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1.1 root 1: .\" @(#)g1 6.1 (Berkeley) 5/22/86
2: .\"
3: .if t .2C
4: .SC Introduction
5: .PP
6: .UC EQN
7: is a
8: program for typesetting mathematics
9: on the Graphics Systems phototypesetters on the
10: .UX
11: operating system.
12: The
13: .UC EQN
14: language was designed to be easy to use
15: by people who know neither mathematics
16: nor typesetting.
17: Thus
18: .UC EQN
19: knows relatively little about mathematics.
20: In particular, mathematical symbols like
21: +, \(mi, \(mu, parentheses, and so on have no special meanings.
22: .UC EQN
23: is quite happy to set garbage (but it will look good).
24: .PP
25: .UC EQN
26: works as a preprocessor for the typesetter formatter,
27: .UC TROFF [1],
28: so the normal mode of operation is to prepare
29: a document with both mathematics and ordinary text
30: interspersed,
31: and let
32: .UC EQN
33: set the mathematics while
34: .UC TROFF
35: does the body of the text.
36: .PP
37: On
38: .UC UNIX ,
39: .UC EQN
40: will also produce mathematics on
41: .UC DASI
42: and
43: .UC GSI
44: terminals and on
45: Model 37 teletypes.
46: The input is identical, but you have to use the programs
47: .UC NEQN
48: and
49: .UC NROFF
50: instead of
51: .UC EQN
52: and
53: .UC TROFF .
54: Of course, some things won't look as good
55: because terminals
56: don't provide the variety of characters, sizes and fonts
57: that a typesetter does,
58: but the output is usually adequate for proofreading.
59: .PP
60: To use
61: .UC EQN
62: on
63: .UC UNIX ,
64: .P1
65: eqn files | troff
66: .P2
67: .SC Displayed Equations
68: .PP
69: To tell
70: .UC EQN
71: where a mathematical expression begins and ends,
72: we mark it with lines beginning
73: .UC .EQ
74: and
75: .UC .EN .
76: Thus
77: if you type the lines
78: .P1
79: ^EQ
80: x=y+z
81: ^EN
82: .P2
83: your output will look like
84: .EQ
85: x=y+z
86: .EN
87: The
88: .UC .EQ
89: and
90: .UC .EN
91: are copied through untouched;
92: they
93: are not otherwise processed
94: by
95: .UC EQN .
96: This means that you have to take care
97: of things like centering, numbering, and so on
98: yourself.
99: The most common way is to use the
100: .UC TROFF
101: and
102: .UC NROFF
103: macro package package `\(mims'
104: developed by M. E. Lesk[3],
105: which allows you to center, indent, left-justify and number equations.
106: .PP
107: With the `\(mims' package,
108: equations are centered by default.
109: To left-justify an equation, use
110: .UC \&.EQ\ L
111: instead of
112: .UC .EQ .
113: To indent it, use
114: .UC .EQ\ I .
115: Any of these can be followed by an arbitrary `equation number'
116: which will be placed at the right margin.
117: For example, the input
118: .P1
119: ^EQ I (3.1a)
120: x = f(y/2) + y/2
121: ^EN
122: .P2
123: produces the output
124: .EQ I (3.1a)
125: x = f(y/2) + y/2
126: .EN
127: .PP
128: There is also a shorthand notation so
129: in-line expressions
130: like
131: $pi sub i sup 2$
132: can be entered without
133: .UC .EQ
134: and
135: .UC .EN .
136: We will talk about it in section 19.
137: .SC Input spaces
138: .PP
139: Spaces and newlines within an expression are thrown away by
140: .UC EQN .
141: (Normal text is left absolutely alone.)
142: Thus
143: between
144: .UC .EQ
145: and
146: .UC .EN ,
147: .P1
148: x=y+z
149: .P2
150: and
151: .P1
152: x = y + z
153: .P2
154: and
155: .P1
156: x = y
157: + z
158: .P2
159: and so on
160: all produce the same
161: output
162: .EQ
163: x=y+z
164: .EN
165: You should use spaces and newlines freely to make your input equations
166: readable and easy to edit.
167: In particular, very long lines are a bad idea,
168: since they are often hard to fix if you make a mistake.
169: .SC Output spaces
170: .PP
171: To force extra spaces into the
172: .ul
173: output,
174: use a tilde ``\|~\|''
175: for each space you want:
176: .P1
177: x~=~y~+~z
178: .P2
179: gives
180: .EQ
181: x~=~y~+~z
182: .EN
183: You can also use a circumflex ``^'',
184: which gives a space half the width of a tilde.
185: It is mainly useful for fine-tuning.
186: Tabs may also be used to position pieces
187: of an expression,
188: but the tab stops must be set by
189: .UC TROFF
190: commands.
191: .SC "Symbols, Special Names, Greek"
192: .PP
193: .UC EQN
194: knows some mathematical symbols,
195: some mathematical names, and the Greek alphabet.
196: For example,
197: .P1
198: x=2 pi int sin ( omega t)dt
199: .P2
200: produces
201: .EQ
202: x = 2 pi int sin ( omega t)dt
203: .EN
204: Here the spaces in the input are
205: .B
206: necessary
207: .R
208: to tell
209: .UC EQN
210: that
211: .ul
212: int,
213: .ul
214: pi,
215: .ul
216: sin
217: and
218: .ul
219: omega
220: are separate entities that should get special treatment.
221: The
222: .ul
223: sin,
224: digit 2, and parentheses are set in roman type instead of italic;
225: .ul
226: pi
227: and
228: .ul
229: omega
230: are made Greek;
231: and
232: .ul
233: int
234: becomes the integral sign.
235: .PP
236: When in doubt, leave spaces around separate parts of the input.
237: A
238: .ul
239: very
240: common error is to type
241: .ul
242: f(pi)
243: without leaving spaces on both sides of the
244: .ul
245: pi.
246: As a result,
247: .UC EQN
248: does not recognize
249: .ul
250: pi
251: as a special word, and it appears as
252: $f(pi)$
253: instead of
254: $f( pi )$.
255: .PP
256: A complete list of
257: .UC EQN
258: names appears in section 23.
259: Knowledgeable users can also use
260: .UC TROFF
261: four-character names
262: for anything
263: .UC EQN
264: doesn't know about,
265: like
266: .ul
267: \\(bs
268: for the Bell System sign \(bs.
269: .SC "Spaces, Again"
270: .PP
271: The only way
272: .UC EQN
273: can deduce that some sequence
274: of letters might be special
275: is if that sequence is separated from the letters
276: on either side of it.
277: This can be done by surrounding a special word by ordinary spaces
278: (or tabs or newlines),
279: as we did in the previous section.
280: .PP
281: .tr ~~
282: You can also make special words stand out by surrounding them
283: with tildes or circumflexes:
284: .P1
285: x~=~2~pi~int~sin~(~omega~t~)~dt
286: .P2
287: is much the same as the last example,
288: except that the tildes
289: not only
290: separate the magic words
291: like
292: .ul
293: sin,
294: .ul
295: omega,
296: and so on,
297: but also add extra spaces,
298: one space per tilde:
299: .EQ
300: x~=~2~pi~int~sin~(~omega~t~)~dt
301: .EN
302: .PP
303: Special words can also be separated by braces { }
304: and double quotes "...",
305: which have special meanings that we will
306: see soon.
307: .tr ~
308: .SC "Subscripts and Superscripts"
309: .PP
310: Subscripts and superscripts are
311: obtained with the words
312: .ul
313: sub
314: and
315: .ul
316: sup.
317: .P1
318: x sup 2 + y sub k
319: .P2
320: gives
321: .EQ
322: x sup 2 + y sub k
323: .EN
324: .UC EQN
325: takes care of all the size changes and vertical motions
326: needed to make the output look right.
327: The words
328: .ul
329: sub
330: and
331: .ul
332: sup
333: must be surrounded by spaces;
334: .ul
335: x sub2
336: will give you
337: $x sub2$ instead of $x sub 2$.
338: Furthermore, don't forget to leave a space
339: (or a tilde, etc.)
340: to mark the end of a subscript or superscript.
341: A common error is to say
342: something like
343: .P1
344: y = (x sup 2)+1
345: .P2
346: which causes
347: .EQ
348: y = (x sup 2)+1
349: .EN
350: instead of
351: the intended
352: .EQ
353: y = (x sup 2 )+1
354: .EN
355: .PP
356: Subscripted subscripts and superscripted superscripts
357: also work:
358: .P1
359: x sub i sub 1
360: .P2
361: is
362: .EQ
363: x sub i sub 1
364: .EN
365: A subscript and superscript on the same thing
366: are printed one above the other
367: if the subscript comes
368: .ul
369: first:
370: .P1
371: x sub i sup 2
372: .P2
373: is
374: .EQ
375: x sub i sup 2
376: .EN
377: .PP
378: Other than this special case,
379: .ul
380: sub
381: and
382: .ul
383: sup
384: group to the right, so
385: .ul
386: x\ sup\ y\ sub\ z
387: means
388: $x sup {y sub z}$, not ${x sup y} sub z$.
389: .SC "Braces for Grouping"
390: .PP
391: Normally, the end of a subscript or superscript is marked
392: simply by a blank (or tab or tilde, etc.)
393: What if the subscript or superscript is something that has to be typed
394: with blanks in it?
395: In that case, you can use the braces
396: { and } to mark the
397: beginning and end of the subscript or superscript:
398: .P1
399: e sup {i omega t}
400: .P2
401: is
402: .EQ
403: e sup {i omega t}
404: .EN
405: .sp
406: Rule: Braces can
407: .ul
408: always
409: be used to force
410: .UC EQN
411: to treat something as a unit,
412: or just to make your intent perfectly clear.
413: Thus:
414: .P1
415: x sub {i sub 1} sup 2
416: .P2
417: is
418: .EQ
419: x sub {i sub 1} sup 2
420: .EN
421: with braces, but
422: .P1
423: x sub i sub 1 sup 2
424: .P2
425: is
426: .EQ
427: x sub i sub 1 sup 2
428: .EN
429: which is rather different.
430: .PP
431: Braces can occur within braces if necessary:
432: .P1
433: e sup {i pi sup {rho +1}}
434: .P2
435: is
436: .EQ
437: e sup {i pi sup {rho +1}}
438: .EN
439: The general rule is that anywhere you could use some single
440: thing like
441: .ul
442: x,
443: you can use an arbitrarily complicated thing if you enclose
444: it in braces.
445: .UC EQN
446: will look after all the details of positioning it and making
447: it the right size.
448: .PP
449: In all cases, make sure you have the
450: right number of braces.
451: Leaving one out or adding an extra will cause
452: .UC EQN
453: to complain bitterly.
454: .PP
455: Occasionally you will have to
456: print braces.
457: To do this,
458: enclose them in double quotes,
459: like "{".
460: Quoting is discussed in more detail in section 14.
461: .SC Fractions
462: .PP
463: To make a fraction,
464: use the word
465: .ul
466: over:
467: .P1
468: a+b over 2c =1
469: .P2
470: gives
471: .EQ
472: a+b over 2c =1
473: .EN
474: The line is made the right length and positioned automatically.
475: Braces can be used to make clear what goes over what:
476: .P1
477: {alpha + beta} over {sin (x)}
478: .P2
479: is
480: .EQ
481: {alpha + beta} over {sin (x)}
482: .EN
483: What happens when there is both an
484: .ul
485: over
486: and a
487: .ul
488: sup
489: in the same expression?
490: In such an apparently ambiguous case,
491: .UC EQN
492: does the
493: .ul
494: sup
495: before the
496: .ul
497: over,
498: so
499: .P1
500: \(mib sup 2 over pi
501: .P2
502: is
503: $-b sup 2 over pi$
504: instead of
505: $-b sup {2 over pi}$
506: The rules
507: which decide which operation is done first in cases like this
508: are summarized in section 23.
509: When in doubt, however,
510: .ul
511: use braces
512: to make clear what goes with what.
513: .SC "Square Roots"
514: .PP
515: To draw a square root, use
516: .ul
517: sqrt:
518: .P1 2
519: sqrt a+b + 1 over sqrt {ax sup 2 +bx+c}
520: .P2
521: is
522: .EQ
523: sqrt a+b + 1 over sqrt {ax sup 2 +bx+c}
524: .EN
525: Warning _ square roots of tall quantities look lousy,
526: because a root-sign
527: big enough to cover the quantity is
528: too dark and heavy:
529: .P1
530: sqrt {a sup 2 over b sub 2}
531: .P2
532: is
533: .EQ
534: sqrt{a sup 2 over b sub 2}
535: .EN
536: Big square roots are generally better written as something
537: to the power \(12:
538: .EQ
539: (a sup 2 /b sub 2 ) sup half
540: .EN
541: which is
542: .P1
543: (a sup 2 /b sub 2 ) sup half
544: .P2
545: .SC "Summation, Integral, Etc."
546: .PP
547: Summations, integrals, and similar constructions
548: are easy:
549: .P1
550: sum from i=0 to {i= inf} x sup i
551: .P2
552: produces
553: .EQ
554: sum from i=0 to {i= inf} x sup i
555: .EN
556: Notice that we used
557: braces to indicate where the upper
558: part
559: $i= inf$
560: begins and ends.
561: No braces were necessary for the lower part $i=0$,
562: because it contained no blanks.
563: The braces will never hurt,
564: and if the
565: .ul
566: from
567: and
568: .ul
569: to
570: parts contain any blanks, you must use braces around them.
571: .PP
572: The
573: .ul
574: from
575: and
576: .ul
577: to
578: parts are both optional,
579: but if both are used,
580: they have to occur in that order.
581: .PP
582: Other useful characters can replace the
583: .ul
584: sum
585: in our example:
586: .P1
587: int prod union inter
588: .P2
589: become, respectively,
590: .EQ
591: int ~~~~~~ prod ~~~~~~ union ~~~~~~ inter
592: .EN
593: Since the thing before the
594: .ul
595: from
596: can be anything,
597: even something in braces,
598: .ul
599: from-to
600: can often be used in unexpected ways:
601: .P1
602: lim from {n \(mi> inf} x sub n =0
603: .P2
604: is
605: .EQ
606: lim from {n-> inf} x sub n =0
607: .EN
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