%!PS-Adobe-2.0 %%Creator: dvips 5.58 Copyright 1986, 1994 Radical Eye Software %%Title: manual.dvi %%CreationDate: Wed Jul 12 19:08:42 1995 %%Pages: 19 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSCommandLine: dvips manual.dvi %DVIPSParameters: dpi=300, comments removed %DVIPSSource: TeX output 1995.07.12:1908 %%BeginProcSet: tex.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR matrix currentmatrix dup dup 4 get round 4 exch put dup dup 5 get round 5 exch put setmatrix}N /@landscape{/isls true N}B /@manualfeed{ statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{/nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{/sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]N df-tail}B /E{ pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get} B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 add]{ ch-image}imagemask restore}B /D{/cc X dup type /stringtype ne{]}if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{cc 1 add D }B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore showpage userdict /eop-hook known{eop-hook}if}N /@start{userdict /start-hook known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V {}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7 getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false} ifelse}{false}ifelse end{{gsave TR -.1 -.1 TR 1 1 scale rulex ruley false RMat{BDot}imagemask grestore}}{{gsave TR -.1 -.1 TR rulex ruley scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave transform round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail} B /c{-4 M}B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{ 3 M}B /k{4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{ 3 2 roll p a}B /bos{/SS save N}B /eos{SS restore}B end %%EndProcSet %%BeginProcSet: /u/levy/texts/geomsty/math.pro % This file is adapted from the PostScript code that gets % included by the psfix filter, provided with Mathematica. % The only differences are the addition of the first two lines % (MyDict) and of the abbreviations at the end (starting with /Ma). %$Revision: 1.3 $ %$Date: 95/06/27 12:16:53 $ /MyDict 200 dict def MyDict begin % The externally visible functions are: % MathPictureStart- start page. % MathPictureEnd - finish off page. % MathSubStart - start a sub-page. % MathSubEnd - finish off a sub-page. % Mdot - draw a dot. % Mtetra - draw a filled tetragon. % Metetra - draw a filled tetragon with black edges. % Mistroke - intermediate stroke of multi-stroke line/curve. % Mfstroke - final stroke of multi-stroke line/curve. % Msboxa - compute coordinates of text bounding box. % Mshowa - plot characters. % MathScale - compute scaling info to contain array of points. % The following are only for backwards compatibility with earlier versions % of Mathematica: % Mpstart - identical to MathPictureStart. % Mpend - identical to MathPictureEnd. % Mscale - like MathScale but without user coordinate info. /Mpstart { % - Mpstart - MathPictureStart } bind def /Mpend { % - Mpend - MathPictureEnd } bind def /Mscale { % [pnts] Mscale - 0 1 0 1 % [pnts] xbias xscale ybias yscale 5 -1 roll % xbias xscale ybias yscale [pnts] MathScale % - } bind def %start of ISOLatin1 stuff /ISOLatin1Encoding dup where { pop pop } { [ /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /minus /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent /dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron /space /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def } ifelse /MFontDict 50 dict def /MStrCat % string1 string2 MStrCat string { exch % s2 s1 dup length % s2 s1 len 2 index length add % s2 s1 len string % s2 s1 s dup 3 1 roll % s2 s s1 s copy % s2 s s1 length % s2 s where exch dup % s2 where s s 4 2 roll exch % s s where s2 putinterval } def /MCreateEncoding % name encoding MCreateEncoding newname { % get base name 1 index % name encoding name % concatenate (-) and encoding to the name 255 string cvs (-) MStrCat 1 index MStrCat cvn exch % basename newname encoding % make encoding name (Encoding) MStrCat cvn dup where { exch get } { pop StandardEncoding } ifelse 3 1 roll % vector basename newname % make the font if we haven't before dup MFontDict exch known not { 1 index findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding 3 index def currentdict end 1 index exch definefont pop MFontDict 1 index null put } if exch pop % vector newname exch pop % newname } def /ISOLatin1 { (ISOLatin1) MCreateEncoding } def /ISO8859 { (ISOLatin1) MCreateEncoding } def %end of ISOLatin1 stuff % % Include old font names for backward compatibility % /Mcopyfont { % procedure to copy font dup maxlength dict exch { 1 index /FID eq { pop pop } { 2 index 3 1 roll put } ifelse } forall } def /Plain /Courier findfont Mcopyfont definefont pop /Bold /Courier-Bold findfont Mcopyfont definefont pop /Italic /Courier-Oblique findfont Mcopyfont definefont pop % Set up for the start of a page. /MathPictureStart { % - MathPictureStart - gsave % - Mtransform % possibly rotate to landscape mode Mlmarg % left_margin Mbmarg % bottom_margin translate % - Mwidth % init_width Mlmarg Mrmarg add % init_width lmarg+rmarg sub % true_width /Mwidth exch def % Mheight % init_height Mbmarg Mtmarg add % init_height tmarg+bmarg sub % true_height /Mheight exch def /Mtmatrix % /Mtmatrix matrix currentmatrix % /Mtmatrix text_matrix def /Mgmatrix % /Mgmatrix matrix currentmatrix % /Mgmatrix graphics_matrix def % - } bind def % Finish off a page. /MathPictureEnd { grestore } bind def %MFill fills the drawing area with the current color. /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def % xmin xmax ymin ymax MPlotRegion alters the origin, Mwidth and Mheight % so that the picture fills the altered region /MPlotRegion { % xmin xmax ymin ymax MPlotRegion 3 index % xmin xmax ymin ymax xmin Mwidth mul % xmin xmax ymin ymax xmin_pos 2 index % xmin xmax ymin ymax xmin_pos ymin Mheight mul % xmin xmax ymin ymax xmin_pos ymin_pos translate % xmin xmax ymin ymax exch sub % xmin xmax ymax-ymin Mheight mul % xmin xmax new_height /Mheight exch def % xmin xmax exch sub % xmax-xmin Mwidth mul % new-width /Mwidth exch def } bind def % Given a rectangle, set it up as a sub-picture. /MathSubStart { % xmin ymin xmax ymax MathSubStart Momatrix Mgmatrix Mtmatrix Mwidth Mheight % xmin ymin xmax ymax 7 -2 roll % xmin ymin xmax ymax moveto % xmin ymin Mtmatrix setmatrix % xmin ymin currentpoint % xmin ymin xmax(t) ymax(t) Mgmatrix setmatrix % xmin ymin xmax(t) ymax(t) 9 -2 roll % xmax(t) ymax(t) xmin ymin moveto % xmax(t) ymax(t) Mtmatrix setmatrix % xmax(t) ymax(t) currentpoint % xmax(t) ymax(t) xmin(t) ymin(t) 2 copy translate % xmax ymax xmin ymin /Mtmatrix matrix currentmatrix def 3 -1 roll % xmax xmin ymin ymax exch sub % xmax xmin height /Mheight exch def % xmax xmin sub % width /Mwidth exch def % } bind def % Restore the saved state left by the matching MathSubStart. % Note, we also leave with the new Mgmatrix as the current matrix. /MathSubEnd { % gmat tmat lm rm bm tm w h MathSubStart - /Mheight exch def % gmat tmat lm rm bm tm w /Mwidth exch def % gmat tmat lm rm bm tm /Mtmatrix exch def % gmat dup setmatrix % gmat /Mgmatrix exch def % - /Momatrix exch def % - } bind def % Given a point, draw a dot. /Mdot { % x y Mdot - moveto % - 0 0 rlineto % - stroke % - } bind def % Given 4 points, draw the corresponding filled tetragon. /Mtetra { % x0 y0 x1 y1 x2 y2 x3 y3 Mtetra - moveto % x0 y0 x1 y1 x2 y2 lineto % x0 y0 x1 y1 lineto % x0 y0 lineto % - fill % - } bind def % Given 4 points, draw the corresponding filled tetragon with black edges. % Note, this leaves the gray level at 0 (for compatibility with the old % C code. /Metetra { % x0 y0 x1 y1 x2 y2 x3 y3 Metetra - moveto % x0 y0 x1 y1 x2 y2 lineto % x0 y0 x1 y1 lineto % x0 y0 lineto % - closepath % - gsave % - fill % - grestore % - 0 setgray % - stroke % - } bind def % Mistroke is called to stroke intermediate parts of a path. It makes % sure to resynchronize the dashing pattern and to leave the current point % as the final point of the path. /Mistroke { % - Mistroke - flattenpath % - 0 0 0 % length x y { % length x y new_x new_y (for moves) 4 2 roll % length new_x new_y x y pop pop % length new_x new_y } { % length x y new_x new_y (for lines) 4 -1 roll % length y new_x new_y x 2 index % length y new_x new_y x new_x sub dup mul % length y new_x new_y dx*dx 4 -1 roll % length new_x new_y dx*dx y 2 index % length new_x new_y dx*dx y new_y sub dup mul % length new_x new_y dx*dx dy*dy add sqrt % length new_x new_y dlen 4 -1 roll % new_x new_y dlen length add % new_x new_y new_length 3 1 roll % new_length new_x new_y } { % length x y x1 y1 x2 y2 x3 y3 (for curves) stop % should never be called } { % length x y (for closepaths) stop % should never be called } pathforall % length x y pop pop % length currentpoint % length final_x final_y stroke % length final_x final_y moveto % length currentdash % length dash_array dash_offset 3 -1 roll % dash_array dash_offset length add % dash_array new_offset setdash % - } bind def % Mfstroke is called to stroke the final parts of a path. It resets % the dashing pattern to compensate for any adjustments made by Mistroke. /Mfstroke { % - Mfstroke - stroke % - currentdash % dash_array dash_offset pop 0 % dash_array 0 setdash % - } bind def % Mrotsboxa is the same as Msboxa except that it takes an angle % form the stack and the box is calculated for text rendered at this angle. % It gsaves in case we are starting a MathSubStart % save Mrot so that Msboxa can convert bouding box back to the non-rotated % coordinate system % call Mrotcheck to alter the offsets into the rotated system % converts Mtmatrix to render in the rotated system % the calls Msboxa which does all the work % at the end Mtmatrix is restored and Mrot is reset to 0 /Mrotsboxa { % [str..] gx gy sx sy ang Mrotsboxa ... Msboxa gsave % in case in MathSubStart dup % [str..] gx gy sx sy ang ang /Mrot exch def % [str..] gx gy sx sy ang Mrotcheck % [str..] gx gy sx_new sy_new ang Mtmatrix % [str..] gx gy sx sy ang Mtmatrix dup setmatrix 7 1 roll % Mtmatrix [str..] gx gy sx sy ang 4 index % Mtmatrix [str..] gx gy sx sy ang gx 4 index % Mtmatrix [str..] gx gy sx sy ang gx gy translate % Mtmatrix [str..] gx gy sx sy ang rotate % Mtmatrix [str..] gx gy sx sy 3 index % Mtmatrix [str..] gx gy sx sy gx -1 mul % Mtmatrix [str..] gx gy sx sy -gx 3 index % Mtmatrix [str..] gx gy sx sy -gx gy -1 mul % Mtmatrix [str..] gx gy sx sy -gx -gy translate % Mtmatrix [str..] gx gy sx sy /Mtmatrix % now change Mtmatrix to be this new currentmatrix matrix currentmatrix def grestore % grestore to deal with MathSubStart Msboxa % Mtmatrix [ x y x y] [ x y x y] 3 -1 roll % [x y x y ] [x y x y] Mtmatrix /Mtmatrix exch def % restore Mtmatrix /Mrot 0 def % restore Mrot } bind def % Given an array of strings ([str...]), which represent consecutive lines % of text, a position in graphics coordinates (gx,gy) and a position in % the bounding box coordinates (sx,sy), compute the low and high coordinates % of the resulting text, in the [gx gy tx ty] form, which corresponds to % the point (gx,gy) (in graphics coordinates) plus the offset (tx,ty) (in % text coordinates). % Note, Msboxa assumes that the current matrix is the text matrix. % Mboxout is called in case we are in Mouter to make the box bigger % Mboxrot adjusts the box to account for a rotation to convert the box % into a nonrotated coordinate system % /Msboxa { % [str...] gx gy sx sy Msboxa [gx gy tlx tly] [gx gy thx thy] newpath % [str...] gx gy sx sy (just in case) 5 -1 roll % gx gy sx sy [str...] Mvboxa % gx gy sx sy blx bly bhx bhy [off...] pop % gx gy sx sy blx bly bhx bhy Mboxout % adjust box for Minner 6 -1 roll % gx gy sy blx bly bhx bhy sx 5 -1 roll % gx gy sy bly bhx bhy sx blx 4 -1 roll % gx gy sy bly bhy sx blx bhx Msboxa1 % gx gy sy bly bhy tlx thx 5 -3 roll % gx gy tlx thx sy bly bhy Msboxa1 % gx gy tlx thx tly thy Mboxrot % adjust box for rotation [ % gx gy tlx thx tly thy mark 7 -2 roll % tlx thx tly thy mark gx gy 2 copy % tlx thx tly thy mark gx gy gx gy [ % tlx thx tly thy mark gx gy gx gy mark 3 1 roll % tlx thx tly thy mark gx gy mark gx gy 10 -1 roll % thx tly thy mark gx gy mark gx gy tlx 9 -1 roll % thx thy mark gx gy mark gx gy tlx tly ] % thx thy mark gx gy [gx gy tlx tly] 6 1 roll % [gx gy tlx tly] thx thy mark gx gy 5 -2 roll % [gx gy tlx tly] mark gx gy thx thy ] % [gx gy tlx tly] [gx gy thx thy] } bind def % Msboxa1 is an internal function which, given a bounding box coordinate % (sz), and the bounding box limits (blz and bhz), computes the actual % offsets (tlz = (blz-bhz)(sz+1)/2, thz = (blz-bhz)(sz-1)/2). /Msboxa1 { % sz blz bhz Msboxa1 tlz thz sub % sz blz-bhz 2 div % sz (blz-bhz)/2 dup % sz (blz-bhz)/2 (blz-bhz)/2 2 index % sz (blz-bhz)/2 (blz-bhz)/2 sz 1 add % sz (blz-bhz)/2 (blz-bhz)/2 sz+1 mul % sz (blz-bhz)/2 tlz 3 -1 roll % (blz-bhz)/2 tlz sz -1 add % (blz-bhz)/2 tlz sz-1 3 -1 roll % tlz sz-1 (blz-bhz)/2 mul % tlz thz } bind def % Given a (non-empty) array of strings ([str...]) calculate the % bounding box. We do this for fixedwidth fonts or nonfixedwidth fonts % depending upon the setting of Mfixwid. Mvboxa1 actually does a lot % of the work. For nonfixedwidth fonts the length of the bounding % box length is made to be the summation of [(str)..] Mwidthcal % ie the maximum length of the strings and xlow % /Mvboxa { % [str...] Mvboxa xlow ylow xhigh yhigh [off...] Mfixwid { Mvboxa1 } { dup % [str...] [str...] Mwidthcal % [str...] [ w1 w2...] 0 exch % [str...] 0 [ w1 w2...] { add } forall % [str...] length exch Mvboxa1 % length xlow ylow xhigh yhigh [off...] 4 index % length xlow ylow xhigh yhigh [off...] xlow 7 -1 roll % xlow ylow xhigh yhigh [off...] xlow length add % xlow ylow xhigh yhigh [off...] new_xhigh 4 -1 roll pop % xlow ylow yhigh [off...] new_xhigh 3 1 roll % xlow ylow new_xhigh yhigh [off...] } ifelse } bind def % Given a (non-empty) array of strings ([str...]) which represent consecutive % lines of text, compute the total bounding box assuming that we start at % (0,0) and the array of y offsets to place the lines correctly. % Note, Mvboxa assumes that the current matrix is the text matrix. % Note, Mvboxa does not alter the current path. % The vertical spacing is set so that the bounding boxes of adjacent lines % are .3 times the width of an `m' apart. /Mvboxa1 { % [str...] Mvboxa xlow ylow xhigh yhigh [off...] gsave % [str...] newpath % [str...] (clear path fragments) [ true % [str...] mark true 3 -1 roll % mark true [str...] { % mark {true -or- off... Xl Yl Xh Yh false} str Mbbox % mark {true -or- off... Xl Yl Xh Yh false} xl yl xh yh 5 -1 roll % mark { - -or- off... Xl Yl Xh Yh} xl yl xh yh first? { % mark xl yl xh yh 0 % mark xl yl xh yh off1 5 1 roll % mark off1 xl yl xh yh } % mark off1 XL YL XH YH { % mark off... Xl Yl Xh Yh xl yl xh yh 7 -1 roll % mark off... Xl Xh Yh xl yl xh yh Yl exch sub % mark off... Xl Xh Yh xl yl xh yh-Yl (m) stringwidth pop % mark off... Xl Xh Yh xl yl xh yh-Yl pntsize .3 mul % mark off... Xl Xh Yh xl yl xh yh-Yl fudge sub % mark off... Xl Xh Yh xl yl xh off 7 1 roll % mark off... off Xl Xh Yh xl yl xh 6 -1 roll % mark off... off Xh Yh xl yl xh Xl 4 -1 roll % mark off... off Xh Yh yl xh Xl xl Mmin % mark off... off Xh Yh yl xh XL 3 -1 roll % mark off... off Xh Yh xh XL yl 5 index % mark off... off Xh Yh xh XL yl off add % mark off... off Xh Yh xh XL YL 5 -1 roll % mark off... off Yh xh XL YL Xh 4 -1 roll % mark off... off Yh XL YL Xh xh Mmax % mark off... off Yh XL YL XH 4 -1 roll % mark off... off XL YL XH YH } % mark off... XL YL XH YH ifelse % mark off... XL YL XH YH false % mark off... XL YL XH YH false } % mark off... XL YL XH YH false forall % mark off... xlow ylow xhigh yhigh false { stop } if % mark off... xlow ylow xhigh yhigh counttomark % mark off... xlow ylow xhigh yhigh (#off's+4) 1 add % mark off... xlow ylow xhigh yhigh (#off's+5) 4 roll % xlow ylow xhigh yhigh mark off... ] % xlow ylow xhigh yhigh [off...] grestore % xlow ylow xhigh yhigh [off...] } bind def % Given a string, compute the bounding box assuming that we start at (0,0). % Note, the path is assumed to be empty, and we are assumed to be in text % coordinates. Allows for long strings. /Mbbox { % str Mbbox xlow ylow xhigh yhigh 1 dict begin 0 0 moveto % str /temp (T) def { gsave currentpoint newpath moveto temp 0 3 -1 roll put temp false charpath flattenpath currentpoint pathbbox grestore moveto lineto moveto} forall pathbbox newpath end } bind def % Compute the minimum of two numbers. /Mmin { % p q Mmin min(p,q) 2 copy % p q p q gt % p q p>q? { exch } if % min(p,q) max(p,q) pop % min(p,q) } bind def % Compute the maximum of two numbers. /Mmax { % p q Mmax max(p,q) 2 copy % p q p q lt % p q p 1 /Mfixdashp { % str dup length % str n 1 gt % str bool 1 index % str bool str true exch % str bool true str { 45 eq and } forall and % str bool { gsave (--) stringwidth pop (-) stringwidth pop sub 2 div % str lenfix 0 rmoveto % str dup % str str length 1 sub % str len-1 { (-) show } repeat grestore } if % x y str } bind def % This is for non-fixedwidth fonts % It shows each character individually advancing the x position by % the maximum width of any character in that position % /Mshoway { 3 index % [str...] [off...] x y [str...] Mwidthcal % [str...] [off...] x y [w1 w2 w3...] 5 1 roll % [w1 w2 w3..] [str...] [off...] x y 0 1 % [w1 w2 w3..] [str...] [off...] x y 0 1 4 index length % [w1 w2 w3..] [str...] [off...] x y 0 1 (#strings) -1 add % [w1 w2 w3..] [str...] [off...] x y 0 1 (#strings-1) { % [w1 w2 w3..] [str...] [off...] x y strnum 2 index % [w1 w2 w3..] [str...] [off...] x y strnum x 4 index % [w1 w2 w3..] [str...] [off...] x y strnum x [off...] 2 index % [w1 w2 w3..] [str...] [off...] x y % strnum [off...] strnum get % [w1 w2 w3..] [str...] [off...] x y strnum x off 3 index % [w1 w2 w3..] [str...] [off...] x y strnum x off y add % [w1 w2 w3..] [str...] [off...] x y strnum x Y moveto % [w1 w2 w3..] [str...] [off...] x y strnum 4 index % [w1 w2 w3..] [str...] [off...] x y strnum [str...] exch get % [w1 w2 w3..] [str...] [off...] x y str [ 6 index % [w1 w2 w3..] [str...] [off...] x y str [ [w1 w2..] aload length % [w1 w2 w3..] [str...] [off...] x y str [ w1 w2.. len 2 add -1 roll % [w1 w2 w3..] [str...] [off...] x y [ w1 w2.. str { pop % [w1 w2 w3..] [str...] [off...] x y [ w1 c2.. str am Strform % [w1 w2 w3..] [str...] [off...] x y [ w1 w2.. str 1str stringwidth pop neg exch % [w1 w2 w3..] [str...] [off...] x y [ w1 w2.. % str -cm cn add 0 rmoveto % [w1 w2 w3..] [str...] [off...] x y [ w1 w2.. str } exch kshow % [w1 w2 w3..] [str...] [off...] x y [ cleartomark } for % [w1 w2 w3..] [str...] [off...] x y pop } bind def % % This is a central mechanism for dealing with non-fixedwidth fonts. % Given an array of strings Mwidthcal returns an array of the lengths % of the longest character in the corresponding positions in the arrays. % Thus the 4th element of the result is the maximum character width of % each strin at the 4th position. % /Mwidthcal { % [(abc) (abc) ..] Mwidthcal [w1 w2 w3 ...] [ exch % [ [(abc) (abd) ..] { Mwidthcal1 } forall ] % [[w w w] [w w w] ..] [ % call this [chr ..] now exch % [ [chr ..] dup % [ [chr ..] [chr ..] Maxlen % [ [chr ..] maxlen -1 add 0 1 3 -1 roll % [chr ..] [ [chr ..] 0 1 maxlen-1 { [ % [chr ..] [ [chr ..] n [ exch % [chr ..] [ [chr ..] [ n 2 index % [chr ..] [ [chr ..] [ n [chr ..] { 1 index Mget % [chr ..] [ [chr ..] [ n [w1 w2 ..] n exch % [chr ..] [ [chr ..] [ wn n } forall pop % [chr ..] [ [chr ..] [ w1 w2 w3 Maxget % [chr ..] [ [chr ..] wmax exch % [chr ..] [ wmax [chr ..] } for pop ] % [ wmax1 wmax2 wmax3 ..] Mreva } bind def %Reverse an array /Mreva { %[a b c ..] Mreva [.. c b a] [ exch %[ [a b c ..] aload length %[a b c .. len -1 1 %[a b c .. len -1 1 {1 roll} for ] %[.. c b a] } bind def % take an array and an index and return that element if index exits % if array not long enougth return zero /Mget { %[a b c d..] index 1 index length %[a b c d..] index len -1 add 1 index %[a b c d..] index (len-1) index ge { get %if long enough return entry } { pop pop 0 %if not long enough return zero } ifelse } bind def %Take an array of arrays and return the longest length /Maxlen { %[ arr1 arr2 arr3 ] Maxlen maxlen [ %[ arr1 arr2 arr3 ] [ exch %[ [ arr1 arr2 arr3 ] { length } forall %[ len1 len2 len3.. Maxget } bind def %Take a series of numbers starting with [ and return the largest member /Maxget { %[n1 n2 n3 .. Maxget nmax counttomark %[n1 n2 n3 .. len -1 add %[n1 n2 n3 .. len-1 1 1 %[n1 n2 n3 .. len 1 1 3 -1 roll %[n1 n2 n3 .. 1 1 (len-1) { pop Mmax } for %[ nmax exch % nmax [ pop % nmax } bind def %Take a string and return an array of the lengths of the characters /Mwidthcal1 { % str Mwidthcal1 [w1 w2 w3 ..] [ exch %[ (str) { Strform stringwidth pop } forall %[w1 w2 w3 .. ] %[w1 w2 w3 ..] } bind def %put a string onto the stack /Strform { % num /tem (x) def tem 0 3 -1 roll put tem } bind def %/Mwidmax { % [str...] % dup % [str...] [str...] % [ % [str...] [str...] [ % exch % [str...] [ [str...] % { % stringwidth % pop % } % forall % [str...] [ w1 w2 ... wm wn % 0 % counttomark % [str...] [ w1 w2 ... wm wn 0 n % -2 add % [str...] [ w1 w2 ... wm wn 0 (n-1) % 1 exch % [str...] [ w1 w2 ... wm wn 0 1 (n-1) % 1 exch % [str...] [ w1 w2 ... wm wn 0 1 1 (n-1) % { % 3 index % [str...] [ w1 w2 ... wm wn num pos wm % 3 index % [str...] [ w1 w2 ... wm wn num pos wm wn % ge % { % wm >= wn % exch pop % exch pop % [str...] [ w1 w2 ... wm num % } % { % wm < wn % pop % 3 -1 roll % pop % [str...] [ w1 w2 ... wn pos < pos -> num > % } % ifelse % [str...] [ w1 w2 ... wmax nmax % } % for % [str...] [ wmax nmax % 4 1 roll % pop pop % nmax [str...] % length % nmax len % -1 add % nmax (len - 1) % exch % sub % max_pos %} bind def % Mshowa1 is an internal routine which, given a bounding box coordinate % (sz), and the bounding box limits if we started drawing at 0 (tlz and thz), % computes the offset at which to start drawing % (relz = (sz-1)tlz/2 - (sz+1)thz/2 = sz(tlz-thz)/2-(tlz+thz)/2). /Mshowa1 { % sz tlz thz Mshowa1 relz 2 copy % sz tlz thz tlz thz add % sz tlz thz tlz+thz 4 1 roll % tlz+thz sz tlz thz sub % tlz+thz sz tlz-thz mul % tlz+thz sz(tlz-thz) sub % tlz+thz-sz(tlz-thz) -2 div % sz(tlz-thz)/2-(tlz+thz)/2 } bind def % Given the x and y scaling to user coordinates and an array of points to % fit (xbias xscale ybias yscale [pnts]), set up the scaling. The array % must contain atleast two points, and the last two must be of the form % [gxlow gylow 0 0] and [gxhigh gyhigh 0 0]. % Note, MathScale assumes that we are already scaled so that the active area % is the rectangle [0,Mwidth-Mlmarg-Mrmarg]x[0,Mheight-Mbmarg-Mtmarg]. % also keep bias and scale info for PostScript commands /MathScale { % [pnts] MathScale - Mwidth % [pnts] width Mheight % [pnts] width height Mlp % Ax Ay Bx By translate % Ax Ay scale % /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix % this transforms from xscale yscale matrix scale % Original to Display coordinates xbias ybias matrix translate matrix concatmatrix def /Mgmatrix % /Mgmatrix matrix currentmatrix % /Mgmatrix graphics_matrix def % - } bind def % Given a non-empty array of points to fit ([p]) and a maximum width (sx) % and height (sy) find the largest scale (Ax and Ay) and offsets (Bx and By) % such that the transformation % [gx gy tx ty] -> (Ax gx + tx + bx, Ay gy + ty + By) % maps the points into the rectangle [0,sx]x[0,sy] /Mlp { % [p] sx sy Mlp Ax Ay Bx By 3 copy % [p] sx sy [p] sx sy Mlpfirst % [p] sx sy Ax Ay { % [p] sx sy Ax Ay Mnodistort % [p] sx sy Ax Ay nodistort? { % [p] sx sy Ax Ay Mmin % [p] sx sy A dup % [p] sx sy Ax Ay } if % [p] sx sy Ax Ay 4 index % [p] sx sy Ax Ay [p] 2 index % [p] sx sy Ax Ay [p] Ax 2 index % [p] sx sy Ax Ay [p] Ax Ay Mlprun % [p] sx sy Ax Ay ctx wtx cgx wgx cty wty cgy wgy 11 index % [p] sx sy Ax Ay ctx wtx cgx wgx cty wty cgy wgy sx 11 -1 roll % [p] sx sy Ay ctx wtx cgx wgx cty wty cgy wgy sx Ax 10 -4 roll % [p] sx sy Ay cty wty cgy wgy sx Ax ctx wtx cgx wgx Mlp1 % [p] sx sy Ay cty wty cgy wgy Ax Bx xok? 8 index % [p] sx sy Ay cty wty cgy wgy Ax Bx xok? sy 9 -5 roll % [p] sx sy Ax Bx xok? sy Ay cty wty cgy wgy Mlp1 % [p] sx sy Ax Bx xok? Ay By yok? 4 -1 roll % [p] sx sy Ax Bx Ay By yok? xok? and % [p] sx sy Ax Bx Ay By ok? { exit } if % [p] sx sy Ax Bx Ay By 3 -1 roll % [p] sx sy Ax Ay Bx By pop pop % [p] sx sy Ax Ay } loop % [p] sx sy Ax Bx Ay By exch % [p] sx sy Ax Bx By Ay 3 1 roll % [p] sx sy Ax Ay Bx By 7 -3 roll % Ax Ay Bx By [p] sx sy pop pop pop % Ax Ay Bx By } bind def % Given an array of points in the [gx gy tx ty] form, with the last two % being [gxlow gylow 0 0] and [gxhigh gyhigh 0 0], and the width and height % (sx and sy) in which to fit them, compute the maximum scaling (Ax and Ay). /Mlpfirst { % [pnts] sx sy Mlpfirst Ax Ay 3 -1 roll % sx sy [pnts] dup length % sx sy [pnts] #pnts 2 copy % sx sy [pnts] #pnts [pnts] #pnts -2 add % sx sy [pnts] #pnts [pnts] #pnts-2 get % sx sy [pnts] #pnts [gxl gyl 0 0] aload % sx sy [pnts] #pnts gxl gyl 0 0 [gxl gyl 0 0] pop pop pop % sx sy [pnts] #pnts gxl gyl 4 -2 roll % sx sy gxl gyl [pnts] #pnts -1 add % sx sy gxl gyl [pnts] #pnts-1 get % sx sy gxl gyl [gxh gyh 0 0] aload % sx sy gxl gyl gxh gyh 0 0 [gxh gyh 0 0] pop pop pop % sx sy gxl gyl gxh gyh 6 -1 roll % sy gxl gyl gxh gyh sx 3 -1 roll % sy gxl gyl gyh sx gxh 5 -1 roll % sy gyl gyh sx gxh gxl sub % sy gyl gyh sx delx div % sy gyl gyh Ax 4 1 roll % Ax sy gyl gyh exch sub % Ax sy dely div % Ax Ay } bind def % Given a non-empty array of points to fit ([pnts]) and scale factors % for graphics->text (Ax and Ay), compute the limiting points. /Mlprun { % [pnts] Ax Ay Mlprun ctx wtx cgx wgx cty wty cgy wgy 2 copy % [pnts] Ax Ay Ax Ay 4 index % [pnts] Ax Ay Ax Ay [pnts] 0 get % [pnts] Ax Ay Ax Ay [first] dup % [pnts] Ax Ay Ax Ay [first] [first] 4 1 roll % [pnts] Ax Ay [first] Ax Ay [first] Mlprun1 % [pnts] Ax Ay [first] fx fy 3 copy % [pnts] Ax Ay [low] lx ly [high] hx hy 8 -2 roll % [pnts] [low] lx ly [high] hx hy Ax Ay 9 -1 roll % [low] lx ly [high] hx hy Ax Ay [pnts] { % [low] lx ly [high] hx hy Ax Ay [pnt] 3 copy % [low] lx ly [high] hx hy Ax Ay [pnt] Ax Ay [pnt] Mlprun1 % [low] lx ly [high] hx hy Ax Ay [pnt] px py 3 copy % [low] lx ly [high] hx hy Ax Ay [pnt] px py [pnt] px py 11 -3 roll % [low] lx ly Ax Ay [pnt] px py [pnt] px py [high] hx hy /gt Mlpminmax % [low] lx ly Ax Ay [pnt] px py [high] hx hy 8 3 roll % [low] lx ly [high] hx hy Ax Ay [pnt] px py 11 -3 roll % [high] hx hy Ax Ay [pnt] px py [low] lx ly /lt Mlpminmax % [high] hx hy Ax Ay [low] lx ly 8 3 roll % [low] lx ly [high] hx hy Ax Ay } forall % [low] lx ly [high] hx hy Ax Ay pop pop pop pop % [low] lx ly [high] 3 1 roll % [low] [high] lx ly pop pop % [low] [high] aload pop % [low] hgx hgy htx hty 5 -1 roll % hgx hgy htx hty [low] aload pop % hgx hgy htx hty lgx lgy ltx lty exch % hgx hgy htx hty lgx lgy lty ltx 6 -1 roll % hgx hgy hty lgx lgy lty ltx htx Mlprun2 % hgx hgy hty lgx lgy lty ctx wtx 8 2 roll % ctx wtx hgx hgy hty lgx lgy lty 4 -1 roll % ctx wtx hgx hgy lgx lgy lty hty Mlprun2 % ctx wtx hgx hgy lgx lgy cty wty 6 2 roll % ctx wtx cty wty hgx hgy lgx lgy 3 -1 roll % ctx wtx cty wty hgx lgx lgy hgy Mlprun2 % ctx wtx cty wty hgx lgx cgy wgy 4 2 roll % ctx wtx cty wty cgy wgy hgx lgx exch % ctx wtx cty wty cgy wgy lgx hgx Mlprun2 % ctx wtx cty wty cgy wgy cgx wgx 6 2 roll % ctx wtx cgx wgx cty wty cgy wgy } bind def % Given scale factors for graphics->text (Ax and Ay) and a point in the % [gx gy tx ty] form, return the text x and y coordinate that results. /Mlprun1 { % Ax Ay [gx gy tx ty] Mlprun1 rx ry aload pop % Ax Ay gx gy tx ty exch % Ax Ay gx gy ty tx 6 -1 roll % Ay gx gy ty tx Ax 5 -1 roll % Ay gy ty tx Ax gx mul add % Ay gy ty rx 4 -2 roll % ty rx Ay gy mul % ty rx Ay*gy 3 -1 roll % rx Ay*gy ty add % rx ry } bind def % Given a low and high coordinate, compute the center and width. /Mlprun2 { % low high Mlprun2 center width 2 copy % low high low high add 2 div % low high (low+high)/2 3 1 roll % (low+high)/2 low high exch sub % (low+high)/2 high-low } bind def % Given two points stored as [gx gy tx ty] followed by the scaled % result (rx, ry), and a comparison function (lt or gt) leave the % point which is the minimum (or maximum) in each dimension. /Mlpminmax { % [pnt1] r1x r1y [pnt2] r2x r2y cmp Mlpminmax [pnt] x y cvx % [pnt1] r1x r1y [pnt2] r2x r2y cmp 2 index % [pnt1] r1x r1y [pnt2] r2x r2y cmp r2x 6 index % [pnt1] r1x r1y [pnt2] r2x r2y cmp r2x r1x 2 index % [pnt1] r1x r1y [pnt2] r2x r2y cmp r2x r1x cmp exec % [pnt1] r1x r1y [pnt2] r2x r2y cmp take2? { % [pnt1] r1x r1y [pnt2] r2x r2y cmp 7 -3 roll % [pnt2] r2x r2y cmp [pnt1] r1x r1y 4 -1 roll % [pnt2] r2x r2y [pnt1] r1x r1y cmp } if % [pnt1] r1x r1y [pnt2] r2x r2y cmp 1 index % [pnt1] r1x r1y [pnt2] r2x r2y cmp r2y 5 index % [pnt1] r1x r1y [pnt2] r2x r2y cmp r2y r1y 3 -1 roll % [pnt1] r1x r1y [pnt2] r2x r2y r2y r1y cmp exec % [pnt1] r1x r1y [pnt2] r2x r2y take2y? { % [gx ? tx ?] rx ? [? gy ? ty] ? ry 4 1 roll % [gx ? tx ?] rx ry ? [? gy ? ty] ? pop % [gx ? tx ?] rx ry ? [? gy ? ty] 5 -1 roll % rx ry ? [? gy ? ty] [gx ? tx ?] aload % rx ry ? [? gy ? ty] gx ? tx ? [gx ? tx ?] pop pop % rx ry ? [? gy ? ty] gx ? tx 4 -1 roll % rx ry ? gx ? tx [? gy ? ty] aload pop % rx ry ? gx ? tx ? gy ? ty [ % rx ry ? gx ? tx ? gy ? ty mark 8 -2 roll % rx ry ? tx ? gy ? ty mark gx ? pop % rx ry ? tx ? gy ? ty mark gx 5 -2 roll % rx ry ? tx ? ty mark gx gy ? pop % rx ry ? tx ? ty mark gx gy 6 -2 roll % rx ry ? ty mark gx gy tx ? pop % rx ry ? ty mark gx gy tx 5 -1 roll % rx ry ? mark gx gy tx ty ] % rx ry ? [pnt] 4 1 roll % [pnt] rx ry ? pop % [pnt] rx ry } { % [gx gy tx ty] rx ry ? ? ? pop pop pop % [pnt] rx ry } ifelse % [pnt] rx ry } bind def % Given a size (s), graphics->text scale (A), text center (ct), text % width (wt), graphics center (cg) and graphics width (wg), compute % a new graphics->text scale (Anew) and offset (B) and whether or not % we are done. % Note, the mysterious .99999 is magic juju which is supposed to ward % off the possibility that floating point errors would cause this % routine to return the old A and yet claim not-done. /Mlp1 { % s A ct wt cg wg Mlp1 Anew B done? 5 index % s A ct wt cg wg s 3 index sub % s A ct wt cg wg s-wt 5 index % s A ct wg cg wg s-wt A 2 index mul % s A ct wg cg wg s-wt A*wg 1 index % s A ct wg cg wg s-wt A*wg s-wt le % s A ct wg cg wg s-wt fits? 1 index % s A ct wg cg wg s-wt fits? s-wt 0 le % s A ct wg cg wg s-wt fits? impossible? or % s A ct wg cg wg s-wt done? dup % s A ct wg cg wg s-wt done? done? not % s A ct wg cg wg s-wt done? notdone? { % s A ct wg cg wg s-wt done? (not done case) 1 index % s A ct wg cg wg s-wt done? s-wt 3 index div % s A ct wg cg wg s-wt done? (s-wt)/wg .99999 mul % s A ct wg cg wg s-wt done? Anew 8 -1 roll % s ct wg cg wg s-wt done? Anew A pop % s ct wg cg wg s-wt done? Anew 7 1 roll % s Anew ct wg cg wg s-wt done? } if % s Anew ct wg cg wg s-wt done? 8 -1 roll % Anew ct wg cg wg s-wt done? s 2 div % Anew ct wg cg wg s-wt done? s/2 7 -2 roll % Anew cg wg s-wt done? s/2 ct wg pop sub % Anew cg wg s-wt done? s/2-ct 5 index % Anew cg wg s-wt done? s/2-ct Anew 6 -3 roll % Anew done? s/2-ct Anew cg wg s-wt pop pop % Anew done? s/2-ct Anew cg mul sub % Anew done? s/2-ct-Anew*cg exch % Anew B done? } bind def % The following are the workings of the tick, axes and plot labels. % NOTE a possible source of confusion is that for xticks ie tickmarks on % the x axis we keep y information and vice versa for yticks % % When Minner is found then % % assumes that box starts at zero on the left lower side % % 0) if outflag = 1 then intop = 0, inrht = 0 outflag = 0 % 1) Save intop largest top of box % 2) Save inrht largest rht of box % 3) set inflag notifies that inner marks are present % % When Mouter is found then % % if inflag is set then % 1) get vecx and vecy off the stack (points in direcn to move) % 2) vecx < 1 xadrht = inrht*abs(vecx) % 3) vecx > 1 xadlft = inrht*abs(vecx) % 4) vecy < 1 yadtop = intop*abs(vecy) % 5) vecy > 1 yadbot = intop*abs(vecy) % 6) set outflag = 1 % 7) clear inflag, inrht, intop % guaranteed to be zero if no inner is present?? % % % These all have effects in Mrotsboxa and Mrotshowa % check inflag and if set % % 1) increase top of bbox by yadtop % 2) decrease bot of bbox by yadbot % 3) increase rht of bbox by xadrht % 4) increase lft of bbox by xadlft % 5) clear outflag, yadtop, yadbot, % xadrht, xadlft % %/ /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def % This saves the top right corner of the bounding box as a side effect % This is to allow the adjustment of text placed with Mouter so that % it misses the Minner text. It is assumed that the ang is 0 % in the same way it is assumed that the text of Mouter is 0 or 90 % /Minner { % [(str)] gx gy sx sy ang Minner [(str)] gx gy sx sy ang outflag % do a bit of tidying up if necessary 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index % [(str)] gx gy sx sy ang [(str)] gsave Mtmatrix setmatrix Mvboxa pop % [(str)] gx gy sx sy ang xlow ylow xhigh yhigh grestore 3 -1 roll % [(str)] gx gy sx sy ang xlow xhigh yhigh ylow pop % [(str)] gx gy sx sy ang xlow xhigh yhigh dup % [(str)] gx gy sx sy ang xlow xhigh yhigh yhigh intop % is intop smaller than yhigh ? gt { /intop % update if it is exch def } { pop } % pop if it is not ifelse % [(str)] gx gy sx sy ang xlow xhigh dup % [(str)] gx gy sx sy ang xlow xhigh xhigh inrht % is inrht smaller than xhigh gt { /inrht % update if it is exch def } { pop } % pop if it is no ifelse % [(str)] gx gy sx sy ang xlow pop % [(str)] gx gy sx sy ang /inflag % set the inflag 1 def } bind def % This takes two number off the stack and uses them as a vector in graphics % coordinates which points in the direction in which the Mouter text is to move % it calculates the bouding box adjustments yadtop yadbot xadrht and xadlft % these are in Mboxout to adjust the bounding box to compensate. /Mouter { % vecx vecy Mouter .. /xadrht 0 def % reset everything /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag % was there an inflag ? 1 eq { dup % vecx vecy vecy 0 lt { dup % vecx vecy vecy intop % vecx vecy vecy intop mul neg % vecx vecy -vecy*intop /yadtop % make into yadtop exch def % vecx vecy } if dup % vecx vecy vecy 0 gt { dup % vecx vecy vecy intop % vecx vecy vecy intop mul % vecx vecy vecy*intop /yadbot % make into yadbot exch def % vecx vecy } if pop % vecx dup % vecx vecx 0 lt { dup % vecx vecx inrht % vecx vecx inrht mul neg % vecx -vecx*inrht /xadrht % make into xadrht exch def % vecx } if dup % vecx vecx 0 gt { dup % vecx vecx inrht % vecx vecx inrht mul % vecx vecx*inrht /xadlft % make into xadlft exch def } if pop % /outflag 1 def % set outflag } { pop pop} % ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def % % This adjusts the bounding box to account for adjacent text % This allows the two text strings to avoid each other % current matrix is the text matrix /Mboxout { % tlx tly thx thy Mboxout new_tlx new_tly new_thx new_thy outflag % do nothing unless Minner was found 1 eq { 4 -1 roll % tly thx thy tlx xadlft leadjust add % tly thx thy tlx xadlft+lead sub % tly thx thy tlx_new 4 1 roll % tlx_new tly thx thy 3 -1 roll % tlx_new thx thy tly yadbot % tlx_new thx thy tly yadbot leadjust % tlx_new thx thy tly yadbot lead add % tlx_new thx thy tly yadbot+lead sub % tlx_new thx thy tly_new 3 1 roll % tlx_new tly_new thx thy exch % tlx_new tly_new thy thx xadrht % tlx_new tly_new thy thx xadrht leadjust % tlx_new tly_new thy thx xadrht lead add % tlx_new tly_new thy thx xadrht+lead add % tlx_new tly_new thy thx_new exch % tlx_new tly_new thx_new thy yadtop % tlx_new tly_new thx_new thy yadtop leadjust % tlx_new tly_new thx_new thy yadtop lead add % tlx_new tly_new thx_new thy yadtop+lead add % tlx_new tly_new thx_new thy_new /outflag 0 def % reset everything to 0 /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def % The offsets sx and sy refer to the graphics coordinate system % thus they must be altered if a rotation has taken place. % We must also change the bounding box computations for Minner % /Mrotcheck { % sx sy ang Mrotcheck new_sx new_sy ang dup 90 eq { % % Mouter only applies to strings which are either at 0 or 90 % sort out the box adjust factors % % xadrht -> yadbot % xadlft -> yadtop % yadtop -> xadrht % yadbot -> xadlft yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup % sx sy ang ang cos % sx sy ang Cos 1 index % sx sy ang Cos ang sin % sx sy ang Cos Sin Checkaux % new_sx sx sy ang dup % new_sx sx sy ang ang cos % new_sx sx sy ang Cos 1 index % new_sx sx sy ang Cos ang sin neg % new_sx sx sy ang Cos -Sin exch % new_sx sx sy ang -Sin Cos Checkaux % new_sx new_sy sx sy ang 3 1 roll % new_sx new_sy ang sx sy pop pop % new_sx new_sy ang } bind def % % Checkaux is an auxilliary function for Mrotcheck it multiplies a % row vector by a column vector % /Checkaux { % r1 r2 dumy c1 c2 Checkaux r1 r2 dumy r1*c1+r2*c2 4 index % r1 r2 dumy c1 c2 r1 exch % r1 r2 dumy c1 r1 c2 4 index % r1 r2 dumy c1 r1 c2 r2 mul % r1 r2 dumy c1 r1 c2*r2 3 1 roll % r1 r2 dumy c2*r2 c1 r1 mul add % r1 r2 dumy c2*r2+c1*r1 4 1 roll % c2*r2+c1*r1 r1 r2 dumy } bind def % % Mboxrot converts the bounding box back from the rotated coordinate % system to the Mgmatrix system to compensate for a rotation % It has the opposite functionality of Mrotcheck % This is not the most neatest or most efficient implementation but it works % /Mboxrot { % tlx thx tly thy Mboxrot new_tlx new_thx new_tly new_thy Mrot 90 eq { % old tlx thx tly thy % new -thy -tly tlx thx % brotaux % tlx thx -thy -tly 4 2 roll % -thy -tly tlx thx } if Mrot 180 eq { % old tlx thx tly thy % new -thx -tlx -thx -tly % 4 2 roll % tly thy tlx thx brotaux % tly thy -thx -tlx 4 2 roll % -thx -tlx tlx thy brotaux % -thx -tlx -thy -tly } if Mrot 270 eq { % old tlx thx tly thy % new tly thy -thx -tlx % 4 2 roll % tly thy tlx thx brotaux % tly thy -thx -tlx } if } bind def % % auxilliary function negate and reverse /brotaux { % x y boxrotaux -y -x neg exch neg } bind def % % Mabsproc takes a measurement in the default user units and converts % it to the present units. This allows absolute thickness and dashing % to work. It works by using a {0, x} vector and using the RMS of the result. /Mabsproc { % abs thing Mabsproc 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def % % Mabswid allows the linewidth to be specified in absolute coordinates % It does this by recording the graphics transformation matrix at the % begining of the plot. % This will break if the scaling in the x and y directions is % different. This is the case if Mnodistort is false % /Mabswid { %abswid Mabswid Mabsproc setlinewidth } bind def % Mabsdash allows the dashing pattern to be specified in absolute coordinates % It does this by recording the graphics transformation matrix at the % begining of the plot. % This will break if the scaling in the x and y directions is % different. This is the case if Mnodistort is false % /Mabsdash { %[d1 d2 d3 .. ] off Mabsdash exch % off [d1 d2 d3 ..] [ % off [d1 d2 d3 ..] exch % off [ [d1 d2 d3 ..] { Mabsproc } forall ] % off [ fact*d1 fact*d2 fact*d3 .. ] exch % [ nd1 nd2 nd3 .. ] off setdash } bind def %MBeginOrig start coordinates in user coordinates /MBeginOrig { Momatrix concat} bind def %MEndOrig start coordinates in user coordinates /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { % str rate nsamp bs proc bool nchan exch pop % str rate nsamp bs proc nchan exch % str rate nsamp bs nchan proc 5 1 roll % str proc rate nsamp bs nchan mul 4 idiv % str proc rate nsamp bs*nchan/4 mul % str proc rate nsamp*bs*nchan/4 2 idiv % str proc rate nbytes exch pop % str proc nbytes exch % str nbytes proc /Mtempproc exch def { Mtempproc pop} repeat } bind def } ifelse % % now simple conversion of cmykcolor to rgbcolor % subtract k and then take complements /setcmykcolor where { pop} { /setcmykcolor { % c m y k 4 1 roll % k c m y [ % k c m y [ 4 1 roll % k [ c m y ] % k [ c m y ] { 1 index % k elem k sub % k elem-k 1 sub neg % k 1-(elem-k) dup 0 lt { pop 0 } if dup 1 gt { pop 1 } if exch % 1-(elem-k) k } forall % r g b k pop setrgbcolor } bind def } ifelse /Mcharproc % max { currentfile (x) readhexstring pop % max val 0 get exch % val max div % nval } bind def /Mshadeproc % max ncols { dup % max ncols ncols 3 1 roll % ncols max ncols { % ncols max dup % ncols max max Mcharproc % ncols max val 3 1 roll % v1.. ncols max } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc % x0 x1 y0 y1 { 3 index % x0 x1 y0 y1 x0 2 index % x0 x1 y0 y1 x0 y0 moveto % x0 x1 y0 y1 2 index % x0 x1 y0 y1 x1 3 -1 roll % x0 x1 y1 x1 y0 lineto % x0 x1 y1 dup % x0 x1 y1 y1 3 1 roll % x0 y1 x1 y1 lineto % x0 y1 lineto fill } bind def /Mcolorimage % nx ny depth matrix proc bool ncols { 7 1 roll % ncols nx ny depth matrix proc bool pop pop matrix invertmatrix concat % ncols nx ny depth 2 exch exp % ncols nx ny 2^depth 1 sub % ncols nx ny max 3 1 roll % ncols max nx ny 1 1 % ncols max nx ny 1 1 2 index % ncols max nx ny 1 1 ny { % ncols max nx ny iy 1 1 % ncols max nx ny iy 1 1 4 index % ncols max nx ny iy 1 1 nx { % ncols max nx ny iy ix dup % ncols max nx ny iy ix ix 1 sub % ncols max nx ny iy ix x0 exch % ncols max nx ny iy x0 x1 2 index % ncols max nx ny iy x0 x1 iy dup % ncols max nx ny iy x0 x1 iy iy 1 sub % ncols max nx ny iy x0 x1 iy y0 exch % ncols max nx ny iy x0 x1 y0 y1 7 index % ncols max nx ny iy x0 x1 y0 y1 max 9 index % ncols max nx ny iy x0 x1 y0 y1 max ncols Mshadeproc % ncols max nx ny iy x0 x1 y0 y1 Mrectproc % max nx ny iy } for % x loop pop % max nx ny } for % y loop pop pop pop pop } bind def /Mimage % nx ny depth matrix proc { pop matrix invertmatrix concat % nx ny depth 2 exch exp % nx ny 2^depth 1 sub % nx ny max 3 1 roll % max nx ny 1 1 % max nx ny 1 1 2 index % max nx ny 1 1 ny { % max nx ny iy 1 1 % max nx ny iy 1 1 4 index % max nx ny iy 1 1 nx { % max nx ny iy ix dup % max nx ny iy ix ix 1 sub % max nx ny iy ix x0 exch % max nx ny iy x0 x1 2 index % max nx ny iy x0 x1 iy dup % max nx ny iy x0 x1 iy iy 1 sub % max nx ny iy x0 x1 iy y0 exch % max nx ny iy x0 x1 y0 y1 7 index % max nx ny iy x0 x1 y0 y1 max Mcharproc % max nx ny iy x0 x1 y0 y1 val setgray % max nx ny iy x0 x1 y0 y1 Mrectproc % max nx ny iy } for % x loop pop % max nx ny } for % y loop pop pop pop } bind def /Ma /Mabswid load def /a /arc load def /c /curveto load def /C /curveto load def /d /setdash load def /f /fill load def /F /fill load def /g /setgray load def /gr /grestore load def /gs /gsave load def /k /stroke load def /l /lineto load def /L /lineto load def /lw /setlinewidth load def /m /moveto load def /n /newpath load def /p /gsave load def /P /grestore load def /r /setrgbcolor load def /s /stroke load def /w /setlinewidth load def /beginmath /MBeginOrig load def /endmath /MEndOrig load def end %%EndProcSet %%BeginProcSet: special.pro TeXDict begin /SDict 200 dict N SDict begin /@SpecialDefaults{/hs 612 N /vs 792 N /ho 0 N /vo 0 N /hsc 1 N /vsc 1 N /ang 0 N /CLIP 0 N /rwiSeen false N /rhiSeen false N /letter{}N /note{}N /a4{}N /legal{}N}B /@scaleunit 100 N /@hscale{@scaleunit div /hsc X}B /@vscale{@scaleunit div /vsc X}B /@hsize{/hs X /CLIP 1 N}B /@vsize{/vs X /CLIP 1 N}B /@clip{ /CLIP 2 N}B /@hoffset{/ho X}B /@voffset{/vo X}B /@angle{/ang X}B /@rwi{ 10 div /rwi X /rwiSeen true N}B /@rhi{10 div /rhi X /rhiSeen true N}B /@llx{/llx X}B /@lly{/lly X}B /@urx{/urx X}B /@ury{/ury X}B /magscale true def end /@MacSetUp{userdict /md known{userdict /md get type /dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N /note{}N /legal{} N /od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{itransform lineto} }{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{ itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{ closepath}}pathforall newpath counttomark array astore /gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}if}N /txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N /cp {pop pop showpage pm restore}N end}if}if}N /normalscale{Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale}if 0 setgray} N /psfts{S 65781.76 div N}N /startTexFig{/psf$SavedState save N userdict maxlength dict begin /magscale false def normalscale currentpoint TR /psf$ury psfts /psf$urx psfts /psf$lly psfts /psf$llx psfts /psf$y psfts /psf$x psfts currentpoint /psf$cy X /psf$cx X /psf$sx psf$x psf$urx psf$llx sub div N /psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR /showpage{}N /erasepage{}N /copypage{}N /p 3 def @MacSetUp}N /doclip{ psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N /endTexFig{end psf$SavedState restore}N /@beginspecial{SDict begin /SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count /ocount X /dcount countdictstack N}N /@setspecial {CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if /showpage{}N /erasepage{}N /copypage{}N newpath }N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{ end}repeat grestore SpecialSave restore end}N /@defspecial{SDict begin} N /@fedspecial{end}B /li{lineto}B /rl{rlineto}B /rc{rcurveto}B /np{ /SaveX currentpoint /SaveY X N 1 setlinecap newpath}N /st{stroke SaveX SaveY moveto}N /fil{fill SaveX SaveY moveto}N /ellipse{/endangle X /startangle X /yrad X /xrad X /savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet TeXDict begin 40258437 52099154 1000 300 300 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([Lam86],)f(but)h(pro)o(vides)h(a)f(n)o(um)o(b)q(er)g(of)g(additional)i (features,)d(suc)o(h)i(as:)143 367 y FA(\017)22 b FD(inclusion)c(of)c (P)o(ostScript)h(\014gures)h(in)g(the)f(do)q(cumen)o(t,)g(and)h(of)e(T) 1314 377 y(E)1340 367 y(X)h(text)g(within)h(\014gures;)143 442 y FA(\017)22 b FD(automatic)15 b(creation)g(of)g(index)h(en)o (tries)g(and)f(cross-reference)h(lab)q(els)h(where)e(appropriate;)143 516 y FA(\017)22 b FD(no)e(restriction)h(on)f(the)g(use)g(of)g(macros)f (and)h(sp)q(ecial)i(c)o(haracters)d(in)i(titles,)h(cross-references,) 188 572 y(captions,)15 b(etc.;)143 647 y FA(\017)22 b FD(greater)14 b(v)o(ersatilit)o(y)i(in)g(de\014ning)h(theorem-lik)o(e)f (en)o(vironmen)o(ts;)143 721 y FA(\017)22 b FD(uprigh)o(t)16 b(digits)f(in)i(an)e(italics)h(en)o(vironmen)o(t)g(\(optionally\);)f (and)143 795 y FA(\017)22 b FD(pro)q(o\014ng)15 b(aids)h(suc)o(h)f(as)g (v)o(ersion)h(n)o(um)o(b)q(ers)f(and)g(a)g(running)i(index.)105 885 y(There)e(are)g(also)g(purely)i(esthetic)f(di\013erences,)g(man)o (y)e(of)h(whic)o(h)h(can)g(b)q(e)f(con)o(trolled)h(b)o(y)g(the)f(user.) 188 941 y(This)h(st)o(yle)f(had)h(its)f(inception)j(in)e(a)f(set)g(of)g (L)974 935 y Fw(a)995 941 y FD(T)1020 955 y(E)1045 941 y(X)h(macros)e(written)i(for)e(the)i(formatting)e(of)h(Bill)105 998 y(Th)o(urston's)20 b Fv(Thr)n(e)n(e-Dimensional)g(Ge)n(ometry)h (and)h(T)m(op)n(olo)n(gy)p FD(,)f(\014rst)f(b)o(y)h(Y)l(air)g(Minsky)g (and)g(subse-)105 1054 y(quen)o(tly)15 b(b)o(y)f(me.)19 b(After)14 b(three)g(y)o(ears)g(of)g(gestation,)f(the)h(macros)g (started)f(b)q(eing)i(used)g(in)o(tensiv)o(ely)h(b)o(y)105 1111 y(some)c(other)g(p)q(eople|notably)j(Th)o(urston,)d(Da)o(vid)g (Epstein)i(and)e(a)g(n)o(um)o(b)q(er)h(of)f(studen)o(ts)g(at)g(W)l (arwic)o(k)105 1167 y(Univ)o(ersit)o(y|and)20 b(more)f(mo)q (di\014cations,)h(includin)q(g)h(a)e(complete)h(rewrite,)f(w)o(ere)g (made.)31 b(The)19 b(\014rst)105 1223 y(b)q(o)q(ok)c(published)j(using) e(the)f FB(geom)g FD(st)o(yle)g([ECL)941 1207 y Fu(+)969 1223 y FD(92])f(came)h(out)g(in)h(F)l(ebruary)f(1992.)188 1280 y(The)e(App)q(endix)h(to)e(this)g(do)q(cumen)o(t)h(describ)q(es)h FB(mathfig)p FD(,)e(a)g(system)f(for)h(t)o(yp)q(esetting)h(T)1721 1290 y(E)1746 1280 y(X)f(lab)q(els)105 1336 y(in)18 b(Mathematica)f (\014gures.)28 b(\(Mathematica)16 b(is)j(describ)q(ed)g(in)g([W)l (ol91]\).)25 b(This)19 b(system)e(can)h(also)f(b)q(e)105 1393 y(used)f(indep)q(enden)o(tly)i(of)d FB(geom)p FD(.)188 1449 y(This)i(release)g(o)o(w)o(es)e(m)o(uc)o(h)h(to)f(the)i(patience)g (of)f(these)g(\014rst)g(users)g(and)g(the)g(feedbac)o(k)h(they)f(pro-) 105 1506 y(vided,)i(for)d(whic)o(h)j(I)e(am)g(v)o(ery)h(grateful.)23 b(Naturally)l(,)17 b(m)o(y)f(debt)h(to)f(the)g(p)q(eople)i(on)e(whose)h (w)o(ork)e(I'v)o(e)105 1562 y(built|Don)k(Kn)o(uth,)g(Leslie)g(Lamp)q (ort,)f(Rainer)h(Sc)o(h\177)-23 b(opf,)18 b(F)l(rank)f(Mittelbac)o(h,)i (T)l(rev)o(or)e(Darrell)h(and)105 1619 y(others|is)e(imp)q(ossible)i (to)d(quan)o(tify)l(.)22 b(I)16 b(wish)h(to)e(tak)o(e)g(this)h(opp)q (ortunit)o(y)g(to)f(thank)h(them,)f(and)h(also)105 1675 y(John)j(Ra)o(wnsley)l(,)h(who)e(pro)o(vided)i(the)e(p)q(ort)h(to)f(L) 982 1669 y Fw(a)1003 1675 y FD(T)1028 1689 y(E)1053 1675 y(X2)1110 1682 y Ft(")1128 1675 y FD(.)30 b(I)19 b(also)f(thank)h(Al)g (Marden,)g(the)f(F)l(ound-)105 1732 y(ing)h(Director)f(of)f(the)i (Geometry)e(Cen)o(ter,)h(for)g(creating)g(the)g(conditions)i(needed)f (for)f(this)g(w)o(ork)g(to)105 1788 y(happ)q(en.)105 1914 y FE(2.)24 b(Ov)n(erall)18 b(Organization)105 2015 y FD(In)26 b(order)e(to)g(use)i(this)f(st)o(yle,)i(y)o(ou)e(need)g(to)g (b)q(e)g(running)h(a)f(v)o(ersion)g(of)f(L)1495 2009 y Fw(a)1516 2015 y FD(T)1541 2029 y(E)1567 2015 y(X)h(that)f(supp)q (orts)105 2072 y(the)g(so-called)i(new)f(fon)o(t)e(selection)j(sc)o (heme)f(\(NFSS\),)f(due)h(to)e(F)l(rank)h(Mittelbac)o(h)h(and)g(Rainer) 105 2128 y(Sc)o(h\177)-23 b(opf.)34 b(If)19 b(y)o(our)h(v)o(ersion)g (of)f(L)668 2122 y Fw(a)689 2128 y FD(T)714 2142 y(E)739 2128 y(X)h(is)g(L)855 2122 y Fw(a)876 2128 y FD(T)901 2142 y(E)927 2128 y(X2)984 2135 y Ft(")1001 2128 y FD(,)h(y)o(ou)e(are) h(automatically)g(using)g(NFSS.)g(If)f(y)o(our)105 2185 y(v)o(ersion)i(is)h(L)329 2179 y Fw(a)350 2185 y FD(T)375 2198 y(E)401 2185 y(X2.09,)f(y)o(ou)g(m)o(ust)g(c)o(hec)o(k)g(whether)g (it)h(supp)q(orts)f(NFSS.)g(Start)g(L)1597 2179 y Fw(a)1618 2185 y FD(T)1643 2198 y(E)1668 2185 y(X)g(and)h(t)o(yp)q(e)105 2241 y FB(\\show\\selectfont)p FD(.)c(If)d(the)g(resp)q(onse)h (includes)147 2335 y Fs(>)21 b(\\selectfont=undefi)o(ned.)105 2435 y FD(this)12 b(is)g(the)g(wrong)f(L)452 2429 y Fw(a)473 2435 y FD(T)498 2448 y(E)523 2435 y(X.)g(Don't)g(despair)h(y)o(et;)g (the)g(righ)o(t)f(L)1138 2429 y Fw(a)1159 2435 y FD(T)1184 2448 y(E)1210 2435 y(X)g(ma)o(y)g(b)q(e)h(a)o(v)m(ailable)i(at)d(y)o (our)g(site,)h(but)105 2491 y(under)19 b(a)e(di\013eren)o(t)h(name|try) g FB(amslatex)p FD(,)f(or)g(ask)g(y)o(our)h(lo)q(cal)h(guru.)27 b(\(Strictly)19 b(sp)q(eaking,)g FA(A)1813 2501 y(M)1862 2491 y(S)p FD(-)105 2548 y(L)117 2542 y Fw(a)138 2548 y FD(T)163 2561 y(E)189 2548 y(X)e([Ame])g(is)h(a)f(set)h(of)f(L)603 2542 y Fw(a)624 2548 y FD(T)649 2561 y(E)674 2548 y(X)h(st)o(yle)f (\014les)i(that)e(em)o(ulate)g FA(A)1229 2557 y(M)1279 2548 y(S)p FD(-T)1347 2557 y(E)1372 2548 y(X.)g(Since)i(their)f(use)g (requires)105 2604 y(NFSS)d(and)g(the)f(necessary)h(mo)q(di\014cations) h(used)f(to)f(b)q(e)h(supplied)i(with)e(the)g FA(A)1486 2614 y(M)1536 2604 y(S)p FD(-L)1591 2598 y Fw(a)1612 2604 y FD(T)1637 2618 y(E)1662 2604 y(X)g(st)o(yle)f(\014les,)105 2729 y(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 3 3 3 2 bop 105 -25 a Fz(3.)17 b(Installation)1546 b(3)-225 116 y FL(\045)10 b(Installation)-225 145 y(calling)j Fy(geom)-225 174 y FL(Section)d(\\Installation")-225 203 y(\045)h(Ov)o(erall)i(Organiza-)-183 232 y(tion)105 120 y FD(the)18 b(name)g(is)h(sometimes)f(used)g(for)g(L)773 114 y Fw(a)794 120 y FD(T)819 134 y(E)844 120 y(X+NFSS.\))g(If)h(y)o (ou)e(can't)h(\014nd)h(L)1436 114 y Fw(a)1457 120 y FD(T)1482 134 y(E)1507 120 y(X+NFSS)g(at)e(all,)j(see)105 177 y(further)15 b(instructions)h(in)g(Section)g(3.)188 233 y(Unlik)o(e)21 b(most)e(other)g(L)586 227 y Fw(a)607 233 y FD(T)632 247 y(E)658 233 y(X)h(st)o(yles,)g FB(geom)g FD(comes)f(in)i(sev)o (eral)f(\014les,)h(dev)o(oted)f(to)f(di\013eren)o(t)h(ca-)105 289 y(pabilities)g(suc)o(h)d(as)g(cross-referencing,)h(\014gures,)g (indexing)h(and)e(so)g(on.)26 b(The)17 b(\014les)h(curren)o(tly)g(in)g (the)105 346 y(distribution)f(are:)105 427 y Fs(dvips.chg)105 476 y(geom.sty)105 526 y(geomar10.sty)105 576 y(geomar11.sty)105 626 y(geomar12.sty)105 676 y(geomart.sty)105 725 y(geombk10.sty)105 775 y(geombk11.sty)105 825 y(geombk12.sty)490 427 y Fr(driv)o(er)d(dep) q(endencies)490 476 y(master)g(\014le)490 526 y(c)o(hanges)h(to)e Fs(art10.sty)490 576 y Fr(c)o(hanges)i(to)e Fs(art11.sty)490 626 y Fr(c)o(hanges)i(to)e Fs(art12.sty)490 676 y 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FB(book)f FD(or)g FB(article)p FD(.)31 b(That)19 b(is,)i(to)d(use)i(the)g(stu\013)105 1051 y(describ)q(ed)d(in)f(this)g (do)q(cumen)o(t,)f(y)o(our)g(text)f(\014le)j(should)f(start)e(with)h(a) g(line)i(suc)o(h)f(as)147 1146 y Fs(\\documentstyle[)o(12pt,)o(geom,)o (...]{)o(book)o(})105 1248 y FD(When)e FB(geom.sty)f FD(is)i(loaded)f(in,)h(it)f(guesses)g(what)g(y)o(our)f(main)h(st)o(yle) g(is,)h(and)f(reads)g(in)g(some)g(c)o(hanges)105 1304 y(to)h(that)f(st)o(yle,)h(con)o(tained)h(in)g(the)f(\014les)h FB(geombook.sty)p FD(,)d FB(geombk12.sty)p FD(,)h(and)h(so)g(on.)188 1360 y(The)h(\014le)h FB(multicol.sty)d FD(is)i(part)f(of)g(the)h(pac)o (k)m(age)g(\014les)g(dev)o(elop)q(ed)i(b)o(y)d(F)l(rank)g(Mittelbac)o (h)i(and)105 1417 y(Rainer)i(Sc)o(h\177)-23 b(opf)18 b(at)g(the)g(Univ)o(ersit)o(y)h(of)e(Mainz.)29 b(It)18 b(is)h(accompanied)g(b)o(y)f FB(multicol.doc)p FD(,)f(whic)o(h)h(is)105 1473 y(a)g(\\source")g(\014le)h(with)g(do)q(cumen)o(tation.)30 b(T)l(o)18 b(obtain)h(more)f(of)g(the)g(excellen)o(t)i(soft)o(w)o(are)d (written)h(b)o(y)105 1530 y(Mittelbac)o(h)e(and)f(Sc)o(h\177)-23 b(opf,)15 b(c)o(hec)o(k)h(the)f(CT)l(AN)g(arc)o(hiv)o(es)h(\(see)f(the) g(Installation)h(section)g(b)q(elo)o(w\).)188 1586 y(The)k(rest)g(of)g (this)g(do)q(cumen)o(t)h(describ)q(es)h(the)e(installation)h(of)f FB(geom)g FD(\(skip)g(if)h(it's)f(already)g(in-)105 1643 y(stalled\),)j(its)f(ma)s(jor)e(features,)i(and)g(ho)o(w)e(y)o(ou)i (can)f(tak)o(e)g(adv)m(an)o(tage)g(of)g(them)g(and)h(\(sometimes\))105 1699 y(mo)q(dify)17 b(them.)25 b(Some)17 b(material)g(that)f(is)i (either)f(v)o(ery)g(tec)o(hnical)h(or)e(unlik)o(ely)k(to)c(b)q(e)h (needed)h(except)105 1756 y(under)e(un)o(usual)g(circumstances)g(is)g (prin)o(ter)f(in)h(smaller)g(t)o(yp)q(e)g(and)f(in)o(tro)q(duced)h(b)o (y)g(an)f(asterisk)g FA(\003)p FD(.)105 1882 y FE(3.)24 b(Installation)105 1983 y FD(Y)l(ou)e(only)f(need)i(to)d(read)i(this)f (section)h(if)g(y)o(ou)f(are)g(in)h(c)o(harge)f(of)g(installing)j FB(geom)c FD(at)h(y)o(our)g(site.)105 2040 y(Installation)16 b(is)f(v)o(ery)f(simple)i(if)f(y)o(our)f(L)787 2034 y Fw(a)808 2040 y FD(T)833 2053 y(E)858 2040 y(X)h(supp)q(orts)g(NFSS)f (and)h(y)o(our)f(T)1437 2049 y(E)1463 2040 y(X-to-P)o(ostScript)g(driv) o(er)105 2096 y(is)i(T)l(om)f(Rokic)o(ki's)h FB(dvips)e FD([Rok].)188 2152 y(T)l(o)g(c)o(hec)o(k)h(whether)g(y)o(ou)g(ha)o(v)o (e)f(L)752 2146 y Fw(a)773 2152 y FD(T)798 2166 y(E)824 2152 y(X+NFSS,)h(see)g(the)f(b)q(eginning)j(of)e(Section)g(2.)20 b(If)14 b(y)o(ou)h(don't,)105 2209 y(it's)e(time)h(to)f(switc)o(h)g(o)o (v)o(er)g(to)g(L)635 2203 y Fw(a)656 2209 y FD(T)681 2223 y(E)706 2209 y(X2)763 2216 y Ft(")781 2209 y FD(.)19 b(Get)13 b(it)h(b)o(y)f(ftp)g(from)g(one)h(of)f(the)g(w)o(orldwide)h (CT)l(AN)g(arc)o(hiv)o(es)105 2265 y(\(curren)o(tly)h FB(pip.shsu.edu)p FD(,)f FB(ftp.uni-stuttgart.de)p FD(,)e(and)j FB(tex.ac.uk)p FD(\).)188 2322 y(If)g(y)o(our)g(driv)o(er)g(is)g(not)g FB(dvips)p FD(,)e(y)o(ou)i(ha)o(v)o(e)f(t)o(w)o(o)g(c)o(hoices:)21 b(either)15 b(install)h FB(dvips)p FD(,)e(whic)o(h)i(is)f(almost)105 2378 y(certainly)22 b(a)f(go)q(o)q(d)g(idea)h(\(get)e(it)i(b)o(y)f(ftp) g(from)f(a)h(CT)l(AN)g(arc)o(hiv)o(e\);)j(or)c(mak)o(e)h(a)g(cop)o(y)g (of)g(the)g(\014le)105 2435 y FB(dvips.chg)12 b FD(in)i(this)f (distribution,)i(and)e(mo)q(dify)h(it)g(so)e(it)i(writes)f(the)g FB(\\special)f FD(commands)h(required)105 2491 y(b)o(y)i(y)o(our)g (driv)o(er.)21 b(If)15 b(y)o(ou)g(adapt)g FB(dvips.chg)f FD(for)h(y)o(our)g(driv)o(er,)g(giv)o(e)g(the)h(new)f(\014le)i(a)e (di\013eren)o(t)g(name,)105 2548 y(and)i(replace)h(with)f(this)g(name)f (all)i(o)q(ccurrences)g(of)e FB(dvips.chg)f FD(in)j(the)f(rest)f(of)g (this)h(section.)25 b(Also,)105 2604 y(please)16 b(send)g(me)f(a)g(cop) o(y)g(of)g(the)g(\014le,)h(so)f(I)g(can)h(include)h(it)f(in)g(future)f (distributions.)105 2729 y(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 4 4 4 3 bop 105 -25 a Fz(4.)17 b(No)c(More)g(F)m(ragile)h(Commands)1261 b(4)-225 116 y FL(Section)15 b(\\No)-183 145 y(More)e(F)n(ragile)-183 174 y(Commands")188 120 y FD(As)18 b(I)h(w)o(as)e(sa)o(ying)h(b)q (efore)h(I)f(got)g(sidetrac)o(k)o(ed,)h(installation)g(is)g(simple.)30 b(If)19 b(y)o(ou're)e(on)h(a)g(UNIX)105 177 y(system,)f(edit)g(the)h FB(Makefile)d FD(to)i(mak)o(e)f(sure)i(the)f(pathnames)g(are)f(correct) h(for)f(y)o(our)h(site,)g(and)h(run)105 233 y FB(make)23 b(install)p FD(.)c(If)d(y)o(ou're)e(not)h(on)g(a)g(UNIX)h(system,)e (here)i(are)f(the)g(step-b)o(y-step)h(instructions:)188 289 y(Place)g(the)f(\014les)h(listed)g(in)g(the)f(previous)g(section)h (\(all)g(the)f(distribution)h(\014les)g(that)e(end)i(in)g FB(.sty)p FD(,)105 346 y FB(.chg)j FD(or)h FB(.doc)p FD(\))f(in)i(the)f(system-wide)h(directory)f(for)f(T)1114 356 y(E)1140 346 y(X)h(input)h(\014les.)35 b(Create)20 b(a)f(sym)o(b)q(olic)j(link)105 402 y FB(driver.chg)c FD(in)j(this)f(directory)l(,)h(p)q(oin)o(ting)g(to)e FB(dvips.chg)p FD(.)33 b(\(If)20 b(y)o(our)f(system)g(do)q(es)h(not)g (supp)q(ort)105 459 y(sym)o(b)q(olic)c(links,)h(cop)o(y)e FB(dvips.chg)f FD(to)g FB(driver.chg)p FD(.\))188 515 y(Cop)o(y)h(the)h(\014le)h FB(mathlabels.orig)d FD(to)h FB(mathlabels)g FD(and)h(edit)g(its)h(\014rst)e(line)j(to)d(b)q(e)h (the)g(correct)105 572 y(pathname)f(of)g(the)h(p)q(erl)g(executable)h (on)e(y)o(our)g(system.)20 b(\(If)15 b(y)o(ou)g(don't)g(ha)o(v)o(e)g FB(perl)g FD(at)f(all,)i(y)o(ou)f(don't)105 628 y(kno)o(w)10 b(what)h(y)o(ou're)f(missing|get)i(it)f(as)g(so)q(on)f(as)h(p)q (ossible.\))20 b(Decide)12 b(on)f(a)f(directory)h(where)g(y)o(ou)g(w)o (an)o(t)105 685 y(to)j(install)i(the)f(auxiliary)h(scripts)g FB(mathlabels)d FD(and)i FB(geomfix)f FD(\(whic)o(h)h(are)f(used)i(b)o (y)f FB(mathfig)p FD(\),)e(and)105 741 y(put)i(copies)g(of)f(them)h (there.)20 b(Cop)o(y)14 b(the)h(\014le)g FB(mathfig.orig)e FD(to)h FB(mathfig)g FD(and)h(edit)g(the)g(lines)h(at)e(the)105 798 y(top)h(to)g(sp)q(ecify)h(the)g(lo)q(cation)g(of)f(the)g FB(mathlabels)f FD(and)i FB(geomfix)e FD(scripts,)h(then)h(cop)o(y)f FB(mathlabels)105 854 y FD(to)g(a)f(system-wide)i(directory)g(for)e (executables.)188 910 y(Finally)l(,)20 b(cop)o(y)d FB(math.pro)g FD(and)h FB(illustrator.pro)d FD(in)o(to)j(the)g(directory)g(where)g(y) o(our)f(T)1775 920 y(E)1800 910 y(X-to-)105 967 y(P)o(ostScript)d(driv) o(er)h(lo)q(oks)g(for)e(prolog)i(\014les.)20 b(\(This)15 b(assumes)f(y)o(our)g(driv)o(er)h(supp)q(orts)f(the)h(inclusion)h(of) 105 1023 y(prolog)f(\014les;)h(switc)o(h)f(to)g FB(dvips)f FD(if)i(it)f(do)q(esn't.\))105 1149 y FE(4.)24 b(No)19 b(More)f(F)-5 b(ragile)18 b(Commands)105 1251 y FD(In)13 b(standard)e(L)357 1245 y Fw(a)378 1251 y FD(T)403 1264 y(E)429 1251 y(X,)g(commands)h(suc)o(h)g(as)g FB(\\section)f FD(ha)o(v)o(e)g Fv(moving)i(ar)n(guments)p FD(,)f(that)f(is,)i(argumen) o(ts)105 1307 y(that)k(migrate)g(to)f(an)i(auxiliary)g(\014le)h Fv(jobname)p FB(.aux)d FD(to)h(b)q(e)h(used)g(later)f(in)i(t)o(yp)q (esetting)e(the)h(table)f(of)105 1364 y(con)o(ten)o(ts)g(and)h(so)f(on) h([Lam86,)f(33{34].)25 b(In)19 b(this)f(pro)q(cess,)g(macros)f(in)i (the)e(b)q(o)q(dy)i(of)e(the)h(argumen)o(t)105 1420 y(are)d(expanded,)h (so)f(that)f(when)i(y)o(ou)f(t)o(yp)q(e,)g(sa)o(y)l(,)147 1514 y Fs(\\section{Annoyi)o(ng)k(\\TeX)i(nicalities})105 1615 y FD(what)15 b(go)q(es)g(in)o(to)g(the)g(auxiliary)i(\014le)f(is)g (something)f(lik)o(e)147 1710 y Fs(\\@writefile{toc)o(}{\\st)o(ring\\)o (conte)o(ntsl)o(ine\\s)o(pace)j({chapter}{\\string\\n)o(umber)o(line\\) o(space)147 1760 y({1}Annoying)h(T\\kern)i(-.1667em\\lower)d (.5ex\\hbox)i({E}\\kern)h(-.125emXnicalit)o(ies}{)o(1}})105 1861 y FD(where)15 b(the)h(second)f(line)i(con)o(tains)f(the)f (expansion)h(of)f(the)g(macro)g FB(\\TeX)p FD(.)188 1917 y(There)i(are)g(sev)o(eral)g(problems)g(with)g(this.)25 b(First,)17 b(the)g(expansion,)h(and)f(consequen)o(tly)g(the)g(line)105 1974 y(where)12 b(it)h(o)q(ccurs)f(in)h(the)g(auxiliary)g(\014le,)h (can)e(b)q(e)h(v)o(ery)f(long,)h(whic)o(h)g(in)g(some)f(implemen)o (tations)h(means)105 2030 y(that)j(T)230 2040 y(E)255 2030 y(X)h(cannot)f(read)g(the)h(line)h(bac)o(k)f(in.)24 b(Secondly)l(,)18 b(the)f(expansion)g(migh)o(t)g(not)f(mak)o(e)g (sense,)g(or)105 2086 y(migh)o(t)f(do)f(the)h(wrong)f(thing,)h(at)g (the)g(time)g(when)g(it)g(is)g(read)g(in)h(again.)k(Ev)o(en)14 b(w)o(orse,)g(the)h(expansion)105 2143 y(of)g FB(\\section{\\small)22 b(foo})p FD(,)14 b(for)g(example,)i(actually)g(causes)f(an)h (in\014nite)h(lo)q(op.)105 2216 y Fq(\003)78 b Fr(Exp)q(erienced)19 b(users)e(of)f(T)622 2225 y(E)645 2216 y(X)h(who)f(w)o(an)o(t)f(to)i (kno)o(w)e(wh)o(y)h(this)h(happ)q(ens)g(can)g(try)f(t)o(yping)g(the)h (follo)o(wing)105 2266 y(lines)d(to)g(plain)e(T)377 2275 y(E)400 2266 y(X:)147 2360 y Fs(\\def\\foo{\\let\\b)o(ar\\fo)o(o})147 2410 y(\\foo)435 b(\045Nothing)20 b(much)h(happens)147 2460 y(\\immediate\\writ)o(e0{\\f)o(oo})e(\045Disaster)g(strikes)105 2554 y Fr(The)13 b(problem)e(is)h(that)h(at)f(the)h(time)f(of)f(the)i Fs(\\write)f Fr(no)g(assignmen)o(t)f(is)i(taking)e(place,)i(so)f(the)h Fs(\\foo)f Fr(at)g(the)h(end)105 2604 y(of)g(the)i(expansion)f(is)f (not)h(handled)g(as)g(a)f(literal.)105 2729 y FD(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 5 5 5 4 bop 105 -25 a Fz(5.)17 b(Lab)q(els)d(and)g(Cross-References)1257 b(5)-225 116 y FL(\045)13 b(Theorems)d(and)-183 145 y(Their)g(F)n (riends)-225 174 y(\045)g(P)o(ostScript)i(Figures)-225 203 y(Section)f(\\Lab)q(els)h(and)-183 232 y(Cross-References")-225 261 y(\045)h(Theorems)d(and)-183 290 y(Their)g(F)n(riends)188 120 y FD(Standard)k(L)396 114 y Fw(a)417 120 y FD(T)442 134 y(E)468 120 y(X's)f(solution)i(to)f(these)g(problems)h(is)f(for)g (the)g(user)g(to)f(precede)j(\\fragile")e(macros)105 177 y(with)19 b(the)h FB(\\protect)d FD(command)i([Lam86,)g(33{34].)30 b(By)19 b(con)o(trast,)f(in)i(the)f FB(geom)g FD(st)o(yle,)h(y)o(ou)e (don't)105 233 y(ha)o(v)o(e)d(to)f(w)o(orry)g(ab)q(out)h(\\fragile")h (commands)f(in)h(the)f(follo)o(wing)h(situations:)143 323 y FA(\017)22 b FD(in)16 b(the)f(argumen)o(ts)g(of)f(the)i (sectioning)g(commands)f FB(\\chapter)p FD(,)f FB(\\section)p FD(,)f(and)j(so)f(on;)143 398 y FA(\017)22 b FD(in)16 b(the)f(optional)h(argumen)o(t)f(to)f(the)h FB(theorem)g FD(en)o(vironmen)o(t)g(and)g(its)h(relativ)o(es)f(\(Section)h(6\);)143 472 y FA(\017)22 b FD(in)16 b(the)f(argumen)o(ts)g(to)f FB(\\caption)p FD(,)g FB(\\fig)h FD(and)g(its)g(relativ)o(es)h (\(Section)g(10\);)143 546 y FA(\017)22 b FD(in)16 b(the)f(argumen)o (ts)g(to)f FB(\\markright)g FD(and)h FB(\\markboth)p FD(;)143 621 y FA(\017)22 b FD(in)16 b(the)f(argumen)o(t)g(to)f FB(\\cite)p FD(.)105 711 y(This)g(co)o(v)o(ers)e(almost)h(all)h(imp)q (ortan)o(t)e(situations)i(where)f(fragile)h(commands)f(need)g(to)g(b)q (e)h FB(\\protect)p FD(ed)105 768 y([Lam86,)20 b(151].)35 b(In)21 b(future)f(v)o(ersions)h(I)g(hop)q(e)g(to)f(extend)h(this)f(p)q (ermissiv)o(eness)j(to)c(the)i(remaining)105 824 y(situations.)188 880 y(Notice,)g(ho)o(w)o(ev)o(er,)f(that)f(the)h FB(\\verb|...|)f FD(construction)h(con)o(tin)o(ues)g(to)f(b)q(e)i(forbidden)g(inside)105 937 y(argumen)o(ts)15 b(to)g(most)h(commands.)22 b(This)16 b(is)h(due)f(to)f(reasons)h(deeply)h(em)o(b)q(edded)h(in)f(T)1633 947 y(E)1658 937 y(X)f(itself,)h(and)105 993 y(is)f(unlik)o(ely)h(ev)o (er)e(to)g(c)o(hange.)105 1067 y Fq(\003)77 b Fr(In)14 b(some)g(circumstances)h(y)o(ou)g(migh)o(t)d(w)o(an)o(t)i(the)i(old)d (L)1080 1062 y Fp(a)1099 1067 y Fr(T)1122 1079 y(E)1146 1067 y(X)i(b)q(eha)o(vior)f(of)g(macro)f(expansion)i(inside)f(the)105 1116 y(argumen)o(t)g(of)g Fs(\\chapter)p Fr(,)f(sa)o(y)m(.)20 b(F)m(or)14 b(instance,)i(y)o(ou)e(migh)o(t)f(ha)o(v)o(e)i(a)f(lo)q (cally)f(de\014ned)j(macro)e(whose)h(de\014nition)105 1166 y(will)g(b)q(e)i(unkno)o(wn)f(at)h(the)g(time)e(the)i(table)f(of)g (con)o(ten)o(ts)i(is)e(read.)26 b(In)17 b(this)f(case)i(y)o(ou)e(can)g (use)i(the)f(follo)o(wing)105 1216 y(construction:)147 1311 y Fs(\\edef\\mystring{)o(...})h(\045)k(where)f(...)g(stands)f(for) i(the)f(argument)f(to)h(be)h(expanded)147 1361 y(\\expandafter\\ch)o (apter)o(\\expa)o(ndaft)o(er{\\)o(mystr)o(ing})105 1486 y FE(5.)i(Lab)r(els)18 b(and)h(Cross-References)105 1588 y FD(In)i(standard)f(L)374 1582 y Fw(a)395 1588 y FD(T)420 1602 y(E)445 1588 y(X,)g(the)g(argumen)o(t)g(to)f(the)i FB(\\label)e FD(command)h(cannot)g(con)o(tain)g(an)o(ything)h(but)105 1644 y(c)o(haracters)10 b(\(after)g(expansion\).)19 b(In)12 b(the)f FB(geom)g FD(st)o(yle,)g(this)h(restriction)f(is)h(lifted,)h (so)d(lab)q(els)j(con)o(tain)e(just)105 1701 y(ab)q(out)17 b(an)o(ything.)25 b(F)l(or)16 b(example,)h FB(\\label{\\TeX})f FD(and)h FB(\\label{Isometries)k(of)j($\\bold)f(R^2$})105 1757 y FD(are)15 b(acceptable.)21 b(Macros)14 b(are)h(no)g(longer)g (expanded.)188 1814 y(One)j(adv)m(an)o(tage)g(of)f(this)h(\015exibilit) o(y)i(is)f(that)e(sub)q(divisions)j(can)e(b)q(e)g(automatically)g(lab)q (eled)i(b)o(y)105 1870 y(their)e(titles.)28 b(In)18 b(the)f FB(geom)g FD(format,)g(b)o(y)g(default,)i(ev)o(ery)e(sectioning)i (command)e(suc)o(h)h(as)f FB(\\section)105 1927 y FD(generates)g(a)h (lab)q(el)h(with)f(its)g(title.)29 b(If)18 b(this)g(feature)f(causes)h (y)o(ou)g(to)f(run)h(out)f(of)h(memory)l(,)f(y)o(ou)h(can)105 1983 y(turn)d(it)h(o\013)e(b)o(y)h(sa)o(ying)g FB(\\autolabelfalse)e FD(in)j(y)o(our)f(do)q(cumen)o(t's)g(pream)o(ble.)188 2040 y(T)l(o)31 b(refer)g(to)f(the)h(place)h(where)f(a)g(lab)q(el)i(o)q (ccurs,)i(y)o(ou)30 b(can)i(still)g(use)f(the)h FB(\\ref)e FD(com-)105 2096 y(mand,)20 b(as)f(in)i(standard)e(L)573 2090 y Fw(a)594 2096 y FD(T)619 2110 y(E)644 2096 y(X.)g(This)h(giv)o (es)g(a)f(bald)h(n)o(um)o(b)q(er|for)g(example,)h FB(\\ref{Isometries) 105 2152 y(of)j($\\bold)f(R^2$})g FD(will)j(prin)o(t)e(\\8.3")f(if)i (Section)g(8.3)e(starts)g(with)h FB(\\section{Isometries)d(of)105 2209 y($\\bold)i(R^2$})15 b FD(while)h(automatic)f(lab)q(eling)i(is)f (in)g(e\013ect.)188 2265 y(A)g(new)g(feature)f(is)i(that)e(y)o(ou)g (can)h(replace)h FB(\\ref)e FD(b)o(y)h FB(\\fullref)e FD(or)i FB(\\Fullref)p FD(,)e(to)h(get)h(\\section)105 2322 y(8.3")j(or)h(\\Section)i(8.3",)e(resp)q(ectiv)o(ely)l(.)38 b(The)21 b(w)o(a)o(y)e FB(\\fullref)g FD(w)o(orks)h(is)h(b)o(y)g (storing)f(in)h(a)g(certain)105 2378 y(register)c(the)g(t)o(yp)q(e)h (of)e(en)o(vironmen)o(t)i(in)g(whic)o(h)g(a)f(lab)q(el)i(w)o(as)d (created.)26 b(Th)o(us,)17 b(when)h(a)f(new)g(section)105 2435 y(starts,)d(this)i(register)g(gets)f(the)h(v)m(alue)h(\\section".) k(When)16 b(a)f FB(\\begin)g FD(command)h(in)o(tro)q(ducing)h(one)e(of) 105 2491 y(the)g(en)o(vironmen)o(ts)f(describ)q(ed)j(in)e(Section)g(6)f (is)h(encoun)o(tered)h(inside)g(this)f(section,)g(the)f(register)g (gets)105 2548 y(up)q(dated)j(to)e(the)h(t)o(yp)q(e)g(of)f(that)g(en)o (vironmen)o(t,)h(sa)o(y)f(\\theorem".)21 b(It)16 b(rev)o(erts)f(to)g (\\section")h(when)g(the)105 2604 y(matc)o(hing)f FB(\\end)g FD(command)g(is)h(read.)105 2729 y(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 6 6 6 5 bop 105 -25 a Fz(6.)17 b(Theorems)c(and)h(Their)g(F)m(riends)1256 b(6)-225 116 y FL(Theorem)8 b(\\Erd\177)-15 b(os")-225 145 y Fx(Kur)o(dish)-225 174 y FL(\045)10 b(Erd\177)-15 b(os)-225 203 y(\045)10 b(circle)-225 232 y(\045)g(Kurdish)-225 261 y(Erd\177)-15 b(os)-225 290 y(\045)10 b(circle)-225 319 y(\045)g(circle)-225 348 y(Section)i(\\Theorems)-183 377 y(and)e(Their)g(F)n(riends")188 120 y FD(Ev)o(en)17 b(if)h(y)o(ou)e(ha)o(v)o(e)h(nested)g(en)o(vironmen)o(ts,)g(lab)q(els)i (placed)f(in)g(eac)o(h)f(of)g(them)g(are)f(assigned)i(the)105 177 y(correct)d(t)o(yp)q(e.)20 b(Consider)15 b(the)h(input)147 276 y Fs(\\newtheorem[{\\p)o(ar\\la)o(rge}{)o(\\it}])o({the)o(orem})o ({Theo)o(rem}[)o(secti)o(on])147 326 y(\\equationwith{t)o(heore)o(m}) 389 b(\045)22 b(These)f(two)g(lines)g(are)g(explained)147 376 y(...)805 b(\045)22 b(in)f(later)g(sections)147 426 y(\\begin{theorem})o([Erd\\)o("os])147 475 y(A)g(theorem)f(both)h(deep) g(and)h(profound)e(/)h(Is)h(that)f(a)g(circle)g(is)g(round:)147 525 y(\\begin{equation)o(})147 575 y(\\mathrm{curvatu)o(re}\\,)o (S^1=\\)o(mathr)o(m)e({const}.)147 625 y(\\label{circle})147 675 y(\\end{equation})147 725 y(In)i(a)g(paper)g(by)h(Erd\\"os)e(/)i (Written)e(in)h(Kurdish)g(/)g(A)h(counterexample)d(is)i(found.)147 774 y(\\label{Kurdish})147 824 y(\\end{theorem})105 930 y FD(whic)o(h)16 b(giv)o(es)105 1038 y FE(Theorem)c(5.1)h(\(Erd\177)-28 b(os\).)22 b Fo(A)13 b(the)n(or)n(em)g(b)n(oth)g(de)n(ep)h(and)f(pr)n (ofound)g(/)g(Is)g(that)h(a)f(cir)n(cle)h(is)g(r)n(ound:)778 1142 y FH(curv)m(ature)8 b Fn(S)1021 1122 y Fm(1)1055 1142 y FH(=)14 b(const)p Fn(:)573 b FH(\(5.2\))105 1246 y Fo(In)18 b(a)f(p)n(ap)n(er)f(by)i(Er)n(d\177)-25 b(os)16 b(/)h(Written)h(in)g(Kur)n(dish)f(/)g(A)h(c)n(ounter)n(example)g(is)g (found.)105 1352 y FD(No)o(w)f FB(\\Fullref{Erd\\"os})e FD(giv)o(es)j(\\Theorem)f(5.1",)g FB(\\Fullref{circle})e FD(giv)o(es)j(\\Equation)g(5.2",)105 1409 y(and)h FB (\\Fullref{Kurdish})d FD(giv)o(es)i(\\Theorem)g(5.1".)29 b(F)l(urthermore,)18 b FB(\\ref*{Erd\\"os})f FD(giv)o(es)h(\\5.1)105 1465 y(\(Erd\177)-23 b(os\)",)19 b(that)f(is,)i(it)g(prin)o(ts)f(the)h (\(optional\))f(tag)f(asso)q(ciated)i(with)f(theorems)g(and)g(the)h (lik)o(e.)33 b(Of)105 1522 y(course)15 b(y)o(ou)g(can)g(also)h(use)f FB(\\fullref*)f FD(and)h FB(\\Fullref*)p FD(.)105 1596 y Fq(\003)73 b Fr(If)11 b(y)o(ou)g(disagree)h(with)f(L)574 1591 y Fp(a)593 1596 y Fr(T)616 1609 y(E)639 1596 y(X's)g(idea)g(of)g (what)g(the)h(lab)q(el)e(t)o(yp)q(e)i(should)f(b)q(e)h(at)f(a)g (particular)g(p)q(oin)o(t,)g(y)o(ou)g(can)105 1646 y(o)o(v)o(erride)h (is)f(using)g Fs(\\setlabeltype)p Fr(.)k(F)m(or)c(example,)f(if)h(w)o (e)h(had)f Fs(\\setlabeltype{form)o(ula})d Fr(righ)o(t)j(b)q(efore)h (the)105 1696 y Fs(\\label)f Fr(command)e(in)i(the)i(previous)f (example,)f(the)h(result)h(of)e Fs(\\Fullref{circle})e Fr(w)o(ould)i(b)q(e)h(\\F)m(orm)o(ula)d(5.2")105 1746 y(instead)14 b(of)f(\\Equation)h(5.2".)188 1827 y FD(Before)25 b FB(\\ref)f FD(actually)h(prin)o(ts)g(the)g(n)o(um)o(b)q(er)f(of)h(a)f (cross-reference,)j(it)e(applies)h(the)f(macro)105 1883 y FB(\\preref)17 b FD(to)h(it.)29 b(By)18 b(default,)h(this)g(macro)e (do)q(es)i(nothing;)h(but)e(y)o(ou)g(can)g(rede\014ne)h(it)g(to)e(do)h (what-)105 1940 y(ev)o(er)i(y)o(ou)f(w)o(an)o(t)g(with)h(the)f(n)o(um)o (b)q(er.)34 b(If)20 b(y)o(ou)f(w)o(an)o(t)g(the)h(n)o(um)o(b)q(er)g(to) f(app)q(ear)h(uprigh)o(t)g(ev)o(en)g(if)g(the)105 1996 y(surrounding)c(text)f(is)g(in)h(italics,)h(y)o(ou)e(can)g(sa)o(y)147 2096 y Fs(\\def\\preref#1{{)o(\\norm)o(alsha)o(pe#1})o(})105 2202 y FD(The)g(output)g(of)g FB(\\pageref)f FD(and)i(of)e FB(\\cite)h FD(is)h(also)f(passed)g(to)g FB(\\pageref)f FD(b)q(efore)h(b)q(eing)i(prin)o(ted.)105 2329 y FE(6.)24 b(Theorems)17 b(and)i(Their)f(F)-5 b(riends)105 2430 y FD(Standard)13 b(L)312 2424 y Fw(a)333 2430 y FD(T)358 2444 y(E)383 2430 y(X)g(pro)o(vides)g(the)g FB(\\newtheorem)e FD(command)i(to)f(create)g(en)o(vironmen)o(ts)h(for)f(statemen)o(ts)105 2487 y(lik)o(e)19 b(theorems,)e(lemmas,)h(and)g(so)f(on.)27 b(The)18 b(basic)g(idea)h(can)f(b)q(e)g(adapted)f(for)g(other)h(t)o(yp) q(es)f(of)g(text)105 2543 y(that)c(should)i(stand)f(out,)f(suc)o(h)h (an)g(exercises,)h(con)o(v)o(en)o(tions,)f(and)g(so)f(on.)20 b(Not)13 b(all)i(of)e(these)h(should)h(b)q(e)105 2600 y(treated)g(t)o(yp)q(ographically)h(the)f(same:)20 b(for)14 b(example,)i(y)o(ou)f(migh)o(t)g(w)o(an)o(t)f(exercises)i(in)g(smaller) g(t)o(yp)q(e.)105 2729 y(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 7 7 7 6 bop 105 -25 a Fz(6.)17 b(Theorems)c(and)h(Their)g(F)m(riends)1256 b(7)-225 116 y FL(\045)14 b(Lab)q(els)g(and)-183 145 y(Cross-References)-225 174 y(\045)g(Lab)q(els)g(and)-183 203 y(Cross-References)-225 232 y Fl(\045)e(Erd\177)-17 b(os)188 120 y FD(The)16 b FB(geom)f FD(st)o(yle)h(extends)g(L)678 114 y Fw(a)699 120 y FD(T)724 134 y(E)750 120 y(X's)f FB(\\newtheorem)g FD(command)g(to)g(allo)o(w)h(y)o(ou)g(to)f(do)h(this) g(easily)l(.)105 177 y(Recall)j(from)e([Lam86,)g(58])f(that)h FB(\\newtheorem)f FD(has)h(t)o(w)o(o)g(required)h(argumen)o(ts:)24 b(the)17 b(name)h(of)f(the)105 233 y(new)g(en)o(vironmen)o(t)f(\(sa)o (y)g(\\theorem"\),)f(and)h(the)g(text)g(used)h(to)f(in)o(tro)q(duce)h (it)g(\(sa)o(y)e(\\Theorem"\).)22 b(In)105 289 y(standard)15 b(L)307 283 y Fw(a)328 289 y FD(T)353 303 y(E)379 289 y(X)h(it)g(also)g(tak)o(es)f(an)h(optional)g(argumen)o(t,)f(whose)h (meaning)g(dep)q(ends)i(on)e(whether)g(it)105 346 y(comes)f(b)q(efore)h (or)e(after)h(the)g(second)h(required)g(argumen)o(t.)188 402 y(In)e(the)f FB(geom)g FD(st)o(yle,)h(y)o(ou)f(can)g(use)h(y)o(et)f (another)g(optional)h(argumen)o(t,)e(righ)o(t)h(after)g FB(\\newtheorem)p FD(,)105 459 y(to)k(tell)i(L)256 453 y Fw(a)277 459 y FD(T)302 473 y(E)327 459 y(X)f(ho)o(w)f(this)h(en)o (vironmen)o(t)g(di\013ers)g(from)f(a)g(v)m(anilla)j(theorem-lik)o(e)f (en)o(vironmen)o(t.)27 b(This)105 515 y(optional)12 b(argumen)o(t)e (should)i(consist)g(of)f(t)o(w)o(o)e(sequences)k(of)e(commands,)g(eac)o (h)g(surrounded)h(b)o(y)f(braces,)105 572 y(lik)o(e)16 b(this:)147 666 y Fs(\\newtheorem[{\\p)o(ar\\la)o(rge}{)o(\\it}])o ({the)o(orem})o({Theo)o(rem}[)o(secti)o(on])105 766 y FD(\(This)f(is)h(the)f(same)g(de\014nition)i(used)f(for)f(the)g (example)h(in)g(Section)g(5.\))188 822 y(The)k(\014rst)f(sequence)h(of) f(commands)g(in)h(braces,)g FB(\\par\\large)p FD(,)f(will)i(b)q(e)f (executed)g(as)f(so)q(on)g(as)105 879 y(L)117 873 y Fw(a)138 879 y FD(T)163 893 y(E)189 879 y(X)c(sees)h(a)f FB(\\begin{theorem})p FD(.)k(This)d(means)g(the)f(theorem)h(will)h(come)e(out)h(in)g(larger)f (t)o(yp)q(e)h(\(see)105 935 y(the)h(output)f(in)h(Section)h(5\).)23 b(L)639 929 y Fw(a)660 935 y FD(T)685 949 y(E)711 935 y(X)16 b(implicitly)k(starts)15 b(a)h(new)h(lev)o(el)h(of)e(braces)h (when)g(it)g(encoun)o(ters)105 992 y(a)e FB(\\begin)f FD(command|c)o(hanges)h(inside)i(the)f(en)o(vironmen)o(t)f(are)g(lo)q (cal,)g(so)g(the)g FB(\\large)g FD(will)h(cease)g(to)105 1048 y(ha)o(v)o(e)f(e\013ect)g(at)f(the)i(end)f(of)g(the)g(en)o (vironmen)o(t.)188 1105 y(The)i(second)f(sequence)i(of)e(commands)g(is) h(inserted)g(righ)o(t)f(after)g(the)g(in)o(tro)q(ductory)h(text)34 b Fk(The-)105 1161 y(orem)18 b(5.1)g(\(Erd\177)-26 b(os\))p FD(.)23 b(It)17 b(a\013ects)e(ev)o(erything)i(from)e(that)g(p)q(oin)o (t)i(till)h(the)e(end)h(of)f(the)g(en)o(vironmen)o(t.)105 1218 y(Here)h(w)o(e'v)o(e)e(used)i FB(\\it)p FD(,)f(so)g(the)h (statemen)o(t)e(of)h(the)g(theorem)h(is)f(prin)o(ted)i(in)f(italics.)25 b(Note)16 b(that,)f(un-)105 1274 y(lik)o(e)i(the)f(standard)f FB(article)g FD(and)h FB(book)g FD(st)o(yles,)f FB(geom)h FD(do)q(es)g(not)f(italicize)k(theorems)c(b)o(y)h(default.)23 b(If)105 1331 y(w)o(e)18 b(didn't)g(ha)o(v)o(e)g(the)g FB(\\it)f FD(in)i(the)f FB(\\newtheorem)e FD(command,)i(the)g(text)g (of)f(the)h(theorem)g(w)o(ould)g(b)q(e)105 1387 y(uprigh)o(t.)105 1460 y Fq(\003)76 b Fr(Y)m(ou)14 b(can)h(also)f(con)o(trol)g(the)h(app) q(earance)h(of)d(the)i(in)o(tro)q(ductory)g(text)g(itself)f(b)o(y)h(c)o (hanging)e(the)i(de\014nition)105 1510 y(of)e Fs(\\theoremintro)p Fr(,)e(whic)o(h)j(b)o(y)f(default)h(is)147 1604 y Fs(\\def\\theoremint) o(ro#1{)o(\\norm)o(alsha)o(pe\\b)o(f#1})105 1698 y Fr(The)g(argumen)o (t)f Fs(#1)h Fr(stands)g(for)g(the)g(in)o(tro)q(ductory)g(text.)188 1777 y FD(Y)l(ou)f(need)h(t)o(w)o(o)d(pairs)i(of)g(braces)g(in)g(the)g (new)g(optional)h(argumen)o(t)e(to)g FB(\\newtheorem)p FD(,)f(ev)o(en)j(if)f(one)105 1834 y(is)k(empt)o(y)l(.)23 b(If)17 b(b)q(oth)f(are)h(empt)o(y)l(,)f(the)g(b)q(eha)o(vior)h(is)g (the)g(same)f(as)g(if)h(the)f(optional)h(argumen)o(t)f(w)o(eren't)105 1890 y(there.)188 1947 y(Another)c(enhancemen)o(t)i(to)e FB(\\newtheorem)e FD(in)k(the)e FB(geom)g FD(st)o(yle)h(is)g(automatic) f(lab)q(eling.)21 b(Supp)q(ose)105 2003 y(y)o(ou)15 b(sa)o(y)147 2097 y Fs(\\newtheorem{def)o(initi)o(on}[t)o(heore)o(m]{D)o(efini)o (tion})105 2197 y FD(\(recall)k(from)e([Lam86,)h(59])f(that)h(the)g (use)h(of)e FB([theorem])g FD(causes)i(de\014nitions)h(to)d(b)q(e)i(n)o (um)o(b)q(ered)g(in)105 2254 y(the)g(same)g(sequence)i(as)e(theorems,)g (assuming)h(the)f FB(theorem)f FD(en)o(vironmen)o(t)i(has)f(b)q(een)i (previously)105 2310 y(de\014ned\).)g(No)o(w)14 b(sa)o(ying)147 2404 y Fs(\\begin{definiti)o(on}[u)o(niver)o(se])147 2454 y(The)21 b(universe)f(is)h(a)h(Hubble)e(bubble.)147 2504 y(\\end{definition)o(})105 2604 y FD(prin)o(ts)105 2729 y(Revision:)i(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 8 8 8 7 bop 105 -25 a Fz(7.)17 b(The)c(Pro)q(of)g(En)o(vironmen)o(t)1335 b(8)-225 116 y FL(Def.)12 b(\\univ)o(erse")-225 145 y(\045)i(Lab)q(els) g(and)-183 174 y(Cross-References)-225 203 y(\045)c(univ)o(erse)-225 232 y(\045)k(Lab)q(els)g(and)-183 261 y(Cross-References)-225 290 y(\045)c(univ)o(erse)-225 319 y(\045)k(Lab)q(els)g(and)-183 348 y(Cross-References)-225 377 y(Section)d(\\The)g(Pro)q(of)-183 406 y(En)o(vironmen)o(t")105 120 y Fk(De\014nition)19 b(6.1)e(\(univ)o(erse\).)22 b FD(The)15 b(univ)o(erse)i(is)e(a)g (Hubble)i(bubble.)105 214 y(and)k(implicitly)j(calls)e FB(\\label{universe})p FD(.)34 b(\(As)21 b(men)o(tioned)g(in)h(Section) g(5,)f(y)o(ou)g(can)g(turn)g(this)105 270 y(feature)16 b(o\013)f(b)o(y)h(sa)o(ying)g FB(\\autolabelfalse)p FD(.\))21 b(The)16 b(en)o(vironmen)o(t)h(kno)o(ws)e(its)h(t)o(yp)q(e)h(at)e(the)h (time)h(the)105 327 y(lab)q(el)g(is)f(made,)e(so)h(sa)o(ying)g FB(\\Fullref{universe})e FD(will)k(prin)o(t)e(\\De\014nition)i(6.1".) 105 402 y Fq(\003)86 b Fr(The)24 b(t)o(yp)q(e)g(is)f(usually)g(just)h (the)g(en)o(vironmen)o(t)e(name,)j(but)e(it)h(can)f(b)q(e)i(o)o(v)o (erridden)f(b)o(y)f(including)105 451 y Fs(\\setlabeltype)10 b Fr(\(Section)j(5\))g(in)f(the)h(\014rst)h(optional)d(argumen)o(t)g (to)i Fs(\\newtheorem)p Fr(.)i(Th)o(us)e(if)f(the)h Fs(definition)105 501 y Fr(en)o(vironmen)o(t)g(had)h(b)q(een)h(created)g(with)147 601 y Fs(\\newtheorem[{\\s)o(etlab)o(eltyp)o(e{def)o(.}}{)o(}]{de)o (finit)o(ion}[)o(theor)o(em]{D)o(efin)o(ition)o(})105 700 y(\\Fullref{universe)o(})c Fr(w)o(ould)i(app)q(ear)i(as)e(\\Def.)g (6.1".)105 782 y FD(The)h(preferred)g(st)o(yle)g(of)f(some)g (publishing)k(houses)c(calls)i(for)e(digits)h(and)g(punctuation)h(to)e (b)q(e)h(t)o(yp)q(eset)105 838 y(uprigh)o(t)20 b(in)h(theorems)f(and)g (suc)o(h,)h(amidst)g(surrounding)f(text)g(in)h(italics.)36 b(The)20 b(con)o(trol)g(sequence)105 895 y FB(\\specialdigits)11 b FD(ac)o(hiev)o(es)j(this.)20 b(It)14 b(causes)f(eac)o(h)h(digit)g(in) g(text,)f(as)g(w)o(ell)h(as)g(paren)o(theses,)f(commas,)105 951 y(colon,)19 b(semicolons)g(and)f(p)q(erio)q(ds,)i(to)d(e\013ectiv)o (ely)i(b)q(e)g(preceded)g(b)o(y)f FB(\\normalshape)p FD(.)27 b(Y)l(ou)18 b(can)h(use)105 1008 y FB(\\specialdigits)13 b FD(after)i FB(\\it)f FD(in)i(the)g(de\014nition)h(of)e(a)f(new)i(en)o (vironmen)o(t)f(with)h FB(\\newtheorem)p FD(.)105 1082 y Fq(\003)79 b Fr(The)17 b(w)o(a)o(y)f Fs(\\specialdigits)d Fr(w)o(orks)k(is)g(b)o(y)f(making)e(digits)i(and)h(punctuation)g(in)o (to)f(activ)o(e)g(c)o(haracters)105 1132 y(\(c)o(hanging)h(their)i Fs(\\catcode)p Fr(s)e(to)g(13\).)31 b(This)17 b(has)i(t)o(w)o(o)e (consequences.)34 b(First,)18 b(c)o(haracters)i(that)e(arise)h(from)105 1182 y(macro)c(expansion)i(don't)f(get)g(the)h(sp)q(ecial)g(treatmen)o (t,)g(b)q(ecause)h(their)f Fs(\\catcode)p Fr(s)e(are)i(frozen)g(b)q (eforehand;)105 1232 y(this)d(is)g(true,)g(in)f(particular,)h(of)f(the) h(expansion)g(of)f Fs(\\ref)g Fr(commands)f(\(but)i(see)h(the)g(end)f (of)f(Section)i(5\).)188 1282 y(The)21 b(second)h(consequence)h(is)d (that)h(the)g(digits)f(and)h(decimal)e(p)q(oin)o(t)h(no)g(longer)h(w)o (ork)f(in)g(sp)q(ecifying)105 1331 y(dimensions:)g(if)15 b(y)o(ou)g(write)h Fs(\\vskip)k(1in)15 b Fr(while)g Fs(\\specialdigits) e Fr(is)i(in)g(e\013ect,)j(y)o(ou)d(get)g(an)h(error)g(message)105 1381 y(complaining)h(that)j(a)f(n)o(um)o(b)q(er)g(w)o(as)h(exp)q (ected.)38 b(T)m(o)19 b(get)h(around)g(this,)g(y)o(ou)g(can)g(temp)q (orarily)e(cancel)i(the)105 1431 y(sp)q(ecialness)d(with)e Fs(\\regulardigits)p Fr(.)20 b(If)c(y)o(ou)f(run)g(in)o(to)g(this)h (problem)e(more)h(than)g(once)h(or)g(t)o(wice,)g(it's)f(b)q(est)105 1481 y(to)j(create)i(a)e(macro,)f(outside)i(the)g(scop)q(e)g(of)f Fs(\\specialdigits)p Fr(,)d(that)k(expands)g(to)f(the)g(desired)i (command)105 1531 y(\()p Fs(\\def\\inch{\\vskip)f(1in})p Fr(\).)105 1682 y FE(7.)24 b(The)19 b(Pro)r(of)f(En)n(vironmen)n(t)105 1784 y FD(Theorems)e(and)g(pro)q(ofs)g(go)f(hand)h(in)h(hand.)23 b(The)16 b FB(proof)g FD(en)o(vironmen)o(t)g(in)h FB(geom)p FD(,)e(in)i(its)f(most)f(basic)105 1840 y(form,)e(prin)o(ts)g Fv(Pr)n(o)n(of.)20 b FD(at)13 b(the)g(b)q(eginning)j(of)d(the)h(pro)q (of,)f(and)g(an)h(end-of-pro)q(of)g(sym)o(b)q(ol)f Fj(\003)h FD(at)f(the)h(end.)105 1897 y(With)h(an)h(optional)f(argumen)o(t)g(it)g (b)q(eha)o(v)o(es)h(lik)o(e)g(this:)147 1996 y Fs(\\begin{proof}[P)o (oinca)o(r\\'e)i(conjecture])147 2046 y(Notice)i(first)h(that)g(...)147 2096 y(...)g(as)g(we)g(wished)g(to)g(show.)147 2146 y(\\end{proof})105 2252 y Fv(Pr)n(o)n(of)16 b(of)g(Poinc)n(ar)o(\023)-22 b(e)16 b(c)n(onje)n(ctur)n(e.)k FD(Notice)c(\014rst)f(that)f FC(:)8 b(:)g(:)21 b FD(as)15 b(w)o(e)g(wished)h(to)e(sho)o(w.)p 1529 2271 376 2 v 1529 2325 2 54 v 1539 2308 a Fr(P)o(oincar)o(\023)-20 b(e)14 b(conjecture)p 1903 2325 V 1529 2327 376 2 v 22 2408 a Fq(\003)79 b Fr(The)18 b(formatting)c(of)j(the)h(pro)q(of)s('s)f (in)o(tro)q(ductory)g(text)h(is)f(con)o(trolled)g(b)o(y)g(the)g(macro)f Fs(\\proofintro)p Fr(,)f(whose)105 2458 y(single)d(argumen)o(t)e(is)i (the)h(optional)d(argumen)o(t)h(to)h Fs(\\begin{proof})p Fr(|in)c(this)13 b(case,)f(\\P)o(oincar)o(\023)-20 b(e)12 b(conjecture".)19 b(If)105 2508 y(the)14 b(optional)f(argumen)o(t)f(is) i(not)g(used,)g Fs(\\proofintro)d Fr(is)j(passed)h(an)e(empt)o(y)g (argumen)o(t.)k(The)d(default)g(setting)105 2557 y(of)f Fs(\\proofintro)f Fr(is)105 2729 y FD(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 9 9 9 8 bop 105 -25 a Fz(8.)17 b(Equations)1568 b(9)-225 116 y FL(Section)10 b(\\Equations")-225 145 y(\045)k(Lab)q(els)g(and) -183 174 y(Cross-References)147 120 y Fs(\\def\\proofintro)o(#1{\\d)o (ef\\@t)o(empa{)o(#1}\045)190 170 y({\\it)21 b(Proof\\ifx\\@tempa\\e)o (mpty\\)o(else)o(\\)e(of)i(#1\\fi.)g(}\\ignorespaces})105 270 y Fr(Y)m(ou)14 b(can)h(probably)e(\014gure)i(out)g(ho)o(w)f(it)g (decides)i(whether)g(to)e(write)h Fi(Pr)n(o)n(of)f Fr(or)g Fi(Pr)n(o)n(of)h(of)p Fh(:)7 b(:)g(:)e Fr(.)20 b(Y)m(ou)14 b(can)h(c)o(hange)105 319 y(its)f(de\014nition)f(to)h(obtain)f(other)i (e\013ects.)188 369 y(Lik)o(ewise,)26 b(the)e(formatting)d(of)j(the)g (b)q(o)o(x)f(at)h(the)g(end)g(of)g(the)g(pro)q(of)f(is)h(con)o(trolled) f(b)o(y)h(the)g(macro)105 419 y Fs(\\provedboxcontent)o(s)p Fr(,)11 b(whic)o(h)i(is)h(en)o(tirely)g(analogous.)j(Its)d(standard)h (setting)f(is)147 519 y Fs(\\def\\provedboxc)o(onten)o(ts#1{)o(\\def\\) o(@tem)o(pa{#1)o(}\045)190 568 y(\\ifx\\@tempa\\empty$)o(\\squa)o (re$\\e)o(lse\\)o(fbox{)o(\\smal)o(l#1}\\)o(fi})105 675 y FD(T)l(o)j(iden)o(tify)i(y)o(our)f(pro)q(ofs)f(with)h(the)g(n)o(um)o (b)q(er)g(of)f(their)h(corresp)q(onding)h(theorems,)f(lemmas,)g(corol-) 105 731 y(laries,)g(etc.,)f(use)g FB(\\setprooftag)f FD(in)i(the)f(de\014nition)i(of)d(these)i(en)o(vironmen)o(ts.)25 b(F)l(or)17 b(instance,)h(after)105 788 y(y)o(ou)d(sa)o(y)147 887 y Fs(\\newtheorem[{\\s)o(etpro)o(oftag)o(}{\\it)o(}]{t)o(heore)o (m}{Th)o(eorem)o(}[sec)o(tion])147 937 y(\\newtheorem[{\\s)o(etpro)o (oftag)o(}{\\it)o(}]{c)o(oroll)o(ary}[)o(theor)o(em]{C)o(oroll)o(ary}) 105 1043 y FB(\\begin{proof})c FD(will)j(b)q(eha)o(v)o(e)g(as)e(if)h(y) o(ou)g(w)o(ere)f(passing)h(it)h(as)e(its)h(optional)g(argumen)o(t)f (the)h(n)o(um)o(b)q(er)g(of)105 1100 y(the)g(most)f(recen)o(t)g (theorem)h(or)f(corollary)l(.)19 b(Nested)13 b(pro)q(ofs)g(k)o(eep)g (trac)o(k)f(of)g(their)h(argumen)o(ts)f(correctly)l(,)105 1156 y(so)j(the)g(b)q(o)o(x)g(at)g(the)g(end)h(of)f(eac)o(h)g(gets)g (the)g(same)g(tag)f(as)h(the)g Fv(Pr)n(o)n(of)h(of)p FC(:)8 b(:)g(:)21 b FD(at)15 b(the)g(b)q(eginning.)105 1213 y(Ho)o(w)o(ev)o(er,)f(certain)i(situations)g(are)f(to)q(o)g (confusing)h(for)f FB(\\setprooftag)p FD(.)k(F)l(or)c(example,)h(if)g (y)o(ou)f(state)105 1269 y(a)i(corollary)h(b)q(et)o(w)o(een)g(a)f (theorem)g(and)h(its)g(pro)q(of,)f(the)h(pro)q(of)f(will)i(incorrectly) g(get)e(the)g(corollary's)105 1326 y(n)o(um)o(b)q(er,)e(whic)o(h)g(is)h (more)e(recen)o(t.)20 b(In)15 b(this)g(situation)h(y)o(ou)e(ha)o(v)o(e) g(to)h(use)g(the)f(optional)i(argumen)o(t.)j(Of)105 1382 y(course,)c(it's)g(b)q(est)h(to)e(use)i FB(\\ref{...})e FD(as)h(the)g(argumen)o(t,)f(rather)h(than)g(an)g(explicit)j(n)o(um)o (b)q(er,)d(whic)o(h)105 1438 y(migh)o(t)g(c)o(hange)g(later.)188 1495 y(If)20 b(a)f(pro)q(of)g(ends)g(with)h(a)f(displa)o(y)o(ed)i(form) o(ula,)e(it)h(is)g(recommen)o(ted)f(that)g(the)g(pro)o(v)o(ed)g(b)q(o)o (x)g(b)q(e)105 1551 y(placed)f(next)e(to)g(the)h(form)o(ula)f(\(as)g (if)h(it)g(w)o(ere)f(a)h(tag\).)23 b(This)17 b(is)g(done)g(b)o(y)f (inserting)i FB(\\proved)e FD(b)q(efore)105 1608 y(the)c(closing)g FB($$)p FD(.)19 b(Lik)o(ewise,)13 b(if)f(the)g(last)f(line)i(of)e(the)h (pro)q(of)f(is)h(part)f(of)g(an)h FB(\\item)p FD(,)f(y)o(ou)g(can)h (use)g FB(\\proved)105 1664 y FD(b)q(efore)i(the)g(closing)h FB(\\end{enumerate})c FD(\(or)i(whatev)o(er\))g(so)h(the)f(pro)o(v)o (ed)h(b)q(o)o(x)g(w)o(on't)e(b)q(e)j(set)e(on)h(a)f(line)105 1721 y(b)o(y)i(itself.)22 b(In)16 b(ev)o(en)g(more)f(di\016cult)i (cases|for)e(instance,)h(a)f(form)o(ula)g(that)g(already)h(has)f(a)g (tag,)f(or)h(is)105 1777 y(part)g(of)f(a)h(m)o(ulti-line)j(displa)o (y|plop)g FB(\\box\\provedbox)13 b FD(where)i(y)o(ou)g(w)o(an)o(t)f (the)i(b)q(o)o(x)f(to)f(b)q(e.)105 1904 y FE(8.)24 b(Equations)105 2005 y FD(The)19 b FB(geom)g FD(st)o(yle)g(reinstates)g(the)g(plain)i (T)861 2015 y(E)887 2005 y(X)e(macro)f FB(\\eqalign)p FD(,)h(whic)o(h)h(is)f(not)g(part)g(of)f(standard)105 2062 y(L)117 2056 y Fw(a)138 2062 y FD(T)163 2075 y(E)189 2062 y(X)d(but)h(is)g(nonetheless)h(v)o(ery)e(useful.)23 b(Unlik)o(e)17 b(the)f FB(eqnarray)e FD(en)o(vironmen)o(t,)i FB(\\eqalign)e FD(creates)105 2118 y(math)j(alignmen)o(ts)i(that)e(are) g(not)h(treated)f(as)g(whole)i(lines,)g(and)f(so)g(can)g(b)q(e)g(com)o (bined)h(with)f(other)105 2175 y(elemen)o(ts.)188 2231 y(The)11 b(example)h(in)h(Section)f(5)f(has)g FB (\\equationwith{theorem})d FD(after)i(the)h FB(theorem)g FD(en)o(vironmen)o(t)105 2288 y(is)j(created.)20 b(This)14 b(causes)g(equations)g(made)g(with)g(the)g FB(equation)f FD(and)h(the)g FB(eqnarray)f FD(en)o(vironmen)o(ts)105 2344 y(to)20 b(b)q(e)h(n)o(um)o(b)q(ered)g(in)g(the)f(same)g(sequence)i (as)e(theorems.)35 b(Y)l(ou)20 b(can)h(replace)g FB(theorem)f FD(with)g(an)o(y)105 2400 y(en)o(vironmen)o(t)14 b(that)f(w)o(as)f (de\014ned)j(with)f FB(\\newtheorem)e FD(and)i(that)f(has)g(a)h(coun)o (ter)f(with)h(its)g(name)f(\(the)105 2457 y(en)o(vironmen)o(t)18 b(has)g(a)g(coun)o(ter)g(with)h(its)f(name)g(if)h(there)f(w)o(as)f(no)h (optional)h(argumen)o(t)e(b)q(et)o(w)o(een)i(the)105 2513 y(\014rst)c(and)g(second)h(required)g(argumen)o(ts)f(to)f FB(\\newtheorem)p FD(\).)188 2570 y(If)h(y)o(ou)g(load)h(the)f (optional)h(st)o(yle)f FB(geomeqns)p FD(|that)f(is,)h(if)h(y)o(our)f (do)q(cumen)o(t)g(starts)f(with)105 2729 y(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 10 10 10 9 bop 105 -25 a Fz(9.)17 b(The)c Fg(Figure)d Fz(and)k Fg(Table)d Fz(en)o(vironmen)o(ts)1099 b(10)-225 116 y FL(Section)14 b(\\The)-183 145 y Fy(Figure)f FL(and)e Fy(Table)-183 174 y 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FD(command)g(to)g(kno)o(w)h(what)f(size)h(b)q(o)o(x)g(to)f (mak)o(e,)g(it)h(needs)h(to)e(\014nd)h(y)o(our)105 1033 y(P)o(ostScript)h(\014gure)g(\014le,)h(and)g(the)f(\014le)h(m)o(ust)f (ha)o(v)o(e)g(near)g(the)g(top)g(a)g(line)i(lik)o(e)f(this:)147 1133 y Fs(\045\045BoundingBox:)i(0)k(30)f(98)h(128)105 1239 y FD(The)15 b(\014rst)f(t)o(w)o(o)f(n)o(um)o(b)q(ers)h(represen)o (t)h(the)f(lo)o(w)h FC(x)p FD(-)f(and)h FC(y)r FD(-co)q(ordinates)g(of) f(the)g(\014gure's)g(b)q(ounding)i(b)q(o)o(x,)105 1296 y(in)j(p)q(oin)o(ts,)g(and)g(the)f(last)g(t)o(w)o(o)f(represen)o(t)h (the)h(high)g FC(x)p FD(-)f(and)g FC(y)r FD(-co)q(ordinates.)30 b(In)19 b(the)f(example)h(just)105 1352 y(giv)o(en,)i(whic)o(h)g (corresp)q(onds)f(to)f(Figure)h(2,)h(the)f(b)q(ounding)h(b)q(o)o(x)f (go)q(es)f(from)h(0)f(to)g(98)h(pt)f(in)i(the)f FC(x)p FD(-)105 1409 y(direction)d(and)f(from)f(30)g(to)h(128)f(pt)g(in)i(the) f FC(y)r FD(-direction,)h(so)e(its)h(heigh)o(t)g(and)g(width)h(are)e(b) q(oth)h(98)f(pt,)105 1465 y(or)e(appro)o(ximately)g(1.35)f(inc)o(hes.) 21 b(The)13 b(corners)g(of)g(the)h(b)q(ounding)h(b)q(o)o(x)e(app)q(ear) g(on)h(the)f(page)g(in)h(pro)q(of)105 1522 y(mo)q(de)h(\(Section)h (13\).)188 1578 y(Note)f(that)f FB(\\psfig)g FD(only)i(cares)f(ab)q (out)g(the)g(heigh)o(t)h(and)f(the)g(width)h(of)f(the)g(b)q(ounding)i (b)q(o)o(x,)d(not)105 1634 y(ab)q(out)k(the)h(actual)g(v)m(alues)g(of)f (the)h(high)g(and)g(lo)o(w)g(co)q(ordinates.)30 b(The)18 b(latter)h(are)f(relev)m(an)o(t)h(only)g(in)105 1691 y(reference)f(to)g(the)f(co)q(ordinates)i(of)e(the)h(ob)s(jects)f (inside)j(the)d(picture,)i(ab)q(out)f(whic)o(h)h FB(\\psfig)e FD(kno)o(ws)105 1747 y(nothing.)31 b(\(Th)o(us)19 b(the)g(b)q(ottom)f (left)h(corner)g(of)g(the)f(square)h(in)h(Figure)f(2)g(has)f(co)q (ordinates)i(\(4)p FC(;)8 b FD(34\),)105 1804 y(whic)o(h)14 b(is)g(a)e(little)j(bit)e(ab)q(o)o(v)o(e)g(and)g(to)g(the)g(righ)o(t)g (of)g(the)g(b)q(ounding)i(b)q(o)o(x's)d(b)q(ottom)g(left)i(corner)f (\(0)p FC(;)8 b FD(30\).\))105 1860 y(If)13 b(one)g(added)h(the)f(same) f(n)o(um)o(b)q(er)h(to)f(the)h FC(x)p FD(-co)q(ordinates)h(of)e(the)h (b)q(ounding)i(b)q(o)o(x)d(and)h(of)g(ev)o(ery)g(ob)s(ject)105 1917 y(in)j(the)f(picture,)h(the)f(result)h(w)o(ould)g(b)q(e)f(exactly) h(the)f(same.)188 1973 y(Normally)l(,)g(the)f FB(\045\045BoundingBox)f FD(line)j(should)g(ha)o(v)o(e)e(b)q(een)h(placed)h(in)f(the)g(P)o (ostScript)f(\014le)h(auto-)105 2030 y(matically)l(,)g(b)o(y)f(whatev)o (er)g(program)f(y)o(ou)h(used)h(to)e(create)h(the)g(\014gure.)20 b(If)14 b(the)h(program)e(did)i(not)f(write)105 2086 y(a)j(line)i(lik)o(e)f(that,)e(y)o(ou)h(ha)o(v)o(e)g(to)f(do)h(it)h(b)o (y)f(hand,)h(and)f(y)o(ou)g(should)h(consider)g(switc)o(hing)g(to)e (another)105 2143 y(program.)188 2199 y(Notice)f(that)e(the)h(lab)q (els)h FC(a)f FD(and)h FC(b)e FD(in)i(Figure)f(2)g(app)q(ear)g(in)h (the)f(same)g(fon)o(t)f(as)h(they)g(w)o(ould)g(in)h(the)105 2255 y(text.)27 b(In)18 b(fact)f(the)h(lab)q(els)h(w)o(ere)f(t)o(yp)q (eset)f(b)o(y)h(T)946 2265 y(E)971 2255 y(X)g(itself,)h(and)f(do)g(not) f(come)g(from)g(the)h(P)o(ostScript)105 2312 y(\014le,)i(where)f(it)g (w)o(ould)g(b)q(e)g(hard)g(to)f(sp)q(ecify)i(them)e(satisfactorily|esp) q(eciall)q(y)j(details)f(suc)o(h)f(as)f(the)105 2368 y(placemen)o(t)f(of)f(the)h(primes)g(and)g(other)f(subscripts)h(and)g (sup)q(erscripts.)25 b(The)16 b(information)h(for)f(these)105 2425 y(lab)q(els)i(is)f(con)o(tained)g(in)g(a)f(\014le)h(with)f(the)h (su\016x)f FB(.lab)p FD(,)g(whic)o(h)h(normally)g(is)f(generated)h(b)o (y)f(the)g(same)105 2481 y(program)j(that)h(creates)g(the)g(P)o (ostScript)h(\014le,)h(or)e(b)o(y)g(a)g(p)q(ostpro)q(cessor.)35 b(If)21 b(y)o(ou)f(w)o(an)o(t)f(to)h(include)105 2538 y Fv(Mathematic)n(a)f FD(graphics,)h(for)e(example,)j(y)o(ou)d(should)i (use)f(the)g FB(mathfig)f FD(utilit)o(y)l(,)i(describ)q(ed)h(in)f(the) 105 2594 y(App)q(endix.)105 2729 y(Revision:)i(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 13 13 13 12 bop 105 -25 a Fz(10.)17 b(P)o(ostScript)e(Figures)1386 b(13)-225 116 y FL(\045)10 b(PStorus)105 120 y Fq(\003)77 b Fr(The)15 b(a)o(v)o(erage)g(user)h(has)f(no)f(need)i(to)f(kno)o(w)f (what)h(the)g Fs(.lab)f Fr(\014le)h(lo)q(oks)f(lik)o(e,)g(but)h(if)f(y) o(ou)h(w)o(an)o(t)f(to)h(write)105 170 y(a)h(new)g(p)q(ostpro)q(cessor) j(in)d(order)g(to)g(implemen)o(t)e(this)i(lab)q(eling)f(sc)o(heme)h(in) g(conjunction)g(with)g(y)o(our)g(fa)o(v)o(orite)105 220 y(dra)o(wing)j(program,)h(here)h(are)f(the)h(details.)36 b(Eac)o(h)20 b(line)f(of)h(the)g(\014le)g(yields)g(one)g(lab)q(el,)h (and)e(con)o(tains)h(the)105 270 y Fs(\\setlabel)11 b Fr(command)f(follo)o(w)o(ed)h(b)o(y)h(\014v)o(e)h(argumen)o(ts:)k(the)c (text)h(of)e(the)h(lab)q(el,)f(to)g(b)q(e)i(t)o(yp)q(eset)g(in)e(math)f (mo)q(de;)105 319 y(the)g Fh(x)p Fr(-)f(and)g Fh(y)q Fr(-co)q(ordinates)i(of)e(the)h(lab)q(el's)e Fi(r)n(efer)n(enc)n(e)i(p) n(oint)p Fr(,)g(in)f(p)q(oin)o(ts;)h(and)f(the)h Fi(r)n(elative)e Fh(x)p Fr(-)h(and)h Fh(y)q Fr(-co)q(ordinates)105 369 y(of)h(the)g(reference)j(p)q(oin)o(t.)i(A)12 b(v)n(alue)f(of)h(1)g(for) f(the)i(last)f(t)o(w)o(o)g(argumen)o(ts)f(means)g(the)i(reference)i(p)q (oin)o(t)c(of)h(the)h(lab)q(el)105 419 y(it)h(at)h(the)g(top)f(or)h (righ)o(t)f(of)g(the)h(lab)q(el's)f(b)q(ounding)g(b)q(o)o(x;)g(a)g(v)n (alue)g(of)g Fq(\000)p Fr(1)h(means)e(b)q(ottom)h(or)g(left,)g(a)g(v)n (alue)g(of)g(0)105 469 y(means)f(middle,)f(and)h(so)h(on.)188 519 y(F)m(or)g(example,)e(here)j(is)e(the)i(\014le)f Fs(PStorus.lab)d Fr(corresp)q(onding)k(to)f(Figure)g(2:)147 604 y Fs(\\setlabel{a}{48)o(.6000)o(00}{3)o(4.162)o(104})o({0}{1)o(}) 147 654 y(\\setlabel{b}{4.)o(16210)o(4}{78)o(.6000)o(00}{)o(1}{0})147 704 y(\\setlabel{a'}{4)o(8.600)o(000}{)o(123.0)o(3789)o(6}{0})o({-1}) 147 753 y(\\setlabel{b'}{9)o(3.037)o(896}{)o(78.60)o(0000)o(}{-1})o ({0})105 839 y Fr(F)m(or)i(the)h(lab)q(el)f Fh(a)p Fr(,)g(the)h (reference)i(p)q(oin)o(t)d(is)g(at)g(the)h(top)f(middle)f(of)h(the)g (lab)q(el's)g(b)q(ounding)g(b)q(o)o(x,)g(so)h(the)g(lab)q(el)105 888 y(itself)d(will)e(b)q(e)i(cen)o(tered)i(under)f(the)g(p)q(oin)o(t)e (with)h(co)q(ordinates)g(\(48)p Fh(:)p Fr(6)p Fh(;)7 b Fr(34)p Fh(:)p Fr(1\).)188 938 y(If)19 b(y)o(ou)g(w)o(an)o(t)g(to)h (t)o(yp)q(eset)h(a)e(lab)q(el)g(outside)h(math)e(mo)q(de,)h(use)h(L) 1260 933 y Fp(a)1279 938 y Fr(T)1302 951 y(E)1326 938 y(X's)f Fs(\\mbox)g Fr(command)d(\(or)k(T)1823 947 y(E)1846 938 y(X's)105 988 y Fs(\\hbox)p Fr(\).)d(The)d(fon)o(t)e(used)j(b)o(y)e (default)g(in)g(this)g(case)h(is)f(the)h(same)f(as)g(for)g(captions.)18 b(Th)o(us,)13 b(to)g(get)h(the)g(lab)q(el)f Fc(fo)q(o)105 1038 y Fr(y)o(ou'll)f(probably)h(w)o(an)o(t)h(to)f(t)o(yp)q(e)i(the)f (string)g Fs(\\hbox{foo})e Fr(in)o(to)h(y)o(our)h(\014gure-making)e (program.)188 1088 y(Sometimes)k(the)j(fact)f(that)g(the)h(source)h Fs(\\hbox{foo})c Fr(has)i(man)o(y)f(more)g(c)o(haracters)j(than)e(the)h (output)105 1138 y(causes)14 b(problems|for)c(example,)h(the)i (\014gure-making)e(program)g(migh)o(t)f(lea)o(v)o(e)i(to)q(o)g(m)o(uc)o (h)f(space)j(for)e(the)h(lab)q(el.)105 1187 y(The)18 b(macro)e Fs(\\hyperactivelabels)e Fr(pro)o(vides)k(a)f(w)o(a)o(y)g (around)h(this.)29 b(This)17 b(macro)g(is)g(called)h(ev)o(ery)g(time)e (a)105 1237 y(lab)q(el)f(is)g(ab)q(out)g(to)g(b)q(e)g(t)o(yp)q(eset,)i (and)e(y)o(ou)f(can)i(de\014ne)g(it)f(at)g(will,)e(to)i(allo)o(w)f (abbreviations,)g(sa)o(y)m(.)21 b(Th)o(us,)16 b(after)105 1287 y(the)e(commands)147 1372 y Fs(\\def\\hyperactiv)o(elabe)o(ls{\\m) o(athco)o(de`:)o(="800)o(0})147 1422 y(\\def\\activecolo)o(n#1:{)o (\\hbox)o({#1}})147 1472 y({\\catcode`\\:=\\a)o(ctive)o(\\glob)o (al\\le)o(t:=\\)o(activ)o(ecolo)o(n})105 1557 y Fr(the)k(construction)g Fs(:foo:)e Fr(has)h(exactly)h(the)g(same)e(e\013ect)j(as)e Fs(\\hbox{foo})p Fr(|but)e(only)h(inside)i(lab)q(els.)27 b(\(The)105 1607 y(command)11 b Fs(\\mathcode`:="80)o(00)f Fr(causes)15 b(the)f(colon)f(to)g(b)q(e)h(treated)h(as)e(an)g(activ)o (e)h(c)o(haracter)h(in)e(math)e(mo)q(de;)105 1657 y(the)j(next)h(t)o(w) o(o)e(lines)h(sa)o(y)m(,)f(in)g(a)h(roundab)q(out)g(w)o(a)o(y)m(,)e (what)i(this)g(activ)o(e)g(c)o(haracter)h(should)f(do.\))188 1734 y FD(Utilities)j(\(programs\))12 b(that)i(generate)g(P)o (ostScript)h(graphics)g(\014les)g(generally)h(start)d(the)i(\014le)h (with)105 1791 y(a)23 b(\\signature")f(\(a)g(commen)o(t)h(line)h (stating)f(the)g(utilit)o(y's)h(name)e(and)i(v)o(ersion\))e(and)h(a)g (c)o(h)o(unk)g(of)105 1847 y(P)o(ostScript)c(co)q(de|call)i(it)f(a)f (header|establishing)j(abbreviations,)e(subroutines,)h(fon)o(ts)d(and)i (the)105 1904 y(lik)o(e.)37 b(The)21 b(header)g(is)g(alw)o(a)o(ys)f (the)h(same,)g(so)f(if)h(y)o(ou)g(ha)o(v)o(e)f(dozens)h(of)f(\014gures) h(generated)f(b)o(y)h(the)105 1960 y(same)e(utilit)o(y)i(it's)e(go)q(o) q(d)h(to)f(factor)g(out)g(this)h(commonalit)o(y)l(,)g(if)g(p)q (ossible.)35 b(With)20 b(certain)g(utilities,)105 2016 y(y)o(ou)15 b(can)g(sa)o(v)o(e)g(y)o(our)g(\014les)h(without)f(the)h (header.)k(Then)c(they)g(w)o(on't)e(prin)o(t)h(on)h(their)g(o)o(wn;)e (but)h(when)105 2073 y FB(\\psfig)h FD(lo)q(oks)h(in)o(to)g(them,)g(if) h(it)f(can)g(recognize)h(the)f(utilit)o(y's)h(signature,)f(it)g(puts)g (in)o(to)g(the)g(dvi)h(\014le)105 2129 y(a)e(command)g(that)f(causes)i (the)f(inclusion)j(of)d(the)g(header)g(at)g(prin)o(ting)h(time.)23 b(This)17 b(w)o(a)o(y)e(the)i(header)105 2186 y(is)i(included)i(only)f (once)f(for)f(all)h(\014gures,)g(sa)o(ving)g(memory)f(and)h(time.)30 b(The)19 b(utilities)i(that)d FB(\\psfig)105 2242 y FD(curren)o(tly)e (kno)o(ws)e(ab)q(out)h(are)g(Mathematica)g([W)l(ol91])f(and)h(Adob)q(e) h(Illustrator)f([S)1569 2226 y Fu(+)1597 2242 y FD(88].)k(With)c (Illus-)105 2299 y(trator,)h(sa)o(ving)h(without)g(the)h(header)g(is)f (accomplished)j(b)o(y)d(clic)o(king)i(on)e(the)h(appropriate)f(en)o (try)g(in)105 2355 y(the)e(\\Sa)o(v)o(e)g(As")g(dialog)h(b)q(o)o(x.)j (F)l(or)c(Mathematica,)f(see)i(the)f(App)q(endix.)105 2426 y Fq(\003)72 b Fr(F)m(or)9 b(the)h(signature)g(to)f(b)q(e)h(seen)h (b)o(y)f Fs(\\psfig)p Fr(,)e(it)h(m)o(ust)g(app)q(ear)h(near)g(the)g (top)g(of)f(the)h(\014le;)g(the)g(actual)g(n)o(um)o(b)q(er)105 2476 y(of)j(lines)h(that)g Fs(\\psfig)e Fr(scans)j(is)e(con)o(trolled)h (b)o(y)f(the)i(coun)o(ter)f Fs(\\maxheaderlines)p Fr(.)h(The)f Fs(\045\045BoundingBox)d Fr(line)105 2525 y(m)o(ust)k(also)h(lie)g(in)g (that)h(same)e(initial)g(stretc)o(h.)27 b(The)17 b(default)f(v)n(alue)g (of)f Fs(\\maxheaderlines)f Fr(is)i(100,)g(whic)o(h)g(is)105 2575 y(almost)c(alw)o(a)o(ys)h(adequate.)105 2729 y FD(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 14 14 14 13 bop 105 -25 a Fz(11.)17 b(F)m(on)o(ts)1605 b(14)-225 116 y FL(Section)10 b(\\F)n(on)o(ts")-225 145 y(\045)h(Ov)o(erall)i (Organiza-)-183 174 y(tion)-225 203 y(Section)e(\\The)g(Index,)-183 232 y(the)h(T)n(able)h(of)-183 261 y(Con)o(ten)o(ts)d(and)i(the)-183 290 y(Glossary")-225 319 y(\045)i(Lab)q(els)g(and)-183 348 y(Cross-References)-225 377 y(\045)f(Theorems)d(and)-183 406 y(Their)g(F)n(riends)-225 435 y(\045)g(Pro)q(o\014ng)h(Aids)105 120 y FE(11.)25 b(F)-5 b(on)n(ts)105 222 y FD(As)11 b(men)o(tioned)g (in)h(Section)f(2,)g(the)g FB(geom)f FD(st)o(yle)h(requires)h(NFSS,)e (a)h(rational)f(fon)o(t)g(managemen)o(t)g(system)105 278 y(that)k(mak)o(es)h(the)g(use)h(of)f(new)g(fon)o(ts)f(easier)i (than)f(under)h(old)g(L)1203 272 y Fw(a)1224 278 y FD(T)1249 292 y(E)1274 278 y(X.)188 334 y(Under)j(this)f(sc)o(heme,)h(unlik)o(e)h (the)e(old,)h(if)g(y)o(ou)f(sa)o(y)f FB(\\bf...)23 b(\\small...)p FD(,)17 b(the)i FB(\\small)e FD(has)h(no)105 391 y(e\013ect)e(on)g(the) h(b)q(oldness)g(of)f(the)h(curren)o(t)f(fon)o(t|size,)h(b)q(oldness,)g (st)o(yle)g(and)f(so)g(on)h(are)f(indep)q(enden)o(t)105 447 y(attributes.)41 b(This)23 b(is)g(generally)g(go)q(o)q(d,)h(but)f (it)f(do)q(es)h(create)f(bac)o(kw)o(ard)g(incompatibilities.)45 b(F)l(or)105 504 y(example,)20 b(if)f(y)o(ou)f(ha)o(v)o(e)g(an)g(old)h (L)699 498 y Fw(a)720 504 y FD(T)745 518 y(E)771 504 y(X)f(do)q(cumen)o(t)h(where)g(y)o(ou'v)o(e)f(relied)i(on)e FB(\\small)g FD(to)g(reset)g(the)105 560 y(w)o(eigh)o(t)j(of)g(the)g (fon)o(t,)h(y)o(ou're)f(in)h(for)e(a)h(surprise.)39 b(Also,)23 b FB(\\rm)e FD(should)h(generally)h(b)q(e)f(replaced)g(b)o(y)105 617 y FB(\\normalshape)p FD(.)c(F)l(or)d(a)g(list)h(of)e(all)j(suc)o(h) e(di\013erences,)h(see)g([Ame].)188 673 y(Another)24 b(case)g(of)g(con\015icting)h(ideas)g(on)f(what)f(fon)o(t-c)o(hange)h (commands)g(should)h(do)e(is)i(in-)105 730 y(side)e(math)e(mo)q(de.)41 b(Under)22 b(NFSS,)g FB(\\bf)g FD(has)f(no)h(e\013ect)g(inside)i(math)d (mo)q(de|y)o(ou)i(need)f(to)g(sa)o(y)105 786 y FB($\\mathbf{xyz}$)p FD(,)15 b(for)i(example.)27 b(The)17 b FB(geom)g FD(st)o(yle)g(will)i (prin)o(t)e(a)g(w)o(arning)g(on)g(y)o(our)g(terminal)h(if)g(it)105 843 y(sees)d FB(\\bf)g FD(in)h(math)f(mo)q(de.)188 899 y(In)20 b(addition)g(to)f(the)g(math-mo)q(de)h(commands)f FB(\\mathbf)p FD(,)g FB(\\mathrm)f FD(and)h FB(\\mathit)p FD(,)g(the)h FB(geom)105 955 y FD(st)o(yle)c(de\014nes)g FB(\\mathss)f FD(and)h FB(\\mathtt)e FD(as)h(the)h(math)f(mo)q(de)h (coun)o(terparts)f(of)g FB(\\sf)g FD(\(sans-serif)t(\))g(and)105 1012 y FB(\\tt)g FD(\(t)o(yp)q(ewriter)g(t)o(yp)q(e\).)188 1068 y(Supp)q(ort)e(for)g(F)l(raktur)f(\(\\gothic"\))g(and)h(blac)o(kb) q(oard-b)q(old)h(fon)o(ts)e(is)i(pro)o(vided,)g(as)e(w)o(ell)i(as)f (for)f(the)105 1125 y(fon)o(ts)h FB(msam)h FD(and)g FB(msbm)p FD(,)f(whic)o(h)i(con)o(tain)f(a)g(plethora)g(of)g(mathematical)g(sym)o (b)q(ols.)20 b(This)15 b(is)f(all)h(thanks)105 1181 y(to)h(the)h(AMS,)g (and)g(y)o(ou)f(should)i(turn)f(to)f(the)h FA(A)964 1191 y(M)1014 1181 y(S)p FD(-L)1069 1175 y Fw(a)1090 1181 y FD(T)1115 1195 y(E)1140 1181 y(X)g(distribution)i([Ame])d(if)h(y)o (our)g(site)g(lac)o(ks)105 1238 y(the)e(fon)o(ts)g(themselv)o(es)g(or)g (the)g(prerequisite)i(auxiliary)g(\014les)f FB(amsfonts.sty)d FD(and)j FB(amssymb.sty)p FD(.)105 1364 y FE(12.)25 b(The)18 b(Index,)f(the)i(T)-5 b(able)18 b(of)h(Con)n(ten)n(ts)g(and)h(the)e (Glossary)105 1466 y FD(The)d(basic)h(command)f(for)g(putting)g (something)g(in)o(to)g(the)h(index)g(is)g FB(\\index)p FD(,)d(as)i(in)h(standard)f(L)1787 1460 y Fw(a)1808 1466 y FD(T)1833 1480 y(E)1858 1466 y(X.)105 1522 y(But)f FB(\\index)f FD(do)q(es)h(not)g(prin)o(t)g(its)g(argumen)o(t.)19 b(T)l(o)14 b(index)h(a)e(w)o(ord)h(that)f(actually)i(app)q(ears)f(in)g (the)g(text)105 1579 y(sa)o(y)c FB(\\ix{...})p FD(.)17 b(T)l(o)11 b(index)h(mathematical)f(notation)f(sa)o(y)g FB(\\ixn$...$)g FD(or)g FB(\\ixninv$...$)p FD(,)g(dep)q(ending)105 1635 y(on)17 b(whether)h(the)f(con)o(ten)o(ts)g(should)i(app)q(ear)e (or)g(not.)26 b(And,)19 b(just)e(for)f(symmetry)l(,)i(y)o(ou)f(can)g (also)h(use)105 1692 y FB(\\ixinv)p FD(,)c(whic)o(h)i(equals)g FB(\\index)p FD(:)799 1781 y(T)l(ext)311 b(Notation)375 1863 y(Visible)291 b FB(\\ix)330 b(\\ixn)375 1919 y FD(In)o(visible)261 b FB(\\ixinv)d(\\ixninv)188 2021 y FD(An)14 b(index)g(en)o(try)f(is)h (made)g(automatically)g(for)e(an)o(y)h FB(\\label)g FD(or)g FB(\\ref)g FD(command.)19 b(In)14 b(the)f(second)105 2078 y(case)i(the)g(en)o(try)g(go)q(es)g(in)o(to)g(the)h(index)g (\014le)g(preceded)h(b)o(y)e(a)g FB(\045)p FD(.)188 2134 y(Remem)o(b)q(er)g(that,)d(unless)j(y)o(ou)f(ha)o(v)o(e)f(issued)i(the) f(command)f FB(\\autolabelfalse)p FD(,)f(there)i(are)f(lots)105 2191 y(of)h(situations)h(in)g(whic)o(h)g(a)f(lab)q(el,)i(and)e (consequen)o(tly)i(an)e(index)i(en)o(try)l(,)e(is)h(generated)f (automatically:)105 2247 y(in)19 b(particular,)h(this)f(happ)q(ens)g (for)f(eac)o(h)g(sectioning)i(command)e(\(Section)h(5\))f(and)g(for)g (eac)o(h)h(tagged)105 2304 y(theorem,)i(lemma,)g(and)f(so)f(on)h (\(Section)h(6\).)33 b(This)21 b(pro)o(vides)f(a)g(w)o(ealth)g(of)g (index)h(en)o(tries,)g(whic)o(h)105 2360 y(later)15 b(y)o(ou)h(can)f (winno)o(w)h(out)f(semi-automatically)l(,)h(if)g(necessary)l(,)g(since) g(en)o(tries)g(of)f(this)h(sort)f(app)q(ear)105 2416 y(in)j(quotation)e(marks,)g(preceded)i(b)o(y)f(their)g(t)o(yp)q(e.)25 b(Y)l(ou)17 b(can)g(see)g(all)g(the)g(en)o(tries)g(that)f(a)h(giv)o(en) g(page)105 2473 y(con)o(tributes)j(to)f(the)h(index)h(b)o(y)f(lo)q (oking)h(at)e(the)h(small)g(prin)o(t)g(on)g(the)g(top)f(left)i(of)e (the)h(page)f(when)105 2529 y(pro)q(o\014ng)c(mo)q(de)h(is)f(on)g (\(Section)h(13\).)105 2729 y(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 15 15 15 14 bop 105 -25 a Fz(13.)17 b(Pro)q(o\014ng)d(Aids)1466 b(15)-225 116 y FL(F)n(rank)10 b(Mittelbac)o(h)-225 145 y Fa(y)p FL(dagger)-225 174 y(\045)i(No)g(More)g(F)n(ragile)-183 203 y(Commands)-225 232 y(Section)g(\\Pro)q(o\014ng)-183 261 y(Aids")105 120 y Fq(\003)76 b Fr(The)14 b Fs(geom)g Fr(st)o(yle)g(mo)q(di\014es)f(the)h Fs(\\theindex)e Fr(format)h(of)g (standard)h(L)1297 115 y Fp(a)1316 120 y Fr(T)1339 133 y(E)1363 120 y(X)g(so)g(that)g(the)h(index)f(is)g(prin)o(ted)105 170 y(in)20 b(smaller)g(t)o(yp)q(e.)39 b(Moreo)o(v)o(er,)22 b(it)f(ac)o(hiev)o(es)g(a)g(double-column)e(format)g(not)h(b)o(y)h (using)f(standard)i(L)1781 165 y Fp(a)1800 170 y Fr(T)1823 182 y(E)1846 170 y(X's)105 220 y Fs(\\twocolumn)11 b Fr(command,)f(whic)o(h)i(starts)i(a)f(new)g(page,)g(but)g(rather)h(F)m (rank)e(Mittelbac)o(h's)h Fs(multicols)e Fr(en)o(viron-)105 270 y(men)o(t)h([Mit89],)e(whic)o(h)j(is)f(implemen)o(ted)e(in)i(the)h (\014le)g Fs(multicol.sty)p Fr(.)i(Using)d(this)h(en)o(vironmen)o(t)e (y)o(ou)h(can)h(ha)o(v)o(e)105 319 y(single-column)f(and)i (double-column)e(text)i(on)g(the)g(same)f(page.)19 b(If)13 b(y)o(ou)h(w)o(an)o(t)f(to)h(add)g(an)f(explanation)g(b)q(efore)105 369 y(the)h(index,)g(for)f(example,)g(y)o(ou)g(migh)o(t)f(sa)o(y)h (something)g(lik)o(e)g(this:)147 463 y Fs(\\begin{theindex)o(})147 512 y(\\null)260 b(\045)22 b(this)f(avoids)f(what)h(seems)g(to)g(be)h (a)f(bug)g(in)h(multicol.sty)147 562 y(\\end{multicols})40 b(\045)22 b(end)f(double)f(column)h(format)f(started)h(by)g (\\begin{theindex})147 662 y(Numbers)f(in)h(parentheses)f(refer)h(to)g (pages)g(where)f(the)i(entry)e(should)h(be)147 712 y(discussed)e(but)j (isn't,)e(due)h(to)h(laziness)e(on)h(the)g(author's)g(part.)147 811 y(\\begin{multicol)o(s}2)e(\045)i(restart)g(double)f(column)h (format)147 861 y(\\item)f(aardvark...)147 911 y(\\end{theindex})105 1011 y FD(Supp)q(ort)13 b(for)f(a)h(glossary)f(is)h(somewhat)f(more)h (extensiv)o(e)g(than)g(in)h(standard)e(L)1464 1005 y Fw(a)1485 1011 y FD(T)1510 1025 y(E)1536 1011 y(X.)g(Y)l(ou)h(can)g (mark)f(a)105 1067 y(w)o(ord)g(as)h(a)g(glossary)g(en)o(try)f(b)o(y)i (sa)o(ying)f FB(\\glo{...})p FD(;)f(this)i(causes)f(a)1293 1051 y Fb(y)1310 1067 y FD(dagger)g(to)f(b)q(e)i(placed)g(b)q(efore)g (the)105 1124 y(w)o(ord,)j(and)g(an)g(index)h(en)o(try)f(for)g(the)g(w) o(ord)f(to)h(b)q(e)h(generated)f(in)h(the)f(\014le)h Fv(jobname)p FB(.idx)p FD(,)f(preceded)105 1180 y(b)o(y)e FB(\\dag)p FD(.)105 1253 y Fq(\003)75 b Fr(Note)14 b(that)g(the)g Fs(geom)e Fr(st)o(yle)i(do)q(es)g(not)g(use)g(a)f(separate)i Fi(jobname)p Fs(.glo)e Fr(\014le;)g(although)g(standard)h(L)1781 1248 y Fp(a)1800 1253 y Fr(T)1823 1266 y(E)1846 1253 y(X's)105 1303 y Fs(\\glossary)e Fr(command)g(is)i(still)g(a)o(v)n (ailable)e(if)i(y)o(ou)g(insist)g(in)g(writing)f(en)o(tries)j(to)e (that)h(\014le,)f(this)g(command)e(has)105 1353 y(not)i(b)q(een)h(made) e(robust)h(in)f(the)i(w)o(a)o(y)e(that)h Fs(\\index)f Fr(and)g Fs(\\label)g Fr(ha)o(v)o(e.)18 b(\(See)d(Section)f(4.\))188 1432 y FD(The)22 b(glossary)g(itself)h(is)g(delimited)i(b)o(y)d FB(\\begin{theglossary})d FD(and)k FB(\\end{theglossary})p FD(.)105 1489 y(Glossary)15 b(en)o(tries)g(start)f(lik)o(e)i(this:)147 1582 y Fs(\\entry{doohicke)o(y})j(...)147 1632 y(\\entry[\\cite{..)o (.}]{t)o(hinga)o(majig)o(})g(...)105 1732 y FD(The)d(en)o(try)g(name)h (is)f(prin)o(ted)h(in)g(b)q(oldface,)g(follo)o(w)o(ed)g(b)o(y)f(a)g(p)q (erio)q(d.)24 b(The)17 b(con)o(ten)o(ts)e(of)h(the)g(optional)105 1788 y(argumen)o(t)e(are)h(prin)o(ted)h(immediately)h(after)d(the)i(en) o(try)e(name,)h(b)q(efore)h(the)f(p)q(erio)q(d.)21 b(The)16 b(commen)o(ts)105 1845 y(made)f(ab)q(o)o(v)o(e)g(ab)q(out)g (double-column)j(formatting)c(apply)i(to)e(the)i(glossary)e(as)h(w)o (ell.)188 1901 y(The)d(table)g(of)g(con)o(ten)o(ts)f(is)h(treated)g(in) h(m)o(uc)o(h)e(the)h(same)g(w)o(a)o(y)f(as)g(in)i(standard)e(L)1551 1895 y Fw(a)1572 1901 y FD(T)1597 1915 y(E)1623 1901 y(X,)g(but)h(there)g(is)105 1958 y(one)j(imp)q(ortan)o(t)f (di\013erence:)21 b(starred)13 b(sectioning)j(commands,)e(lik)o(e)i FB(\\section*)p FD(,)d(do)i(sho)o(w)e(up)i(in)h(the)105 2014 y(table)g(of)f(con)o(ten)o(ts,)f(unless)i(y)o(ou'v)o(e)f(said)g FB(\\starredcontentsfalse)p FD(.)j(Since)e(one)g(generally)g(do)q (esn't)105 2071 y(w)o(an)o(t)e(the)g(table)h(of)f(con)o(ten)o(ts)g(to)g (include)j(an)e(en)o(try)f(for)g(the)h(table)g(of)f(con)o(ten)o(ts)g (itself,)h(the)g(de\014nition)105 2127 y(of)g FB(\\tableofcontents)e FD(in)j FB(geomart.sty)d FD(starts)h(lik)o(e)j(this:)147 2220 y Fs(\\def\\tableofcon)o(tents)o({{\\st)o(arred)o(cont)o(entsf)o (alse\\)o(secti)o(on*{C)o(onten)o(ts}.)o(..}})105 2320 y FD(The)e(extra)g(pair)h(of)e(braces)i(limits)g(the)f(action)h(of)f FB(\\starredcontentsfalse)d FD(to)i(this)i(en)o(try)f(only)l(.)105 2446 y FE(13.)25 b(Pro)r(o\014ng)18 b(Aids)105 2548 y FD(The)e FB(geom)f FD(st)o(yle)h(pro)o(vides)h(a)e(n)o(um)o(b)q(er)h (of)g(pro)q(o\014ng)g(aids)g(that)f(y)o(ou)h(can)g(turn)f(on)h(and)g (o\013)f(b)o(y)h(sa)o(ying)105 2604 y FB(\\proofingtrue)c FD(and)i FB(\\proofingfalse)p FD(.)k(The)c(default)h(is)f(for)f(pro)q (o\014ng)h(to)g(b)q(e)g(on.)20 b(These)14 b(facilities)105 2729 y(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 16 16 16 15 bop 105 -25 a Fz(App)q(endix:)19 b Fg(mathfig)p Fz(|A)10 b(System)k(for)f(Doing)h(T)o(yp)q(esetting)h(in)e(Mathematica) 573 b(16)-225 116 y FL(\045)12 b(The)g(Index,)f(the)-183 145 y(T)n(able)f(of)h(Con)o(ten)o(ts)-183 174 y(and)f(the)g(Glossary) -225 203 y(R)o(CS)-225 232 y(Section)h(\\App)q(endix:)-183 261 y Fy(mathfig)p FL(|A)-183 290 y(System)e(for)i(Doing)-183 319 y(T)o(yp)q(esetting)h(in)-183 348 y(Mathematica")105 120 y FD(are)17 b(indep)q(enden)o(t)j(of)e(standard)f(L)702 114 y Fw(a)723 120 y FD(T)748 134 y(E)774 120 y(X's)g FB(draft)g FD(option)h(to)f(the)g FB(book)g FD(and)h FB(article)f FD(st)o(yle,)h(whose)105 177 y(only)e(e\013ect)f(is)g(to)g (mak)o(e)g(o)o(v)o(erfull)g(b)q(o)o(x)h(mark)o(ers)e(visible.)188 233 y(If)22 b(y)o(ou)f(use)g(L)428 227 y Fw(a)449 233 y FD(T)474 247 y(E)500 233 y(X's)g FB(\\includeonly)e FD(mec)o(hanism)j([Lam86,)g(76],)f(y)o(ou)g(can)h(prin)o(t)f(y)o(our)g (\014nal)105 289 y(v)o(ersion)e(b)o(y)g(passing)g(the)f(macro)g FB(\\noproofing)f FD(as)i(the)g(argumen)o(t)e(to)h FB(\\includeonly)p FD(.)29 b(This)19 b(not)105 346 y(only)d(turns)g(o\013)f(all)i(pro)q (o\014ng)f(aids,)g(but)g(also)f(prev)o(en)o(ts)h(L)1109 340 y Fw(a)1130 346 y FD(T)1155 360 y(E)1180 346 y(X)g(from)f(starting) h(a)f(new)h(page)g(for)f(eac)o(h)105 402 y(input)g(\014le.)20 b(\(Naturally)l(,)14 b(the)g(page)g(breaks)g(will)h(lik)o(ely)h(b)q(e)e (di\013eren)o(t)g(b)q(ecause)h(of)e(that,)g(so)h(y)o(ou'll)g(need)105 459 y(to)h(run)g(the)g(job)g(t)o(wice)h(to)e(get)h(cross-references)h (righ)o(t.\))105 532 y Fq(\003)76 b Fr(Normally)11 b(y)o(ou)j(ha)o(v)o (e)f(t)o(w)o(o)h(lines)f(lik)o(e)h(this)g(in)f(the)h(main)e(\014le)i (for)g(y)o(our)f(do)q(cumen)o(t:)147 627 y Fs(\\typein[\\sectio)o (nstoi)o(nclud)o(e]{En)o(ter)18 b(the)k(sections)e(that)h(should)f(be)i (processed:)d(})147 677 y(\\includeonly{\\s)o(ectio)o(nstoi)o(nclud)o (e})105 772 y Fr(so)f(y)o(ou)f(can)i(t)o(yp)q(e)f(in)f(the)i(sections)g (to)f(b)q(e)g(included)g(from)e(the)j(terminal,)e(without)g(ha)o(ving)g (to)h(mo)q(dify)d(the)105 822 y(source)g(\014le.)j(The)d(macro)d Fs(\\noproofing)g Fr(w)o(orks)i(in)f(this)h(mo)q(de,)e(to)q(o.)188 902 y FD(By)j(the)h(w)o(a)o(y)l(,)e(if)h(y)o(ou)g(are)g(using)h(the)f FB(book)g FD(st)o(yle,)g(the)g(construction)h FB(\\chap1{345})d FD(expands)j(to)147 997 y Fs(chap1/1.3,chap1)o(/1.4,)o(chap1)o(/1.5)105 1098 y FD(This)23 b(has)f(nothing)h(to)e(do)h(with)h(pro)q(o\014ng,)h (but)e(it)g(pro)o(vides)h(a)f(useful)h(shorthand)f(for)g(use)h(with)105 1155 y FB(\\includeonly)p FD(.)29 b(Braces)19 b(should)h(b)q(e)g(used)f (around)g(a)f(section)i(or)e(c)o(hapter)h(n)o(um)o(b)q(er)g(ha)o(ving)g (more)105 1211 y(than)c(one)g(digit.)188 1268 y(In)20 b(pro)q(o\014ng)g(mo)q(de)g(y)o(ou)f(get,)h(to)f(the)g(left)h(of)f(the) h(main)g(text,)g(a)f(column)i(in)f(tin)o(y)g(prin)o(t)g(with)105 1324 y(all)e(the)f(index)h(en)o(tries)f(con)o(tributed)h(b)o(y)f(that)f (page.)25 b(This)17 b(includes)j(automatic)c(en)o(tries)h(with)g(their) 105 1381 y(resp)q(ectiv)o(e)f(pre\014xes)g(\(see)f(Section)h(12\).)188 1437 y(If)f(y)o(ou)f(are)g(in)h(pro)q(of)f(mo)q(de)h(and)g(the)f (macros)g FB(\\leftfoot)f FD(and)i FB(\\rightfoot)e FD(are)h (de\014ned,)i(they)105 1494 y(will)k(b)q(e)f(t)o(yp)q(eset)g(\015ush)g (left)g(and)g(\015ush)g(righ)o(t)f(on)h(the)f(fo)q(otline.)31 b(These)19 b(macros)f(are)g(often)h(de\014ned)105 1550 y(to)g(con)o(tain)g(information)h(ab)q(out)f(draft)f(v)o(ersion,)j (date)e(of)g(last)g(mo)q(di\014cation,)i(etc.,)f(whic)o(h)g(can)f(b)q (e)105 1607 y(up)q(dated)d(automatically)l(.)105 1680 y Fq(\003)76 b Fr(Near)14 b(the)h(top)f(of)f(the)h(source)i(\014le)d (for)h(this)g(do)q(cumen)o(t,)f(I)h(wrote)g(the)h(lines)147 1775 y Fs(\\def\\leftfoot{\\)o(RCSst)o(ring$)o(Revis)o(ion:)j(1.12)j ($})147 1825 y(\\def\\rightfoot{)o(\\RCSs)o(tring)o($Date)o(:)e (95/07/03)h(15:57:22)g($})147 1875 y(\\def\\RCSstring$)o(#1)f(${#1})105 1970 y Fr(The)c(\014rst)g(t)o(w)o(o)f(lines)g(are)h(automatically)d(up) q(dated)j(b)o(y)f(the)h(UNIX)g(utilit)o(y)e(R)o(CS)h(\(Revision)g(Con)o (trol)f(System\))105 2019 y(whenev)o(er)19 b(I)f(c)o(hec)o(k)h(the)g (\014le)f(in)f(or)h(out.)31 b(R)o(CS)17 b(requires)i(that)f(the)h(k)o (eyw)o(ords)f Fs(Revision)p Fr(,)f Fs(Date)g Fr(and)h(so)g(on)105 2069 y(b)q(e)f(found)f(within)f(dollar)h(signs,)g(and)g(it)g(tac)o(ks)h (on)f(a)g(blank)g(b)q(efore)h(the)g(closing)e Fs($)h Fr(for)g(go)q(o)q(d)g(measure.)26 b(The)105 2119 y Fs(\\RCSstring)12 b Fr(macro)g(eliminates)h(this)h(extraneous)h(stu\013.)105 2269 y FE(App)r(endix:)24 b Ff(mathfig)p FE(|A)16 b(System)h(for)h (Doing)h(T)n(yp)r(esetting)e(in)h(Mathematica)105 2372 y(W)-5 b(arning.)22 b FH(The)33 b(soft)o(w)o(are)g(describ)q(ed)g(in)f (this)h(App)q(endix)f(dep)q(ends)h(on)h(Mathematica)105 2430 y([W)l(ol91].)21 b(I)15 b(mak)o(e)f(no)i(represen)o(tation)f (whatso)q(ev)o(er)h(concerning)f(its)g(p)q(erformance.)20 b(Although)105 2488 y(I)d(ha)o(v)o(e)f(used)h Ff(mathfig)e FH(under)i(Mathematica)f(v)o(ersions)h(1.2,)g(2.0)g(and)h(2.1,)g(I)e (emphasize)g(that)105 2546 y Ff(mathfig)c FH(ma)o(y)i(fail)g(to)h(w)o (ork)g(as)h(describ)q(ed)e(here)g(and)i(that)f(I)g(tak)o(e)f(no)h(resp) 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b(usage)g(of)g(this)g(program)f(is)i(the)f(follo)o(wing:) 147 378 y Fs(mathfig)e Fr([)h Fs(-d)h Fi(dir)n(e)n(ctory)f Fr(])g([)g Fs(-i)h Fi(init\014le)f Fr(])h Fi(\014les)105 466 y FD(The)j FB(-d)f FD(option)h(mak)o(es)f(all)i(\014le)g(names)e (relativ)o(e)h(to)f(the)h(sp)q(eci\014ed)i(directory)l(.)25 b(The)17 b FB(-i)f FD(option)h(tells)105 522 y(Mathematica)c(to)g(read) g(an)h(initialization)j(\014le.)j(An)o(y)14 b(n)o(um)o(b)q(er)f(of)h (\014les)g(can)g(b)q(e)g(passed)g(as)f(subsequen)o(t)105 579 y(argumen)o(t;)f FB(\\mathfig)e FD(pro)q(cesses)j(one)f(at)f(a)g (time,)i(starting)e(a)h(new)g(Mathematica)f(session)h(eac)o(h)g(time.) 188 635 y(The)17 b(steps)g(p)q(erformed)g(b)o(y)g FB(mathfig)f FD(when)h(pro)q(cessing)h(the)f(\014le)h FB(foo.m)e FD(are)g(the)h (follo)o(wing.)26 b(It)105 692 y(calls)c FB(math)e FD(and)g(giv)o(es)h (it)g(the)g(commands)f FB(Get[")p Fv(init\014le)p FB("])e FD(\(if)j(an)f(initialization)k(\014le)e(w)o(as)d(sp)q(eci-)105 748 y(\014ed\))f(and)f 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b(if)f(y)o(ou)g(assign)g(v)n(alues)f(to)i(the)f(v)n(ariables)g Fs($xlo)p Fr(,)g Fs($xhi)p Fr(,)h Fs($ylo)e Fr(and)h Fs($yhi)p Fr(,)h(the)f(\014gure)105 1545 y(pro)q(duced)13 b(b)o(y)f(Mathematica)f(will)f(b)q(e)j(clipp)q(ed)f(to)g(a)f(windo)o(w) h(with)f(the)i(giv)o(en)e(b)q(oundaries,)i(and)f(rescaled)h(so)f(as)105 1595 y(to)f(\014t)h(in)f(a)g(b)q(o)o(x)g(of)g(the)h(giv)o(en)f(heigh)o (t)h(and)f(width.)17 b(F)m(or)11 b(example,)f(setting)i Fs($xlo=$ylo=.1)d Fr(and)i Fs($xhi=$yhi=.9)105 1645 y Fr(will)i(trim)f(10\045)h(o\013)h(the)h(size)g(of)e(the)i(b)q(o)o(x)f (around)g(eac)o(h)g(edge,)h(and)e(the)i(remaining)d(graphics)i(will)f (b)q(e)i(rescaled)105 1695 y(b)o(y)h(a)f(factor)h(of)g(1)p Fh(=)p Fr(\()p Fh(:)p Fr(9)9 b Fq(\000)i Fh(:)p Fr(1\))k(=)g(1)p Fh(:)p Fr(25.)23 b(Under)17 b(Mathematica)e(1.2,)g(this)h(is)f(the)i (only)e(w)o(a)o(y)h(I)f(kno)o(w)h(to)g(mak)o(e)e(a)105 1745 y(3D-graphics)i(ob)r(ject)i(o)q(ccup)o(y)g(the)f(whole)g(b)q (ounding)f(b)q(o)o(x.)27 b(Unfortunately)17 b(the)g(v)n(alues)g(of)f Fs($xlo)g Fr(and)h(so)g(on)105 1794 y(ha)o(v)o(e)d(to)f(b)q(e)i (determined)f(b)o(y)f(trial)h(and)f(error.)188 1844 y(The)j(sym)o(b)q (ols)f Fs($height)p Fr(,)f Fs($width)p Fr(,)h Fs($xlo)p Fr(,)g Fs($ylo)p Fr(,)g Fs($xhi)p Fr(,)g Fs($yhi)g Fr(and)h Fs($Def)f Fr(should)h(not)f(b)q(e)i(used)g(in)e(y)o(our)105 1894 y(Mathematica)e(source)i(\014le)f(except)h(with)e(the)i(meanings)d (describ)q(ed)k(ab)q(o)o(v)o(e.)i(\()p Fs($Def)13 b Fr(is)h(used)g(in)o (ternally)m(.\))188 1944 y(When)j(Mathematica)f(generates)j(a)e (picture)h(with)f(lab)q(els,)g(the)h(scaling)f(computations)e(are)j (implicit)c(in)105 1994 y(the)f(resulting)f(P)o(ostScript)i(co)q(de,)f (and)f(they)h(tak)o(e)f(in)o(to)g(accoun)o(t)h(the)g(dimensions)e(of)g (the)i(lab)q(els)f(presen)o(t)i(in)e(the)105 2043 y(co)q(de.)19 b(Th)o(us)14 b(the)h(graph)e(generated)i(b)o(y)147 2127 y Fs(Plot[x,{x,0,1}])105 2210 y Fr(lo)q(oks)e(a)h(bit)f(smaller)g(on)g (the)i(screen)h(than)e(the)g(one)g(generated)i(b)o(y)147 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673 y([Lam86])52 b(Leslie)13 b(Lamp)q(ort.)g(L)653 667 y Fw(a)674 673 y FD(T)699 686 y(E)725 673 y(X)p Fv(:)f(A)g(Do)n (cument)h(Pr)n(ep)n(ar)n(ation)f(System)p FD(.)g(Addison-W)l(esley)l(,) i(Read-)318 729 y(ing,)i(MA,)e(1986.)105 804 y([Mit89])69 b(F)l(rank)15 b(Mittelbac)o(h.)21 b(An)15 b(en)o(vironmen)o(t)h(for)f (m)o(ulti-column)i(output.)j Fv(TUGb)n(o)n(at)p FD(,)14 b(10:407{)318 861 y(415,)g(1989.)105 936 y([Rok])107 b(T)l(om)15 b(Rokic)o(ki.)21 b(D)o(VIPS:)15 b(A)g(T)846 946 y(E)871 936 y(X)g(driv)o(er)h(\(v)o(ersion)f(5.490,)e(1992\).)18 b(Distributed)e(with)g(the)318 992 y(soft)o(w)o(are)e(\(use)h(anon)o (ymous)f(ftp)h(from)g FB(labrea.stanford.edu)p FD(\).)105 1068 y([S)143 1051 y Fu(+)170 1068 y FD(88])89 b(Mik)o(e)16 b(Sc)o(h)o(uster)f(et)g(al.)20 b Fv(A)n(dob)n(e)c(Il)r(lustr)n(ator)p FD(.)j(Adob)q(e)d(Systems,)f(P)o(alo)g(Alto,)f(CA,)h(1988.)105 1143 y([W)l(ol91])63 b(Stephen)13 b(W)l(olfram.)h Fv(Mathematic)n(a:)20 b(A)13 b(System)f(for)i(Doing)f(Mathematics)g(by)h(Computer)p FD(.)318 1199 y(Addison-W)l(esley)l(,)j(Reading,)f(MA,)f(2nd)g (edition,)h(1991.)105 2729 y(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Page: 19 19 19 18 bop 105 -25 a Fz(Index)1669 b(19)-225 116 y FL(Section)10 b(\\Index")105 120 y FE(Index)105 2729 y FD(Revision:)22 b(1.12)1029 b(Date:)19 b(95/07/03)13 b(15:57:22)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF