1 dfc67f9b 2004-05-16 devnull .TH EQN 1
  2 dfc67f9b 2004-05-16 devnull .EQ
  3 dfc67f9b 2004-05-16 devnull delim $$
  4 dfc67f9b 2004-05-16 devnull .EN
  5 dfc67f9b 2004-05-16 devnull .SH NAME
  6 dfc67f9b 2004-05-16 devnull eqn  \- typeset mathematics
  7 dfc67f9b 2004-05-16 devnull .SH SYNOPSIS
  8 dfc67f9b 2004-05-16 devnull .B eqn
  9 dfc67f9b 2004-05-16 devnull [
 10 dfc67f9b 2004-05-16 devnull .I option ...
 11 dfc67f9b 2004-05-16 devnull ]
 12 dfc67f9b 2004-05-16 devnull [
 13 dfc67f9b 2004-05-16 devnull .I file ...
 14 dfc67f9b 2004-05-16 devnull ]
 15 dfc67f9b 2004-05-16 devnull .SH DESCRIPTION
 16 dfc67f9b 2004-05-16 devnull .I Eqn
 17 dfc67f9b 2004-05-16 devnull is a
 18 d32deab1 2020-08-16 rsc .MR troff (1)
 19 dfc67f9b 2004-05-16 devnull preprocessor
 20 dfc67f9b 2004-05-16 devnull for typesetting mathematics
 21 dfc67f9b 2004-05-16 devnull on a typesetter.
 22 dfc67f9b 2004-05-16 devnull Usage is almost always
 23 dfc67f9b 2004-05-16 devnull .IP
 24 dfc67f9b 2004-05-16 devnull .L
 25 dfc67f9b 2004-05-16 devnull eqn file ... | troff
 26 dfc67f9b 2004-05-16 devnull .PP
 27 dfc67f9b 2004-05-16 devnull If no files are specified, 
 28 dfc67f9b 2004-05-16 devnull .I eqn
 29 dfc67f9b 2004-05-16 devnull reads from the standard input.
 30 dfc67f9b 2004-05-16 devnull .I Eqn
 31 dfc67f9b 2004-05-16 devnull prepares output for the typesetter 
 32 dfc67f9b 2004-05-16 devnull named in the
 33 dfc67f9b 2004-05-16 devnull .BI -T dest
 34 dfc67f9b 2004-05-16 devnull option (default
 35 dfc67f9b 2004-05-16 devnull .BR -Tutf ;
 36 dfc67f9b 2004-05-16 devnull see
 37 d32deab1 2020-08-16 rsc .MR troff (1) ).
 38 dfc67f9b 2004-05-16 devnull When run with other preprocessor filters,
 39 dfc67f9b 2004-05-16 devnull .I eqn
 40 dfc67f9b 2004-05-16 devnull usually comes last.
 41 dfc67f9b 2004-05-16 devnull .PP
 42 dfc67f9b 2004-05-16 devnull A line beginning with
 43 dfc67f9b 2004-05-16 devnull .B .EQ
 44 dfc67f9b 2004-05-16 devnull marks the start of an equation;
 45 dfc67f9b 2004-05-16 devnull the end of an equation
 46 dfc67f9b 2004-05-16 devnull is marked by a line beginning with
 47 dfc67f9b 2004-05-16 devnull .BR .EN .
 48 dfc67f9b 2004-05-16 devnull Neither of these lines is altered,
 49 dfc67f9b 2004-05-16 devnull so they may be defined in macro packages
 50 dfc67f9b 2004-05-16 devnull to get
 51 dfc67f9b 2004-05-16 devnull centering, numbering, etc.
 52 dfc67f9b 2004-05-16 devnull It is also possible to set two characters
 53 dfc67f9b 2004-05-16 devnull as `delimiters';
 54 dfc67f9b 2004-05-16 devnull text between delimiters is also
 55 dfc67f9b 2004-05-16 devnull .I eqn
 56 dfc67f9b 2004-05-16 devnull input.
 57 dfc67f9b 2004-05-16 devnull Delimiters may be set to characters
 58 dfc67f9b 2004-05-16 devnull .I x
 59 dfc67f9b 2004-05-16 devnull and
 60 dfc67f9b 2004-05-16 devnull .I y
 61 dfc67f9b 2004-05-16 devnull with the option
 62 dfc67f9b 2004-05-16 devnull .BI -d xy
 63 dfc67f9b 2004-05-16 devnull or (more commonly) with
 64 dfc67f9b 2004-05-16 devnull .B delim
 65 dfc67f9b 2004-05-16 devnull .I xy
 66 dfc67f9b 2004-05-16 devnull between
 67 dfc67f9b 2004-05-16 devnull .B .EQ
 68 dfc67f9b 2004-05-16 devnull and
 69 dfc67f9b 2004-05-16 devnull .BR .EN .
 70 dfc67f9b 2004-05-16 devnull Left and right delimiters may be identical.
 71 dfc67f9b 2004-05-16 devnull (They are customarily taken to be
 72 dfc67f9b 2004-05-16 devnull $font L "$$" )$.
 73 dfc67f9b 2004-05-16 devnull Delimiters are turned off by
 74 dfc67f9b 2004-05-16 devnull .LR "delim off" .
 75 dfc67f9b 2004-05-16 devnull All text that is neither between delimiters nor between
 76 dfc67f9b 2004-05-16 devnull .B .EQ
 77 dfc67f9b 2004-05-16 devnull and
 78 dfc67f9b 2004-05-16 devnull .B .EN
 79 dfc67f9b 2004-05-16 devnull is passed through untouched.
 80 dfc67f9b 2004-05-16 devnull .PP
 81 dfc67f9b 2004-05-16 devnull Tokens within
 82 dfc67f9b 2004-05-16 devnull .I eqn
 83 dfc67f9b 2004-05-16 devnull are separated by
 84 dfc67f9b 2004-05-16 devnull spaces, tabs, newlines, braces, double quotes,
 85 dfc67f9b 2004-05-16 devnull tildes or circumflexes.
 86 dfc67f9b 2004-05-16 devnull Braces {} are used for grouping;
 87 dfc67f9b 2004-05-16 devnull generally speaking,
 88 dfc67f9b 2004-05-16 devnull anywhere a single character like
 89 dfc67f9b 2004-05-16 devnull .L x
 90 dfc67f9b 2004-05-16 devnull could appear, a complicated construction
 91 dfc67f9b 2004-05-16 devnull enclosed in braces may be used instead.
 92 dfc67f9b 2004-05-16 devnull Tilde
 93 dfc67f9b 2004-05-16 devnull .L ~
 94 dfc67f9b 2004-05-16 devnull represents a full space in the output,
 95 dfc67f9b 2004-05-16 devnull circumflex
 96 dfc67f9b 2004-05-16 devnull .L ^
 97 dfc67f9b 2004-05-16 devnull half as much.
 98 dfc67f9b 2004-05-16 devnull .PP
 99 dfc67f9b 2004-05-16 devnull .vs 13p
100 dfc67f9b 2004-05-16 devnull Subscripts and superscripts are produced with the keywords
101 dfc67f9b 2004-05-16 devnull .B sub
102 dfc67f9b 2004-05-16 devnull and
103 dfc67f9b 2004-05-16 devnull .BR sup .
104 dfc67f9b 2004-05-16 devnull Thus
105 dfc67f9b 2004-05-16 devnull .L "x sub i" 
106 dfc67f9b 2004-05-16 devnull makes
107 dfc67f9b 2004-05-16 devnull $x sub i$, 
108 dfc67f9b 2004-05-16 devnull .L "a sub i sup 2"
109 dfc67f9b 2004-05-16 devnull produces
110 dfc67f9b 2004-05-16 devnull $a sub i sup 2$,
111 dfc67f9b 2004-05-16 devnull and
112 dfc67f9b 2004-05-16 devnull .L "e sup {x sup 2 + y sup 2}"
113 dfc67f9b 2004-05-16 devnull gives
114 dfc67f9b 2004-05-16 devnull $e sup {x sup 2 + y sup 2}$.
115 dfc67f9b 2004-05-16 devnull .PP
116 dfc67f9b 2004-05-16 devnull .B Over
117 dfc67f9b 2004-05-16 devnull makes fractions:
118 dfc67f9b 2004-05-16 devnull .L "a over b"
119 dfc67f9b 2004-05-16 devnull yields $a over b$.
120 dfc67f9b 2004-05-16 devnull .PP
121 dfc67f9b 2004-05-16 devnull .B Sqrt
122 dfc67f9b 2004-05-16 devnull produces square roots:
123 dfc67f9b 2004-05-16 devnull .L "1 over sqrt {ax sup 2 +bx+c}"
124 dfc67f9b 2004-05-16 devnull results in
125 dfc67f9b 2004-05-16 devnull $1 over sqrt {ax sup 2 +bx+c}$ .
126 dfc67f9b 2004-05-16 devnull .PP
127 dfc67f9b 2004-05-16 devnull The keywords
128 dfc67f9b 2004-05-16 devnull .B from
129 dfc67f9b 2004-05-16 devnull and
130 dfc67f9b 2004-05-16 devnull .B to
131 dfc67f9b 2004-05-16 devnull introduce lower and upper
132 dfc67f9b 2004-05-16 devnull limits on arbitrary things:
133 dfc67f9b 2004-05-16 devnull $lim from {n -> inf} sum from 0 to n x sub i$
134 dfc67f9b 2004-05-16 devnull is made with
135 dfc67f9b 2004-05-16 devnull .LR "lim from {n -> inf} sum from 0 to n x sub i" .
136 dfc67f9b 2004-05-16 devnull .PP
137 dfc67f9b 2004-05-16 devnull Left and right brackets, braces, etc., of the right height are made with
138 dfc67f9b 2004-05-16 devnull .B left
139 dfc67f9b 2004-05-16 devnull and
140 dfc67f9b 2004-05-16 devnull .BR right :
141 dfc67f9b 2004-05-16 devnull .L "left [ x sup 2 + y sup 2 over alpha right ] ~=~1"
142 dfc67f9b 2004-05-16 devnull produces
143 dfc67f9b 2004-05-16 devnull $left [ x sup 2 + y sup 2 over alpha right ] ~=~1$.
144 dfc67f9b 2004-05-16 devnull The
145 dfc67f9b 2004-05-16 devnull .B right
146 dfc67f9b 2004-05-16 devnull clause is optional.
147 dfc67f9b 2004-05-16 devnull Legal characters after 
148 dfc67f9b 2004-05-16 devnull .B left
149 dfc67f9b 2004-05-16 devnull and
150 dfc67f9b 2004-05-16 devnull .B right
151 dfc67f9b 2004-05-16 devnull are braces, brackets, bars,
152 dfc67f9b 2004-05-16 devnull .B c
153 dfc67f9b 2004-05-16 devnull and
154 dfc67f9b 2004-05-16 devnull .B f
155 dfc67f9b 2004-05-16 devnull for ceiling and floor,
156 dfc67f9b 2004-05-16 devnull and
157 dfc67f9b 2004-05-16 devnull .B
158 dfc67f9b 2004-05-16 devnull ""
159 dfc67f9b 2004-05-16 devnull for nothing at all (useful for a right-side-only bracket).
160 dfc67f9b 2004-05-16 devnull .PP
161 dfc67f9b 2004-05-16 devnull Vertical piles of things are made with 
162 dfc67f9b 2004-05-16 devnull .BR pile ,
163 dfc67f9b 2004-05-16 devnull .BR lpile ,
164 dfc67f9b 2004-05-16 devnull .BR cpile ,
165 dfc67f9b 2004-05-16 devnull and
166 dfc67f9b 2004-05-16 devnull .BR rpile :
167 dfc67f9b 2004-05-16 devnull .L "pile {a above b above c}"
168 dfc67f9b 2004-05-16 devnull produces
169 dfc67f9b 2004-05-16 devnull $pile {a above b above c}$.
170 dfc67f9b 2004-05-16 devnull There can be an arbitrary number of elements in a pile.
171 dfc67f9b 2004-05-16 devnull .B lpile
172 dfc67f9b 2004-05-16 devnull left-justifies,
173 dfc67f9b 2004-05-16 devnull .B pile
174 dfc67f9b 2004-05-16 devnull and
175 dfc67f9b 2004-05-16 devnull .B cpile
176 dfc67f9b 2004-05-16 devnull center, with different vertical spacing,
177 dfc67f9b 2004-05-16 devnull and 
178 dfc67f9b 2004-05-16 devnull .B rpile
179 dfc67f9b 2004-05-16 devnull right justifies.
180 dfc67f9b 2004-05-16 devnull .PP
181 dfc67f9b 2004-05-16 devnull Matrices are made with
182 dfc67f9b 2004-05-16 devnull .BR matrix :
183 dfc67f9b 2004-05-16 devnull .L "matrix { lcol { x sub i above y sub 2 } ccol { 1 above 2 } }"
184 dfc67f9b 2004-05-16 devnull produces
185 dfc67f9b 2004-05-16 devnull $matrix { lcol { x sub i above y sub 2 } ccol { 1 above 2 } }$.
186 dfc67f9b 2004-05-16 devnull In addition, there is
187 dfc67f9b 2004-05-16 devnull .B rcol
188 dfc67f9b 2004-05-16 devnull for a right-justified column.
189 dfc67f9b 2004-05-16 devnull .PP
190 dfc67f9b 2004-05-16 devnull .vs 12p
191 dfc67f9b 2004-05-16 devnull Diacritical marks are made with
192 dfc67f9b 2004-05-16 devnull .BR prime ,
193 dfc67f9b 2004-05-16 devnull .BR dot ,
194 dfc67f9b 2004-05-16 devnull .BR dotdot ,
195 dfc67f9b 2004-05-16 devnull .BR hat ,
196 dfc67f9b 2004-05-16 devnull .BR tilde ,
197 dfc67f9b 2004-05-16 devnull .BR bar ,
198 dfc67f9b 2004-05-16 devnull .BR under ,
199 dfc67f9b 2004-05-16 devnull .BR vec ,
200 dfc67f9b 2004-05-16 devnull .BR dyad ,
201 dfc67f9b 2004-05-16 devnull and
202 dfc67f9b 2004-05-16 devnull .BR under :
203 dfc67f9b 2004-05-16 devnull .L "x sub 0 sup prime = f(t) bar + g(t) under"
204 dfc67f9b 2004-05-16 devnull is
205 dfc67f9b 2004-05-16 devnull $x sub 0 sup prime = f(t) bar + g(t) under$,
206 dfc67f9b 2004-05-16 devnull and
207 dfc67f9b 2004-05-16 devnull .L "x vec = y dyad"
208 dfc67f9b 2004-05-16 devnull is
209 dfc67f9b 2004-05-16 devnull $x vec = y dyad$.
210 dfc67f9b 2004-05-16 devnull .PP
211 dfc67f9b 2004-05-16 devnull Sizes and fonts can be changed with prefix operators
212 dfc67f9b 2004-05-16 devnull .B size 
213 dfc67f9b 2004-05-16 devnull .IR n ,
214 dfc67f9b 2004-05-16 devnull .B size
215 dfc67f9b 2004-05-16 devnull .BI ± n \f1,
216 dfc67f9b 2004-05-16 devnull .BR fat ,
217 dfc67f9b 2004-05-16 devnull .BR roman ,
218 dfc67f9b 2004-05-16 devnull .BR italic ,
219 dfc67f9b 2004-05-16 devnull .BR bold ,
220 dfc67f9b 2004-05-16 devnull or
221 dfc67f9b 2004-05-16 devnull .BR font
222 dfc67f9b 2004-05-16 devnull .IR n .
223 dfc67f9b 2004-05-16 devnull Size and fonts can be changed globally in a document by
224 dfc67f9b 2004-05-16 devnull .B gsize
225 dfc67f9b 2004-05-16 devnull .I n
226 dfc67f9b 2004-05-16 devnull and
227 dfc67f9b 2004-05-16 devnull .B gfont
228 dfc67f9b 2004-05-16 devnull .IR n ,
229 dfc67f9b 2004-05-16 devnull or by the command-line arguments
230 dfc67f9b 2004-05-16 devnull .BI -s n
231 dfc67f9b 2004-05-16 devnull and
232 dfc67f9b 2004-05-16 devnull .BI -f n\f1.
233 dfc67f9b 2004-05-16 devnull .PP
234 dfc67f9b 2004-05-16 devnull Normally subscripts and superscripts are reduced by
235 dfc67f9b 2004-05-16 devnull 3 point sizes from the previous size;
236 dfc67f9b 2004-05-16 devnull this may be changed by the command-line argument
237 dfc67f9b 2004-05-16 devnull .BI -p n\f1.
238 dfc67f9b 2004-05-16 devnull .PP
239 dfc67f9b 2004-05-16 devnull Successive display arguments can be lined up.
240 dfc67f9b 2004-05-16 devnull Place
241 dfc67f9b 2004-05-16 devnull .B mark
242 dfc67f9b 2004-05-16 devnull before the desired lineup point in the first equation;
243 dfc67f9b 2004-05-16 devnull place
244 dfc67f9b 2004-05-16 devnull .B lineup
245 dfc67f9b 2004-05-16 devnull at the place that is to line up vertically in subsequent equations.
246 dfc67f9b 2004-05-16 devnull .PP
247 dfc67f9b 2004-05-16 devnull Shorthands may be defined
248 dfc67f9b 2004-05-16 devnull or existing keywords redefined with
249 dfc67f9b 2004-05-16 devnull .BR define :
250 dfc67f9b 2004-05-16 devnull .L define
251 dfc67f9b 2004-05-16 devnull .I thing
252 dfc67f9b 2004-05-16 devnull .L %
253 dfc67f9b 2004-05-16 devnull .I replacement
254 dfc67f9b 2004-05-16 devnull .L %
255 dfc67f9b 2004-05-16 devnull defines a new token called
256 dfc67f9b 2004-05-16 devnull .I thing
257 dfc67f9b 2004-05-16 devnull which will be replaced by
258 dfc67f9b 2004-05-16 devnull .I replacement
259 dfc67f9b 2004-05-16 devnull whenever it appears thereafter.
260 dfc67f9b 2004-05-16 devnull The 
261 dfc67f9b 2004-05-16 devnull .L %
262 dfc67f9b 2004-05-16 devnull may be any character that does not occur in
263 dfc67f9b 2004-05-16 devnull .LR replacement .
264 dfc67f9b 2004-05-16 devnull .PP
265 dfc67f9b 2004-05-16 devnull Keywords like 
266 dfc67f9b 2004-05-16 devnull .L sum
267 dfc67f9b 2004-05-16 devnull .EQ
268 dfc67f9b 2004-05-16 devnull ( sum ),
269 dfc67f9b 2004-05-16 devnull .EN
270 dfc67f9b 2004-05-16 devnull .L int
271 dfc67f9b 2004-05-16 devnull .EQ
272 dfc67f9b 2004-05-16 devnull ( int ),
273 dfc67f9b 2004-05-16 devnull .EN
274 dfc67f9b 2004-05-16 devnull .L inf
275 dfc67f9b 2004-05-16 devnull .EQ
276 dfc67f9b 2004-05-16 devnull ( inf ),
277 dfc67f9b 2004-05-16 devnull .EN
278 dfc67f9b 2004-05-16 devnull and shorthands like
279 dfc67f9b 2004-05-16 devnull .L >=
280 dfc67f9b 2004-05-16 devnull .EQ
281 dfc67f9b 2004-05-16 devnull (>=),
282 dfc67f9b 2004-05-16 devnull .EN
283 dfc67f9b 2004-05-16 devnull .L ->
284 dfc67f9b 2004-05-16 devnull .EQ
285 dfc67f9b 2004-05-16 devnull (->),
286 dfc67f9b 2004-05-16 devnull .EN
287 dfc67f9b 2004-05-16 devnull and
288 dfc67f9b 2004-05-16 devnull .L !=
289 dfc67f9b 2004-05-16 devnull .EQ
290 dfc67f9b 2004-05-16 devnull ( != )
291 dfc67f9b 2004-05-16 devnull .EN
292 dfc67f9b 2004-05-16 devnull are recognized.
293 dfc67f9b 2004-05-16 devnull Greek letters are spelled out in the desired case, as in
294 dfc67f9b 2004-05-16 devnull .L alpha
295 dfc67f9b 2004-05-16 devnull or
296 dfc67f9b 2004-05-16 devnull .LR GAMMA .
297 dfc67f9b 2004-05-16 devnull Mathematical words like
298 dfc67f9b 2004-05-16 devnull .LR sin ,
299 dfc67f9b 2004-05-16 devnull .LR cos ,
300 dfc67f9b 2004-05-16 devnull .L log
301 dfc67f9b 2004-05-16 devnull are made Roman automatically.
302 d32deab1 2020-08-16 rsc .MR Troff (1)
303 dfc67f9b 2004-05-16 devnull four-character escapes like
304 dfc67f9b 2004-05-16 devnull .L \e(lh
305 dfc67f9b 2004-05-16 devnull (\(lh) can be used anywhere.
306 dfc67f9b 2004-05-16 devnull Strings enclosed in double quotes " "
307 dfc67f9b 2004-05-16 devnull are passed through untouched;
308 dfc67f9b 2004-05-16 devnull this permits keywords to be entered as text,
309 dfc67f9b 2004-05-16 devnull and can be used to communicate
310 dfc67f9b 2004-05-16 devnull with 
311 dfc67f9b 2004-05-16 devnull .I troff
312 dfc67f9b 2004-05-16 devnull when all else fails.
313 dfc67f9b 2004-05-16 devnull .SH FILES
314 dfc67f9b 2004-05-16 devnull .TF /sys/lib/troff/font/devutf
315 dfc67f9b 2004-05-16 devnull .TP
316 dfc67f9b 2004-05-16 devnull .B /sys/lib/troff/font/devutf
317 dfc67f9b 2004-05-16 devnull font descriptions for PostScript
318 dfc67f9b 2004-05-16 devnull .SH SOURCE
319 c3674de4 2005-01-11 devnull .B \*9/src/cmd/eqn
320 dfc67f9b 2004-05-16 devnull .SH "SEE ALSO"
321 dfc67f9b 2004-05-16 devnull .IR troff (1), 
322 d32deab1 2020-08-16 rsc .MR tbl (1)
323 dfc67f9b 2004-05-16 devnull .br
324 dfc67f9b 2004-05-16 devnull J. F. Ossanna and B. W. Kernighan,
325 dfc67f9b 2004-05-16 devnull ``Troff User's Manual''.
326 dfc67f9b 2004-05-16 devnull .br
327 dfc67f9b 2004-05-16 devnull B. W. Kernighan and L. L. Cherry,
328 dfc67f9b 2004-05-16 devnull ``Typesetting Mathematics\(emUser's Guide'', 
329 dfc67f9b 2004-05-16 devnull .I
330 dfc67f9b 2004-05-16 devnull Unix Research System Programmer's Manual,
331 dfc67f9b 2004-05-16 devnull Tenth Edition, Volume 2.
332 dfc67f9b 2004-05-16 devnull .SH BUGS
333 dfc67f9b 2004-05-16 devnull To embolden digits, parens, etc.,
334 dfc67f9b 2004-05-16 devnull it is necessary to quote them,
335 dfc67f9b 2004-05-16 devnull as in 
336 dfc67f9b 2004-05-16 devnull .LR bold\ "12.3" .
337 dfc67f9b 2004-05-16 devnull .EQ
338 dfc67f9b 2004-05-16 devnull delim off
339 dfc67f9b 2004-05-16 devnull .EN