1eqn(1) General Commands Manual eqn(1)
2
6 eqn - format mathematics (equations) for groff or MathML
7
9 eqn [-CNrR] [-d xy] [-f F] [-m n] [-M dir] [-p n] [-s n] [-T dev]
10 [file ...]
11 eqn --help
13 eqn -v
15 eqn --version
16
18 The GNU implementation of eqn is part of the groff(7) document format‐
19 ting system. eqn is a troff(1) preprocessor that translates expres‐
20 sions in its own language, embedded in roff(7) input files, into mathe‐
21 matical notation typeset by troff(1). It copies each file's contents
22 to the standard output stream, translating each equation between lines
23 starting with .EQ and .EN, or within a pair of user-specified delim‐
24 iters. Normally, eqn is not executed directly by the user, but invoked
25 by specifying the -e option to groff(1). While GNU eqn's input syntax
26 is highly compatible with AT&T eqn, the output eqn produces cannot be
27 processed by AT&T troff; GNU troff (or a troff implementing relevant
28 GNU extensions) must be used. If no file operands are given on the
29 command line, or if file is “-”, eqn reads the standard input stream.
30 Unless the -R option is used, eqn searches for the file eqnrc in the
32 directories given with the -M option first, then in /etc/groff/
33 site-tmac, and finally in the standard macro directory /usr/share/
34 groff/1.23.0/tmac. If it exists and is readable, eqn processes it be‐
35 fore any input files.
36 This man page primarily discusses the differences between GNU eqn and
38 AT&T eqn. Most of the new features of the GNU eqn input language are
39 based on TeX. There are some references to the differences between TeX
40 and GNU eqn below; these may safely be ignored if you do not know TeX.
41 Three points are worth special note.
43 • GNU eqn emits Presentation MathML output when invoked with the
45 “-T MathML” option.
46 • GNU eqn does not support terminal devices well, though it may suffice
48 for simple inputs.
49 • GNU eqn sets the input token “...” as an ellipsis on the text base‐
51 line, not the three centered dots of AT&T eqn. Set an ellipsis on
52 the math axis with the GNU extension macro cdots.
53 Anatomy of an equation
55 eqn input consists of tokens. Consider a form of Newton's second law
56 of motion. The input
57 .EQ
59 F =
60 m a
61 .EN
62 becomes F=ma. Each of F, =, m, and a is a token. Spaces and newlines
64 are interchangeable; they separate tokens but do not break lines or
65 produce space in the output.
66 The following input characters not only separate tokens, but manage
68 their grouping and spacing as well.
69 { } Braces perform grouping. Whereas “e sup a b” expresses “(e to
71 the a) times b”, “e sup { a b }” means “e to the (a times b)”.
72 When immediately preceded by a “left” or “right” primitive, a
73 brace loses its special meaning.
74 ^ ~ are the half space and full space, respectively. Use them to
76 tune the appearance of the output.
77 Tab and leader characters separate tokens as well as advancing the
79 drawing position to the next tab stop, but are seldom used in eqn in‐
80 put. When they occur, they must appear at the outermost lexical scope.
81 This roughly means that they can't appear within braces that are neces‐
82 sary to disambiguate the input; eqn will diagnose an error in this
83 event. (See subsection “Macros” below for additional token separation
84 rules.)
85 Other tokens are primitives, macros, an argument to either of the fore‐
87 going, or components of an equation.
88 Primitives are fundamental keywords of the eqn language. They can con‐
90 figure an aspect of the preprocessor's state, as when setting a
91 “global” font selection or type size (gfont and gsize), or declaring or
92 deleting macros (“define” and undef); these are termed commands. Other
93 primitives perform formatting operations on the tokens after them (as
94 with fat, over, sqrt, or up).
95 Equation components include mathematical variables, constants, numeric
97 literals, and operators. eqn remaps some input character sequences to
98 groff special character escape sequences for economy in equation entry
99 and to ensure that glyphs from an unstyled font are used; see
100 groff_char(7).
101 + \[pl] ' \[fm]
103 - \[mi] <= \[<=]
104 = \[eq] >= \[>=]
105 Macros permit primitives, components, and other macros to be collected
107 and referred to by a single token. Predefined macros make convenient
108 the preparation of eqn input in a form resembling its spoken expres‐
109 sion; for example, consider cos, hat, inf, and lim.
110 Spacing and typeface
112 GNU eqn imputes types to the components of an equation, adjusting the
113 spacing between them accordingly. Recognized types are as follows;
114 most affect spacing only, whereas the “letter” subtype of “ordinary”
115 also assigns a style.
116 ordinary character such as “1”, “a”, or “!”
118 letter character to be italicized by default
119 digit n/a
120 operator large operator such as “Σ”
121 binary binary operator such as “+”
122 relation relational operator such as “=”
123 opening opening bracket such as “(”
124 closing closing bracket such as “)”
125 punctuation punctuation character such as “,”
126 inner sub-formula contained within brackets
127 suppress component to which automatic spacing is not applied
128 Two primitives apply types to equation components.
130 type t e
132 Apply type t to expression e.
133 chartype t text
135 Assign each character in (unquoted) text type t, persistently.
136 eqn sets up spacings and styles as if by the following commands.
138 chartype "letter" abcdefghiklmnopqrstuvwxyz
140 chartype "letter" ABCDEFGHIKLMNOPQRSTUVWXYZ
141 chartype "letter" \[*a]\[*b]\[*g]\[*d]\[*e]\[*z]
142 chartype "letter" \[*y]\[*h]\[*i]\[*k]\[*l]\[*m]
143 chartype "letter" \[*n]\[*c]\[*o]\[*p]\[*r]\[*s]
144 chartype "letter" \[*t]\[*u]\[*f]\[*x]\[*q]\[*w]
145 chartype "binary" *\[pl]\[mi]
146 chartype "relation" <>\[eq]\[<=]\[>=]
147 chartype "opening" {([
148 chartype "closing" })]
149 chartype "punctuation" ,;:.
150 chartype "suppress" ^~
151 eqn assigns all other ordinary and special roff characters, including
153 numerals 0–9, the “ordinary” type. (The “digit” type is not used, but
154 is available for customization.) In keeping with common practice in
155 mathematical typesetting, lowercase, but not uppercase, Greek letters
156 are assigned the “letter” type to style them in italics. The macros
157 for producing ellipses, “...”, cdots, and ldots, use the “inner” type.
158 Primitives
160 eqn supports without alteration the AT&T eqn primitives above, back,
161 bar, bold, define, down, fat, font, from, fwd, gfont, gsize, italic,
162 left, lineup, mark, matrix, ndefine, over, right, roman, size, sqrt,
163 sub, sup, tdefine, to, under, and up.
164 New primitives
166 The GNU extension primitives “type” and chartype are discussed in sub‐
167 section “Spacing and typeface” above; “set” in subsection “Customiza‐
168 tion” below; and grfont and gbfont in subsection “Fonts” below. In the
169 following synopses, X can be any character not appearing in the parame‐
170 ter thus bracketed.
171 e1 accent e2
173 Set e2 as an accent over e1. e2 is assumed to be at the appro‐
174 priate height for a lowercase letter without an ascender; eqn
175 vertically shifts it depending on e1's height. For example, hat
176 is defined as follows.
177 accent { "^" }
179 dotdot, dot, tilde, vec, and dyad are also defined using the
181 accent primitive.
182 big e Enlarge the expression e; semantics like those of CSS “large”
184 are intended. In troff output, the type size is increased by 5
185 scaled points. MathML output emits the following.
186 <mstyle mathsize='big'>
188 copy file
190 include file
191 Interpolate the contents of file, omitting lines beginning with
192 .EQ or .EN. If a relative path name, file is sought relative to
193 the current working directory.
194 ifdef name X anything X
196 If name is defined as a primitive or macro, interpret anything.
197 nosplit text
199 As "text", but since text is not quoted it is subject to macro
200 expansion; it is not split up and the spacing between characters
201 not adjusted per subsection “Spacing and typeface” above.
202 e opprime
204 As prime, but set the prime symbol as an operator on e. In the
205 input “A opprime sub 1”, the “1” is tucked under the prime as a
206 subscript to the “A” (as is conventional in mathematical type‐
207 setting), whereas when prime is used, the “1” is a subscript to
208 the prime character. The precedence of opprime is the same as
209 that of bar and “under”, and higher than that of other primi‐
210 tives except accent and uaccent. In unquoted text, a neutral
211 apostrophe (') that is not the first character on the input line
212 is treated like opprime.
213 sdefine name X anything X
215 As “define”, but name is not recognized as a macro if called
216 with arguments.
217 e1 smallover e2
219 As over, but reduces the type size of e1 and e2, and puts less
220 vertical space between e1 and e2 and the fraction bar. The over
221 primitive corresponds to the TeX \over primitive in displayed
222 equation styles; smallover corresponds to \over in non-display
223 (“inline”) styles.
224 space n
226 Set extra vertical spacing around the equation, replacing the
227 default values, where n is an integer in hundredths of an em.
228 If positive, n increases vertical spacing before the equation;
229 if negative, it does so after the equation. This primitive pro‐
230 vides an interface to groff's \x escape sequence, but with the
231 opposite sign convention. It has no effect if the equation is
232 part of a pic(1) picture.
233 special troff-macro e
235 Construct an object by calling troff-macro on e. The troff
236 string 0s contains the eqn output for e, and the registers 0w,
237 0h, 0d, 0skern, and 0skew the width, height, depth, subscript
238 kern, and skew of e, respectively. (The subscript kern of an
239 object indicates how much a subscript on that object should be
240 “tucked in”, or placed to the left relative to a non-subscripted
241 glyph of the same size. The skew of an object is how far to the
242 right of the center of the object an accent over it should be
243 placed.) The macro must modify 0s so that it outputs the de‐
244 sired result, returns the drawing position to the text baseline
245 at the beginning of e, and updates the foregoing registers to
246 correspond to the new dimensions of the result.
247 Suppose you want a construct that “cancels” an expression by
249 drawing a diagonal line through it.
250 .de Ca
252 . ds 0s \
253 \Z'\\*(0s'\
254 \v'\\n(0du'\
255 \D'l \\n(0wu -\\n(0hu-\\n(0du'\
256 \v'\\n(0hu'
257 ..
258 .EQ
259 special Ca "x \[mi] 3 \[pl] x" ~ 3
260 .EN
261 We use the \[mi] and \[pl] special characters instead of + and -
263 because they are part of the argument to a troff macro, so eqn
264 does not transform them to mathematical glyphs for us. Here's a
265 more complicated construct that draws a box around an expres‐
266 sion; the bottom of the box rests on the text baseline. We de‐
267 fine the eqn macro box to wrap the call of the troff macro Bx.
268 .de Bx
270 .ds 0s \
271 \Z'\\h'1n'\\*[0s]'\
272 \v'\\n(0du+1n'\
273 \D'l \\n(0wu+2n 0'\
274 \D'l 0 -\\n(0hu-\\n(0du-2n'\
275 \D'l -\\n(0wu-2n 0'\
276 \D'l 0 \\n(0hu+\\n(0du+2n'\
277 \h'\\n(0wu+2n'
278 .nr 0w +2n
279 .nr 0d +1n
280 .nr 0h +1n
281 ..
282 .EQ
283 define box ' special Bx $1 '
284 box(foo) ~ "bar"
285 .EN
286 split "text"
288 As text, but since text is quoted, it is not subject to macro
289 expansion; it is split up and the spacing between characters ad‐
290 justed per subsection “Spacing and typeface” above.
291 e1 uaccent e2
293 Set e2 as an accent under e1. e2 is assumed to be at the appro‐
294 priate height for a letter without a descender; eqn vertically
295 shifts it depending on whether e1 has a descender. utilde is
296 predefined using uaccent as a tilde accent below the baseline.
297 undef name
299 Remove definition of macro or primitive name, making it unde‐
300 fined.
301 vcenter e
303 Vertically center e about the math axis, a horizontal line upon
304 which fraction bars and characters such as “+” and “−” are
305 aligned. MathML already behaves this way, so eqn ignores this
306 primitive when producing that output format. The built-in sum
307 macro is defined as if by the following.
308 define sum ! { type "operator" vcenter size +5 \(*S } !
310 Extended primitives
312 GNU eqn extends the syntax of some AT&T eqn primitives, introducing one
313 deliberate incompatibility.
314 delim on
316 eqn recognizes an “on” argument to the delim primitive spe‐
317 cially, restoring any delimiters previously disabled with “delim
318 off”. If delimiters haven't been specified, neither command has
319 effect. Few eqn documents are expected to use “o” and “n” as
320 left and right delimiters, respectively. If yours does, con‐
321 sider swapping them, or select others.
322 col n { ... }
324 ccol n { ... }
325 lcol n { ... }
326 rcol n { ... }
327 pile n { ... }
328 cpile n { ... }
329 lpile n { ... }
330 rpile n { ... }
331 The integer value n (in hundredths of an em) increases the ver‐
332 tical spacing between rows, using groff's \x escape sequence
333 (the value has no effect in MathML mode). Negative values are
334 accepted but have no effect. If more than one n occurs in a ma‐
335 trix or pile, the largest is used.
336 Customization
338 When eqn generates troff input, the appearance of equations is con‐
339 trolled by a large number of parameters. They have no effect when gen‐
340 erating MathML, which delegates typesetting to a MathML rendering en‐
341 gine. Configure these parameters with the set primitive.
342 set p n
344 assigns parameter p the integer value n; n is interpreted in
345 units of hundredths of an em unless otherwise stated. For exam‐
346 ple,
347 set x_height 45
349 says that eqn should assume that the font's x-height is
351 0.45 ems.
352 Available parameters are as follows; defaults are shown in
354 parentheses. We intend these descriptions to be expository
355 rather than rigorous.
356 minimum_size sets a floor for the type size (in scaled
358 points) at which equations are set (5).
359 fat_offset The fat primitive emboldens an equation by
361 overprinting two copies of the equation hori‐
362 zontally offset by this amount (4). In MathML
363 mode, components to which fat_offset applies
364 instead use the following.
365 <mstyle mathvariant='double-struck'>
366 over_hang A fraction bar is longer by twice this amount
368 than the maximum of the widths of the numerator
369 and denominator; in other words, it overhangs
370 the numerator and denominator by at least this
371 amount (0).
372 accent_width When bar or under is applied to a single char‐
374 acter, the line is this long (31). Normally,
375 bar or under produces a line whose length is
376 the width of the object to which it applies; in
377 the case of a single character, this tends to
378 produce a line that looks too long.
379 delimiter_factor Extensible delimiters produced with the left
381 and right primitives have a combined height and
382 depth of at least this many thousandths of
383 twice the maximum amount by which the sub-equa‐
384 tion that the delimiters enclose extends away
385 from the axis (900).
386 delimiter_shortfall
388 Extensible delimiters produced with the left
389 and right primitives have a combined height and
390 depth not less than the difference of twice the
391 maximum amount by which the sub-equation that
392 the delimiters enclose extends away from the
393 axis and this amount (50).
394 null_delimiter_space
396 This much horizontal space is inserted on each
397 side of a fraction (12).
398 script_space The width of subscripts and superscripts is in‐
400 creased by this amount (5).
401 thin_space This amount of space is automatically inserted
403 after punctuation characters. It also config‐
404 ures the width of the space produced by the ^
405 token (17).
406 medium_space This amount of space is automatically inserted
408 on either side of binary operators (22).
409 thick_space This amount of space is automatically inserted
411 on either side of relations. It also config‐
412 ures the width of the space produced by the ~
413 token (28).
414 x_height The height of lowercase letters without ascen‐
416 ders such as “x” (45).
417 axis_height The height above the baseline of the center of
419 characters such as “+” and “−” (26). It is im‐
420 portant that this value is correct for the font
421 you are using.
422 default_rule_thickness
424 This should be set to the thickness of the
425 \[ru] character, or the thickness of horizontal
426 lines produced with the \D escape sequence (4).
427 num1 The over primitive shifts up the numerator by
429 at least this amount (70).
430 num2 The smallover primitive shifts up the numerator
432 by at least this amount (36).
433 denom1 The over primitive shifts down the denominator
435 by at least this amount (70).
436 denom2 The smallover primitive shifts down the denomi‐
438 nator by at least this amount (36).
439 sup1 Normally superscripts are shifted up by at
441 least this amount (42).
442 sup2 Superscripts within superscripts or upper lim‐
444 its or numerators of smallover fractions are
445 shifted up by at least this amount (37). Con‐
446 ventionally, this is less than sup1.
447 sup3 Superscripts within denominators or square
449 roots or subscripts or lower limits are shifted
450 up by at least this amount (28). Convention‐
451 ally, this is less than sup2.
452 sub1 Subscripts are normally shifted down by at
454 least this amount (20).
455 sub2 When there is both a subscript and a super‐
457 script, the subscript is shifted down by at
458 least this amount (23).
459 sup_drop The baseline of a superscript is no more than
461 this much below the top of the object on which
462 the superscript is set (38).
463 sub_drop The baseline of a subscript is at least this
465 much below the bottom of the object on which
466 the subscript is set (5).
467 big_op_spacing1 The baseline of an upper limit is at least this
469 much above the top of the object on which the
470 limit is set (11).
471 big_op_spacing2 The baseline of a lower limit is at least this
473 much below the bottom of the object on which
474 the limit is set (17).
475 big_op_spacing3 The bottom of an upper limit is at least this
477 much above the top of the object on which the
478 limit is set (20).
479 big_op_spacing4 The top of a lower limit is at least this much
481 below the bottom of the object on which the
482 limit is set (60).
483 big_op_spacing5 This much vertical space is added above and be‐
485 low limits (10).
486 baseline_sep The baselines of the rows in a pile or matrix
488 are normally this far apart (140). Usually
489 equal to the sum of num1 and denom1.
490 shift_down The midpoint between the top baseline and the
492 bottom baseline in a matrix or pile is shifted
493 down by this much from the axis (26). Usually
494 equal to axis_height.
495 column_sep This much space is added between columns in a
497 matrix (100).
498 matrix_side_sep This much space is added at each side of a ma‐
500 trix (17).
501 draw_lines If non-zero, eqn draws lines using the troff \D
503 escape sequence, rather than the \l escape se‐
504 quence and the \[ru] special character. The
505 eqnrc file sets the default: 1 on ps, html, and
506 the X11 devices, otherwise 0.
507 body_height is the presumed height of an equation above the
509 text baseline; eqn adds any excess as extra
510 pre-vertical line spacing with troff's \x es‐
511 cape sequence (85).
512 body_depth is the presumed depth of an equation below the
514 text baseline; eqn adds any excess as extra
515 post-vertical line spacing with troff's \x es‐
516 cape sequence (35).
517 nroff If non-zero, then ndefine behaves like define
519 and tdefine is ignored, otherwise tdefine be‐
520 haves like define and ndefine is ignored. The
521 eqnrc file sets the default: 1 on ascii,
522 latin1, utf8, and cp1047 devices, otherwise 0.
523 Macros
525 In GNU eqn, macros can take arguments. A word defined by any of the
526 define, ndefine, or tdefine primitives followed immediately by a left
527 parenthesis is treated as a parameterized macro call: subsequent tokens
528 up to a matching right parenthesis are treated as comma-separated argu‐
529 ments. In this context only, commas and parentheses also serve as to‐
530 ken separators. A macro argument is not terminated by a comma inside
531 parentheses nested within it. In a macro definition, $n, where n is
532 between 1 and 9 inclusive, is replaced by the nth argument; if there
533 are fewer than n arguments, it is replaced by nothing.
534 Predefined macros
536 GNU eqn supports the predefined macros offered by AT&T eqn: and,
537 approx, arc, cos, cosh, del, det, dot, dotdot, dyad, exp, for, grad,
538 half, hat, if, inter, Im, inf, int, lim, ln, log, max, min, nothing,
539 partial, prime, prod, Re, sin, sinh, sum, tan, tanh, tilde, times,
540 union, vec, ==, !=, +=, ->, <-, <<, >>, and “...”. The lowercase clas‐
541 sical Greek letters are available as alpha, beta, chi, delta, epsilon,
542 eta, gamma, iota, kappa, lambda, mu, nu, omega, omicron, phi, pi, psi,
543 rho, sigma, tau, theta, upsilon, xi, and zeta. Spell them with an ini‐
544 tial capital letter (Alpha) or in full capitals (ALPHA) to obtain up‐
545 percase forms.
546 GNU eqn further defines the macros cdot, cdots, and utilde (all dis‐
548 cussed above), dollar, which sets a dollar sign, and ldots, which sets
549 an ellipsis on the text baseline.
550 Fonts
552 eqn uses up to three typefaces to set an equation: italic (oblique),
553 roman (upright), and bold. Assign each a groff typeface with the prim‐
554 itives gfont, grfont, and gbfont. The defaults are the styles I, R,
555 and B (applied to the current font family). The chartype primitive
556 (see above) sets a character's type, which determines the face used to
557 set it. The “letter” type is set in italics; others are set in roman.
558 Use the bold primitive to select an (upright) bold style.
559 gbfont f
561 Select f as the bold font. This is a GNU extension.
562 gfont f
564 Select f as the italic font.
565 grfont f
567 Select f as the roman font. This is a GNU extension.
568
570 --help displays a usage message, while -v and --version show version
571 information; all exit afterward.
572 -C Recognize .EQ and .EN even when followed by a character other
574 than space or newline.
575 -d xy Specify delimiters x for left and y for right ends of equations
577 not bracketed by .EQ/.EN. x and y need not be distinct. Any
578 “delim xy” statements in the source file override this option.
579 -f F is equivalent to “gfont F”.
581 -m n is equivalent to “set minimum_size n”.
583 -M dir Search dir for eqnrc before those listed in section “Descrip‐
585 tion” above.
586 -N Prohibit newlines within delimiters. This option allows eqn to
588 recover better from missing closing delimiters.
589 -p n Set sub- and superscripts n points smaller than the surrounding
591 text. This option is deprecated. eqn normally sets sub- and
592 superscripts at 70% of the type size of the surrounding text.
593 -r Reduce the type size of subscripts at most once relative to the
595 base type size for the equation.
596 -R Don't load eqnrc.
598 -s n is equivalent to “gsize n”. This option is deprecated.
600 -T dev Prepare output for the device dev. In most cases, the effect of
602 this is to define a macro dev with a value of 1; eqnrc uses this
603 to provide definitions appropriate for the device. However, if
604 the specified driver is “MathML”, the output is MathML markup
605 rather than troff input, and eqnrc is not loaded at all. The
606 default output device is ps.
607
609 /usr/share/groff/1.23.0/tmac/eqnrc
610 Initialization file.
611
613 MathML is designed on the assumption that it cannot know the exact
614 physical characteristics of the media and devices on which it will be
615 rendered. It does not support control of motions and sizes to the same
616 degree troff does.
617 • eqn customization parameters have no effect on generated MathML.
619 • The special, up, down, fwd, and back primitives cannot be imple‐
621 mented, and yield a MathML “<merror>” message instead.
622 • The vcenter primitive is silently ignored, as centering on the math
624 axis is the MathML default.
625 • Characters that eqn sets extra large in troff mode—notably the inte‐
627 gral sign—may appear too small and need to have their “<mstyle>”
628 wrappers adjusted by hand.
629 As in its troff mode, eqn in MathML mode leaves the .EQ and .EN tokens
631 in place, but emits nothing corresponding to delim delimiters. They
632 can, however, be recognized as character sequences that begin with
633 “<math>”, end with “</math>”, and do not cross line boundaries.
634
636 Tokens must be double-quoted in eqn input if they are not to be recog‐
637 nized as names of macros or primitives, or if they are to be inter‐
638 preted by troff. In particular, short ones, like “pi” and “PI”, can
639 collide with troff identifiers. For instance, the eqn command “gfont
640 PI” does not select groff's Palatino italic font for the global italic
641 face; you must use “gfont "PI"” instead.
642 Delimited equations are set at the type size current at the beginning
644 of the input line, not necessarily that immediately preceding the open‐
645 ing delimiter.
646 Unlike TeX, eqn does not inherently distinguish displayed and inline
648 equation styles; see the smallover primitive above. However, macro
649 packages frequently define EQ and EN macros such that the equation
650 within is displayed. These macros may accept arguments permitting the
651 equation to be labeled or captioned; see the package's documentation.
652
654 eqn abuses terminology—its “equations” can be inequalities, bare ex‐
655 pressions, or unintelligible gibberish. But there's no changing it
656 now.
657 In nroff mode, lowercase Greek letters are rendered in roman instead of
659 italic style.
660 In MathML mode, the mark and lineup features don't work. These could,
662 in theory, be implemented with “<maligngroup>” elements.
663 In MathML mode, each digit of a numeric literal gets a separate “<mn>
665 </mn>” pair, and decimal points are tagged with “<mo></mo>”. This is
666 allowed by the specification, but inefficient.
667
669 We first illustrate eqn usage with a trigonometric identity.
670 .EQ
672 sin ( alpha + beta ) = sin alpha cos beta + cos alpha sin beta
673 .EN
674 It can be convenient to set up delimiters if mathematical content will
676 appear frequently in running text.
677 .EQ
679 delim $$
680 .EN
681 Having cached a table of logarithms,
682 the property $ln ( x y ) = ln x + ln y$ sped calculations.
683 The quadratic formula illustrates use of fractions and radicals, and
685 affords an opportunity to use the full space token ~.
686 .EQ
688 x = { - b ~ \[+-] ~ sqrt { b sup 2 - 4 a c } } over { 2 a }
689 .EN
690 Alternatively, we could define the plus-minus sign as a binary opera‐
692 tor. Automatic spacing puts 0.06 em less space on either side of the
693 plus-minus than ~ does, this being the difference between the widths of
694 the medium_space parameter used by binary operators and that of the
695 full space. Independently, we can define a macro “frac” for setting
696 fractions.
697 .EQ
699 chartype "binary" \[+-]
700 define frac ! { $1 } over { $2 } !
701 x = frac(- b \[+-] sqrt { b sup 2 - 4 a c }, 2 a)
702 .EN
703
705 “Typesetting Mathematics—User's Guide” (2nd edition), by Brian W.
706 Kernighan and Lorinda L. Cherry, 1978, AT&T Bell Laboratories Computing
707 Science Technical Report No. 17.
708 The TeXbook, by Donald E. Knuth, 1984, Addison-Wesley Professional.
710 Appendix G discusses many of the parameters from section “Customiza‐
711 tion” above in greater detail.
712 groff_char(7), particularly subsections “Logical symbols”, “Mathemati‐
714 cal symbols”, and “Greek glyphs”, documents a variety of special char‐
715 acter escape sequences useful in mathematical typesetting.
716 groff(1), troff(1), pic(1), groff_font(5)
718groff 1.23.0 2 November 2023 eqn(1)