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1.1 root 1: .\" @(#)g2 6.1 (Berkeley) 5/22/86
2: .\"
3: .SC "Size and Font Changes"
4: .PP
5: By default, equations are set in 10-point type (the same size as this guide),
6: with standard mathematical conventions
7: to determine what characters are in roman and what in italic.
8: Although
9: .UC EQN
10: makes a valiant attempt to use
11: esthetically pleasing sizes and fonts,
12: it is not perfect.
13: To change sizes and fonts, use
14: .ul
15: size n
16: and
17: .ul
18: roman, italic,
19: .ul
20: bold
21: and
22: .ul
23: fat.
24: Like
25: .ul
26: sub
27: and
28: .ul
29: sup,
30: size
31: and font changes affect only the thing that follows
32: them, and revert to the normal situation
33: at the end of it. Thus
34: .P1
35: bold x y
36: .P2
37: is
38: .EQ
39: bold x y
40: .EN
41: and
42: .P1
43: size 14 bold x = y +
44: size 14 {alpha + beta}
45: .P2
46: gives
47: .EQ
48: size 14 bold x = y +
49: size 14 {alpha + beta}
50: .EN
51: As always, you can use braces if you want to affect something
52: more complicated than a single letter.
53: For example, you can change the size of an entire equation by
54: .P1
55: size 12 { ... }
56: .P2
57: .PP
58: Legal sizes which may follow
59: .ul
60: size
61: are
62: 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 24, 28, 36.
63: You can also change the size
64: .ul
65: by
66: a given amount;
67: for example, you can say
68: .ul
69: size~+2
70: to make the size two points bigger,
71: or
72: .ul
73: size~\(mi3
74: to make it three points smaller.
75: This has the advantage that you don't have
76: to know what the current size is.
77: .PP
78: If you are using fonts other than roman, italic and bold,
79: you can say
80: .ul
81: font X
82: where
83: .ul
84: X
85: is a one character
86: .UC TROFF
87: name or number for the font.
88: Since
89: .UC EQN
90: is tuned for roman, italic and bold,
91: other fonts may not give quite as good an appearance.
92: .PP
93: The
94: .ul
95: fat
96: operation takes the current font and widens it by overstriking:
97: .ul
98: fat\ grad
99: is
100: $fat grad$ and
101: .ul
102: fat {x sub i}
103: is
104: $fat {x sub i}$.
105: .PP
106: If an entire document is to be in a non-standard size
107: or font, it is a severe nuisance
108: to have to write out a size and font change for each
109: equation.
110: Accordingly, you can set a ``global'' size or font
111: which thereafter affects all equations.
112: At the beginning of any equation, you might say, for instance,
113: .P1
114: ^EQ
115: gsize 16
116: gfont R
117: ...
118: ^EN
119: .P2
120: to set the size to 16 and the font to roman thereafter.
121: In place of R, you can use any of the
122: .UC TROFF
123: font names.
124: The size after
125: .ul
126: gsize
127: can be a relative change with + or \(mi.
128: .PP
129: Generally,
130: .ul
131: gsize
132: and
133: .ul
134: gfont
135: will appear at the beginning of a document
136: but they can also appear
137: thoughout a document: the global font and size
138: can be changed as often as needed.
139: For example, in a footnote\(dd
140: .FS
141: \(ddLike this one, in which we have a
142: $gsize -2$few random
143: expressions like $x sub i$ and $pi sup 2$.
144: The sizes for these were set by the command
145: .ul
146: gsize~\(mi2.
147: .FE $gsize +2$
148: you will typically want the size of equations to match
149: the size of the footnote text, which is two points smaller
150: than the main text.
151: Don't forget to reset the global size
152: at the end of the footnote.
153: .SC "Diacritical Marks"
154: .PP
155: To get funny marks on top of letters,
156: there are several words:
157: .P1
158: .tr ^^
159: .tr ~~
160: .ta 1i
161: x dot $x dot$
162: x dotdot $x dotdot$
163: x hat $x hat$
164: x tilde $x tilde$
165: x vec $x vec$
166: x dyad $x dyad$
167: x bar $x bar$
168: x under $x under$
169: .P2
170: The diacritical mark is placed at the right height.
171: The
172: .ul
173: bar
174: and
175: .ul
176: under
177: are made the right length for the entire construct,
178: as in $x+y+z bar$;
179: other marks are centered.
180: .SC "Quoted Text"
181: .PP
182: Any input entirely within quotes (\|"..."\|)
183: is not subject to any of the font changes and spacing
184: adjustments normally done by the equation setter.
185: This provides a way to do your own spacing and adjusting if needed:
186: .P1
187: italic "sin(x)" + sin (x)
188: .P2
189: is
190: .EQ
191: italic "sin(x)" + sin (x)
192: .EN
193: .PP
194: Quotes are also used to get braces and other
195: .UC EQN
196: keywords printed:
197: .P1
198: "{ size alpha }"
199: .P2
200: is
201: .EQ
202: "{ size alpha }"
203: .EN
204: and
205: .P1
206: roman "{ size alpha }"
207: .P2
208: is
209: .EQ
210: roman "{ size alpha }"
211: .EN
212: .PP
213: The construction "" is often used as a place-holder
214: when grammatically
215: .UC EQN
216: needs something, but you don't actually want anything in your output.
217: For example, to make
218: $"" sup 2 roman He$,
219: you can't just type
220: .ul
221: sup 2 roman He
222: because a
223: .ul
224: sup
225: has to be a superscript
226: .ul
227: on
228: something.
229: Thus you must say
230: .P1
231: "" sup 2 roman He
232: .P2
233: .PP
234: To get a literal quote
235: use ``\\"''.
236: .UC TROFF
237: characters like
238: .ul
239: \e(bs
240: can appear unquoted, but more complicated things like
241: horizontal and vertical motions with
242: .ul
243: \eh
244: and
245: .ul
246: \ev
247: should
248: always
249: be quoted.
250: (If you've never heard of
251: .ul
252: \\h
253: and
254: .ul
255: \\v,
256: ignore this section.)
257: .SC "Lining Up Equations"
258: .PP
259: Sometimes it's necessary to line up a series of equations
260: at some horizontal position, often at an equals sign.
261: This is done with two operations called
262: .ul
263: mark
264: and
265: .ul
266: lineup.
267: .PP
268: The word
269: .ul
270: mark
271: may appear once at any place in an equation.
272: It remembers the horizontal position where it appeared.
273: Successive equations can contain one occurrence of the word
274: .ul
275: lineup.
276: The place where
277: .ul
278: lineup
279: appears is made to line up
280: with the place marked by the previous
281: .ul
282: mark
283: if at all possible.
284: Thus, for example,
285: you can say
286: .P1
287: ^EQ I
288: x+y mark = z
289: ^EN
290: ^EQ I
291: x lineup = 1
292: ^EN
293: .P2
294: to produce
295: .EQ I
296: x+y mark = z
297: .EN
298: .EQ I
299: x lineup = 1
300: .EN
301: For reasons too complicated to talk about,
302: when you use
303: .UC EQN
304: and
305: `\(mims',
306: use either
307: .UC .EQ\ I
308: or
309: .UC .EQ\ L .
310: mark
311: and
312: .ul
313: lineup
314: don't work with centered equations.
315: Also bear in mind that
316: .ul
317: mark
318: doesn't look ahead;
319: .P1
320: x mark =1
321: ...
322: x+y lineup =z
323: .P2
324: isn't going to work, because there isn't room
325: for the
326: .ul
327: x+y
328: part after the
329: .ul
330: mark
331: remembers where the
332: .ul
333: x
334: is.
335: .SC "Big Brackets, Etc."
336: .PP
337: .tr ~
338: To get big brackets [~],
339: braces {~}, parentheses (~), and bars |~|
340: around things, use the
341: .ul
342: left
343: and
344: .ul
345: right
346: commands:
347: .tr ~~
348: .P1
349: left { a over b + 1 right }
350: ~=~ left ( c over d right )
351: + left [ e right ]
352: .P2
353: is
354: .EQ
355: left { a over b + 1 right } ~=~ left ( c over d right ) + left [ e right ]
356: .EN
357: The resulting brackets are made big enough to cover whatever they enclose.
358: Other characters can be used besides these,
359: but the are not likely to look very good.
360: One exception is the
361: .ul
362: floor
363: and
364: .ul
365: ceiling
366: characters:
367: .P1
368: left floor x over y right floor
369: <= left ceiling a over b right ceiling
370: .P2
371: produces
372: .EQ
373: left floor x over y right floor
374: <= left ceiling a over b right ceiling
375: .EN
376: .PP
377: Several warnings about brackets are in order.
378: First, braces are typically bigger than brackets and parentheses,
379: because they are made up of three, five, seven, etc., pieces,
380: while brackets can be made up of two, three, etc.
381: Second, big left and right parentheses often look poor,
382: because the character set is poorly designed.
383: .PP
384: The
385: .ul
386: right
387: part may be omitted:
388: a ``left something'' need not have a
389: corresponding
390: ``right
391: something''.
392: If the
393: .ul
394: right
395: part is omitted,
396: put braces around the thing you want the left bracket
397: to encompass.
398: Otherwise, the resulting brackets may be too large.
399: .PP
400: If you want to omit the
401: .ul
402: left
403: part, things are more complicated,
404: because technically you can't have a
405: .ul
406: right
407: without a corresponding
408: .ul
409: left.
410: Instead you have to say
411: .P1
412: left "" ..... right )
413: .P2
414: for example.
415: The
416: .ul
417: left ""
418: means a ``left nothing''.
419: This satisfies the rules without hurting your output.
420: .SC "Piles"
421: .PP
422: There is a general facility for making vertical piles
423: of things; it comes in several flavors.
424: For example:
425: .P1
426: .tr ~~
427: A ~=~ left [
428: pile { a above b above c }
429: ~~ pile { x above y above z }
430: right ]
431: .P2
432: will make
433: .EQ
434: A ~=~ left [
435: pile { a above b above c } ~~ pile { x above y above z }
436: right ]
437: .EN
438: The elements of the pile (there can be as many as you want)
439: are centered one above another, at the right height for
440: most purposes.
441: The keyword
442: .ul
443: above
444: is used to separate the pieces;
445: braces are used around the entire list.
446: The elements of a pile can be as complicated as needed, even containing more piles.
447: .PP
448: Three other forms of pile exist:
449: .ul
450: lpile
451: makes a pile with the elements left-justified;
452: .ul
453: rpile
454: makes a right-justified pile;
455: and
456: .ul
457: cpile
458: makes a centered pile, just like
459: .ul
460: pile.
461: The vertical spacing between the pieces
462: is somewhat larger for
463: .ul
464: l-,
465: .ul
466: r-
467: and
468: .ul
469: cpiles
470: than it is for ordinary piles.
471: .P1 2
472: roman sign (x)~=~
473: left {
474: lpile {1 above 0 above -1}
475: ~~ lpile
476: {if~x>0 above if~x=0 above if~x<0}
477: .P2
478: makes
479: .EQ
480: roman sign (x)~=~
481: left {
482: lpile {1 above 0 above -1}
483: ~~ lpile
484: {if~x>0 above if~x=0 above if~x<0}
485: .EN
486: Notice the left brace
487: without a matching right one.
488: .SC Matrices
489: .PP
490: It is also possible to make matrices.
491: For example, to make
492: a neat array like
493: .EQ
494: matrix {
495: ccol { x sub i above y sub i }
496: ccol { x sup 2 above y sup 2 }
497: }
498: .EN
499: you have to type
500: .P1
501: matrix {
502: ccol { x sub i above y sub i }
503: ccol { x sup 2 above y sup 2 }
504: }
505: .P2
506: This produces a matrix with
507: two centered columns.
508: The elements of the columns are then listed just as for a pile,
509: each element separated by the word
510: .ul
511: above.
512: You can also use
513: .ul
514: lcol
515: or
516: .ul
517: rcol
518: to left or right adjust columns.
519: Each column can be separately adjusted,
520: and there can be as many columns as you like.
521: .PP
522: The reason for using a matrix instead of two adjacent piles, by the way,
523: is that if the elements of the piles don't all have the same height,
524: they won't line up properly.
525: A matrix forces them to line up,
526: because it looks at the entire structure before deciding what
527: spacing to use.
528: .PP
529: A word of warning about matrices _
530: .ul
531: each column must have the same number of elements in it.
532: The world will end if you get this wrong.
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