Typesetting Mathematics - User's Guide USD:27-1Typesetting Mathematics - User's Guide(Second Edition)Brian W. Kernighan and Lorinda L. Cherry AT&T Bell Laboratories Murray Hill, New Jersey 07974ABSTRACTThis is the user's guide for a system for typesetting mathematics, using the phototypesetters on the UNIX-operating system. Mathematical expressions are described in a language designed to be easy to use by people who know neither mathematics nor typesetting. Enough of the language to set in-line expres- sions like lim (tan x)sin 2x = 1 or display equations like x->i̅i̅/2 | | G(z) = eln G(z) = exp|_k__k_| Sk|k/k | ≥̅ k |__2_z_4_+...| |||≥1 | S2k≥1 |... | | |__z__+...||_2__2_+ | km | =| | S1 ||1+ 2 22.2! k2___m___|zm |1+|1z+ 2! || k1___2___... km | =|≥̅ |___1___k2 m km!| can be learned0in an hou̅r or so. k1 2 k2! | | k1,k2,...,km≥0 1 k1! The language1interfaceskdirectly with the phototypesetting language TROFF, so mathematical expressions can be embedded in the running text of a manuscript, and the entire document pro- duced in one process. This user's guide is an example of its out- put. The same language may be used with the UNIX formatter NROFF to set mathematical expressions on DASI and GSI terminals and Model 37 teletypes. --------------------------UNIX is a registered trademark of AT&T Bell Labora- tories in the USA and other countries. February 8, 2016 USD:27-2 Typesetting Mathematics - User's Guide1. IntroductionEQN is a program for typesetting mathematics on the Graphics Systems phototypesetters on the UNIX operating system. The EQN language was designed to be easy to use by people who know nei- ther mathematics nor typesetting. Thus EQN knows relatively lit- tle about mathematics. In particular, mathematical symbols like +, -, x, parentheses, and so on have no special meanings. EQN is quite happy to set garbage (but it will look good). EQN works as a preprocessor for the typesetter formatter, TROFF[1], so the normal mode of operation is to prepare a docu- ment with both mathematics and ordinary text interspersed, and let EQN set the mathematics while TROFF does the body of the text. On UNIX, EQN will also produce mathematics on DASI and GSI terminals and on Model 37 teletypes. The input is identical, but you have to use the programs NEQN and NROFF instead of EQN and TROFF. Of course, some things won't look as good because termi- nals don't provide the variety of characters, sizes and fonts that a typesetter does, but the output is usually adequate for proofreading. To use EQN on UNIX, eqn files | troff2. Displayed EquationsTo tell EQN where a mathematical expression begins and ends, we mark it with lines beginning .EQ and .EN. Thus if you type the lines .EQ x=y+z .EN your output will look like x=y+z The .EQ and .EN are copied through untouched; they are not other- wise processed by EQN. This means that you have to take care of things like centering, numbering, and so on yourself. The most common way is to use the TROFF and NROFF macro package package `-ms' developed by M. E. Lesk[3], which allows you to center, indent, left-justify and number equations. With the `-ms' package, equations are centered by default. To left-justify an equation, use .EQ L instead of .EQ. To indent it, use .EQ I. Any of these can be followed by an arbitrary `equation number' which will be placed at the right margin. For example, the input February 8, 2016 Typesetting Mathematics - User's Guide USD:27-3 .EQ I (3.1a) x = f(y/2) + y/2 .EN produces the output x=f(y/2)+y/2 (3.1a) The2ecanabeoenteredtwithoutt.EQoands.EN.nWeiwilletalksaboutitkins̅e̅ction 19.3. Input spacesSpaces and newlines within an expression are thrown away by EQN. (Normal text is left absolutely alone.) Thus between .EQ and .EN, x=y+z and x = y + z and x = y + z and so on all produce the same output x=y+z You should use spaces and newlines freely to make your input equations readable and easy to edit. In particular, very long lines are a bad idea, since they are often hard to fix if you make a mistake.4. Output spacesTo force extra spaces into theoutput, use a tilde ``~'' for each space you want: x~=~y~+~z gives x = y + z You can also use a circumflex ``^'', which gives a space half the width of a tilde. It is mainly useful for fine-tuning. Tabs may also be used to position pieces of an expression, but the tab stops must be set by TROFF commands. February 8, 2016 USD:27-4 Typesetting Mathematics - User's Guide5. Symbols,Special Names,GreekEQN knows some mathematical symbols, some mathematical names, and the Greek alphabet. For example, x=2 pi int sin ( omega t)dt produces x=2i̅i̅sin(wt)dt Here the spaces in the input arenecessaryto tell EQN thatint,pi,sinandomegaare separate entities that should get special treatment. Thesin, digit 2, and parentheses are set in roman type instead of italic;piandomegaare made Greek; andintbecomes the integral sign. When in doubt, leave spaces around separate parts of the input. Averycommon error is to typef(pi) without leaving spaces on both sides of thepi. As a result, EQN does not recog- nizepias a special word, and it appears as f(pi) instead of f(i̅i̅). A complete list of EQN names appears in section 23. Knowledgeable users can also use TROFF four-character names for anything EQN doesn't know about, like \(bsfor the Bell System sign .6. Spaces,AgainThe only way EQN can deduce that some sequence of letters might be special is if that sequence is separated from the letters on either side of it. This can be done by surrounding a special word by ordinary spaces (or tabs or newlines), as we did in the previous section. You can also make special words stand out by surrounding them with tildes or circumflexes: x~=~2~pi~int~sin~(~omega~t~)~dt is much the same as the last example, except that the tildes not only separate the magic words likesin,omega, and so on, but also add extra spaces, one space per tilde: x = 2 i̅i̅ sin ( w t ) dt Special words can also be separated by braces { } and double quotes "...", which have special meanings that we will see soon.7. Subscripts and SuperscriptsSubscripts and superscripts are obtained with the wordssubandsup. February 8, 2016 Typesetting Mathematics - User's Guide USD:27-5 x sup 2 + y sub k gives x2+yk EQN takes care of all the size changes and vertical motions needed to make the output look right. The wordssubandsupmust be surrounded by spaces;x sub2will give you xsub2 instead of x2. Furthermore, don't forget to leave a space (or a tilde, etc.) to mark the end of a subscript or superscript. A common error is to say something like y = (x sup 2)+1 which causes y=(x2)+1 instead of the intended y=(x2)+1 Subscripted subscripts and superscripted superscripts also work: x sub i sub 1 is xi1 A subscript and superscript on the same thing are printed one above the other if the subscript comesfirst: x sub i sup 2 is 2 xi Other than this special cayz,subandsupgroup to the right, sox sup y sub zmeans x , not xyz.8. Braces for GroupingNormally, the end of a subscript or superscript is marked simply by a blank (or tab or tilde, etc.) What if the subscript or superscript is something that has to be typed with blanks in it? In that case, you can use the braces { and } to mark the beginning and end of the subscript or superscript: e sup {i omega t} is February 8, 2016 USD:27-6 Typesetting Mathematics - User's Guide eiwt Rule: Braces canalwaysbe used to force EQN to treat something as a unit, or just to make your intent perfectly clear. Thus: x sub {i sub 1} sup 2 is 2 with braces, but xi1 x sub i sub 1 sup 2 is x 2 which is rather different. i1 Braces can occur within braces if necessary: e sup {i pi sup {rho +1}} is eii̅i̅p+1 The general rule is that anywhere you could use some single thing likex, you can use an arbitrarily complicated thing if you enclose it in braces. EQN will look after all the details of positioning it and making it the right size. In all cases, make sure you have the right number of braces. Leaving one out or adding an extra will cause EQN to complain bitterly. Occasionally you will have to print braces. To do this, enclose them in double quotes, like "{". Quoting is discussed in more detail in section 14.9. FractionsTo make a fraction, use the wordover: a+b over 2c =1 gives_±_=1 The line is made the right length and positioned automatically. Braces can be used to make clear what goes over what: {alpha + beta} over {sin (x)} February 8, 2016 Typesetting Mathematics - User's Guide USD:27-7 is__(_±|__ What happens when there is bothnan)overand asupin the same expression? In such an apparently ambiguous case, EQN does thesupbefore theover, so -b sup 2 ove_2_pi i̅i̅ The rules which decide which operation is don_e_2_firstein caseslike this are summarized in section 23. Whenin d̅o̅ubt, however,use bracesto make clear what goes with what.10. Square RootsTo draw a square root, usesqrt: sqrt a+b + 1 over sqrt {ax sup 2 +bx+c} is _____________ \|a+b+ ________ Warning - square roots of tall\quantities look lousy, because a root-sign big enough to cover the quantity is too dark and heavy: sqrt {a sup 2 over b sub 2} is __ |_2_ Big square roots are generallybetter written as something to the power 1/2: \| (a2/b2)1/2 which is (a sup 2 /b sub 2 ) sup half11. Summation,Integral,Etc. Summations, integrals, and similar constructions are easy: sum from i=0 to {i= inf} x sup i produces i=oo ≥̅ xi Notice that we used braces toiindicate where the upper part i=oo begins and ends. No braces were necessary for the lower part i=0, because it contained no blanks. The braces will never hurt, and February 8, 2016 USD:27-8 Typesetting Mathematics - User's Guide if thefromandtoparts contain any blanks, you must use braces around them. Thefromandtoparts are both optional, but if both are used, they have to occur in that order. Other useful characters can replace thesumin our example: int prod union inter become, respectively, TT (̅)̅_)_ Since the thing before thefromcan be anything, even something in braces,from-tocan often be used in unexpected ways: lim from {n -> inf} x sub n =0 is lim xn=0 n->oo12. Size and Font ChangesBy default, equations are set in 10-point type (the same size as this guide), with standard mathematical conventions to determine what characters are in roman and what in italic. Although EQN makes a valiant attempt to use esthetically pleasing sizes and fonts, it is not perfect. To change sizes and fonts, usesize nandroman,italic,boldandfat. Likesubandsup, size and font changes affect only the thing that follows them, and revert to the normal situation at the end of it. Thus bold x y is xy and size 14 bold x = y + size 14 {alpha + beta} gives x=y+(+|As always, you can use braces if you want to affect something more complicated than a single letter. For example, you can change the size of an entire equation by size 12 { ... } Legal sizes which may followsizeare 6, 7, 8, 9, 10, 11, February 8, 2016 Typesetting Mathematics - User's Guide USD:27-9 12, 14, 16, 18, 20, 22, 24, 28, 36. You can also change the sizebya given amount; for example, you can saysize+2to make the size two points bigger, orsize -3to make it three points smaller. This has the advantage that you don't have to know what the current size is. If you are using fonts other than roman, italic and bold, you can sayfont XwhereXis a one character TROFF name or number for the font. Since EQN is tuned for roman, italic and bold, other fonts may not give quite as good an appearance. Thefatoperation takes the current font and widens it by overstriking:fat gradis\̅̅/̅̅ andfat{x sub i} isxi. If an entire document is to be in a non-standard size or font, it is a severe nuisance to have to write out a size and font change for each equation. Accordingly, you can set a ``glo- bal'' size or font which thereafter affects all equations. At the beginning of any equation, you might say, for instance, .EQ gsize 16 gfont R ... .EN to set the size to 16 and the font to roman thereafter. In place of R, you can use any of the TROFF font names. The size aftergsizecan be a relative change with + or -. Generally,gsizeandgfontwill appear at the beginning of a document but they can also appear thoughout a document: the glo- bal font and size can be changed as often as needed. For example, in a footnote=you will typically want the size of equations to match the size of the footnote text, which is two points smaller than the main text. Don't forget to reset the global size at the end of the footnote.13. Diacritical MarksTo get funny marks on top of letters, there are several words: -------------------------=Like this one, in which we have a few random expres- sions like xi and i̅i̅2. The sizes for these were set by the commandgsize -2. February 8, 2016 USD:27-10 Typesetting Mathematics - User's Guide . x dot.. x dotdot x x hat^x tilde-̅x vec-x dyad _x x bar x x under _x The diacritical mark is placed at the right height. Thebarandu_n_d_e_r_are made the right length for the entire construct, as in x+y+z; other marks are centered.14. Quoted TextAny input entirely within quotes ("...") is not subject to any of the font changes and spacing adjustments normally done by the equation setter. This provides a way to do your own spacing and adjusting if needed: italic "sin(x)" + sin (x) is sin(x)+sin(x) Quotes are also used to get braces and other EQN keywords printed: "{ size alpha }" is { size alpha } and roman "{ size alpha }" is { size alpha } The construction "" is often used as a place-holder when grammatically EQN needs something, but you don't actually want anything in your output. For example, to make 2He, you can't just typesup 2 roman Hebecause asuphas to be a superscriptonsomething. Thus you must say "" sup 2 roman He To get a literal quote use ``\"''. TROFF characters like\(bscan appear unquoted, but more complicated things like February 8, 2016 Typesetting Mathematics - User's Guide USD:27-11 horizontal and vertical motions with\hand\vshould always be quoted. (If you've never heard of \hand \v, ignore this sec- tion.)15. Lining Up EquationsSometimes it's necessary to line up a series of equations at some horizontal position, often at an equals sign. This is done with two operations calledmarkandlineup. The wordmarkmay appear once at any place in an equation. It remembers the horizontal position where it appeared. Succes- sive equations can contain one occurrence of the wordlineup. The place wherelineupappears is made to line up with the place marked by the previousmarkif at all possible. Thus, for exam- ple, you can say .EQ I x+y mark = z .EN .EQ I x lineup = 1 .EN to produce x+y=z x=1 For reasons too complicated to talk about, when you use EQN and `-ms', use either .EQ I or .EQ L. mark andlineupdon't work with centered equations. Also bear in mind thatmarkdoesn't look ahead; x mark =1 ... x+y lineup =z isn't going to work, because there isn't room for thex+ypart after themarkremembers where thexis.16. Big Brackets,Etc. To get big brackets [ ], braces { }, parentheses ( ), and bars |~| around things, use theleftandrightcommands: left { a over b + 1 right } ~=~ left ( c over d right ) + left [ e right ] is | |_+1| = |_||b | |d|+| | |e| | The resulting brackets are made big enough to cover whatever they enclose. Other characters can be used besides these, but the are February 8, 2016 USD:27-12 Typesetting Mathematics - User's Guide not likely to look very good. One exception is thefloorandceilingcharacters: left floor x over y right floor <= left ceiling a over b right ceiling produces |_||y|≤|_||b| Several warnings about brackets are in order. First, braces are typically bigger than brackets and parentheses, because they are made up of three, five, seven, etc., pieces, while brackets can be made up of two, three, etc. Second, big left and right parentheses often look poor, because the character set is poorly designed. Therightpart may be omitted: a ``left something'' need not have a corresponding ``right something''. If therightpart is omitted, put braces around the thing you want the left bracket to encompass. Otherwise, the resulting brackets may be too large. If you want to omit theleftpart, things are more compli- cated, because technically you can't have arightwithout a correspondingleft. Instead you have to say left "" ..... right ) for example. Theleft"" means a ``left nothing''. This satisfies the rules without hurting your output.17. PilesThere is a general facility for making vertical piles of things; it comes in several flavors. For example: A ~=~ left [ pile { a above b above c } ~~ pile { x above y above z } right ] will make |a x| A = |b y| The elements of the pile (there|canzbe as many as you want) are centered one above another, at the right height for most pur- poses. The keywordaboveis used to separate the pieces; braces are used around the entire list. The elements of a pile can be as complicated as needed, even containing more piles. Three other forms of pile exist:lpilemakes a pile with the elements left-justified;rpilemakes a right-justified pile; andcpilemakes a centered pile, just likepile. The vertical spacing between the pieces is somewhat larger forl-,r-andcpilesthan February 8, 2016 Typesetting Mathematics - User's Guide USD:27-13 it is for ordinary piles. roman sign (x)~=~ left { lpile {1 above 0 above -1} ~~ lpile {if~x>0 above if~x=0 above if~x<0} makes | |1 sign(x) = |0 if x>0 |-1 if x=0 | if x<0 Notice the left brace without a matching right one.18. MatricesIt is also possible to make matrices. For example, to make a neat array like xi x2 yi y2 you have to type matrix { ccol { x sub i above y sub i } ccol { x sup 2 above y sup 2 } } This produces a matrix with two centered columns. The elements of the columns are then listed just as for a pile, each element separated by the wordabove. You can also uselcolorrcolto left or right adjust columns. Each column can be separately adjusted, and there can be as many columns as you like. The reason for using a matrix instead of two adjacent piles, by the way, is that if the elements of the piles don't all have the same height, they won't line up properly. A matrix forces them to line up, because it looks at the entire structure before deciding what spacing to use. A word of warning about matrices -each column must have thesame number of elements in it. The world will end if you get this wrong.19. Shorthand for In-line EquationsIn a mathematical document, it is necessary to follow mathematical conventions not just in display equations, but also in the body of the text, for example by making variable names like x italic. Although this could be done by surrounding the appropriate parts with .EQ and .EN, the continual repetition of .EQ and .EN is a nuisance. Furthermore, with `-ms', .EQ and .EN February 8, 2016 USD:27-14 Typesetting Mathematics - User's Guide imply a displayed equation. EQN provides a shorthand for short in-line expressions. You can define two characters to mark the left and right ends of an in-line equation, and then type expressions right in the middle of text lines. To set both the left and right characters to dol- lar signs, for example, add to the beginning of your document the three lines .EQ delim $$ .EN Having done this, you can then say things like Let $alpha sub i$ be the primary variable, and let $beta$ be zero. Then we can show that $x sub 1$ is $>=0$. This works as you might expect - spaces, newlines, and so on are significant in the text, but not in the equation part itself. Multiple equations can occur in a single input line. Enough room is left before and afternline that contains in-line expressions that something like ≥̅ xi does not interfere with the lines surrounding it. i=1 To turn off the delimiters, .EQ delim off .EN Warning: don't use braces, tildes, circumflexes, or double quotes as delimiters - chaos will result.20. DefinitionsEQN provides a facility so you can give a frequently-used string of characters a name, and thereafter just type the name instead of the whole string. For example, if the sequence x sub i sub 1 + y sub i sub 1 appears repeatedly throughout a paper, you can save re-typing it each time by defining it like this: define xy 'x sub i sub 1 + y sub i sub 1' This makesxya shorthand for whatever characters occur between the single quotes in the definition. You can use any character instead of quote to mark the ends of the definition, so long as it doesn't appear inside the definition. Now you can usexylike this: February 8, 2016 Typesetting Mathematics - User's Guide USD:27-15 .EQ f(x) = xy ... .EN and so on. Each occurrence ofxywill expand into what it was defined as. Be careful to leave spaces or their equivalent around the name when you actually use it, so EQN will be able to iden- tify it as special. There are several things to watch out for. First, although definitions can use previous definitions, as in .EQ define xi ' x sub i ' define xi1 ' xi sub 1 ' .ENdon't define something in terms of itself' A favorite error is to say define X ' roman X ' This is a guaranteed disaster, since Xisnow defined in terms of itself. If you say define X ' roman "X" ' however, the quotes protect the second X, and everything works fine. EQN keywords can be redefined. You can make / meanoverby saying define / ' over ' or redefineoveras / with define over ' / ' If you need different things to print on a terminal and on the typesetter, it is sometimes worth defining a symbol dif- ferently in NEQN and EQN. This can be done withndefineandtde-fine. A definition made withndefineonly takes effect if you are running NEQN; if you usetdefine, the definition only applies for EQN. Names defined with plaindefineapply to both EQN and NEQN.21. Local MotionsAlthough EQN tries to get most things at the right place on the paper, it isn't perfect, and occasionally you will need to tune the output to make it just right. Small extra horizontal spaces can be obtained with tilde and circumflex. You can also February 8, 2016 USD:27-16 Typesetting Mathematics - User's Guide sayback nandfwd nto move small amounts horizontally.nis how far to move in 1/100's of an em (an em is about the width of the letter `m'.) Thusback 50moves back about half the width of an m. Similarly you can move things up or down withup nanddown n. As withsuborsup, the local motions affect the next thing in the input, and this can be something arbitrarily complicated if it is enclosed in braces.22. A Large ExampleHere is the complete source for the three display equations in the abstract of this guide. .EQ I G(z)~mark =~ e sup { ln ~ G(z) } ~=~ exp left ( sum from k>=1 {S sub k z sup k} over k right ) ~=~ prod from k>=1 e sup {S sub k z sup k /k} .EN .EQ I lineup = left ( 1 + S sub 1 z + { S sub 1 sup 2 z sup 2 } over 2! + ... right ) left ( 1+ { S sub 2 z sup 2 } over 2 + { S sub 2 sup 2 z sup 4 } over { 2 sup 2 cdot 2! } + ... right ) ... .EN .EQ I lineup = sum from m>=0 left ( sum from pile { k sub 1 ,k sub 2 ,..., k sub m >=0 above k sub 1 +2k sub 2 + ... +mk sub m =m} { S sub 1 sup {k sub 1} } over {1 sup k sub 1 k sub 1 ! } ~ { S sub 2 sup {k sub 2} } over {2 sup k sub 2 k sub 2 ! } ~ ... { S sub m sup {k sub m} } over {m sup k sub m k sub m ! } right ) z sup m .EN23. Keywords,Precedences,Etc. If you don't use braces, EQN will do operations in the order shown in this list.dyad vec under bar tilde hat dot dotdotfwd back down upfat roman italic bold sizesub sup sqrt overfrom toThese operations group to the left:over sqrt left rightFebruary 8, 2016 Typesetting Mathematics - User's Guide USD:27-17 All others group to the right. Digits, parentheses, brackets, punctuation marks, and these mathematical words are converted to Roman font when encountered: sin cos tan sinh cosh tanh arc max min lim log ln exp Re Im and if for det These character sequences are recognized and translated as shown. >= ≥ <= ≤ == _= !=/+- ± -> -> <- <- << << >> >> inf oo partial`half 1/2 prime ' approx~nothing cdot . times x del \̅/̅ grad \̅/̅ ... ... ,..., ,..., sum ≥̅ int prod TT union (̅)̅ inter_)_ To obtain Greek letters, simply spell them out in whatever case you want: DELTA_\_iota i GAMMA I̅ kappa k LAMBDA /\ lambda\OMEGA_mu u PHI|nu v PI TT omega w PSI|omicrono SIGMA ≥̅ phi|THETA-pi i̅i̅ UPSILON Y psi|XI_rho p alpha(sigma o̅ February 8, 2016 USD:27-18 Typesetting Mathematics - User's Guide beta|tau i̅ chi x theta-delta`upsilonu epsilon-xi eta n zeta gamma/These are all the words known to EQN (except for characters with names), together with the section where they are discussed. above 17, 18 lpile 17 back 21 mark 15 bar 13 matrix 18 bold 12 ndefine20 ccol 18 over 9 col 18 pile 17 cpile 17 rcol 18 define 20 right 16 delim 19 roman 12 dot 13 rpile 17 dotdot 13 size 12 down 21 sqrt 10 dyad 13 sub 7 fat 12 sup 7 font 12 tdefine20 from 11 tilde 13 fwd 21 to 11 gfont 12 under 13 gsize 12 up 21 hat 13 vec 13 italic 12 ~, ^ 4, 6 lcol 18 { } 8 left 16 "..." 8, 14 lineup 1524. TroubleshootingIf you make a mistake in an equation, like leaving out a brace (very common) or having one too many (very common) or hav- ing asupwith nothing before it (common), EQN will tell you with the messagesyntax error between lines x and y,file zwherexandyare approximately the lines between which the trou- ble occurred, andzis the name of the file in question. The line numbers are approximate - look nearby as well. There are also self-explanatory messages that arise if you leave out a quote or try to run EQN on a non-existent file. If you want to check a document before actually printing it (on UNIX only), February 8, 2016 Typesetting Mathematics - User's Guide USD:27-19 eqn files >/dev/null will throw away the output but print the messages. If you use something like dollar signs as delimiters, it is easy to leave one out. This causes very strange troubles. The programcheckeqchecks for misplaced or missing dollar signs and similar troubles. In-line equations can only be so big because of an internal buffer in TROFF. If you get a message ``word overflow'', you have exceeded this limit. If you print the equation as a displayed equation this message will usually go away. The message ``line overflow'' indicates you have exceeded an even bigger buffer. The only cure for this is to break the equation into two separate ones. On a related topic, EQN does not break equations by itself - you must split long equations up across multiple lines by your- self, marking each by a separate .EQ ... .EN sequence. EQN does warn about equations that are too long to fit on one line.25. Use on UNIXTo print a document that contains mathematics on the UNIX typesetter, eqn files | troff If there are any TROFF options, they go after the TROFF part of the command. For example, eqn files | troff -ms A compatible version of EQN can be used on devices like teletypes and DASI and GSI terminals which have half-line forward and reverse capabilities. To print equations on a Model 37 tele- type, for example, use neqn files | nroff The language for equations recognized by NEQN is identical to that of EQN, although of course the output is more restricted. To use a GSI or DASI terminal as the output device, neqn files | nroff -Txwherexis the terminal type you are using, such as300or300S. EQN and NEQN can be used with the TBL program[2] for setting tables that contain mathematics. Use TBL before [N]EQN, like February 8, 2016 USD:27-20 Typesetting Mathematics - User's Guide this: tbl files | eqn | troff tbl files | neqn | nroff26. AcknowledgmentsWe are deeply indebted to J. F. Ossanna, the author of TROFF, for his willingness to extend TROFF to make our task easier, and for his continuous assistance during the development and evolution of EQN. We are also grateful to A. V. Aho for advice on language design, to S. C. Johnson for assistance with the YACC compiler-compiler, and to all the EQN users who have made helpful suggestions and criticisms.References[1] J. F. Ossanna, ``NROFF/TROFF User's Manual'', Bell Labora- tories Computing Science Technical Report #54, 1976. [2] M. E. Lesk, ``Typing Documents on UNIX'', Bell Laboratories, 1976. [3] M. E. Lesk, ``TBL - A Program for Setting Tables'', Bell Laboratories Computing Science Technical Report #49, 1976. February 8, 2016

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