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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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