Further customization possibilities More extensive customization capabilities are provided by the amsthm package in the form of a newtheoremstyl command and a mechanism for using package options to load custom theoremstyle definitions As these capabilities are somewhat beyond the needs of the average user discussion of the details is consigned to the example file thmtest tex and to the commentary in amsthm dt x 10 5 Proofs A predefined proof environment provided by the amst hm package produces the heading Proof with appropriate spacing and punctuation The proof environment is primarily intended for short proofs no more than a page or two in length longer proofs are usually better done as a separate A section or subsection in your document A Q E D symbol O is automatically appended at the end of a proof environm
34. m 1 begin align xe y_l y_2 y_3 y_5t y_8 dots amp amp text by eqref eq C amp y Xcirc y amp amp text by eqref eq D amp y 0 y amp amp text by Axiom 1 end align A variant environment alignat allows the space between equation columns to be explicitly specified Here the number of equation columns must also be specified where the number of columns is calculated as 1 amp max 2 with amp max maximum number of amp markers on any line 2 18 X yi yoty3 ystyg by 2 21 2 19 y o0 by 3 1 2 20 y 0 y by Axiom 1 begin alignat 2 X amp y_l y_2 y_3 y_5ty_8 dots amp quad text by eqref eq C amp y cire y amp amp text by eqref eq D amp y 0 y amp amp text by Axiom 1 end alignat 4 2 DISPLAYED EQUATIONS AMSMATH PACKAGE 2 7 Alignment building blocks Some other equation alignment environments such as aligned and gathered construct self contained units that can be used inside of other expressions or set side by side These environments take an optional argument to specify their vertical positioning with respect to the material on either side The default is middle placement with the vertical midpoint of the total unit falling on the math axis For example Q QQ B BBBBB versus 65 Y Y n nnn 9 begin equation begin aligned alpha amp alpha alpha beta amp beta
35. mand accentedsymbol1 is a sort of hybrid of newcommand and savebox you use it in the preamble of your document to store the result of the double accent command in a box 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 IEX 3 7 Roots In ordinary I4TRX the placement of root indices is sometimes not so good Vk sqrt beta k In the amsmath package left root 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 Vk The negative argument used with leftroot moves the f to the right The units are a small amount that is a useful size for such adjustments 8 3 MISCELLANEOUS MATHEMATICS FEATURES 3 8 Boxed formulas The command boxed puts a box around its argument like fbox except that the contents are in math mode 3 2 n lt C 8 n Am 0 5 boxed eta Meg C delta eta Lambda_M 0 delta 3 9 Extensible arrows xleftarrowand 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 superscript possibly empty 3 3 A n u 1 B C xleftarrow n mu 1 quad xrightarrow T n pm i 1 3 10 Affixing
36. mps an 41 an 0 varinjlim lim m lt 0 varprojlim limpesayAp lt 0 7 INTEGRALS AND SUMS AMSMATH AMSINTX PACKAGES 11 4 2 mod and its relatives Commands mod bmod pmod pod are provided by the amsopn package to deal with the special spacing conventions of mod notation bmod and pmod are available in ATEX but with the amsopn 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 4 1 ged n mmodn x y modb x y mode x y d Xgcd n mibmod n quad xlequiv y pmod b quad x equiv y mod c quad x equiv y pod d The text command amstext amsmath packages The text command is defined by the amsmath package through a subordinate package amst ext 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 BIEX command Ambox 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 5 1 fix ix 18 Monotonic i 1 c 1 f_ x_ i 1 x_i text is monotonic quad i 1 dots ctl 6
37. n z or the such that condition in set notation or the evaluated at notation felt o 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 at least not without a significant cost in processing speed and even then not without falling somewhat short of human readers abilities It is recommended therefore 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 as in the notations for absolute value or norm because left and right delimiters are distinct usages that do not relate in the same way to adjacent symbols recommended practice is therefore to define suitable commands in the document preamble for any paired delimiter use of vert bar symbols newcommand abs 1 lvert 1 rvert newcommand norm 1 lVert 1 rVert whereupon the document would contain abs z to produce z and norm v to produce v 4 Operator names amsopn amsmath packages 4 1 Defining new operator names Math functions such as log sin and lim are traditionally typeset in roman type to make them visually more dis
38. n your system and would like to use some of the symbols in it it can be obtained by anonymous FTP from CTAN see or from the e MATH system at e math ams org It can also be ordered on disk from the AMS Customer Services Department at cust serv math ams org or 800 321 4267 B 3 Syntax checking the synt only package If you are working on a relatively slow computer system you might want to try the syntonl y package This makes I4TRx skim through your document only checking for proper syntax and usage of the commands but not producing any printed pages As IXT X runs quite a bit faster under those conditions for early error checking runs of a document this can save you valuable time The syntonly package is a standard I4TRX package so you should find it already on your system to use it write usepackage syntonly syntaxonly When you want to produce pages comment out the second line by adding a percent character syntaxonly B 4 Verbatim and comments the verbat im package The verbatim package is another standard I4TFX package like syntonly In addition to some minor enhancements for the verbat im environment it provides a comment environment that skips everything between begin comment and the next end comment A command verbatiminput is also provided for typesetting a whole file in verbatim style B 5 Commutative diagrams and other diagrams packages diagram xypic pstricks The amscd package for commutative diagram
39. ndently within the display width However it s possible to force a line to the left or right with commands shoveleft shoveright These commands take the entire line as an argument up to but not including the final MM for example 2 10 A begin multline framebox 65 columnwidth A framebox 5 columnwidth B shoveright framebox 55 columnwidth C framebox 65 columnwidth D end multline The value of multlinegap can be changed using BIEX s set length and addtolength commands If the mult line 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 4 Split equations with alignment Like mult Line 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 mult line however the split environment provides for alignment among the split lines using amp to mark alignment points as usual In addition unlike the other amsmath equation structures the split environment Basic ATEX doesn t provide an equat ion environment but rather a functionally equivalent environment named displaymath 2 DISPLAYED EQUATIONS AMSMATH PACKAGE 3 provides no numbering because it is intended to be used only inside some other displayed equation structure usually an equation align or
40. nore the font specification Wizards can fix TFM files using TFtoPL PLtoTF Appendix A ERROR MESSAGES AND OUTPUT PROBLEMS 19 You might try inserting a different font spec e g type I font lt same font id gt lt substitute font name gt 2 Explanation Certain extra sizes of some Computer Modern fonts that were formerly available mainly through the AMSFonts distribution are considered part of standard IATEX 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 I4T X 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 typel 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 Depending on the contents of your document this may be adequate L Foreign command Mover use frac or genfrac instead Example Package amsmath Error Foreign command Mover use frac or genfrac instead See the amsmath package documentation for explanation Type H lt return gt for immediate help 1 49 Fractions 1 over 2 S and Explanation T
41. number in square brackets will be used as a multiplier i e the normal value is 1 0 Dit apt Ointn day t Dot pt 3 1 2141 2 2n n nity Amt Dnt begin pmatrix D_1lt amp a_ 12 t_2 amp dots amp a_ 1in t_n a_ 21 t_1 amp D_2t amp dots amp a_ 2n t_n hdotsfor 2 4 a_ nl t_l amp a_ n2 t_2 amp dots D_nt end pmatrix 3 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 NE thinspace JL negthinspace L MG medspace JL negmedspace A W thickspace JL negthickspace LL quad 3 L qquad JJ L 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 Amspace 18 0mu 3 3 Over and under arrows Basic I4IFX provides overrightarrow and overleftarrow commands Some additional over and under arrow commands are provided by the amsmath package to fill out the set overleftarrow underleftarrow overrightarrow underrightarrow overleftrightarrow underleftrightarrow More precisely The maximum number of columns in a matrix is determined by the counter MaxMat rixCols normal value 10 which you can change if necessary using BIEX s set c
42. ounter or addtocounter commands 3 MISCELLANEOUS MATHEMATICS FEATURES 7 3 4 Dots When the amsmath package is used ellipsis dots should normally be typed as dots Placement on the baseline or centered is determined by whatever follows the dot s If the next thing is a plus sign or other binary symbol the dots will be centered if it s any other kind of symbol they will be on the baseline 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 dot sc for dots with commas or dot sb for dots with binary operators relations or dot sm 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 SA_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 Az the regional sum A Az the orthogonal product A4473 and the infinite integral i 4 k f 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 ISTEX and makes documents more easily adaptable to different conventions
43. ous mathematics features amsmath package 3 1 Matrices The amsmath package provides some environments for matrices beyond the basic array environment of BIEX The pmatrix bmatrix vmatrix and Vmat rix have respectively and delimiters built in For naming consis tency there is amat rix 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 To produce a small matrix suitable for use in text there is a smal lmat r ix environment e g 2 2 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 The above example was produced by bigl begin smallmatrix a amp b c amp d end smallmatrix bigr hdot s for number produces a row of dots in a matrix spanning the given number of columns For example abcd begin matrix a amp b amp c amp d Co EAA e amp hdotsfor 3 end matrix The spacing of the dots can be varied through use of a square bracket option for example Ahdotsfor 1 5 3 The
44. port continued development of free TEX related software There are also many local 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 BIEX 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 s guide Amer Math Soc Providence RI 1994 distributed with the AMSFonts package 2 Instructions for preparation of papers and monographs Am S BT X Amer Math Soc Providence RI 1994 3 Michel Goossens Frank Mittelbach and Alexander Samarin The BTX companion Addison Wesley Reading MA 1994 4 Donald E Knuth The TfXbook Addison Wesley Reading MA 1984 5 Leslie Lamport BTX A document preparation system 2nd revised ed Addison Wesley Reading MA 1994 6 Frank Mittelbach and Rainer Sch pf The new font family selection user interface to standard BIEX TUGboat 11 no 2 June 1990 pp 297 305 7 Michael Spivak The joy of TEX 2nd revised ed Amer Math Soc Providence RI 1990 Index 10 10 10 10 3 7 8 30 32 8 16 above 13 abovewithdelims 13 accentedsymbol 1 12 accents double 12 addtocounter 9 10 addtolength 3 align envi
45. r contents smash can be employed to make them more consistent Compare x y z and x y Z where the latter was produced by sqrt x sqrt smash b y sqrt z S 3 14 Delimiters 3 14 1 Delimiter sizes A subject that escapes mention in the I4TEX book is how to control the size of large delimiters if the automatic sizing done by left and right produces unsatisfactory results The automatic sizing 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 approximately 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 size text left bigl Big biggl Biggl size right bigr Bigr biggr Biggr Result OG 0 00 eS 5 e 5 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 py Up 5 1 p Y di Yxi versus YE di Xij i i i j biggl sum_i a_i Bigl lvert sum_j x_ ij Bigr rvert p biggr 1 p
46. r 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 Li Paragraph ended before xxx was complete Example Runaway argument Paragraph ended before equation was complete lt to be read again gt par Appendix A ERROR MESSAGES AND OUTPUT PROBLEMS 21 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 equation command e g begin equation eriein or by using abbreviations such as beq and eeq for begin equation and end equation beq eeq That kind of abbreviation works in ordinary IATEX but for technical reasons it does not work with any of the displayed equation environments gather align split equation etc when the ansmath package is used Work to re enable the use of such abbreviations is under way but nontrivial technical complications are involved 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 2h The option intlim was not declared in package amsmat
47. ring h There is also a section discussing some output errors i e instances where the printed document has something wrong but there was no I4TpX error during typesetting A 2 Error messages L begin split won t work here Example Package amsmath Error begin split won t work here 1 8 begin split h Did you forget a preceding begin equation If not perhaps the aligned environment is what you want 19 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 2h An extra amp here is so disastrous that you should probably exit and fix things up 19 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 YX and the above error is issued L Font OMX cmex m n 7 cmex7 not loadable Example Font OMX cmex m n 7 cmex7 not loadable Metric TFM file not found lt to be read again gt relax 1 8 Sa b b 2 2h I wasn t able to read the size data for this font so I will ig
48. ronment 2 5 6 34 alignat environment 6 30 32 aligned environment 6 allowdisplaybreaks 8 allowdisplaybreaks environment 7 msalpha bst 29 msart class 29 35 msbook class 29 35 msbsy package 1 18 msbsy dtx 29 mscd package 1 20 21 36 mscd dtx 29 msclass dtx 29 msdtx dtx 29 msfonts package 21 36 MSFonts collection 21 31 36 msgen dtx 29 sintx package 1 19 20 II wo w 3 amsintx dtx 20 29 AmS BTEX user s guide 27 slatex bug 28 slatex faq 28 slatex ins 29 sldoc tex 27 28 smath environment 32 smath package 1 3 5 7 9 19 28 31 34 smath dtx 29 sopn package 1 17 18 sopn dtx 29 splain bst 29 sproc class 29 35 ssymb package 36 LuS T X v mstex package 29 mstex sty 29 mstext package 1 18 mstext dtx 29 m m m 9 9 ooooooayo ow ow 333333333333 sthm package vi 1 22 24 25 29 sthm dtx 25 29 sxtra package 1 12 msxtra dtx 29 array environment 9 10 32 o9oogogoogo ow 25 arrows extensible 13 in commutative diagrams 21 article cls 27 atop 13 atopwithdelims 13 author info 35 BaKoMa fonts 31 big Big bigg delimiters 16 biggl 33 biggr 33 bigl 33 bigr 33 binom 13 14 binomials 14 bmat r ix environment 9 bmod 18 boldsymbol vi 1 18 19 29 35 boxed 13 C 22 cases environment 7 CD environment 1 21 centertags option 1 cfrac 15 classes 27 mbsy 35 bsy5
49. s that is included in the 414S BTEX distribution is quite limited The following packages are worth investigation for authors who need more powerful diagram features diagram xypic pstricks These are available by anonymous FTP from CTAN see The diagram package by Michael Barr focuses on commu tative diagrams and is thus smaller than the others it uses TEX arrows as produced by vector for diagram construction The xypic package by Kristoffer Rose is a more general diagram package it requires special arrow fonts included in the xypic distribution or PostScript capabilities in your system The pst ricks package by Timothy van Zandt also provides general diagram object commands it is strictly for PostScript use as the name implies Appendix D GETTING HELP 23 Appendix C Where to find other information C 1 Technical notes The file technote tex contains some remarks on miscellaneous technical questions related to AMS BIEX they are relegated to a separate document because they are unlikely to be of interest to most users C 2 Differences between 414S IXT EX version 1 1 and Ary S LT X version 1 2 Version 1 2 of AMS BTIEX fills in some gaps and corrects some mistakes in the AMS BIEX 1 1 feature set The significant differences from a user s perspective are described in the document diff12 tex Appendix D Getting help Questions or comments regarding the A 4S I4TRX package should be sent to American Mat
50. 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 10 3 Numbering modifications In addition to the two mandatory arguments newt heorem has two mutually exclusive optional arguments These affect the sequencing and hierarchy of the numbering By default each kind of 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 1em 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 With the optional argument section the prop counter will be reset to 0 whenever the parent counter sect ion is incremented 1
51. sible arrows asteeg e ee 3 10 Affixing symbols to other symbols oaoa a 3 11 Fractions and related constructions o e e a a 3212 Continued fractions w a ia e GY GB ee Ben le 3 13 Smash Opuons de lo al is a Bd We a Sth ae ad Sel es NI SN AA 4 Operator names amsopn amsmath packages 4 1 Defining new Operator names 0 0 0 eee eee ee ee 4 2 modand ats relatives 4 oe iw eae ar OR eee ee eS Se hs 5 The text command amstext amsmath packages 6 The boldsymbol command amsbsy amsmath packages 7 Integrals and sums amsmath amsintx packages 7 1 Multipleintegralsigns 2 2 2 0 0 e 7 2 Multiline subscripts and superscripts 2 2 eee ee ee 713 The sideset command o ra sowo e siese e ea ene o e 0 000 7A The amsintEx package iii a Se 8 Commutative diagrams amscd package 9 Using math fonts 9710 antroduction bi Cm BAe eel BG eh RE be HE Gg EA eS 9 2 Recommended use of math font commands 04 CONTENTS Sesto eee ac tala ARO RA iv 10 DS ae ee 10 dt ewe eee Sate a akg 11 11 11 11 som eng goed ia os 11 iis hig ie Bel st da Wet eta Os 12 Pe A ds ie hs 12 setae tee a pw O BE rad as 12 12 CONTENTS 10 Theorems and related structures amst hm package 10 1 Introduction 102 The newtheoremcommand ece Coe ee 000 a se e e a a e a E a e a o e oe 10 3 Numbering modifications coi e e a OS eS Boe pa 10 4 Changing styles for theorem l
52. te 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 e A boldsymbol command for printing bold versions of individual symbols including things like and lowercase Greek letters e An amsthm package that provides a useful proof environment and some enhancements to the newtheorem command support for multiple theorem styles in a single document and for unnumbered theorem types 1 HOW TO USE AyyS I4TEX 1 1 How to use AmS BTEX 1 1 Using an AMS package in a IAT X document A package in IATEX terminology is an extension written in such a form that it can be used via the usepackage command Many of the principal features of A S I4TEX are provided in separate packages so that they can be used individually on demand The amsmath package is perhaps the single most noteworthy package as it subsumes the amstext amsbsy and amsopn packages and provides a number of other enhancements for mathematical typesetting The current list of pack
53. than here 3 MISCELLANEOUS MATHEMATICS FEATURES 9 To illustrate here is how frac t frac and binom might be defined newcommand frac 2 genfrac 1 2 newcommand tfrac 2 genfrac 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 3 12 Continued fractions The continued fraction 3 6 can be obtained by typing cfrac 1 sqrt 2 cfrac 1 sqrt 2 cfrac 1 sqrt 2 dotsb 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 3 13 Smash options The 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 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 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 thei
54. tinct 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 new ones come up all the time in mathematical papers so the amsopn package provides a general mechanism for defining new operator names As the amsopn package is loaded internally by the amsmath package the following features are available there also 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 automatically add proper spacing on either side when necessary so that you get A xxx 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 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 A few special operator names are predefined by the amsopn package varinjlim varprojlim varliminf and varlimsup varlimsup limy 40Q Un un u lt 0 Wvarliminf li
55. ts between them 1 Actually depending on which font set you use Amat hbf may inconsistently work for cap Greek letters but not for lowercase 12 8 COMMUTATIVE DIAGRAMS AMSCD PACKAGE 7 2 Multiline subscripts and superscripts The substack command can be used to produce a multiline subscript or superscript for example sum_ substack 0 le i le m 0 lt 3 lt n P i 3 produces a two line subscript underneath the sum 7 1 L PGJ 0 lt i lt m O lt j lt n 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 7 2 YP EA 0 lt j lt n sum_ begin subarray 1 i in Lambda 0 lt j lt n end subarray P 1 3 7 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 Y 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_nin display mode 7 3 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 sideset sum_ n lt k text n odd nE_n to get 7 4 Y nE n lt k n odd The extra pa
56. ts msam and msbm do not currently exist so boldsymbol square will merely produce the same result as square alone Also the weight of the fonts cmmib and cmbsy is bold rather than bold extended as for cmbx Depending on the symbol in question and the resolution of your printer or previewer a symbol that was taken from one of those two bold symbol fonts might be nearly indistinguishable from the non bold version Appendix B Other useful items for mathematical documents B 1 AMS documentclasses amsart amsbook amsproc The American Mathematical Society provides custom A 4S I4TgX document classes for AMS journals and book series These may obtained by anonymous FTP from the e MATH system e math ams org directory in the author info area Note that directory structures may occasionally change if you have trouble locating files you need please contact AMS Technical Support see Appendix D Specific and generic classes can be requested by e mail to ams latex math ams org or ordered on floppy disk through the AMS Customer Services Department at cust serv math ams org or 800 321 4267 B 2 Extra math fonts the AMSFonts collection The AMSFonts font collection is a set of extra math fonts that supplements the standard set of IATEX math fonts It includes BIEX packages called ams fonts and amssymb that make it easy to use the extra fonts in a I4TRX document If you don t have the AMSFonts collection already o
57. ugmented set includes equation align gather flalign multline alignat split Although the standard eqnarray environment remains available align or split are recommended instead Except for split each environment has both starred and unstarred forms where the unstarred forms have automatic numbering using I4TRX s equation counter You can suppress the number on any particular line by putting not ag before the AX 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 AMS BIEX sample files testmath texand subeqn tex 2 2 Single equations The equation environment is for a single equation with an automatically generated number The equat ion environment is the same except for omitting the number 2 3 Split equations without alignment The mult line environment is a variation of the equat ion 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 Intermediate lines will be centered indepe
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