diff options
Diffstat (limited to 'doc/design/outfile.ps')
-rw-r--r-- | doc/design/outfile.ps | 722 |
1 files changed, 368 insertions, 354 deletions
diff --git a/doc/design/outfile.ps b/doc/design/outfile.ps index c142bee..469005f 100644 --- a/doc/design/outfile.ps +++ b/doc/design/outfile.ps @@ -1,6 +1,6 @@ %!PS-Adobe-3.0 -%%Creator: Basser Lout Version 3.38 (September 2008) -%%CreationDate: Tue Oct 14 07:37:29 2008 +%%Creator: Basser Lout Version 3.39 (September 2010) +%%CreationDate: Tue Sep 21 13:16:16 2010 %%DocumentData: Binary %%DocumentNeededResources: (atend) %%DocumentSuppliedResources: (atend) @@ -253,6 +253,9 @@ % % % PostScript @SysPrependGraphic file for @Tab % % % +% This file has been placed in the public domain % +% by its author, Jeffrey H. Kingston % +% % % To assist in avoiding name clashes, the names % % of all these symbols begin with "ltab". % % % @@ -371,6 +374,9 @@ % PostScript @SysPrependGraphic file for @Fig Jeffrey H. Kingston % % Version 2.0 (includes CIRCUM label) January 1992 % % % +% This file has been placed in the public domain by its author, % +% Jeffrey H. Kingston % +% % % Although Fig is now obsolete I have updated it 20 October 2002 % % to work with textures, i.e. replacing setrgbcolor with % % LoutSetRGBColor. % @@ -1375,6 +1381,14 @@ end %%BeginResource: procset LoutBasicSetup % @PrependGraphic file /home/jeff/lout.lib/include/bsf.lpg +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % +% PostScript @SysPrependGraphic file for @BasicSetup % +% % +% This file has been placed in the public domain by its author, % +% Jeffrey H. Kingston % +% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % width height linethickness louteuro - % draw a Euro symbol of this width and height with this line thickness @@ -1686,7 +1700,7 @@ grestore 4489(of)s 4760(Sydne)s 3(y)k 5530(2006,)s 4095 10020(Australia)m 3739 9568(27)m 4027(January)s 15(,)k 4863(1993)s 240 fnt2 0 8926(1.)m 291(Intr)s 4(oduction)k -[ /Dest /LOUT18_677_s1_0_1 /DEST pdfmark +[ /Dest /LOUT18_694_s1_0_1 /DEST pdfmark 240 fnt1 480 8495(Lout)m 985([1,)s 1284(2])s 1515(is)s 1718(a)s 1877(high-le)s 6(v)k 3(el)k 2885(language)s 3798(for)s 4129(document)s 5126(formatting,)s 6234(designed)s @@ -1839,7 +1853,7 @@ gsave grestore 0 13256(further)m 709(impro)s 3(v)k 3(ement.)k 240 fnt2 0 12463(2.)m 291(Objects)s -[ /Dest /LOUT18_677_s2_0_1 /DEST pdfmark +[ /Dest /LOUT18_694_s2_0_1 /DEST pdfmark 240 fnt1 480 11987(The)m 923(essence)s 1725(of)s 2011(an)s 3(y)k 2424(mo)s 3(v)k 3(e)k 3021(to)s 3276(a)s 3457(higher)s 4144(le)s 6(v)k 3(el)k @@ -1873,58 +1887,58 @@ grestore 2866(in)s 3106(1984,)s 3690(the)s 4035(Eqn)s 4475(formatting)s 5533(language)s 6450([5])s 6764(stands)s 7410(out)s 7773(lik)s 2(e)k 8182(a)s 8344(beacon.)s 0 8845(In)m 256(Eqn,)s 749(a)s -915(mathematical)s 2256(formula)s 3072(such)s 3568(as)s 167 fnt4 -586 8392(2)m 240 fnt3 480 8332(x)m 240 fnt4 737 8324(+)m -938(1)s gsave -480 8276 translate -240 fnt3 552 0 0 0 240 288 12 LoutGraphic +915(mathematical)s 2256(formula)s 3072(such)s 3568(as)s 168 fnt4 +586 8390(2)m 240 fnt3 480 8330(x)m 240 fnt4 738 8322(+)m +939(1)s gsave +480 8274 translate +240 fnt3 553 0 0 0 240 288 12 LoutGraphic gsave 0 0 moveto xsize 0 lineto 0.05 ft setlinewidth stroke grestore grestore -699 8048(4)m 240 fnt1 0 7537(is)m -210(produced)s 1159(by)s 1453(typing)s 220 fnt5 480 7039({ x sup 2 + 1 } o)m 3(v)k 5(er 4)k -240 fnt1 0 6543(in)m 261(the)s 627(input)s 1197(\207le;)s -220 fnt5 1632 6540(sup)m 240 fnt1 2056 6543(and)m 220 fnt5 -2478 6540(o)m 3(v)k 5(er)k 240 fnt1 2975 6543(are)m +700 8046(4)m 240 fnt1 0 7535(is)m +210(produced)s 1159(by)s 1453(typing)s 220 fnt5 480 7037({ x sup 2 + 1 } o)m 3(v)k 5(er 4)k +240 fnt1 0 6541(in)m 261(the)s 627(input)s 1197(\207le;)s +220 fnt5 1632 6538(sup)m 240 fnt1 2056 6541(and)m 220 fnt5 +2478 6538(o)m 3(v)k 5(er)k 240 fnt1 2975 6541(are)m 3340(binary)s 4023(operators,)s 5037(and)s 5459(braces)s 6138(are)s 6503(used)s 7018(for)s 7374(grouping.)s 8421(This)s 8916(is)s -0 6255(document)m 1017(formatting)s 2091(at)s 2337(a)s 2516(v)s 3(ery)k +0 6253(document)m 1017(formatting)s 2091(at)s 2337(a)s 2516(v)s 3(ery)k 3006(high)s 3502(le)s 6(v)k 3(el,)k 4077(close)s 4638(to)s 4890(the)s 5252(language)s 6185(of)s 6469(mathematics)s -7741(itself,)s 8337(with)s 8833(all)s 0 5967(reference)m 943(to)s +7741(itself,)s 8337(with)s 8833(all)s 0 5965(reference)m 943(to)s 1182(font)s 1627(changes)s 2449(and)s 2853(spacing)s 3637(suppressed.)s -480 5593(Eqn)m 916(pro)s 3(vides)k 1780(a)s 1938(single)s +480 5591(Eqn)m 916(pro)s 3(vides)k 1780(a)s 1938(single)s 2557(data)s 3008(type)s 3468(\(let)s 3837(us)s 4093(call)s -4485(it)s 4669(the)s 240 fnt3 5009 5595(e)m 4(xpr)k 8(ession)k -240 fnt1 6014 5593(\),)m 6192(b)s 4(uilt)k 6679(up)s +4485(it)s 4669(the)s 240 fnt3 5009 5593(e)m 4(xpr)k 8(ession)k +240 fnt1 6014 5591(\),)m 6192(b)s 4(uilt)k 6679(up)s 6964(recursi)s 6(v)k 3(ely)k 8062(in)s 8297(conte)s 3(xt-)k -0 5305(free)m 457(style:)s 1106(where)s 1778(one)s 2212(e)s 3(xpression)k +0 5303(free)m 457(style:)s 1106(where)s 1778(one)s 2212(e)s 3(xpression)k 3321(may)s 3819(appear)s 9(,)k 4586(an)s 3(y)k 5015(e)s 3(xpression)k 6124(may)s 6622(appear)s 13(.)k -7442(This)s 7950(approach)s 8916(is)s 0 5017(common)m 905(in)s +7442(This)s 7950(approach)s 8916(is)s 0 5015(common)m 905(in)s 1158(algebra)s 1931(and)s 2345(programming)s 3710(languages,)s 4785(where)s 5435(its)s 5721(simplicity)s 6740(and)s 7154(e)s 3(xpressi)k 6(v)k 3(eness)k -8625(ha)s 4(v)k 3(e)k 0 4729(long)m 479(been)s +8625(ha)s 4(v)k 3(e)k 0 4727(long)m 479(been)s 987(appreciated;)s 2199(b)s 4(ut)k 2560(Eqn)s 3002(w)s 2(as)k 3423(the)s 3770(\207rst)s 4200(language)s 5119(to)s 5357(demonstrate)s 6581(its)s 6856(utility)s 7479(in)s 7721(document)s 8724(for)s 4(-)k -0 4441(matting.)m 480 4067(Each)m 1015(e)s 3(xpression)k 2092(is)s +0 4439(matting.)m 480 4065(Each)m 1015(e)s 3(xpression)k 2092(is)s 2302(treated)s 3009(by)s 3304(Eqn)s 3747(as)s 3997(a)s -4163(rectangle)s 5094(with)s 5577(a)s 240 fnt3 5743 4069(horizontal)m -6787(axis)s 240 fnt1 7167 4067(,)m 7274(used)s 7771(for)s -8110(alignment)s 0 3779(with)m 482(adjacent)s 1338(e)s 3(xpressions:)k -552 517 0 288 240 288 60 480 2922 LoutGr2 +4163(rectangle)s 5094(with)s 5577(a)s 240 fnt3 5743 4067(horizontal)m +6787(axis)s 240 fnt1 7167 4065(,)m 7274(used)s 7771(for)s +8110(alignment)s 0 3777(with)m 482(adjacent)s 1338(e)s 3(xpressions:)k +553 519 0 288 240 288 60 480 2918 LoutGr2 grestore save gsave 200 dict begin lfigdict begin grestore -552 517 0 288 240 288 60 0 0 LoutGr2 +553 519 0 288 240 288 60 0 0 LoutGr2 /lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore 0.015 cm setlinewidth lfiground setlinecap 0.15 cm /lfigsolid [ lfigbox ] lfigdopath pop pop grestore -552 517 0 288 240 288 60 0 0 LoutGr2 +553 519 0 288 240 288 60 0 0 LoutGr2 0.015 cm setlinewidth lfiground setlinecap 0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd @@ -1932,42 +1946,42 @@ grestore ] lfigdopath pop pop grestore -167 fnt4 106 404(2)m 240 fnt3 0 344(x)m 240 fnt4 -257 336(+)m 458(1)s gsave +168 fnt4 106 404(2)m 240 fnt3 0 344(x)m 240 fnt4 +258 336(+)m 459(1)s gsave 0 288 translate -240 fnt3 552 0 0 0 240 288 12 LoutGraphic +240 fnt3 553 0 0 0 240 288 12 LoutGraphic gsave 0 0 moveto xsize 0 lineto 0.05 ft setlinewidth stroke grestore grestore -219 60(4)m +220 60(4)m grestore grestore end end restore grestore -0 2471(The)m +0 2467(The)m 425(size)s 848(and)s 1248(rendering)s 2213(of)s 2481(the)s 2825(e)s 3(xpression)k 3898(on)s 4191(the)s 4536(printed)s 5267(page)s 5771(are)s 6114(kno)s 6(wn)k 6815(only)s -7291(to)s 7526(the)s 7870(implementa-)s 0 2183(tion,)m 481(ne)s 6(v)k 3(er)k +7291(to)s 7526(the)s 7870(implementa-)s 0 2179(tion,)m 481(ne)s 6(v)k 3(er)k 1066(e)s 3(xplicitly)k 2021(calculated)s 3050(or)s 3312(accessed)s 4208(by)s 4505(the)s 4855(user)s 13(.)k 5407(This)s 5886(prohibition)s 7008(is)s 7221(crucial)s 7927(to)s 8169(the)s -8520(main-)s 0 1895(tenance)m 785(of)s 1055(the)s 1402(conte)s 3(xt-)k +8520(main-)s 0 1891(tenance)m 785(of)s 1055(the)s 1402(conte)s 3(xt-)k 2171(free)s 2596(property)s 3459(in)s 3701(practice.)s 4619(In)s 4874(Lout,)s 5432(for)s 5769(e)s 3(xample,)k 6682(equations,)s -7705(\207gures,)s 8462(tables,)s 0 1607(and)m 393(arbitrary)s 1256(objects)s +7705(\207gures,)s 8462(tables,)s 0 1603(and)m 393(arbitrary)s 1256(objects)s 1972(may)s 2427(be)s 2697(mix)s 3(ed)k 3338(together)s 4169(freely)s 15(.)k 4863(This)s 5327(w)s 2(ould)k 5970(be)s 6241(impossible)s 7321(if)s 7526(size)s 7941(information)s -0 1319(w)m 2(as)k 421(hidden)s 1130(from)s 1654(the)s -2002(implementation)s 3559(in)s 3802(user)s 4260(calculations.)s 480 945(The)m +0 1315(w)m 2(as)k 421(hidden)s 1130(from)s 1654(the)s +2002(implementation)s 3559(in)s 3802(user)s 4260(calculations.)s 480 941(The)m 927(object)s 1591(abstraction)s 2715(of)s 3006(Lout)s 3537(is)s 3767(a)s 3952(direct)s 4575(descendant)s 5717(of)s 6008(the)s 6375(Eqn)s 6838(e)s 3(xpression.)k 8041(It)s 8266(emplo)s 2(ys)k -0 657(the)m 385(same)s 969(conte)s 3(xt-free)k 2212(recursi)s 6(v)k 3(e)k +0 653(the)m 385(same)s 969(conte)s 3(xt-free)k 2212(recursi)s 6(v)k 3(e)k 3171(style)s 3715(of)s 4023(construction,)s 5350(and)s 5791(each)s 6323(object)s 7004(is)s 7251(treated)s 7995(by)s 8326(Lout)s 8876(as)s @@ -3087,14 +3101,14 @@ grestore grestore gsave -2267 7394 translate +2267 7395 translate 180.0000 rotate gsave 0 0 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3114,8 +3128,8 @@ gsave 0 0 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3126,12 +3140,12 @@ grestore grestore gsave -1247 7394 translate +1247 7395 translate 30.0000 rotate gsave 0 1 translate 180 fnt1 -68 -1 0 -1 180 288 45 LoutGraphic +68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3140,7 +3154,7 @@ grestore grestore gsave -1247 7394 translate +1247 7395 translate 180 fnt1 1020 0 0 0 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke @@ -3148,11 +3162,11 @@ grestore grestore gsave -1247 7394 translate +1247 7395 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3198,14 +3212,14 @@ grestore grestore gsave -2267 6213 translate +2267 6214 translate 180.0000 rotate gsave 0 0 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3226,8 +3240,8 @@ gsave 0 0 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3238,11 +3252,11 @@ grestore grestore gsave -1247 6213 translate +1247 6214 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3251,7 +3265,7 @@ grestore grestore gsave -1247 6213 translate +1247 6214 translate 180 fnt1 1020 0 0 0 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke @@ -3259,11 +3273,11 @@ grestore grestore gsave -1247 6213 translate +1247 6214 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3309,7 +3323,7 @@ grestore grestore gsave -2551 4975 translate +2551 4976 translate 180.0000 rotate gsave 0 0 translate @@ -3317,7 +3331,7 @@ gsave gsave 0 1 translate 180 fnt1 -68 -1 0 -1 180 288 45 LoutGraphic +68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3337,8 +3351,8 @@ gsave 0 0 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3349,11 +3363,11 @@ grestore grestore gsave -680 4975 translate +680 4976 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3362,7 +3376,7 @@ grestore grestore gsave -680 4975 translate +680 4976 translate 180 fnt1 1871 0 0 0 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke @@ -3370,12 +3384,12 @@ grestore grestore gsave -680 4975 translate +680 4976 translate -30.0000 rotate gsave -0 0 translate +0 1 translate 180 fnt1 -68 -1 0 0 180 288 45 LoutGraphic +68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3421,14 +3435,14 @@ grestore grestore gsave -2551 3738 translate +2551 3739 translate 180.0000 rotate gsave 0 0 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3448,8 +3462,8 @@ gsave 0 0 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3460,11 +3474,11 @@ grestore grestore gsave -680 3738 translate +680 3739 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3473,7 +3487,7 @@ grestore grestore gsave -680 3738 translate +680 3739 translate 180 fnt1 1871 0 0 0 180 288 45 LoutGraphic gsave @@ -3482,11 +3496,11 @@ grestore grestore gsave -680 3738 translate +680 3739 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3498,14 +3512,14 @@ grestore 180 fnt3 1319 3537(length)m 180 fnt4 1774 3531(,)m 180 fnt3 1854 3537(a)m 180 fnt4 1994 3531(+)m 180 fnt3 2145 3537(b)m 180 fnt4 2240 3531(\))m gsave -1247 4362 translate +1247 4363 translate 180.0000 rotate gsave 0 0 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3525,9 +3539,9 @@ gsave 0 0 translate -30.0000 rotate gsave -0 0 translate +0 1 translate 180 fnt1 -68 -1 0 0 180 288 45 LoutGraphic +68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3538,11 +3552,11 @@ grestore grestore gsave -680 4362 translate +680 4363 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3551,7 +3565,7 @@ grestore grestore gsave -680 4362 translate +680 4363 translate 180 fnt1 567 0 0 0 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke @@ -3559,11 +3573,11 @@ grestore grestore gsave -680 4362 translate +680 4363 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3573,14 +3587,14 @@ grestore grestore 180 fnt3 920 4431(a)m gsave -2551 4362 translate +2551 4363 translate 180.0000 rotate gsave 0 0 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3600,8 +3614,8 @@ gsave 0 0 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3612,11 +3626,11 @@ grestore grestore gsave -2268 4362 translate +2268 4363 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3625,7 +3639,7 @@ grestore grestore gsave -2268 4362 translate +2268 4363 translate 180 fnt1 283 0 0 0 180 288 45 LoutGraphic gsave @@ -3634,11 +3648,11 @@ grestore grestore gsave -2268 4362 translate +2268 4363 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3684,14 +3698,14 @@ grestore grestore gsave -2551 2442 translate +2551 2443 translate 180.0000 rotate gsave 0 0 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3711,8 +3725,8 @@ gsave 0 0 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3723,12 +3737,12 @@ grestore grestore gsave -680 2442 translate +680 2443 translate 30.0000 rotate gsave 0 1 translate 180 fnt1 -68 -1 0 -1 180 288 45 LoutGraphic +68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3737,7 +3751,7 @@ grestore grestore gsave -680 2442 translate +680 2443 translate 180 fnt1 1871 0 0 0 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke @@ -3745,11 +3759,11 @@ grestore grestore gsave -680 2442 translate +680 2443 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3761,14 +3775,14 @@ grestore 1314 2235(\()m 180 fnt3 1377 2241(length)m 180 fnt4 1832 2235(,)m 180 fnt3 1912 2241(a)m 180 fnt4 2007 2235(,)m 180 fnt3 2087 2241(b)m 180 fnt4 2182 2235(\))m gsave -1247 3066 translate +1247 3067 translate 180.0000 rotate gsave 0 0 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3789,8 +3803,8 @@ gsave 0 0 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3801,11 +3815,11 @@ grestore grestore gsave -680 3066 translate +680 3067 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3814,7 +3828,7 @@ grestore grestore gsave -680 3066 translate +680 3067 translate 180 fnt1 567 0 0 0 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke @@ -3822,11 +3836,11 @@ grestore grestore gsave -680 3066 translate +680 3067 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3836,14 +3850,14 @@ grestore grestore 180 fnt3 920 3135(a)m gsave -2551 3066 translate +2551 3067 translate 180.0000 rotate gsave 0 0 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3863,8 +3877,8 @@ gsave 0 0 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3875,12 +3889,12 @@ grestore grestore gsave -2268 3066 translate +2268 3067 translate 30.0000 rotate gsave 0 1 translate 180 fnt1 -68 -1 0 -1 180 288 45 LoutGraphic +68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3889,7 +3903,7 @@ grestore grestore gsave -2268 3066 translate +2268 3067 translate 180 fnt1 283 0 0 0 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke @@ -3897,11 +3911,11 @@ grestore grestore gsave -2268 3066 translate +2268 3067 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3947,14 +3961,14 @@ grestore grestore gsave -2268 1233 translate +2268 1234 translate 180.0000 rotate gsave 0 0 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3974,9 +3988,9 @@ gsave 0 0 translate -30.0000 rotate gsave -0 0 translate +0 1 translate 180 fnt1 -68 -1 0 0 180 288 45 LoutGraphic +68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -3987,11 +4001,11 @@ grestore grestore gsave -0 1233 translate +0 1234 translate 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -4000,7 +4014,7 @@ grestore grestore gsave -0 1233 translate +0 1234 translate 180 fnt1 2268 0 0 0 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke @@ -4008,11 +4022,11 @@ grestore grestore gsave -0 1233 translate +0 1234 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -4029,7 +4043,7 @@ gsave gsave 0 1 translate 180 fnt1 -68 -1 0 -1 180 288 45 LoutGraphic +68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -4049,8 +4063,8 @@ gsave 0 0 translate -30.0000 rotate gsave -0 0 translate -180 fnt1 68 -1 0 0 180 288 45 LoutGraphic +0 1 translate +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -4065,7 +4079,7 @@ gsave 30.0000 rotate gsave 0 1 translate -180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic +180 fnt1 68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -4085,9 +4099,9 @@ gsave 0 734 translate -30.0000 rotate gsave -0 0 translate +0 1 translate 180 fnt1 -68 -1 0 0 180 288 45 LoutGraphic +68 -2 0 -1 180 288 45 LoutGraphic gsave 0 0 moveto xsize 0 lineto stroke grestore @@ -4095,7 +4109,7 @@ grestore grestore grestore -1189 522(curr)m 6(ent)k 1759(bound)s +1189 523(curr)m 6(ent)k 1759(bound)s grestore end end restore grestore @@ -4985,116 +4999,116 @@ grestore 924(mode)s 1512(is)s 1722(mark-to-mark,)s 3155(and)s 3559(so)s 3825(on.)s 4229(Gi)s 6(v)k 3(en)k 4862(an)s 5145(object)s 240 fnt3 480 9992(X)m 240 fnt4 720 9984(=)m -240 fnt3 933 9992(x)m 167 fnt4 1039 9900(1)m 240 fnt4 -1248 9984(|)m 240 fnt3 1293 9992(g)m 167 fnt4 1404 9900(1)m -240 fnt4 1613 9984(\274)m 200 fnt3 1971 10000(^)m 240 fnt4 -2067 9984(|)m 240 fnt3 2112 9992(g)m 167 fnt3 2223 9905(i)m -167 fnt4 2289 9900(-)m 2400(1)s 240 fnt3 2609 9992(x)m -167 fnt3 2715 9905(i)m 240 fnt4 2903 9984(\274)m 3261(|)s -240 fnt3 3306 9992(g)m 167 fnt3 3417 9905(n)m 167 fnt4 -3518 9900(-)m 3629(1)s 240 fnt3 3838 9992(x)m 167 fnt3 -3944 9905(n)m 240 fnt1 0 9449(we)m 335(may)s 801(calculate)s +240 fnt3 933 9992(x)m 168 fnt4 1039 9899(1)m 240 fnt4 +1249 9984(|)m 240 fnt3 1294 9992(g)m 168 fnt4 1405 9899(1)m +240 fnt4 1615 9984(\274)m 200 fnt3 1973 10000(^)m 240 fnt4 +2069 9984(|)m 240 fnt3 2114 9992(g)m 168 fnt3 2225 9905(i)m +168 fnt4 2291 9899(-)m 2403(1)s 240 fnt3 2613 9992(x)m +168 fnt3 2719 9905(i)m 240 fnt4 2907 9984(\274)m 3265(|)s +240 fnt3 3310 9992(g)m 168 fnt3 3421 9905(n)m 168 fnt4 +3523 9899(-)m 3635(1)s 240 fnt3 3845 9992(x)m 168 fnt3 +3951 9905(n)m 240 fnt1 0 9448(we)m 335(may)s 801(calculate)s 1705(its)s 1981(size)s 2408(as)s 2658(follo)s 6(ws:)k -240 fnt3 740 8946(left)m 240 fnt4 1060 8938(\()m 240 fnt3 -1144 8946(X)m 240 fnt4 1312 8938(\))m 1474(=)s 240 fnt3 -1687 8946(left)m 240 fnt4 2007 8938(\()m 240 fnt3 2091 8946(x)m -167 fnt4 2197 8854(1)m 240 fnt4 2274 8938(\))m 2412(+)s -240 fnt3 2613 8946(hgap)m 240 fnt4 3098 8938(\()m 240 fnt3 -3182 8946(x)m 167 fnt4 3288 8854(1)m 240 fnt4 3365 8938(,)m -240 fnt3 3472 8946(g)m 167 fnt4 3583 8854(1)m 240 fnt4 -3660 8938(,)m 240 fnt3 3767 8946(x)m 167 fnt4 3873 8854(2)m -240 fnt4 3964 8938(\))m 4102(+)s 4303(\274)s 4589(+)s -240 fnt3 4790 8946(hgap)m 240 fnt4 5275 8938(\()m 240 fnt3 -5359 8946(x)m 167 fnt3 5465 8859(i)m 167 fnt4 5531 8854(-)m -5642(1)s 240 fnt4 5719 8938(,)m 240 fnt3 5826 8946(g)m -167 fnt3 5937 8859(i)m 167 fnt4 6003 8854(-)m 6114(1)s -240 fnt4 6191 8938(,)m 240 fnt3 6298 8946(x)m 167 fnt3 -6404 8859(i)m 240 fnt4 6460 8938(\))m 240 fnt3 579 8543(right)m -240 fnt4 1060 8535(\()m 240 fnt3 1144 8543(X)m 240 fnt4 -1312 8535(\))m 1474(=)s 240 fnt3 1687 8543(hgap)m 240 fnt4 -2172 8535(\()m 240 fnt3 2256 8543(x)m 167 fnt3 2362 8456(i)m -240 fnt4 2418 8535(,)m 240 fnt3 2525 8543(g)m 167 fnt3 -2636 8456(i)m 240 fnt4 2692 8535(,)m 240 fnt3 2799 8543(x)m -167 fnt3 2905 8456(i)m 167 fnt4 2971 8451(+)m 3083(1)s -240 fnt4 3160 8535(\))m 3298(+)s 3499(\274)s 3785(+)s -240 fnt3 3986 8543(hgap)m 240 fnt4 4471 8535(\()m 240 fnt3 -4555 8543(x)m 167 fnt3 4661 8456(n)m 167 fnt4 4762 8451(-)m -4873(1)s 240 fnt4 4950 8535(,)m 240 fnt3 5057 8543(g)m -167 fnt3 5168 8456(n)m 167 fnt4 5269 8451(-)m 5380(1)s -240 fnt4 5457 8535(,)m 240 fnt3 5564 8543(x)m 167 fnt3 -5670 8456(n)m 240 fnt4 5761 8535(\))m 5899(+)s 240 fnt3 -6100 8543(right)m 240 fnt4 6581 8535(\()m 240 fnt3 6665 8543(x)m -167 fnt3 6771 8456(n)m 240 fnt4 6862 8535(\))m 240 fnt3 -485 8140(abo)m 2(ve)k 240 fnt4 1060 8132(\()m 240 fnt3 -1144 8140(X)m 240 fnt4 1312 8132(\))m 1474(=)s 240 fnt3 -1687 8140(abo)m 2(ve)k 240 fnt4 2262 8132(\()m 240 fnt3 -2346 8140(x)m 167 fnt4 2452 8046(1)m 240 fnt4 2529 8132(\))m -2679(\255)s 2900(\274)s 3198(\255)s 240 fnt3 3419 8140(abo)m 2(ve)k -240 fnt4 3994 8132(\()m 240 fnt3 4078 8140(x)m 167 fnt3 -4184 8051(n)m 240 fnt4 4275 8132(\))m 240 fnt3 480 7737(below)m -240 fnt4 1060 7729(\()m 240 fnt3 1144 7737(X)m 240 fnt4 -1312 7729(\))m 1474(=)s 240 fnt3 1687 7737(below)m 240 fnt4 -2267 7729(\()m 240 fnt3 2351 7737(x)m 167 fnt4 2457 7643(1)m -240 fnt4 2534 7729(\))m 2684(\255)s 2905(\274)s 3203(\255)s -240 fnt3 3424 7737(below)m 240 fnt4 4004 7729(\()m 240 fnt3 -4088 7737(x)m 167 fnt3 4194 7648(n)m 240 fnt4 4285 7729(\))m -240 fnt1 0 7143(where)m 240 fnt4 693 7137(\255)m 240 fnt1 -943 7143(returns)m 1678(the)s 2046(lar)s 4(ger)k 2679(of)s +240 fnt3 740 8945(left)m 240 fnt4 1060 8937(\()m 240 fnt3 +1144 8945(X)m 240 fnt4 1312 8937(\))m 1474(=)s 240 fnt3 +1687 8945(left)m 240 fnt4 2007 8937(\()m 240 fnt3 2091 8945(x)m +168 fnt4 2197 8852(1)m 240 fnt4 2275 8937(\))m 2413(+)s +240 fnt3 2614 8945(hgap)m 240 fnt4 3099 8937(\()m 240 fnt3 +3183 8945(x)m 168 fnt4 3289 8852(1)m 240 fnt4 3367 8937(,)m +240 fnt3 3474 8945(g)m 168 fnt4 3585 8852(1)m 240 fnt4 +3663 8937(,)m 240 fnt3 3770 8945(x)m 168 fnt4 3876 8852(2)m +240 fnt4 3968 8937(\))m 4106(+)s 4307(\274)s 4593(+)s +240 fnt3 4794 8945(hgap)m 240 fnt4 5279 8937(\()m 240 fnt3 +5363 8945(x)m 168 fnt3 5469 8858(i)m 168 fnt4 5535 8852(-)m +5647(1)s 240 fnt4 5725 8937(,)m 240 fnt3 5832 8945(g)m +168 fnt3 5943 8858(i)m 168 fnt4 6009 8852(-)m 6121(1)s +240 fnt4 6199 8937(,)m 240 fnt3 6306 8945(x)m 168 fnt3 +6412 8858(i)m 240 fnt4 6468 8937(\))m 240 fnt3 579 8542(right)m +240 fnt4 1060 8534(\()m 240 fnt3 1144 8542(X)m 240 fnt4 +1312 8534(\))m 1474(=)s 240 fnt3 1687 8542(hgap)m 240 fnt4 +2172 8534(\()m 240 fnt3 2256 8542(x)m 168 fnt3 2362 8455(i)m +240 fnt4 2418 8534(,)m 240 fnt3 2525 8542(g)m 168 fnt3 +2636 8455(i)m 240 fnt4 2692 8534(,)m 240 fnt3 2799 8542(x)m +168 fnt3 2905 8455(i)m 168 fnt4 2971 8449(+)m 3084(1)s +240 fnt4 3162 8534(\))m 3300(+)s 3501(\274)s 3787(+)s +240 fnt3 3988 8542(hgap)m 240 fnt4 4473 8534(\()m 240 fnt3 +4557 8542(x)m 168 fnt3 4663 8455(n)m 168 fnt4 4765 8449(-)m +4877(1)s 240 fnt4 4955 8534(,)m 240 fnt3 5062 8542(g)m +168 fnt3 5173 8455(n)m 168 fnt4 5275 8449(-)m 5387(1)s +240 fnt4 5465 8534(,)m 240 fnt3 5572 8542(x)m 168 fnt3 +5678 8455(n)m 240 fnt4 5770 8534(\))m 5908(+)s 240 fnt3 +6109 8542(right)m 240 fnt4 6590 8534(\()m 240 fnt3 6674 8542(x)m +168 fnt3 6780 8455(n)m 240 fnt4 6872 8534(\))m 240 fnt3 +485 8139(abo)m 2(ve)k 240 fnt4 1060 8131(\()m 240 fnt3 +1144 8139(X)m 240 fnt4 1312 8131(\))m 1474(=)s 240 fnt3 +1687 8139(abo)m 2(ve)k 240 fnt4 2262 8131(\()m 240 fnt3 +2346 8139(x)m 168 fnt4 2452 8044(1)m 240 fnt4 2530 8131(\))m +2680(\255)s 2901(\274)s 3199(\255)s 240 fnt3 3420 8139(abo)m 2(ve)k +240 fnt4 3995 8131(\()m 240 fnt3 4079 8139(x)m 168 fnt3 +4185 8050(n)m 240 fnt4 4277 8131(\))m 240 fnt3 480 7736(below)m +240 fnt4 1060 7728(\()m 240 fnt3 1144 7736(X)m 240 fnt4 +1312 7728(\))m 1474(=)s 240 fnt3 1687 7736(below)m 240 fnt4 +2267 7728(\()m 240 fnt3 2351 7736(x)m 168 fnt4 2457 7641(1)m +240 fnt4 2535 7728(\))m 2685(\255)s 2906(\274)s 3204(\255)s +240 fnt3 3425 7736(below)m 240 fnt4 4005 7728(\()m 240 fnt3 +4089 7736(x)m 168 fnt3 4195 7647(n)m 240 fnt4 4287 7728(\))m +240 fnt1 0 7141(where)m 240 fnt4 693 7135(\255)m 240 fnt1 +943 7141(returns)m 1678(the)s 2046(lar)s 4(ger)k 2679(of)s 2971(its)s 3267(tw)s 2(o)k 3698(parameters.)s 4930(Similar)s 5712(formulas)s 6633(are)s 7001(easily)s 7632(deri)s 6(v)k 3(ed)k -8419(for)s 8778(the)s 0 6855(other)m 551(operators.)s 480 6481(F)m 3(or)k +8419(for)s 8778(the)s 0 6853(other)m 551(operators.)s 480 6479(F)m 3(or)k 866(purposes)s 1765(of)s 2033(e)s 3(xposition)k 3081(we)s 3412(will)s 3835(no)s 6(w)k 4293(mak)s 2(e)k 4862(the)s 5207(simplifying)s 6358(assumptions)s 7589(that)s 8004(all)s -8294(g)s 1(aps)k 8779(are)s 220 fnt5 0 6190(0i)m -240 fnt1 156 6193(,)m 248(all)s 525(column)s 1285(marks)s +8294(g)s 1(aps)k 8779(are)s 220 fnt5 0 6188(0i)m +240 fnt1 156 6191(,)m 248(all)s 525(column)s 1285(marks)s 1904(lie)s 2183(at)s 2399(the)s 2732(left)s 3093(edge,)s 3637(and)s 4025(all)s 4303(ro)s 6(w)k 4707(marks)s 5327(lie)s 5605(at)s 5822(the)s 6154(top)s 6498(edge.)s 7098(Then)s 7632(the)s 7964(size)s 8376(of)s 8631(each)s -0 5905(object)m 644(can)s 1033(be)s 1315(e)s 3(xpressed)k +0 5903(object)m 644(can)s 1033(be)s 1315(e)s 3(xpressed)k 2313(by)s 2607(just)s 3012(tw)s 2(o)k 3422(numbers,)s 4353(width)s 4955(and)s 5359(height,)s 6064(and)s 6468(the)s 6816(four)s 7274(formulas)s 8174(reduce)s 8867(to)s 240 fnt3 -555 5402(width)m 240 fnt4 1094 5394(\()m 240 fnt3 1178 5402(x)m -167 fnt4 1284 5310(1)m 240 fnt4 1433 5394(|)m 1550(\274)s -1848(|)s 240 fnt3 1965 5402(x)m 167 fnt3 2071 5315(n)m -240 fnt4 2162 5394(\))m 2324(=)s 240 fnt3 2537 5402(width)m -240 fnt4 3076 5394(\()m 240 fnt3 3160 5402(x)m 167 fnt4 -3266 5310(1)m 240 fnt4 3343 5394(\))m 3481(+)s 3682(\274)s -3968(+)s 240 fnt3 4169 5402(width)m 240 fnt4 4708 5394(\()m -240 fnt3 4792 5402(x)m 167 fnt3 4898 5315(n)m 240 fnt4 -4989 5394(\))m 240 fnt3 480 4999(height)m 240 fnt4 1094 4991(\()m -240 fnt3 1178 4999(x)m 167 fnt4 1284 4907(1)m 240 fnt4 -1433 4991(|)m 1550(\274)s 1848(|)s 240 fnt3 1965 4999(x)m -167 fnt3 2071 4912(n)m 240 fnt4 2162 4991(\))m 2324(=)s -240 fnt3 2537 4999(height)m 240 fnt4 3151 4991(\()m 240 fnt3 -3235 4999(x)m 167 fnt4 3341 4907(1)m 240 fnt4 3418 4991(\))m -3568(\255)s 3789(\274)s 4087(\255)s 240 fnt3 4308 4999(height)m -240 fnt4 4922 4991(\()m 240 fnt3 5006 4999(x)m 167 fnt3 -5112 4912(n)m 240 fnt4 5203 4991(\))m 240 fnt1 0 4456(The)m +555 5400(width)m 240 fnt4 1094 5392(\()m 240 fnt3 1178 5400(x)m +168 fnt4 1284 5307(1)m 240 fnt4 1434 5392(|)m 1551(\274)s +1849(|)s 240 fnt3 1966 5400(x)m 168 fnt3 2072 5313(n)m +240 fnt4 2164 5392(\))m 2326(=)s 240 fnt3 2539 5400(width)m +240 fnt4 3078 5392(\()m 240 fnt3 3162 5400(x)m 168 fnt4 +3268 5307(1)m 240 fnt4 3346 5392(\))m 3484(+)s 3685(\274)s +3971(+)s 240 fnt3 4172 5400(width)m 240 fnt4 4711 5392(\()m +240 fnt3 4795 5400(x)m 168 fnt3 4901 5313(n)m 240 fnt4 +4993 5392(\))m 240 fnt3 480 4997(height)m 240 fnt4 1094 4989(\()m +240 fnt3 1178 4997(x)m 168 fnt4 1284 4904(1)m 240 fnt4 +1434 4989(|)m 1551(\274)s 1849(|)s 240 fnt3 1966 4997(x)m +168 fnt3 2072 4910(n)m 240 fnt4 2164 4989(\))m 2326(=)s +240 fnt3 2539 4997(height)m 240 fnt4 3153 4989(\()m 240 fnt3 +3237 4997(x)m 168 fnt4 3343 4904(1)m 240 fnt4 3421 4989(\))m +3571(\255)s 3792(\274)s 4090(\255)s 240 fnt3 4311 4997(height)m +240 fnt4 4925 4989(\()m 240 fnt3 5009 4997(x)m 168 fnt3 +5115 4910(n)m 240 fnt4 5207 4989(\))m 240 fnt1 0 4453(The)m 428(corresponding)s 1850(formulas)s 2750(for)s 3088(v)s 3(ertical)k -3855(concatenation)s 5240(are)s 240 fnt3 555 3906(width)m 240 fnt4 -1094 3898(\()m 240 fnt3 1178 3906(x)m 167 fnt4 1284 3814(1)m -240 fnt3 1433 3906(/)m 240 fnt4 1608 3898(\274)m 240 fnt3 -1906 3906(/)m 2081(x)s 167 fnt3 2187 3819(n)m 240 fnt4 -2278 3898(\))m 2440(=)s 240 fnt3 2653 3906(width)m 240 fnt4 -3192 3898(\()m 240 fnt3 3276 3906(x)m 167 fnt4 3382 3814(1)m -240 fnt4 3459 3898(\))m 3609(\255)s 3830(\274)s 4128(\255)s -240 fnt3 4349 3906(width)m 240 fnt4 4888 3898(\()m 240 fnt3 -4972 3906(x)m 167 fnt3 5078 3819(n)m 240 fnt4 5169 3898(\))m -240 fnt3 480 3503(height)m 240 fnt4 1094 3495(\()m 240 fnt3 -1178 3503(x)m 167 fnt4 1284 3411(1)m 240 fnt3 1433 3503(/)m -240 fnt4 1608 3495(\274)m 240 fnt3 1906 3503(/)m 2081(x)s -167 fnt3 2187 3416(n)m 240 fnt4 2278 3495(\))m 2440(=)s -240 fnt3 2653 3503(height)m 240 fnt4 3267 3495(\()m 240 fnt3 -3351 3503(x)m 167 fnt4 3457 3411(1)m 240 fnt4 3534 3495(\))m -3672(+)s 3873(\274)s 4159(+)s 240 fnt3 4360 3503(height)m -240 fnt4 4974 3495(\()m 240 fnt3 5058 3503(x)m 167 fnt3 -5164 3416(n)m 240 fnt4 5255 3495(\))m 240 fnt1 0 2960(According)m +3855(concatenation)s 5240(are)s 240 fnt3 555 3903(width)m 240 fnt4 +1094 3895(\()m 240 fnt3 1178 3903(x)m 168 fnt4 1284 3810(1)m +240 fnt3 1434 3903(/)m 240 fnt4 1609 3895(\274)m 240 fnt3 +1907 3903(/)m 2082(x)s 168 fnt3 2188 3816(n)m 240 fnt4 +2280 3895(\))m 2442(=)s 240 fnt3 2655 3903(width)m 240 fnt4 +3194 3895(\()m 240 fnt3 3278 3903(x)m 168 fnt4 3384 3810(1)m +240 fnt4 3462 3895(\))m 3612(\255)s 3833(\274)s 4131(\255)s +240 fnt3 4352 3903(width)m 240 fnt4 4891 3895(\()m 240 fnt3 +4975 3903(x)m 168 fnt3 5081 3816(n)m 240 fnt4 5173 3895(\))m +240 fnt3 480 3500(height)m 240 fnt4 1094 3492(\()m 240 fnt3 +1178 3500(x)m 168 fnt4 1284 3407(1)m 240 fnt3 1434 3500(/)m +240 fnt4 1609 3492(\274)m 240 fnt3 1907 3500(/)m 2082(x)s +168 fnt3 2188 3413(n)m 240 fnt4 2280 3492(\))m 2442(=)s +240 fnt3 2655 3500(height)m 240 fnt4 3269 3492(\()m 240 fnt3 +3353 3500(x)m 168 fnt4 3459 3407(1)m 240 fnt4 3537 3492(\))m +3675(+)s 3876(\274)s 4162(+)s 240 fnt3 4363 3500(height)m +240 fnt4 4977 3492(\()m 240 fnt3 5061 3500(x)m 168 fnt3 +5167 3413(n)m 240 fnt4 5259 3492(\))m 240 fnt1 0 2956(According)m 1063(to)s 1302(these)s 1849(formulas,)s 2805(the)s 3153(height)s 3811(of)s gsave -480 1266 translate +480 1262 translate 240 fnt3 3044 1354 56 1298 240 288 12 LoutGraphic gsave grestore save gsave 200 dict begin lfigdict begin @@ -5386,34 +5400,34 @@ grestore 6323(we)s 6659(introduce)s 7618(a)s 7784(ne)s 6(w)k 8232(operator)s 9(,)k 240 fnt3 0 8807(COL)m 240 fnt1 466 8805(,)m 573(de\207ned)s 1336(by)s 240 fnt3 480 8255(width)m -240 fnt4 1019 8247(\()m 240 fnt3 1103 8255(x)m 167 fnt4 -1209 8163(1)m 240 fnt3 1346 8255(COL)m 240 fnt4 1884 8247(\274)m -240 fnt3 2170 8255(COL)m 2708(x)s 167 fnt3 2814 8168(n)m -240 fnt4 2905 8247(\))m 3055(=)s 240 fnt3 3268 8255(width)m -240 fnt4 3807 8247(\()m 240 fnt3 3891 8255(x)m 167 fnt4 -3997 8163(1)m 240 fnt4 4074 8247(\))m 4224(\255)s 4445(\274)s -4743(\255)s 240 fnt3 4964 8255(width)m 240 fnt4 5503 8247(\()m -240 fnt3 5587 8255(x)m 167 fnt3 5693 8168(n)m 240 fnt4 -5784 8247(\))m 240 fnt1 0 7712(and)m 440(replace)s 1221(both)s -240 fnt3 1741 7714(a)m 240 fnt1 1952 7712(and)m 240 fnt3 -2393 7714(c)m 240 fnt1 2591 7712(by)m 240 fnt3 2922 7714(a)m -3218(COL)s 3865(c)s 240 fnt1 3967 7712(.)m 4168(T)s 19(o)k -4504(pre)s 6(v)k 3(ent)k 240 fnt3 5309 7714(COL)m -240 fnt1 5871 7712(operators)m 6848(from)s 7408(disturbing)s 8468(height)s -0 7424(calculations,)m 1248(we)s 1583(de\207ne)s 2224(a)s 2390(binary)s -3055(operator)s 3911(called)s 240 fnt3 4539 7426(SPLIT)m 240 fnt1 -5228 7424(by)m 240 fnt3 555 6921(width)m 240 fnt4 1094 6913(\()m -240 fnt3 1178 6921(x)m 1356(SPLIT)s 2057(y)s 240 fnt4 -2171 6913(\))m 2333(=)s 240 fnt3 2546 6921(width)m 240 fnt4 -3085 6913(\()m 240 fnt3 3169 6921(x)m 240 fnt4 3287 6913(\))m -240 fnt3 480 6518(height)m 240 fnt4 1094 6510(\()m 240 fnt3 -1178 6518(x)m 1356(SPLIT)s 2057(y)s 240 fnt4 2171 6510(\))m -2333(=)s 240 fnt3 2546 6518(height)m 240 fnt4 3160 6510(\()m -240 fnt3 3244 6518(y)m 240 fnt4 3358 6510(\))m 240 fnt1 -0 6014(which)m 642(switches)s 1516(height)s 2174(and)s 2578(width)s +240 fnt4 1019 8247(\()m 240 fnt3 1103 8255(x)m 168 fnt4 +1209 8162(1)m 240 fnt3 1347 8255(COL)m 240 fnt4 1885 8247(\274)m +240 fnt3 2171 8255(COL)m 2709(x)s 168 fnt3 2815 8168(n)m +240 fnt4 2907 8247(\))m 3057(=)s 240 fnt3 3270 8255(width)m +240 fnt4 3809 8247(\()m 240 fnt3 3893 8255(x)m 168 fnt4 +3999 8162(1)m 240 fnt4 4077 8247(\))m 4227(\255)s 4448(\274)s +4746(\255)s 240 fnt3 4967 8255(width)m 240 fnt4 5506 8247(\()m +240 fnt3 5590 8255(x)m 168 fnt3 5696 8168(n)m 240 fnt4 +5788 8247(\))m 240 fnt1 0 7711(and)m 440(replace)s 1221(both)s +240 fnt3 1741 7713(a)m 240 fnt1 1952 7711(and)m 240 fnt3 +2393 7713(c)m 240 fnt1 2591 7711(by)m 240 fnt3 2922 7713(a)m +3218(COL)s 3865(c)s 240 fnt1 3967 7711(.)m 4168(T)s 19(o)k +4504(pre)s 6(v)k 3(ent)k 240 fnt3 5309 7713(COL)m +240 fnt1 5871 7711(operators)m 6848(from)s 7408(disturbing)s 8468(height)s +0 7423(calculations,)m 1248(we)s 1583(de\207ne)s 2224(a)s 2390(binary)s +3055(operator)s 3911(called)s 240 fnt3 4539 7425(SPLIT)m 240 fnt1 +5228 7423(by)m 240 fnt3 555 6920(width)m 240 fnt4 1094 6912(\()m +240 fnt3 1178 6920(x)m 1356(SPLIT)s 2057(y)s 240 fnt4 +2171 6912(\))m 2333(=)s 240 fnt3 2546 6920(width)m 240 fnt4 +3085 6912(\()m 240 fnt3 3169 6920(x)m 240 fnt4 3287 6912(\))m +240 fnt3 480 6517(height)m 240 fnt4 1094 6509(\()m 240 fnt3 +1178 6517(x)m 1356(SPLIT)s 2057(y)s 240 fnt4 2171 6509(\))m +2333(=)s 240 fnt3 2546 6517(height)m 240 fnt4 3160 6509(\()m +240 fnt3 3244 6517(y)m 240 fnt4 3358 6509(\))m 240 fnt1 +0 6013(which)m 642(switches)s 1516(height)s 2174(and)s 2578(width)s 3180(calculations)s 4372(onto)s 4851(dif)s 6(ferent)k 5726(subtrees.)s 6673(Then)s 7222(the)s 7570(transformation)s gsave -480 4315 translate +480 4314 translate 240 fnt3 338 1359 56 1298 240 288 12 LoutGraphic gsave grestore save gsave 200 dict begin lfigdict begin @@ -5434,8 +5448,8 @@ grestore grestore end end restore grestore -240 fnt4 1130 5553(\336)m gsave -1671 4315 translate +240 fnt4 1130 5552(\336)m gsave +1671 4314 translate 240 fnt3 2564 1359 56 1298 240 288 12 LoutGraphic gsave grestore save gsave 200 dict begin lfigdict begin @@ -5566,22 +5580,22 @@ grestore end end restore grestore 240 fnt1 -0 3815(widens)m 240 fnt3 740 3817(a)m 240 fnt1 926 3815(to)m -240 fnt3 1176 3817(width)m 240 fnt4 1726 3809(\()m 240 fnt3 -1821 3817(a)m 240 fnt4 1959 3809(\))m 2142(\255)s 240 fnt3 -2396 3817(width)m 240 fnt4 2946 3809(\()m 240 fnt3 3041 3817(c)m -240 fnt4 3166 3809(\))m 240 fnt1 3303 3815(without)m 4105(af)s 6(fecting)k +0 3814(widens)m 240 fnt3 740 3816(a)m 240 fnt1 926 3814(to)m +240 fnt3 1176 3816(width)m 240 fnt4 1726 3808(\()m 240 fnt3 +1821 3816(a)m 240 fnt4 1959 3808(\))m 2142(\255)s 240 fnt3 +2396 3816(width)m 240 fnt4 2946 3808(\()m 240 fnt3 3041 3816(c)m +240 fnt4 3166 3808(\))m 240 fnt1 3303 3814(without)m 4105(af)s 6(fecting)k 5011(its)s 5298(height;)s 6019(it)s 6222(is)s 6443(applied)s 7216(to)s 7466(e)s 6(v)k 3(ery)k 8053(object)s -8708(that)s 0 3527(shares)m 638(its)s 904(column)s 1669(mark)s +8708(that)s 0 3526(shares)m 638(its)s 904(column)s 1669(mark)s 2211(with)s 2683(at)s 2905(least)s 3392(one)s 3784(other)s 4325(object.)s 5063(A)s 5283(similar)s 5995(transformation)s 7448(in)s 9(v)k 4(olving)k -8396(a)s 240 fnt3 8552 3529(R)m 9(O)k 12(W)k -240 fnt1 0 3239(operator)m 856(deals)s 1398(with)s 1880(shared)s +8396(a)s 240 fnt3 8552 3528(R)m 9(O)k 12(W)k +240 fnt1 0 3238(operator)m 856(deals)s 1398(with)s 1880(shared)s 2562(ro)s 6(w)k 2982(marks.)s 3730(The)s 4158(ef)s 6(fect)k 4754(on)s 5051(our)s 5430(little)s 5922(table)s 6442(is)s 6652(to)s 6891(replace)s gsave -480 1545 translate +480 1544 translate 240 fnt3 3044 1354 56 1298 240 288 12 LoutGraphic gsave grestore save gsave 200 dict begin lfigdict begin @@ -5766,7 +5780,7 @@ grestore grestore end end restore grestore -0 1094(by)m +0 1093(by)m grestore 0 0 0 0 240 288 60 1417 -15423 LoutGr2 0 LoutMargSet @@ -6800,13 +6814,13 @@ grestore 2662 3918(f)m 240 fnt4 2823 3910(\))m 2973(\255)s 240 fnt3 3194 3918(width)m 240 fnt4 3733 3910(\()m 240 fnt3 3817 3918(i)m 240 fnt4 3892 3910(\))m -[ /Dest /LOUT12_1731_s2_4_1 /DEST pdfmark +[ /Dest /LOUT12_1748_s2_4_1 /DEST pdfmark 240 fnt3 480 3367(y)m 240 fnt4 666 3359(=)m 240 fnt3 879 3367(width)m 240 fnt4 1418 3359(\()m 240 fnt3 1502 3367(d)m 240 fnt4 1688 3359(\))m 1838(\255)s 240 fnt3 2059 3367(width)m 240 fnt4 2598 3359(\()m 240 fnt3 2682 3367(g)m 240 fnt4 2808 3359(\))m -[ /Dest /LOUT12_1731_s2_4_2 /DEST pdfmark +[ /Dest /LOUT12_1748_s2_4_2 /DEST pdfmark 240 fnt3 480 2816(z)m 240 fnt4 655 2808(=)m 240 fnt3 868 2816(width)m 240 fnt4 1407 2808(\()m 240 fnt3 1491 2816(b)m 240 fnt4 1617 2808(\))m @@ -6814,7 +6828,7 @@ grestore 240 fnt3 2611 2816(e)m 240 fnt4 2722 2808(\))m 2872(\255)s 240 fnt3 3093 2816(width)m 240 fnt4 3632 2808(\()m 240 fnt3 3716 2816(h)m 240 fnt4 3843 2808(\))m -[ /Dest /LOUT12_1731_s2_4_3 /DEST pdfmark +[ /Dest /LOUT12_1748_s2_4_3 /DEST pdfmark 240 fnt1 0 2312(It)m 224(seems)s 878(clear)s 1420(that)s 240 fnt3 1857 2314(y)m 240 fnt1 2038 2312(at)m 2289(least)s 2805(must)s 3349(appear)s @@ -7813,7 +7827,7 @@ grestore 4745(re)s 3(grettably)k 15(,)k 5868(it)s 6060(is)s 6270(not)s 6636(implemented.)s 240 fnt2 0 7547(3.)m 291(De\207nitions)s -[ /Dest /LOUT18_677_s3_0_1 /DEST pdfmark +[ /Dest /LOUT18_694_s3_0_1 /DEST pdfmark 240 fnt1 480 7116(The)m 936(need)s 1474(to)s 1741(pro)s 3(vide)k 2554(a)s 2748(means)s 3438(of)s 3737(packaging)s 4803(useful)s 5470(pieces)s 6146(of)s 6445(code)s 6982(for)s 7348(easy)s @@ -7838,9 +7852,9 @@ grestore 6774(results.)s 7569(F)s 3(or)k 7965(e)s 3(xample,)k 8887(to)s 0 4550(de\207ne)m 641(a)s 807(superscript)s 1915(operator)s 2771(so)s 3037(that)s 220 fnt5 480 4056(2 sup n)m 240 fnt1 -0 3531(appears)m 781(as)s 167 fnt1 1145 3647(n)m 240 fnt4 -1031 3525(2)m 240 fnt1 1226 3531(,)m 1333(the)s 1681(follo)s 6(wing)k -2658(operator)s 3514(de\207nition)s 4488(may)s 4954(be)s 5236(used:)s +0 3531(appears)m 781(as)s 168 fnt1 1145 3647(n)m 240 fnt4 +1031 3525(2)m 240 fnt1 1227 3531(,)m 1334(the)s 1682(follo)s 6(wing)k +2659(operator)s 3515(de\207nition)s 4489(may)s 4955(be)s 5237(used:)s 220 fnt5 480 3032(def sup)m 480 2744( precedence 50)m 480 2456( associativity r)m -3(ight)k 480 2168( left x)m 480 1880( r)m -3(ight y)k 480 1592({)m 480 1304( @OneRo)m 3(w { | {-2p @F)k 6(ont y} ^/0.5fk x })k 480 1016(})m 240 fnt1 0 520(The)m 220 fnt5 481 517(sup)m @@ -8917,7 +8931,7 @@ grestore 6696(the)s 7076(mer)s 4(ging)k 7954(of)s 8257(passes)s 8952(2)s 0 9082(and)m 404(3.)s 240 fnt2 0 8338(5.)m 291(Galleys)s -[ /Dest /LOUT18_677_s5_0_1 /DEST pdfmark +[ /Dest /LOUT18_694_s5_0_1 /DEST pdfmark 240 fnt1 480 7861(W)m 9(ith)k 1022(objects)s 1767(and)s 2188(de\207nitions)s 3266(under)s 3888(control,)s 4689(the)s 5053(author)s 5741(f)s 2(aced)k 6331(the)s 6696(problem)s @@ -11266,48 +11280,48 @@ grestore 5203(just)s 5624(one)s 6042(e)s 3(xample)k 6921(of)s 7208(ho)s 6(w)k 7685(these)s 8248(rules)s 8779(are)s 0 4217(deri)m 6(v)k 3(ed,)k 815(using)s 1387(the)s -1735(object)s 240 fnt3 480 3721(x)m 167 fnt4 586 3629(1)m -220 fnt5 771 3716(/)m 240 fnt3 955 3721(x)m 167 fnt4 -1061 3629(2)m 220 fnt5 1260 3716(/)m 240 fnt3 1444 3721(.)m -1550(.)s 1656(.)s 220 fnt5 1810 3716(/)m 240 fnt3 -1994 3721(x)m 167 fnt3 2100 3634(n)m 240 fnt1 0 3176(where)m -240 fnt3 640 3178(x)m 167 fnt3 746 3091(j)m 240 fnt1 -852 3176(has)m 1222(width)s 240 fnt3 1824 3178(l)m 167 fnt3 -1890 3091(j)m 240 fnt4 1948 3170(,)m 240 fnt3 2055 3178(r)m -167 fnt3 2127 3091(j)m 240 fnt1 2233 3176(for)m 2571(all)s -240 fnt3 2864 3178(j)m 240 fnt1 2930 3176(.)m 480 2802(Suppose)m +1735(object)s 240 fnt3 480 3721(x)m 168 fnt4 586 3628(1)m +220 fnt5 772 3716(/)m 240 fnt3 956 3721(x)m 168 fnt4 +1062 3628(2)m 220 fnt5 1262 3716(/)m 240 fnt3 1446 3721(.)m +1552(.)s 1658(.)s 220 fnt5 1812 3716(/)m 240 fnt3 +1996 3721(x)m 168 fnt3 2102 3634(n)m 240 fnt1 0 3175(where)m +240 fnt3 640 3177(x)m 168 fnt3 746 3090(j)m 240 fnt1 +852 3175(has)m 1222(width)s 240 fnt3 1824 3177(l)m 168 fnt3 +1890 3090(j)m 240 fnt4 1948 3169(,)m 240 fnt3 2055 3177(r)m +168 fnt3 2127 3090(j)m 240 fnt1 2233 3175(for)m 2571(all)s +240 fnt3 2864 3177(j)m 240 fnt1 2930 3175(.)m 480 2801(Suppose)m 1345(the)s 1689(whole)s 2326(object)s 2966(has)s 3333(width)s -3931(constraint)s 240 fnt3 4929 2804(X)m 240 fnt4 5097 2796(,)m -240 fnt3 5204 2804(Y)m 240 fnt4 5367 2796(,)m 240 fnt3 -5474 2804(Z)m 240 fnt1 5619 2802(,)m 5722(and)s 6123(we)s -6454(require)s 7182(the)s 7526(width)s 8124(constraint)s 0 2514(of)m -240 fnt3 271 2516(x)m 167 fnt3 377 2429(i)m 240 fnt1 -421 2514(.)m 586(Let)s 240 fnt3 965 2516(L)m 240 fnt4 -1185 2508(=)m 240 fnt1 1401 2514(max)m 167 fnt3 1808 2429(j)m -240 fnt3 1917 2516(l)m 167 fnt3 1983 2429(j)m 240 fnt1 -2090 2514(and)m 240 fnt3 2495 2516(R)m 240 fnt4 2723 2508(=)m -240 fnt1 2939 2514(max)m 167 fnt3 3346 2429(j)m 240 fnt3 -3455 2516(r)m 167 fnt3 3527 2429(j)m 240 fnt1 3573 2514(,)m -3681(so)s 3948(that)s 240 fnt3 4367 2516(L)m 240 fnt4 -4512 2508(,)m 240 fnt3 4619 2516(R)m 240 fnt1 4821 2514(is)m +3931(constraint)s 240 fnt3 4929 2803(X)m 240 fnt4 5097 2795(,)m +240 fnt3 5204 2803(Y)m 240 fnt4 5367 2795(,)m 240 fnt3 +5474 2803(Z)m 240 fnt1 5619 2801(,)m 5722(and)s 6123(we)s +6454(require)s 7182(the)s 7526(width)s 8124(constraint)s 0 2513(of)m +240 fnt3 271 2515(x)m 168 fnt3 377 2428(i)m 240 fnt1 +421 2513(.)m 586(Let)s 240 fnt3 965 2515(L)m 240 fnt4 +1185 2507(=)m 240 fnt1 1401 2513(max)m 168 fnt3 1808 2428(j)m +240 fnt3 1917 2515(l)m 168 fnt3 1983 2428(j)m 240 fnt1 +2090 2513(and)m 240 fnt3 2495 2515(R)m 240 fnt4 2723 2507(=)m +240 fnt1 2939 2513(max)m 168 fnt3 3346 2428(j)m 240 fnt3 +3455 2515(r)m 168 fnt3 3527 2428(j)m 240 fnt1 3573 2513(,)m +3681(so)s 3948(that)s 240 fnt3 4367 2515(L)m 240 fnt4 +4512 2507(,)m 240 fnt3 4619 2515(R)m 240 fnt1 4821 2513(is)m 5032(the)s 5381(width)s 5984(of)s 6256(the)s 6605(whole)s 7247(object.)s 7996(W)s 19(e)k 8366(assume)s 240 fnt3 -0 2203(L)m 240 fnt4 145 2195(,)m 240 fnt3 252 2203(R)m -240 fnt4 477 2195(\243)m 240 fnt3 687 2203(X)m 240 fnt4 -855 2195(,)m 240 fnt3 962 2203(Y)m 240 fnt4 1125 2195(,)m -240 fnt3 1232 2203(Z)m 240 fnt1 1377 2201(.)m 1541(Then)s -240 fnt3 2090 2203(x)m 167 fnt3 2196 2116(i)m 240 fnt1 -2300 2201(can)m 2689(be)s 2971(enlar)s 4(ged)k 3848(to)s -4087(an)s 3(y)k 4484(size)s 240 fnt3 4911 2203(l)m -167 fnt3 4977 2116(i)m 240 fnt4 5081 2195(,)m 240 fnt3 -5188 2203(r)m 167 fnt3 5260 2116(i)m 240 fnt1 5364 2201(satisfying)m -240 fnt4 480 1608(\()m 240 fnt3 564 1616(l)m 167 fnt3 -630 1529(i)m 240 fnt4 758 1608(\255)m 240 fnt3 979 1616(L)m -240 fnt4 1124 1608(\))m 1202(,)s 1309(\()s 240 fnt3 -1393 1616(r)m 167 fnt3 1465 1529(i)m 240 fnt4 1593 1608(\255)m -240 fnt3 1814 1616(R)m 240 fnt4 1967 1608(\))m 2117(\243)s -240 fnt3 2327 1616(X)m 240 fnt4 2495 1608(,)m 240 fnt3 -2602 1616(Y)m 240 fnt4 2765 1608(,)m 240 fnt3 2872 1616(Z)m +0 2202(L)m 240 fnt4 145 2194(,)m 240 fnt3 252 2202(R)m +240 fnt4 477 2194(\243)m 240 fnt3 687 2202(X)m 240 fnt4 +855 2194(,)m 240 fnt3 962 2202(Y)m 240 fnt4 1125 2194(,)m +240 fnt3 1232 2202(Z)m 240 fnt1 1377 2200(.)m 1541(Then)s +240 fnt3 2090 2202(x)m 168 fnt3 2196 2115(i)m 240 fnt1 +2300 2200(can)m 2689(be)s 2971(enlar)s 4(ged)k 3848(to)s +4087(an)s 3(y)k 4484(size)s 240 fnt3 4911 2202(l)m +168 fnt3 4977 2115(i)m 240 fnt4 5081 2194(,)m 240 fnt3 +5188 2202(r)m 168 fnt3 5260 2115(i)m 240 fnt1 5364 2200(satisfying)m +240 fnt4 480 1607(\()m 240 fnt3 564 1615(l)m 168 fnt3 +630 1528(i)m 240 fnt4 758 1607(\255)m 240 fnt3 979 1615(L)m +240 fnt4 1124 1607(\))m 1202(,)s 1309(\()s 240 fnt3 +1393 1615(r)m 168 fnt3 1465 1528(i)m 240 fnt4 1593 1607(\255)m +240 fnt3 1814 1615(R)m 240 fnt4 1967 1607(\))m 2117(\243)s +240 fnt3 2327 1615(X)m 240 fnt4 2495 1607(,)m 240 fnt3 +2602 1615(Y)m 240 fnt4 2765 1607(,)m 240 fnt3 2872 1615(Z)m grestore 0 0 0 0 240 288 60 1417 -15423 LoutGr2 @@ -11370,34 +11384,34 @@ gsave grestore 0 13253(which)m 642(e)s 3(xpands)k 1475(to)s 1714(eight)s 2252(inequalities:)s 240 fnt3 917 12702(l)m -167 fnt3 983 12615(i)m 240 fnt4 1123 12694(\243)m 240 fnt3 +168 fnt3 983 12615(i)m 240 fnt4 1123 12694(\243)m 240 fnt3 1333 12702(X)m 894 12338(L)m 240 fnt4 1123 12330(\243)m 240 fnt3 -1333 12338(X)m 528 12047(l)m 167 fnt3 594 11960(i)m 240 fnt4 -710 12039(+)m 240 fnt3 911 12047(r)m 167 fnt3 983 11960(i)m +1333 12338(X)m 528 12047(l)m 168 fnt3 594 11960(i)m 240 fnt4 +710 12039(+)m 240 fnt3 911 12047(r)m 168 fnt3 983 11960(i)m 240 fnt4 1123 12039(\243)m 240 fnt3 1333 12047(Y)m 503 11675(l)m -167 fnt3 569 11588(i)m 240 fnt4 685 11667(+)m 240 fnt3 +168 fnt3 569 11588(i)m 240 fnt4 685 11667(+)m 240 fnt3 886 11675(R)m 240 fnt4 1123 11667(\243)m 240 fnt3 1333 11675(Y)m 505 11311(L)m 240 fnt4 710 11303(+)m 240 fnt3 911 11311(r)m -167 fnt3 983 11224(i)m 240 fnt4 1123 11303(\243)m 240 fnt3 +168 fnt3 983 11224(i)m 240 fnt4 1123 11303(\243)m 240 fnt3 1333 11311(Y)m 480 10947(L)m 240 fnt4 685 10939(+)m 240 fnt3 886 10947(R)m 240 fnt4 1123 10939(\243)m 240 fnt3 1333 10947(Y)m -911 10664(r)m 167 fnt3 983 10577(i)m 240 fnt4 1123 10656(\243)m +911 10664(r)m 168 fnt3 983 10577(i)m 240 fnt4 1123 10656(\243)m 240 fnt3 1333 10664(Z)m 886 10300(R)m 240 fnt4 1123 10292(\243)m 240 fnt3 1333 10300(Z)m 240 fnt1 0 9793(Three)m 613(are)s 960(already)s 1717(kno)s 6(wn,)k 2471(and)s 2875(slightly)s 3646(rearranging)s 4800(the)s 5148(others)s 5783(gi)s 6(v)k 3(es)k -240 fnt3 869 9242(l)m 167 fnt3 935 9155(i)m 240 fnt4 -1075 9234(\243)m 240 fnt3 1285 9242(X)m 869 8870(l)m 167 fnt3 +240 fnt3 869 9242(l)m 168 fnt3 935 9155(i)m 240 fnt4 +1075 9234(\243)m 240 fnt3 1285 9242(X)m 869 8870(l)m 168 fnt3 935 8783(i)m 240 fnt4 1075 8862(\243)m 240 fnt3 1285 8870(Y)m 240 fnt4 1508 8862(-)m 240 fnt3 1708 8870(R)m 480 8498(l)m -167 fnt3 546 8411(i)m 240 fnt4 662 8490(+)m 240 fnt3 -863 8498(r)m 167 fnt3 935 8411(i)m 240 fnt4 1075 8490(\243)m -240 fnt3 1285 8498(Y)m 863 8134(r)m 167 fnt3 935 8047(i)m +168 fnt3 546 8411(i)m 240 fnt4 662 8490(+)m 240 fnt3 +863 8498(r)m 168 fnt3 935 8411(i)m 240 fnt4 1075 8490(\243)m +240 fnt3 1285 8498(Y)m 863 8134(r)m 168 fnt3 935 8047(i)m 240 fnt4 1075 8126(\243)m 240 fnt3 1285 8134(Z)m 863 7770(r)m -167 fnt3 935 7683(i)m 240 fnt4 1075 7762(\243)m 240 fnt3 +168 fnt3 935 7683(i)m 240 fnt4 1075 7762(\243)m 240 fnt3 1285 7770(Y)m 240 fnt4 1508 7762(-)m 240 fnt3 1708 7770(L)m 240 fnt1 0 7182(Therefore)m 997(the)s 1345(width)s 1947(constraint)s -2949(of)s 240 fnt3 3220 7184(x)m 167 fnt3 3326 7097(i)m +2949(of)s 240 fnt3 3220 7184(x)m 168 fnt3 3326 7097(i)m 240 fnt1 3430 7182(is)m 480 6644(min)m 240 fnt4 861 6638(\()m 240 fnt3 945 6646(X)m 240 fnt4 1113 6638(,)m 240 fnt3 1220 6646(Y)m 240 fnt4 1443 6638(-)m 240 fnt3 1643 6646(R)m @@ -12011,7 +12025,7 @@ grestore 240 fnt2 0 12672(6.)m 291(Cr)s 4(oss)k 926(r)s 4(efer)k 4(ences)k -[ /Dest /LOUT18_677_s6_0_1 /DEST pdfmark +[ /Dest /LOUT18_694_s6_0_1 /DEST pdfmark 240 fnt1 480 12240(Cross)m 1064(references,)s 2138(such)s 2622(as)s 2859(`see)s 3286(page)s 3782(57')s 4121(and)s 4512(`see)s 4940(Figure)s 5607(5,)s 16(')k 5871(are)s 6205(a)s @@ -12518,7 +12532,7 @@ gsave grestore 0 13253(more)m 547(is)s 757(required.)s 240 fnt2 0 12460(7.)m 291(Conclusion)s -[ /Dest /LOUT18_677_s7_0_1 /DEST pdfmark +[ /Dest /LOUT18_694_s7_0_1 /DEST pdfmark 240 fnt1 480 12028(Since)m 1054(its)s 1316(public)s 1953(release)s 2657(in)s 2886(October)s 3702(1991,)s 4275(the)s 4609(Basser)s 5292(Lout)s @@ -12706,7 +12720,7 @@ grestore 1668(of)s 1939(Computer)s 2956(Science,)s 3806(The)s 4234(Uni)s 6(v)k 3(ersity)k 5288(of)s 5559(Sydne)s 3(y)k 15(,)k 6367(Australia)s 7242(.)s -[ /Dest /LOUT12_1731_s7_0_1 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_1 /DEST pdfmark 0 11716(2.)m 480(Kingston,)s 1492(Jef)s 6(fre)k 3(y)k 2227(H..)s 2652(A)s 2910(ne)s 6(w)k 3385(approach)s 4347(to)s 4613(document)s 5645(formatting)s 6646(.)s 6838(T)s 16(ech.)k @@ -12714,7 +12728,7 @@ grestore 1177(Department)s 2365(of)s 2636(Computer)s 3653(Science,)s 4503(The)s 4931(Uni)s 6(v)k 3(ersity)k 5985(of)s 6256(Sydne)s 3(y)k 15(,)k 7064(Australia)s 7939(.)s -[ /Dest /LOUT12_1731_s7_0_2 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_2 /DEST pdfmark 0 10925(3.)m 480(Kingston,)s 1491(Jef)s 6(fre)k 3(y)k 2224(H..)s 2647(The)s 3101(Basser)s 3824(Lout)s 4362(Document)s 5445(F)s 3(ormatter)k 6383(,)s 6516(1991)s 6971(.)s @@ -12730,7 +12744,7 @@ grestore 1388(for)s 1726(non-)s 240 fnt3 2154 10063(ftp)m 240 fnt1 2459 10061(sites.)m 3047(All)s 3407(enquiries)s 4334(to)s 4573(jef)s 6(f@cs.su.oz.au.)k -[ /Dest /LOUT12_1731_s7_0_3 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_3 /DEST pdfmark 0 9558(4.)m 480(Furuta,)s 1211(Richard,)s 2075(Sco\207eld,)s 2965(Jef)s 6(fre)k 3(y)k 15(,)k 3710(and)s 4113(Sha)s 3(w)k 15(,)k 4734(Alan.)s 5363(Document)s 6419(formatting)s 7480(systems:)s 8402(surv)s 3(e)k 3(y)k 15(,)k @@ -12738,14 +12752,14 @@ grestore 2554 9272(Computing)m 3673(Surve)s 7(ys)k 240 fnt2 4465 9269(14)m 240 fnt1 4699 9270(,)m 4806(417\211472)s 5700(\(1982\))s 6327(.)s -[ /Dest /LOUT12_1731_s7_0_4 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_4 /DEST pdfmark 0 8765(5.)m 480(K)s 6(ernighan,)k 1645(Brian)s 2287(W)s 22(.)k 2649(and)s 3107(Cherry)s 15(,)k 3917(Lorinda)s 4789(L..)s 5213(A)s 5497(system)s 6275(for)s 6667(typesetting)s 7824(mathematics)s 9022(.)s 240 fnt3 480 8479(Communications)m 2158(of)s 2439(the)s 2784(A)s 7(CM)k 240 fnt2 3351 8476(18)m 240 fnt1 3585 8477(,)m 3692(182\211193)s 4576(\(1975\))s 5203(.)s -[ /Dest /LOUT12_1731_s7_0_5 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_5 /DEST pdfmark 0 7977(6.)m 480(Kingston,)s 1488(Jef)s 6(fre)k 3(y)k 2218(H..)s 2638(Fig)s 3033(\211)s 3236(a)s 3425(Lout)s 3961(package)s @@ -12755,7 +12769,7 @@ grestore 3653(Science,)s 4503(The)s 4931(Uni)s 6(v)k 3(ersity)k 5985(of)s 6256(Sydne)s 3(y)k 15(,)k 7064(Australia)s 7939(.)s -[ /Dest /LOUT12_1731_s7_0_6 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_6 /DEST pdfmark 0 7184(7.)m 480(Reid,)s 1042(Brian)s 1634(K..)s 2034(A)s 2268(High-)s 2815(Le)s 6(v)k 3(el)k 3409(Approach)s 4413(to)s 4656(Computer)s 5677(Document)s 6737(Production)s @@ -12766,19 +12780,19 @@ grestore 8773(V)s 26(e-)k 480 6610(gas)m 868(NV)s 240 fnt1 1192 6608(,)m 1299(pages)s 1895(24\21131)s 2470(,)s 2577(1980)s 3052(.)s -[ /Dest /LOUT12_1731_s7_0_7 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_7 /DEST pdfmark 0 6103(8.)m 480(Joseph)s 1207(F)s 19(.)k 1443(Ossanna.)s 2436(Nrof)s 6(f/T)k 8(rof)k 6(f)k 3605(User')s 13(s)k 4284(Manual)s 5010(.)s 5193(T)s 16(ech.)k 5777(Rep.)s 6285(54)s 6597(\(1976\))s 7224(,)s 7349(Bell)s 7821(Laboratories)s 9019(,)s 480 5815(Murray)m 1251(Hill,)s 1729(NJ)s 2051(07974)s 2645(.)s -[ /Dest /LOUT12_1731_s7_0_8 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_8 /DEST pdfmark 0 5310(9.)m 480(Knuth,)s 1186(Donald)s 1949(E..)s 240 fnt3 2319 5312(The)m 2731(T)s 2882 5264(E)m 3033 5312(XBook)m 240 fnt1 3675 5310(.)m 3839(Addison-W)s 19(esle)k 3(y)k 5419(,)s 5526(1984)s 6000(.)s -[ /Dest /LOUT12_1731_s7_0_9 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_9 /DEST pdfmark 0 4807(10.)m 480(Kingston,)s 1485(Jef)s 6(fre)k 3(y)k 2212(H..)s 2629(Eq)s 2973(\211)s 3173(a)s 3359(Lout)s 3892(package)s 4752(for)s @@ -12789,7 +12803,7 @@ grestore 8147(Australia)s 9022(.)s 480 4231(\(Contains)m 1461(an)s 1744(appendix)s 2677(describing)s 3726(the)s 4074(P)s 3(as)k 4454(P)s 3(ascal)k 5116(formatter)s 13(.\))k -[ /Dest /LOUT12_1731_s7_0_10 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_10 /DEST pdfmark 0 3728(11.)m 480(Kingston,)s 1478(Jef)s 6(fre)k 3(y)k 2198(H..)s 2608(A)s 2851(be)s 3(ginners')k 3903(guide)s 4504(to)s 4756(Lout)s 5208(.)s 5385(T)s 16(ech.)k @@ -12798,7 +12812,7 @@ grestore 3156(The)s 3584(Uni)s 6(v)k 3(ersity)k 4638(of)s 4909(Sydne)s 3(y)k 15(,)k 5717(Australia)s 6592(.)s -[ /Dest /LOUT12_1731_s7_0_11 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_11 /DEST pdfmark 0 2937(12.)m 480(Kingston,)s 1475(Jef)s 6(fre)k 3(y)k 2193(H..)s 2600(T)s 19(ab)k 3017(\211)s 3207(a)s 3384(Lout)s 3907(package)s 4757(for)s 5106(formatting)s 6177(tables)s @@ -12807,13 +12821,13 @@ grestore 2636(Computer)s 3653(Science,)s 4503(The)s 4931(Uni)s 6(v)k 3(ersity)k 5985(of)s 6256(Sydne)s 3(y)k 15(,)k 7064(Australia)s 7939(.)s -[ /Dest /LOUT12_1731_s7_0_12 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_12 /DEST pdfmark 0 2146(13.)m 480(Brooks,)s 1279(K)s 6(enneth)k 2141(P)s 26(..)k 2472(Lilac:)s 3068(a)s 3234(tw)s 2(o-vie)k 6(w)k 4183(document)s 5187(editor)s 5744(.)s 240 fnt3 5908 2148(IEEE)m 6490(Computer)s 240 fnt1 7453 2146(,)m 7560(7\21119)s 8091(\(1991\))s 8718(.)s -[ /Dest /LOUT12_1731_s7_0_13 /DEST pdfmark +[ /Dest /LOUT12_1748_s7_0_13 /DEST pdfmark grestore 0 0 0 0 240 288 60 1417 -15423 LoutGr2 |