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pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. 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def /x1 x def } +def +/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def +} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } +/pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +0 } ifelse setdash stroke } def +/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt +{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add +def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if +] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1 +setlinecap stroke } def +/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch +2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +% DG/SR modification end +Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +% def +a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +pop pop } def +% DG/SR modification end +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul +neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add +def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 +div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + currentpoint + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%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 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mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 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y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + currentpoint + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%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 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moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul +neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add +def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 +div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. 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grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] 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a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + currentpoint + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: 8r.enc +% @@psencodingfile@{ +% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry", +% version = "0.6", +% date = "1 July 1998", +% filename = "8r.enc", +% email = "tex-fonts@@tug.org", +% docstring = "Encoding for TrueType or Type 1 fonts +% to be used with TeX." +% @} +% +% Idea is to have all the characters normally included in Type 1 fonts +% available for typesetting. This is effectively the characters in Adobe +% Standard Encoding + ISO Latin 1 + extra characters from Lucida. +% +% Character code assignments were made as follows: +% +% (1) the Windows ANSI characters are almost all in their Windows ANSI +% positions, because some Windows users cannot easily reencode the +% fonts, and it makes no difference on other systems. The only Windows +% ANSI characters not available are those that make no sense for +% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen +% (173). quotesingle and grave are moved just because it's such an +% irritation not having them in TeX positions. +% +% (2) Remaining characters are assigned arbitrarily to the lower part +% of the range, avoiding 0, 10 and 13 in case we meet dumb software. +% +% (3) Y&Y Lucida Bright includes some extra text characters; in the +% hopes that other PostScript fonts, perhaps created for public +% consumption, will include them, they are included starting at 0x12. +% +% (4) Remaining positions left undefined are for use in (hopefully) +% upward-compatible revisions, if someday more characters are generally +% available. +% +% (5) hyphen appears twice for compatibility with both +% ASCII and Windows. +% +/TeXBase1Encoding [ +% 0x00 (encoded characters from Adobe Standard not in Windows 3.1) + /.notdef /dotaccent /fi /fl + /fraction /hungarumlaut /Lslash /lslash + /ogonek /ring /.notdef + /breve /minus /.notdef +% These are the only two remaining unencoded characters, so may as +% well include them. + /Zcaron /zcaron +% 0x10 + /caron /dotlessi +% (unusual TeX characters available in, e.g., Lucida Bright) + /dotlessj /ff /ffi /ffl + /.notdef /.notdef /.notdef /.notdef + /.notdef /.notdef /.notdef /.notdef + % very contentious; it's so painful not having quoteleft and quoteright + % at 96 and 145 that we move the things normally found there to here. + /grave /quotesingle +% 0x20 (ASCII begins) + /space /exclam /quotedbl /numbersign + /dollar /percent /ampersand /quoteright + /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash +% 0x30 + /zero /one /two /three /four /five /six /seven + /eight /nine /colon /semicolon /less /equal /greater /question +% 0x40 + /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O +% 0x50 + /P /Q /R /S /T /U /V /W + /X /Y /Z /bracketleft /backslash /bracketright /asciicircum 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FJ(\))2146 2596 y FU(P)j FG(\))q +FU(;)j(a)p FG(\))156 2732 y FF(Cut)223 2685 y FC( )284 +2732 y FG(\()316 2720 y FQ(h)343 2732 y FU(b)379 2720 +y FQ(i)406 2732 y FF(Not)536 2744 y FS(L)586 2732 y FG(\()618 +2720 y FQ(h)645 2732 y FU(a)689 2720 y FQ(i)716 2732 +y FU(M)8 b(;)14 b(x)p FG(\))q FU(;)959 2720 y FJ(\()985 +2732 y FU(y)1029 2720 y FJ(\))1054 2732 y FU(P)e FG(\))1236 +2696 y FS(x)1173 2732 y FT(\000)-25 b(\000)g(!)22 b FF(Not)1488 +2744 y FS(L)1538 2732 y FG(\()1570 2720 y FQ(h)1597 2732 +y FU(a)1641 2720 y FQ(i)1668 2732 y FF(Cut)1734 2685 +y FC( )1795 2732 y FG(\()1827 2720 y FQ(h)1855 2732 y +FU(b)1891 2720 y FQ(i)1917 2732 y FU(M)9 b(;)2044 2720 +y FJ(\()2069 2732 y FU(y)2113 2720 y FJ(\))2139 2732 +y FU(P)j FG(\))p FU(;)i(x)p FG(\))-57 2868 y FF(Cut)10 +2821 y FC( )70 2868 y FG(\()102 2856 y FQ(h)130 2868 +y FU(d)173 2856 y FQ(i)200 2868 y FF(And)341 2880 y FS(R)395 +2868 y FG(\()427 2856 y FQ(h)454 2868 y FU(a)498 2856 +y FQ(i)525 2868 y FU(M)9 b(;)652 2856 y FQ(h)679 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def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 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pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For copying restrictions, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 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/BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + currentpoint + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%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 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sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h 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LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine 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add chg}{1 add +chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ +1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} +forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn +/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 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 A 1 get A +mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ +SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ +userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X +1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 +index cvrs cvn put}for pop 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/Rx 0 N/Ry 0 N/V{}B/RV/v{ +/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) +(LaserWriter 16/600)]{A length product length le{A length product exch 0 +exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse +end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask +grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} +imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round +exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto +fill grestore}B/a{moveto}B/delta 0 N/tail{A/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: pstricks.pro +%! +% PostScript prologue for pstricks.tex. +% Version 97 patch 3, 98/06/01 +% For distribution, see pstricks.tex. +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Atan { /atan load stopped { pop pop 0 } if } def +/Div { dup 0 eq { pop } { div } ifelse } def +/NET { neg exch neg exch T } def +/Pyth { dup mul exch dup mul add sqrt } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } +def +/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def +} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } +/pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +0 } ifelse setdash stroke } def +/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt +{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add +def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if +] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1 +setlinecap stroke } def +/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch +2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +% DG/SR modification end +Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +% def +a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +pop pop } def +% DG/SR modification end +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul +neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add +def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 +div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + currentpoint + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%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$SavedState +save N userdict maxlength dict begin/magscale true def normalscale +currentpoint TR/psf$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 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def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + currentpoint + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%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 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add def } repeat grestore } +% def +a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +pop pop } def +% DG/SR modification end +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul +neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add +def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 +div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + currentpoint + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%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 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{ 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul +neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add +def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 +div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul 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dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } 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index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + currentpoint + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%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 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moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul +neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add +def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 +div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def +n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + (P) 0 get /BoldPentagon put + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { + 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath + } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { + -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto + closepath + } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +% END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. 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Ff(1)l FZ(<)l Ff(2)p +FC(^)q Ff(f1)d FV(=)f Ff(f2)p FZ(;)k Ff(f1)c FV(=)g Ff(1)5821 +-384 y FC(8)5856 -373 y Fd(L)p 2784 -310 2676 4 v 3165 +-256 a FZ(M)3223 -246 y FP(1)3255 -256 y FZ(;)k(M)3343 +-246 y FP(2)3375 -256 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p +Ff(fx)d FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p +FZ(;)k(S)o(;)f(T)p 3972 -268 6 23 v 3978 -277 25 3 v +68 w Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)e FV(=)f Ff(f3)p +FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)e FV(=)f Ff(f2)p +FZ(;)j Ff(2)l FZ(<)l Ff(3)p FC(^)r Ff(f2)d FV(=)g Ff(f3)q +FZ(;)j Ff(f1)e FV(=)f Ff(1)5459 -301 y FC(^)5500 -290 +y Fd(R)p 3083 -223 2079 4 v 3083 -169 a FZ(M)3141 -159 +y FP(1)3173 -169 y FZ(;)j(M)3260 -159 y FP(2)3293 -169 +y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)g +Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p +3890 -181 6 23 v 3895 -191 25 3 v 57 w FC(9)p Ff(m)p +FZ(:)p FV(\()p Ff(1)l FZ(<)l Ff(m)p FC(^)q Ff(f1)c FV(=)g +Ff(fm)p FV(\))p FZ(;)k Ff(1)l FZ(<)l Ff(2)p FC(^)q 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+FV(\()p Ff(2)l FZ(<)l Ff(m)p FC(^)q Ff(f2)e FV(=)f Ff(fm)o +FV(\))p FZ(;)k Ff(f1)d FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p +FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q +Ff(fn)g FV(=)g Ff(fm)p FV(\))5111 134 y FC(9)5146 145 +y Fd(R)p 3132 209 1981 4 v 3369 262 a FZ(M)3427 272 y +FP(1)3460 262 y FZ(;)j(M)3547 272 y FP(2)3579 262 y FZ(;)p +FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f Ff(0)p FC(_)p +Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 4176 +250 6 23 v 4182 241 25 3 v 67 w Ff(f1)d FV(=)f Ff(1)p +FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l +FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)o FV(\))5111 +220 y FC(9)5146 231 y Fd(R)6003 112 y F3(.)6003 145 y(.)6003 +178 y(.)6003 211 y(.)5968 262 y FZ(X)6018 272 y FP(5)p +3369 295 2699 4 v 3880 349 a FZ(M)3938 359 y FP(1)3971 +349 y FZ(;)j(M)4058 359 y FP(2)4090 349 y FZ(;)p FC(8)p +Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f Ff(0)p FC(_)p Ff(fx)h +FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 4687 337 6 23 +v 4693 327 25 3 v 67 w Ff(f1)d FV(=)f Ff(1)p FC(^)p Ff(f0)g +FV(=)g Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p +FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p +FV(\))6067 303 y FC(^)6108 314 y Fd(R)2490 393 y Fc(|)p +2514 393 1785 8 v 1785 w({z)p 4347 393 V 1785 w(})4283 +455 y Fd(X)4329 467 y FP(6)p 2567 627 247 4 v 2567 678 +a Ff(1)l FC(\024)l Ff(1)p 2675 666 6 23 v 2680 656 25 +3 v 61 w(1)l FC(\024)l Ff(1)p 2474 708 433 4 v 2463 773 +a FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(1)l FC(\024)l Ff(m)2673 +752 y Fe(x)p Fd(;)p Fe(1)2730 773 y FV(\))p 2768 761 +6 23 v 2774 751 25 3 v 59 w Ff(1)l FC(\024)l Ff(1)2906 +720 y FC(8)2941 731 y Fd(L)p 2474 805 433 4 v 2569 857 +a FZ(M)2627 867 y FP(2)p 2673 845 6 23 v 2679 835 25 +3 v 2718 857 a Ff(1)l FC(\024)l Ff(1)2906 817 y FC(8)2941 +828 y Fd(L)p 3034 806 247 4 v 3034 857 a Ff(0)l FZ(<)l +Ff(1)p 3142 845 6 23 v 3148 835 25 3 v 61 w(0)l FZ(<)l +Ff(1)p 2569 887 713 4 v 2671 939 a(1)l FC(\024)l Ff(1)p +FC(\033)q Ff(0)l FZ(<)l Ff(1)p FZ(;)13 b(M)2994 949 y 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FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p +FZ(;)j(S)o(;)h(T)p 4878 835 6 23 v 4883 825 25 3 v 67 +w Ff(f0)d FV(=)f Ff(f1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p +Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h +FV(=)f Ff(fm)p FV(\))5591 802 y FC(\033)5639 813 y Fd(L)p +3441 879 2208 4 v 3430 933 a FC(8)p Ff(y)q FZ(:)p FV(\(\()p +Ff(fy)i FV(=)e Ff(1)p FC(^)o Ff(f0)h FV(=)f Ff(1)p FV(\))p +FC(\033)p Ff(f0)h FV(=)f Ff(fy)q FV(\))p FZ(;)j(M)4185 +943 y FP(1)4218 933 y FZ(;)g(M)4305 943 y FP(2)4337 933 +y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f +Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p +4934 921 6 23 v 4940 911 25 3 v 67 w Ff(f0)d FV(=)f Ff(f1)p +FZ(;)p FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l +FZ(<)l Ff(m)p FC(^)q Ff(fn)h FV(=)f Ff(fm)p FV(\))5648 +891 y FC(8)5683 902 y Fd(L)p 3421 965 2247 4 v 3411 1019 +a FC(8)p Ff(x)p FZ(:)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)i +FV(=)e Ff(1)p FC(^)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FC(\033)p +Ff(fx)h FV(=)f Ff(fy)p FV(\))p FZ(;)k(M)4205 1029 y FP(1)4237 +1019 y FZ(;)g(M)4325 1029 y FP(2)4357 1019 y FZ(;)p FC(8)p +Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)p Ff(fx)g +FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p 4954 1007 6 +23 v 4960 998 25 3 v 68 w Ff(f0)e FV(=)f Ff(f1)p FZ(;)p +FC(9)p Ff(n)p FZ(:)p Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l +Ff(m)p FC(^)q Ff(fn)g FV(=)g Ff(fm)p FV(\))5667 977 y +FC(8)5702 988 y Fd(L)p 3421 1052 2247 4 v 3784 1106 a +FZ(M)3842 1116 y FP(1)3874 1106 y FZ(;)k(M)3962 1116 +y FP(2)3994 1106 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p +Ff(fx)d FV(=)f Ff(0)p FC(_)p Ff(fx)g FV(=)g Ff(1)p FV(\))p +FZ(;)k(S)o(;)g(T)p 4591 1094 6 23 v 4597 1084 25 3 v +67 w Ff(f0)d FV(=)f Ff(f1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p +Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)h +FV(=)f Ff(fm)o FV(\))5667 1064 y FC(8)5702 1075 y Fd(L)p +2768 1138 2538 4 v 3209 1192 a FZ(M)3267 1202 y FP(1)3299 +1192 y FZ(;)j(M)3386 1202 y FP(2)3419 1192 y FZ(;)p FC(8)p +Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)g Ff(0)p FC(_)p 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FC(\033)4916 -791 y Fd(L)p 3700 -725 1181 4 v +3690 -671 a FC(8)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)h FV(=)f +Ff(0)p FC(^)p Ff(f0)g FV(=)g Ff(0)p FV(\))p FC(\033)p +Ff(f0)h FV(=)f Ff(fy)q FV(\))p FZ(;)j Ff(f1)e FV(=)f +Ff(0)p FZ(;)k Ff(f0)d FV(=)f Ff(0)p 4690 -683 6 23 v +4696 -693 25 3 v 59 w(f0)g FV(=)g Ff(f1)4880 -713 y FC(8)4915 +-702 y Fd(L)p 3681 -638 1220 4 v 3670 -584 a FC(8)p Ff(x)p +FZ(:)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)i FV(=)e Ff(0)p +FC(^)o Ff(fx)h FV(=)f Ff(0)p FV(\))p FC(\033)p Ff(fx)h +FV(=)f Ff(fy)q FV(\))p FZ(;)j Ff(f1)e FV(=)f Ff(0)p FZ(;)j +Ff(f0)e FV(=)f Ff(0)p 4709 -596 6 23 v 4715 -606 25 3 +v 59 w(f0)h FV(=)f Ff(f1)4899 -627 y FC(8)4934 -616 y +Fd(L)p 3681 -552 1220 4 v 4006 -501 a Ff(f1)h FV(=)f +Ff(0)p FZ(;)k Ff(f0)c FV(=)g Ff(0)p FZ(;)k(T)p 4384 -513 +6 23 v 4389 -523 25 3 v 67 w Ff(f0)d FV(=)f Ff(f1)4899 +-540 y FC(8)4934 -529 y Fd(L)p 3082 -471 1493 4 v 3381 +-419 a Ff(f1)h FV(=)f Ff(0)p FZ(;)k Ff(1)l FC(\024)l +Ff(1)p FZ(;)h Ff(f0)c FV(=)f Ff(0)p 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FZ(;)k(M)3393 -239 y FP(1)3425 -249 y FZ(;)f(M)3512 +-239 y FP(2)3545 -249 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p +Ff(fx)e FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p +FZ(;)j(S)o(;)h(T)p 4142 -261 6 23 v 4147 -271 25 3 v +67 w Ff(0)l FZ(<)l Ff(1)p FC(^)r Ff(f0)d FV(=)f Ff(f1)p +FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)q +FZ(;)j Ff(f0)e FV(=)f Ff(1)p FZ(;)p FC(9)p Ff(n)p FZ(:)p +Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g +FV(=)g Ff(fm)p FV(\))5626 -291 y FC(8)5661 -280 y Fd(L)p +2960 -216 2594 4 v 2949 -152 a FC(8)p Ff(x)p FZ(:)p FV(\()p +Ff(x)l FC(\024)l Ff(m)3157 -173 y Fe(x)p Fd(;)p Fe(0)3214 +-152 y FV(\))p FZ(;)j Ff(f0)e FV(=)f Ff(0)p FZ(;)k(M)3485 +-142 y FP(1)3517 -152 y FZ(;)f(M)3604 -142 y FP(2)3637 +-152 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f +Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p +4234 -164 6 23 v 4240 -174 25 3 v 68 w Ff(0)l FZ(<)l +Ff(1)p FC(^)q Ff(f0)e FV(=)f Ff(f1)p FZ(;)j Ff(1)l FZ(<)l +Ff(2)p 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Ff(0)4233 +9 y FC(^)4275 20 y Fd(R)p 4372 1 351 4 v 4372 52 a Ff(f2)g +FV(=)g Ff(f3)p 4532 40 6 23 v 4538 30 25 3 v 60 w(f2)g +FV(=)g Ff(f3)p 3566 82 1157 4 v 3611 136 a FV(\()p Ff(f3)h +FV(=)f Ff(0)p FC(^)o Ff(f2)h FV(=)f Ff(0)p FV(\))p FC(\033)p +Ff(f2)h FV(=)f Ff(f3)p FZ(;)k Ff(f3)c FV(=)g Ff(0)p FZ(;)k +Ff(f2)d FV(=)f Ff(0)p 4487 124 6 23 v 4493 114 25 3 v +59 w(f2)g FV(=)g Ff(f3)4722 91 y FC(\033)4770 102 y Fd(L)p +3554 168 1181 4 v 3544 222 a FC(8)p Ff(y)q FZ(:)p FV(\(\()p +Ff(fy)h FV(=)f Ff(0)p FC(^)p Ff(f2)g FV(=)g Ff(0)p FV(\))p +FC(\033)p Ff(f2)h FV(=)f Ff(fy)q FV(\))p FZ(;)k Ff(f3)c +FV(=)g Ff(0)p FZ(;)k Ff(f2)d FV(=)f Ff(0)p 4544 210 6 +23 v 4550 200 25 3 v 59 w(f2)g FV(=)g Ff(f3)4734 180 +y FC(8)4769 191 y Fd(L)p 3535 254 1220 4 v 3524 308 a +FC(8)p Ff(x)p FZ(:)p Ff(y)q FZ(:)p FV(\(\()p Ff(fy)i +FV(=)e Ff(0)p FC(^)o Ff(fx)h FV(=)f Ff(0)p FV(\))p FC(\033)p +Ff(fx)h FV(=)f Ff(fy)q FV(\))p FZ(;)j Ff(f3)e FV(=)f +Ff(0)p FZ(;)j Ff(f2)e FV(=)f Ff(0)p 4563 296 6 23 v 4569 +286 25 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3226 585 +1770 4 v 3226 639 a Ff(3)l FC(\024)l Ff(3)p FZ(;)12 b +Ff(f2)c FV(=)f Ff(0)p FZ(;)j Ff(2)l FC(\024)l Ff(3)p +FZ(;)j Ff(f1)7 b FV(=)g Ff(1)p FZ(;)p FC(8)p Ff(x)p FZ(:)p +FV(\()p Ff(fx)h FV(=)f Ff(0)p FC(_)p Ff(fx)h FV(=)f Ff(1)p +FV(\))p FZ(;)j(S)o(;)h(T)p 4359 627 6 23 v 4364 617 25 +3 v 67 w Ff(2)l FZ(<)l Ff(3)p FC(^)r Ff(f2)c FV(=)g Ff(f3)q +FZ(;)j Ff(1)l FZ(<)l Ff(3)p FC(^)r Ff(f1)d FV(=)g Ff(f3)4995 +597 y FC(8)5030 608 y Fd(L)p 3134 671 1954 4 v 3123 736 +a FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(x)l FC(\024)l Ff(m)3331 +715 y Fe(x)p Fd(;)p Fe(2)3388 736 y FV(\))p FZ(;)j Ff(f2)e +FV(=)f Ff(0)p FZ(;)k Ff(2)l FC(\024)l Ff(3)p FZ(;)h Ff(f1)c +FV(=)f Ff(1)p FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)h +FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p +4451 724 6 23 v 4456 714 25 3 v 67 w Ff(2)l FZ(<)l Ff(3)p +FC(^)r Ff(f2)d FV(=)f Ff(f3)p FZ(;)j Ff(1)l FZ(<)l Ff(3)p +FC(^)r Ff(f1)d FV(=)g Ff(f3)5087 683 y FC(8)5122 694 +y Fd(L)p 3134 768 1954 4 v 3228 822 a Ff(f2)g FV(=)g +Ff(0)p FZ(;)k Ff(2)l FC(\024)l Ff(3)p FZ(;)h Ff(f1)c +FV(=)f Ff(1)p FZ(;)k(M)3728 832 y FP(1)3760 822 y FZ(;)p +FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)o +Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)k(S)o(;)f(T)p 4357 +810 6 23 v 4363 800 25 3 v 68 w Ff(2)l FZ(<)l Ff(3)p +FC(^)q Ff(f2)e FV(=)f Ff(f3)p FZ(;)j Ff(1)l FZ(<)l Ff(3)p +FC(^)r Ff(f1)e FV(=)f Ff(f3)5087 780 y FC(8)5122 791 +y Fd(L)5261 672 y F3(.)5261 705 y(.)5261 738 y(.)5261 +771 y(.)5233 822 y FZ(Y)5269 832 y FP(2)p 3008 855 2532 +4 v 3008 909 a Ff(f2)h FV(=)f Ff(0)p FC(_)o Ff(f2)h FV(=)f +Ff(1)p FZ(;)k Ff(2)l FC(\024)l Ff(3)p FZ(;)h Ff(f1)c +FV(=)f Ff(1)p FZ(;)j Ff(2)l FC(\024)l Ff(2)p FZ(;)j Ff(f1)7 +b FV(=)g Ff(1)p FZ(;)k(M)3962 919 y FP(1)3994 909 y FZ(;)p +FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)f Ff(0)p FC(_)p +Ff(fx)g FV(=)g Ff(1)p FV(\))p FZ(;)k(S)o(;)g(T)p 4591 +897 6 23 v 4597 887 25 3 v 67 w Ff(2)l FZ(<)l Ff(3)p +FC(^)q Ff(f2)d FV(=)f Ff(f3)p FZ(;)k Ff(1)l FZ(<)l Ff(3)p +FC(^)q Ff(f1)d FV(=)f Ff(f3)p FZ(;)k Ff(1)l FZ(<)l Ff(2)p +FC(^)q Ff(f1)d FV(=)f Ff(f2)5538 863 y FC(_)5580 874 +y Fd(L)p 3008 941 2532 4 v 3173 995 a Ff(2)l FC(\024)l +Ff(3)p FZ(;)13 b Ff(f1)7 b FV(=)g Ff(1)p FZ(;)k Ff(2)l +FC(\024)l Ff(2)p FZ(;)h Ff(f1)c FV(=)f Ff(1)p FZ(;)k(M)3797 +1005 y FP(1)3829 995 y FZ(;)p FC(8)p Ff(x)p FZ(:)p FV(\()p +Ff(fx)d FV(=)f Ff(0)p FC(_)o Ff(fx)h FV(=)f Ff(1)p FV(\))p +FZ(;)k(S)o(;)f(T)p 4426 983 6 23 v 4432 973 25 3 v 68 +w Ff(2)l FZ(<)l Ff(3)p FC(^)q Ff(f2)e FV(=)f Ff(f3)p +FZ(;)k Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)d FV(=)f Ff(f3)p +FZ(;)j Ff(1)l FZ(<)l Ff(2)p FC(^)r Ff(f1)d FV(=)g Ff(f2)5538 +953 y FC(8)5573 964 y Fd(L)p 3091 1027 2365 4 v 3091 +1081 a Ff(2)l FC(\024)l Ff(3)p FZ(;)12 b Ff(f1)c FV(=)f +Ff(1)p FZ(;)k Ff(2)l FC(\024)l Ff(2)p FZ(;)h Ff(f1)c +FV(=)f Ff(1)p FZ(;)j(M)3714 1091 y FP(1)3747 1081 y FZ(;)p +FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)d FV(=)g Ff(0)p FC(_)p +Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 4344 +1069 6 23 v 4349 1060 25 3 v 57 w FC(9)p Ff(m)p FZ(:)p +FV(\()p Ff(2)l FZ(<)l Ff(m)p FC(^)q Ff(f2)c FV(=)g Ff(fm)p +FV(\))p FZ(;)k Ff(1)l FZ(<)l Ff(3)p FC(^)q Ff(f1)d FV(=)f +Ff(f3)p FZ(;)k Ff(1)l FZ(<)l Ff(2)p FC(^)q Ff(f1)d FV(=)f +Ff(f2)5455 1039 y FC(9)5490 1050 y Fd(R)p 3067 1114 2413 +4 v 3067 1168 a Ff(2)l FC(\024)l Ff(3)p FZ(;)12 b Ff(f1)c +FV(=)f Ff(1)p FZ(;)k Ff(2)l FC(\024)l Ff(2)p FZ(;)h Ff(f1)c +FV(=)f Ff(1)p FZ(;)j(M)3690 1178 y FP(1)3723 1168 y FZ(;)p +FC(8)p Ff(x)p FZ(:)p FV(\()p Ff(fx)e FV(=)f Ff(0)p FC(_)o +Ff(fx)h FV(=)f Ff(1)p FV(\))p FZ(;)j(S)o(;)h(T)p 4320 +1156 6 23 v 4325 1146 25 3 v 67 w Ff(1)l FZ(<)l Ff(3)p +FC(^)r Ff(f1)c FV(=)g Ff(f3)q FZ(;)j Ff(1)l FZ(<)l Ff(2)p +FC(^)r Ff(f1)d FV(=)g Ff(f2)q FZ(;)p FC(9)p Ff(n)p FZ(:)p +Ff(m)p FZ(:)p FV(\()p Ff(n)l FZ(<)l Ff(m)p FC(^)q Ff(fn)g +FV(=)g Ff(fm)p FV(\))5479 1125 y FC(9)5514 1136 y Fd(R)p +2974 1200 2600 4 v 2963 1265 a FC(8)p Ff(x)p FZ(:)p FV(\()p +Ff(2)l FC(\024)l Ff(m)3173 1244 y Fe(x)p Fd(;)p Fe(2)3230 +1265 y FV(\))p FZ(;)j Ff(f1)e FV(=)f Ff(1)p 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3574 4 62 v Black +277 3811 a Gb(Pr)n(oof)j(of)g(Lemma)f(2.3.1.)p Black +34 w Gg(The)g(only)h(case)h(that)f(is)g(non-tri)n(vial)i(is)e(where)g +Ga(M)36 b Gg(is)26 b(an)h(axiom)g(\(since)277 3924 y(axioms)d +(introduce)j(tw)o(o)c(labels\).)p Black 277 4113 a Gb(Case)h +Ga(M)35 b F6(\021)25 b FL(Ax)p F4(\()p Ga(x;)15 b(b)p +F4(\))p Gb(:)p Black 37 w Gg(Suppose)22 b F6(f)p Ga(\033)s +F6(g)f Gg(and)g F6(f)p Ga(\034)10 b F6(g)21 b Gg(are)g(of)f(the)h(form) +15 b F6(f)-7 b Ga(x)27 b F4(:=)2669 4101 y FX(h)2696 +4113 y Ga(a)2744 4101 y FX(i)2772 4113 y Ga(P)s F6(g)21 +b Gg(and)15 b F6(f)-7 b Ga(b)27 b F4(:=)3269 4101 y F9(\()3296 +4113 y Ga(y)3344 4101 y F9(\))3372 4113 y Ga(Q)-10 b +F6(g)p Gg(,)504 4226 y(respecti)n(v)o(ely)k(.)31 b(W)-7 +b(e)20 b(analyse)i(in)f(turn)g(the)g(cases)h FL(Ax)o +F4(\()p Ga(x;)15 b(b)p F4(\))p F6(f)p Ga(\033)s F6(g)-15 +b(f)p Ga(\034)10 b F6(g)23 b Gg(and)e FL(Ax)o F4(\()p +Ga(x;)15 b(b)p F4(\))p F6(f)p Ga(\034)10 b F6(g)-15 b(f)p +Ga(\033)s F6(f)p Ga(\034)10 b 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4030 y Gc(x)3181 4016 y F6(2)25 b Ga(S)5 +b(N)3401 4030 y Gc(aux)3524 4016 y Gg(.)321 4128 y(By)23 +b(Lemma)g(2.6.7)g(we)g(ha)n(v)o(e)h(the)g(identities)p +Black Black 1140 4370 a F6(j)p FL(Cut)p F4(\()1338 4358 +y FX(h)1366 4370 y Ga(a)1414 4358 y FX(i)1441 4370 y +FL(Not)1584 4384 y Gc(R)1641 4370 y F4(\()1676 4358 y +F9(\()1704 4370 y Ga(x)1756 4358 y F9(\))1784 4370 y +FL(Cut)1862 4322 y FC( )1923 4370 y F4(\()1958 4358 y +FX(h)1986 4370 y Ga(a)2034 4358 y FX(i)2062 4370 y Ga(S)5 +b(;)2163 4358 y F9(\()2190 4370 y Ga(y)2238 4358 y F9(\))2266 +4370 y Ga(T)12 b F4(\))q Ga(;)j(a)p F4(\))q Ga(;)2531 +4358 y F9(\()2558 4370 y Ga(y)2606 4358 y F9(\))2634 +4370 y Ga(T)e F4(\))p F6(j)2760 4384 y Gc(x)969 4483 +y F6(\021)100 b FL(Cut)o F4(\()1312 4471 y FX(h)1340 +4483 y Ga(a)1388 4471 y FX(i)1416 4483 y F6(j)p FL(Not)1584 +4497 y Gc(R)1641 4483 y F4(\()1676 4471 y F9(\()1704 +4483 y Ga(x)1756 4471 y F9(\))1784 4483 y FL(Cut)1862 +4435 y FC( )1923 4483 y F4(\()1958 4471 y FX(h)1986 4483 +y 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b(gi)n(v)o(e)i(one)g(case.)504 533 y Ga(M)36 b +F6(\021)25 b FL(Cut)p F4(\()897 521 y FX(h)924 533 y +Ga(a)972 521 y FX(i)1000 533 y Ga(S)5 b(;)1101 521 y +F9(\()1129 533 y Ga(x)1181 521 y F9(\))1208 533 y Ga(T)13 +b F4(\))1376 496 y Gc(l)q(oc)1334 533 y F6(\000)-31 b(\000)g(!)25 +b FL(Cut)p F4(\()1703 521 y FX(h)1731 533 y Ga(a)1779 +521 y FX(i)1806 533 y Ga(S)1867 500 y FX(0)1890 533 y +Ga(;)1930 521 y F9(\()1958 533 y Ga(x)2010 521 y F9(\))2038 +533 y Ga(T)12 b F4(\))26 b F6(\021)f Ga(N)504 646 y Gg(\(1\))101 +b Ga(S)838 608 y Gc(l)q(oc)796 646 y F6(\000)-31 b(\000)g(!)25 +b Ga(S)1053 613 y FX(0)1099 646 y Gg(and)f Ga(S)p 1253 +661 61 4 v 30 w(>)1410 613 y Gc(r)r(po)1543 646 y Ga(S)1604 +613 y FX(0)p 1543 661 85 4 v 2454 646 a Gg(by)g(assumption)i(and)e +(induction)504 758 y(\(2\))101 b Ga(M)p 710 773 99 4 +v 35 w F4(=)25 b Ga(S)p 929 773 61 4 v 26 w F6(\001)1036 +772 y Gc(m)1123 758 y Ga(T)p 1123 773 66 4 v 60 w Gg(and)50 +b Ga(N)p 1416 773 83 4 v 35 w F4(=)25 b Ga(S)1681 725 +y 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w(>)904 +1177 y Gc(r)r(po)1037 1210 y Ga(N)p 1037 1225 83 4 v +1180 w Gg(if)23 b Ga(m)i F4(=)g Ga(n)p Gg(,)d(then)i(by)g(\(5\))g(and)g +(rpo\(iii\))2315 1323 y(if)f Ga(m)i(>)g(n)p Gg(,)d(then)j(by)e(\(4\))h +(and)g(rpo\(ii\))p Black 277 1503 a Gb(Labelled)f(Cut)f(Reduction:)p +Black 46 w Gg(W)-7 b(e)23 b(gi)n(v)o(e)g(\002)n(v)o(e)g(typical)i +(cases.)504 1655 y Ga(M)36 b F6(\021)22 b FL(Cut)800 +1608 y FC( )861 1655 y F4(\()896 1643 y FX(h)924 1655 +y Ga(c)963 1643 y FX(i)990 1655 y FL(And)1145 1669 y +Gc(R)1203 1655 y F4(\()1238 1643 y FX(h)1266 1655 y Ga(a)1314 +1643 y FX(i)1341 1655 y Ga(S)5 b(;)1442 1643 y FX(h)1470 +1655 y Ga(b)1509 1643 y FX(i)1536 1655 y Ga(T)13 b(;)i(c)p +F4(\))q Ga(;)1757 1643 y F9(\()1785 1655 y Ga(x)1837 +1643 y F9(\))1864 1655 y Ga(U)10 b F4(\))782 1742 y Gc(x)717 +1779 y F6(\000)-31 b(\000)f(!)26 b FL(Cut)o F4(\()1085 +1767 y FX(h)1113 1779 y Ga(c)1152 1767 y FX(i)1180 1779 +y FL(And)1335 1793 y Gc(R)1392 1779 y F4(\()1427 1767 +y FX(h)1455 1779 y 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1903 y Ga(;)15 b(T)p 2185 1918 66 4 v 14 +w F6(h)p Ga(U)p 2287 1918 72 4 v 10 w F6(i)2394 1917 +y Gc(s)2431 1903 y FB(M)21 b F6(\001)2512 1917 y Gc(t)2562 +1903 y Ga(U)p 2562 1918 V 146 w Gg(by)i(De\002nition)i(2.6.17)504 +2027 y(\(2\))146 b Ga(m)26 b F6(\025)f Ga(t;)15 b(r)m(;)g(s)1551 +b Gg(by)23 b(Lemma)g(2.6.19\(i,ii\))504 2152 y(\(3\))p +758 2152 28 4 v 775 2152 V 793 2152 V 211 w F6(h)p 857 +2152 V 875 2152 V 893 2152 V 65 w(i)955 2166 y Gc(m)1047 +2152 y F6(\035)p 1165 2152 V 1183 2152 V 1201 2152 V +110 w(\001)1273 2166 y Gc(t)p 1325 2152 V 1343 2152 V +1360 2152 V 2487 2152 a Gg(by)h(\(2\))f(and)h(De\002nition)h(2.6.14)504 +2276 y(\(4\))146 b FB(L)p Ga(S)p 790 2291 61 4 v 6 w(;)15 +b(T)p 892 2291 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 1028 +2291 72 4 v 11 w F6(i)1136 2290 y Gc(m)1228 2276 y Ga(>)1299 +2243 y Gc(r)r(po)1431 2276 y Ga(S)p 1431 2291 61 4 v +53 w Gg(and)50 b FB(L)p Ga(S)p 1755 2291 V 5 w(;)15 b(T)p +1856 2291 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 1992 2291 +72 4 v 11 w F6(i)2100 2290 y Gc(m)2192 2276 y Ga(>)2263 +2243 y Gc(r)r(po)2396 2276 y Ga(U)p 2396 2291 V 724 w +Gg(by)23 b(rpo\(i\))504 2400 y(\(5\))146 b F6(f)-24 b(j)p +FB(L)p Ga(S)p 836 2415 61 4 v 7 w(;)15 b(T)p 939 2415 +66 4 v 13 w FB(M)p Ga(;)g(U)p 1080 2415 72 4 v 11 w F6(j)-24 +b(g)26 b Ga(>)1296 2356 y Gc(r)r(po)1296 2429 y(mul)q(t)1476 +2400 y F6(f)-24 b(j)p Ga(S)p 1522 2415 61 4 v 6 w(;)15 +b(U)p 1624 2415 72 4 v 10 w F6(j)-24 b(g)1440 b Gg(by)23 +b(rpo\(i\))504 2524 y(\(6\))146 b FB(L)p Ga(S)p 790 2539 +61 4 v 6 w(;)15 b(T)p 892 2539 66 4 v 13 w FB(M)p F6(h)p +Ga(U)p 1028 2539 72 4 v 11 w F6(i)1136 2538 y Gc(m)1228 +2524 y Ga(>)1299 2491 y Gc(r)r(po)1431 2524 y Ga(S)p +1431 2539 61 4 v 5 w F6(h)p Ga(U)p 1527 2539 72 4 v 11 +w F6(i)1635 2538 y Gc(r)2301 2524 y Gg(if)23 b Ga(m)i +F4(=)g Ga(r)s Gg(,)d(then)i(by)g(\(5\))g(and)g(rpo\(iii\))2326 +2648 y(if)f Ga(m)i(>)g(r)s Gg(,)d(then)j(by)e(\(4\))h(and)g(rpo\(ii\)) +504 2773 y(\(7\))146 b FB(L)p Ga(S)p 790 2788 61 4 v +6 w(;)15 b(T)p 892 2788 66 4 v 13 w FB(M)p F6(h)p Ga(U)p +1028 2788 72 4 v 11 w F6(i)1136 2787 y Gc(m)1228 2773 +y Ga(>)1299 2740 y Gc(r)r(po)1431 2773 y Ga(T)p 1431 +2788 66 4 v 13 w F6(h)p Ga(U)p 1532 2788 72 4 v 10 w +F6(i)1639 2787 y Gc(s)2775 2773 y Gg(analogous)26 b(to)e(\(4,5,6\))504 +2897 y(\(8\))146 b FB(L)p Ga(S)p 790 2912 61 4 v 6 w(;)15 +b(T)p 892 2912 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 1028 +2912 72 4 v 11 w F6(i)1136 2911 y Gc(m)1228 2897 y Ga(>)1299 +2864 y Gc(r)r(po)1431 2897 y FB(L)p Ga(S)p 1466 2912 +61 4 v 6 w F6(h)p Ga(U)p 1563 2912 72 4 v 10 w F6(i)1670 +2911 y Gc(r)1708 2897 y Ga(;)g(T)p 1748 2912 66 4 v 14 +w F6(h)p Ga(U)p 1850 2912 72 4 v 10 w F6(i)1957 2911 +y Gc(s)1994 2897 y FB(M)776 b Gg(by)24 b(\(6,7\))g(and)g(rpo\(ii\))504 +3021 y(\(9\))146 b FB(L)p Ga(S)p 790 3036 61 4 v 6 w(;)15 +b(T)p 892 3036 66 4 v 13 w FB(M)p F6(h)p Ga(U)p 1028 +3036 72 4 v 11 w F6(i)1136 3035 y Gc(m)1228 3021 y Ga(>)1299 +2988 y Gc(r)r(po)1431 3021 y Ga(U)p 1431 3036 V 1689 +w Gg(by)23 b(rpo\(i\))504 3145 y(\(10\))101 b Ga(M)p +755 3160 99 4 v 36 w(>)950 3112 y Gc(r)r(po)1082 3145 +y Ga(N)p 1082 3160 83 4 v 1582 w Gg(by)24 b(\(3,8,9\))g(and)g +(rpo\(ii\))504 3386 y Ga(M)36 b F6(\021)25 b FL(Cut)803 +3339 y FC( )863 3386 y F4(\()898 3374 y FX(h)926 3386 +y Ga(d)973 3374 y FX(i)1001 3386 y FL(And)1156 3400 y +Gc(R)1213 3386 y F4(\()1248 3374 y FX(h)1276 3386 y Ga(a)1324 +3374 y FX(i)1352 3386 y Ga(S)5 b(;)1453 3374 y FX(h)1480 +3386 y Ga(b)1519 3374 y FX(i)1547 3386 y Ga(T)13 b(;)i(c)p +F4(\))q Ga(;)1768 3374 y F9(\()1796 3386 y Ga(x)1848 +3374 y F9(\))1875 3386 y Ga(U)10 b F4(\))782 3473 y Gc(x)717 +3510 y F6(\000)-31 b(\000)f(!)26 b FL(And)1067 3524 y +Gc(R)1125 3510 y F4(\()1160 3498 y FX(h)1188 3510 y Ga(a)1236 +3498 y FX(i)1263 3510 y FL(Cut)1342 3463 y FC( )1403 +3510 y F4(\()1438 3498 y FX(h)1466 3510 y Ga(d)1513 3498 +y FX(i)1540 3510 y Ga(S)5 b(;)1641 3498 y F9(\()1669 +3510 y Ga(x)1721 3498 y F9(\))1749 3510 y Ga(U)10 b F4(\))p +Ga(;)1896 3498 y FX(h)1924 3510 y Ga(b)1963 3498 y FX(i)1990 +3510 y FL(Cut)2069 3463 y FC( )2130 3510 y F4(\()2165 +3498 y FX(h)2193 3510 y Ga(d)2240 3498 y FX(i)2267 3510 +y Ga(T)j(;)2373 3498 y F9(\()2401 3510 y Ga(x)2453 3498 +y F9(\))2480 3510 y Ga(U)d F4(\))q Ga(;)15 b(c)p F4(\))26 +b F6(\021)f Ga(N)504 3634 y Gg(\(1\))101 b Ga(M)p 710 +3649 99 4 v 35 w F4(=)25 b FB(L)p Ga(S)p 964 3649 61 +4 v 6 w(;)15 b(T)p 1066 3649 66 4 v 13 w FB(M)g F6(h)p +Ga(U)p 1217 3649 72 4 v 11 w F6(i)1325 3648 y Gc(m)1440 +3634 y Gg(and)49 b Ga(N)p 1619 3649 83 4 v 35 w F4(=)25 +b FB(L)p Ga(S)p 1858 3649 61 4 v 5 w F6(h)p Ga(U)p 1954 +3649 72 4 v 11 w F6(i)2062 3648 y Gc(r)2100 3634 y Ga(;)15 +b(T)p 2140 3649 66 4 v 13 w F6(h)p Ga(U)p 2241 3649 72 +4 v 10 w F6(i)2348 3648 y Gc(s)2386 3634 y FB(M)349 b +Gg(by)23 b(De\002nition)i(2.6.17)504 3759 y(\(2\))101 +b Ga(m)25 b F6(\025)g Ga(r)m(;)15 b(s)1670 b Gg(by)23 +b(Lemma)g(2.6.19\(i,ii\))504 3883 y(\(3\))101 b FB(L)p +Ga(S)p 745 3898 61 4 v 5 w(;)15 b(T)p 846 3898 66 4 v +14 w FB(M)p F6(h)p Ga(U)p 983 3898 72 4 v 10 w F6(i)1090 +3897 y Gc(m)1182 3883 y Ga(>)1253 3850 y Gc(r)r(po)1386 +3883 y Ga(S)p 1386 3898 61 4 v 53 w Gg(and)49 b FB(L)p +Ga(S)p 1709 3898 V 5 w(;)15 b(T)p 1810 3898 66 4 v 14 +w FB(M)p F6(h)p Ga(U)p 1947 3898 72 4 v 10 w F6(i)2054 +3897 y Gc(m)2147 3883 y Ga(>)2218 3850 y Gc(r)r(po)2350 +3883 y Ga(U)p 2350 3898 V 770 w Gg(by)23 b(rpo\(i\))504 +4007 y(\(4\))101 b F6(f)-24 b(j)p FB(L)p Ga(S)p 791 4022 +61 4 v 6 w(;)15 b(T)p 893 4022 66 4 v 14 w FB(M)p Ga(;)g(U)p +1035 4022 72 4 v 10 w F6(j)-24 b(g)27 b Ga(>)1251 3963 +y Gc(r)r(po)1251 4036 y(mul)q(t)1430 4007 y F6(f)-24 +b(j)p Ga(S)p 1476 4022 61 4 v 6 w(;)15 b(U)p 1578 4022 +72 4 v 11 w F6(j)-24 b(g)1485 b Gg(by)23 b(rpo\(i\))504 +4131 y(\(5\))101 b FB(L)p Ga(S)p 745 4146 61 4 v 5 w(;)15 +b(T)p 846 4146 66 4 v 14 w FB(M)p F6(h)p Ga(U)p 983 4146 +72 4 v 10 w F6(i)1090 4145 y Gc(m)1182 4131 y Ga(>)1253 +4098 y Gc(r)r(po)1386 4131 y Ga(S)p 1386 4146 61 4 v +5 w F6(h)p Ga(U)p 1482 4146 72 4 v 10 w F6(i)1589 4145 +y Gc(r)2301 4131 y Gg(if)23 b Ga(m)i F4(=)g Ga(r)s Gg(,)d(then)i(by)g +(\(4\))g(and)g(rpo\(iii\))2326 4255 y(if)f Ga(m)i(>)g(r)s +Gg(,)d(then)j(by)e(\(3\))h(and)g(rpo\(ii\))504 4380 y(\(6\))101 +b FB(L)p Ga(S)p 745 4395 61 4 v 5 w(;)15 b(T)p 846 4395 +66 4 v 14 w FB(M)p F6(h)p Ga(U)p 983 4395 72 4 v 10 w +F6(i)1090 4394 y Gc(m)1182 4380 y Ga(>)1253 4347 y Gc(r)r(po)1386 +4380 y Ga(T)p 1386 4395 66 4 v 13 w F6(h)p Ga(U)p 1487 +4395 72 4 v 10 w F6(i)1594 4394 y Gc(s)2775 4380 y Gg(analogous)26 +b(to)e(\(3,4,5\))504 4504 y(\(7\))101 b Ga(M)p 710 4519 +99 4 v 35 w(>)904 4471 y Gc(r)r(po)1037 4504 y Ga(N)p +1037 4519 83 4 v 1695 w Gg(by)24 b(\(5,6\))g(and)g(rpo\(ii\))504 +4745 y Ga(M)36 b F6(\021)25 b FL(Cut)803 4697 y FC( )863 +4745 y F4(\()898 4733 y FX(h)926 4745 y Ga(a)974 4733 +y FX(i)1002 4745 y FL(Cut)p F4(\()1175 4733 y FX(h)1202 +4745 y Ga(b)1241 4733 y FX(i)1269 4745 y Ga(S)5 b(;)1370 +4733 y F9(\()1398 4745 y Ga(x)1450 4733 y F9(\))1477 +4745 y Ga(T)13 b F4(\))p Ga(;)1618 4733 y F9(\()1646 +4745 y Ga(y)1694 4733 y F9(\))1721 4745 y Ga(U)d F4(\))782 +4832 y Gc(x)717 4869 y F6(\000)-31 b(\000)f(!)26 b FL(Cut)o +F4(\()1085 4857 y FX(h)1113 4869 y Ga(b)1152 4857 y FX(i)1180 +4869 y FL(Cut)1258 4821 y FC( )1319 4869 y F4(\()1354 +4857 y FX(h)1382 4869 y Ga(a)1430 4857 y FX(i)1458 4869 +y Ga(S)5 b(;)1559 4857 y F9(\()1586 4869 y Ga(y)1634 +4857 y F9(\))1662 4869 y Ga(U)10 b F4(\))p Ga(;)1809 +4857 y F9(\()1837 4869 y Ga(x)1889 4857 y F9(\))1916 +4869 y FL(Cut)1995 4821 y FC( )2056 4869 y F4(\()2091 +4857 y FX(h)2119 4869 y Ga(a)2167 4857 y FX(i)2194 4869 +y Ga(T)j(;)2300 4857 y F9(\()2328 4869 y Ga(y)2376 4857 +y F9(\))2403 4869 y Ga(U)d F4(\))q(\))25 b F6(\021)g +Ga(N)504 4993 y Gg(\(1\))101 b Ga(M)p 710 5008 99 4 v +35 w F4(=)25 b(\()p Ga(S)p 964 5008 61 4 v 26 w F6(\001)1071 +5007 y Gc(m)1158 4993 y Ga(T)p 1158 5008 66 4 v 13 w +F4(\))p F6(h)p Ga(U)p 1294 5008 72 4 v 10 w F6(i)1401 +5007 y Gc(n)1497 4993 y Gg(and)49 b Ga(N)p 1676 5008 +83 4 v 35 w F4(=)25 b Ga(S)p 1880 5008 61 4 v 5 w F6(h)p +Ga(U)p 1976 5008 72 4 v 10 w F6(i)2083 5007 y Gc(r)2142 +4993 y F6(\001)2167 5007 y Gc(s)2224 4993 y Ga(T)p 2224 +5008 66 4 v 13 w F6(h)p Ga(U)p 2325 5008 72 4 v 10 w +F6(i)2432 5007 y Gc(t)2770 4993 y Gg(by)e(De\002nition)i(2.6.17)504 +5117 y(\(2\))101 b Ga(n)25 b F6(\025)g Ga(s;)15 b(r)m(;)g(t)1622 +b Gg(by)23 b(Lemma)g(2.6.19\(i,ii\))504 5241 y(\(3\))p +712 5241 28 4 v 730 5241 V 747 5241 V 166 w F6(h)p 812 +5241 V 830 5241 V 847 5241 V 64 w(i)909 5255 y Gc(n)982 +5241 y F6(\035)p 1100 5241 V 1118 5241 V 1135 5241 V +110 w(\001)1208 5255 y Gc(s)p 1267 5241 V 1285 5241 V +1302 5241 V 2487 5241 a Gg(by)h(\(2\))f(and)h(De\002nition)h(2.6.14)p +Black Black eop end +%%Page: 154 166 +TeXDict begin 154 165 bop Black -144 51 a Gb(154)2658 +b(Details)24 b(f)n(or)g(some)g(Pr)n(oofs)p -144 88 3691 +4 v Black 549 384 a Gg(\(4\))100 b F4(\()p Ga(S)p 789 +399 61 4 v 26 w F6(\001)896 398 y Gc(m)983 384 y Ga(T)p +983 399 66 4 v 13 w F4(\))p F6(h)p Ga(U)p 1119 399 72 +4 v 10 w F6(i)1226 398 y Gc(n)1299 384 y Ga(>)1370 351 +y Gc(r)r(po)1502 384 y Ga(S)p 1502 399 61 4 v 53 w Gg(and)50 +b F4(\()p Ga(S)p 1826 399 V 25 w F6(\001)1932 398 y Gc(m)2019 +384 y Ga(T)p 2019 399 66 4 v 13 w F4(\))p F6(h)p Ga(U)p +2155 399 72 4 v 11 w F6(i)2263 398 y Gc(n)2335 384 y +Ga(>)2406 351 y Gc(r)r(po)2539 384 y Ga(U)p 2539 399 +V 625 w Gg(by)23 b(rpo\(i\))549 508 y(\(5\))100 b F6(f)-24 +b(j)p F4(\()p Ga(S)p 835 523 61 4 v 27 w F6(\001)943 +522 y Gc(m)1030 508 y Ga(T)p 1030 523 66 4 v 13 w F4(\))p +Ga(;)15 b(U)p 1171 523 72 4 v 10 w F6(j)-24 b(g)27 b +Ga(>)1387 464 y Gc(r)r(po)1387 537 y(mul)q(t)1566 508 +y F6(f)-24 b(j)p Ga(S)p 1612 523 61 4 v 6 w(;)15 b(U)p +1714 523 72 4 v 11 w F6(j)-24 b(g)1393 b Gg(by)23 b(rpo\(i\))549 +632 y(\(6\))100 b F4(\()p Ga(S)p 789 647 61 4 v 26 w +F6(\001)896 646 y Gc(m)983 632 y Ga(T)p 983 647 66 4 +v 13 w F4(\))p F6(h)p Ga(U)p 1119 647 72 4 v 10 w F6(i)1226 +646 y Gc(n)1299 632 y Ga(>)1370 599 y Gc(r)r(po)1502 +632 y Ga(S)p 1502 647 61 4 v 5 w F6(h)p Ga(U)p 1598 647 +72 4 v 11 w F6(i)1706 646 y Gc(r)2370 632 y Gg(if)23 +b Ga(n)i F4(=)g Ga(r)s Gg(,)d(then)i(by)g(\(5\))g(and)g(rpo\(iii\))2395 +756 y(if)g Ga(n)g(>)h(r)s Gg(,)d(then)j(by)e(\(4\))h(and)g(rpo\(ii\)) +549 881 y(\(7\))100 b F4(\()p Ga(S)p 789 896 61 4 v 26 +w F6(\001)896 895 y Gc(m)983 881 y Ga(T)p 983 896 66 +4 v 13 w F4(\))p F6(h)p Ga(U)p 1119 896 72 4 v 10 w F6(i)1226 +895 y Gc(n)1299 881 y Ga(>)1370 848 y Gc(r)r(po)1502 +881 y Ga(T)p 1502 896 66 4 v 13 w F6(h)p Ga(U)p 1603 +896 72 4 v 10 w F6(i)1710 895 y Gc(t)2819 881 y Gg(analogous)27 +b(to)c(\(4,5,6\))549 1005 y(\(8\))100 b Ga(M)p 754 1020 +99 4 v 36 w(>)949 972 y Gc(r)r(po)1081 1005 y Ga(N)p +1081 1020 83 4 v 1627 w Gg(by)24 b(\(3,6,7\))g(and)g(rpo\(ii\))549 +1294 y Ga(M)35 b F6(\021)25 b FL(Cut)847 1247 y FC( )908 +1294 y F4(\()943 1282 y FX(h)970 1294 y Ga(a)1018 1282 +y FX(i)1046 1294 y FL(Cut)p F4(\()1219 1282 y FX(h)1247 +1294 y Ga(b)1286 1282 y FX(i)1313 1294 y Ga(S)5 b(;)1414 +1282 y F9(\()1442 1294 y Ga(x)1494 1282 y F9(\))1521 +1294 y FL(Ax)p F4(\()p Ga(x;)15 b(a)p F4(\))q(\))p Ga(;)1910 +1282 y F9(\()1938 1294 y Ga(y)1986 1282 y F9(\))2013 +1294 y Ga(U)10 b F4(\))826 1381 y Gc(x)761 1418 y F6(\000)-31 +b(\000)g(!)25 b FL(Cut)p F4(\()1130 1406 y FX(h)1157 +1418 y Ga(b)1196 1406 y FX(i)1224 1418 y FL(Cut)1303 +1371 y FC( )1364 1418 y F4(\()1399 1406 y FX(h)1426 1418 +y Ga(a)1474 1406 y FX(i)1502 1418 y Ga(S)5 b(;)1603 1406 +y F9(\()1631 1418 y Ga(y)1679 1406 y F9(\))1706 1418 +y Ga(U)10 b F4(\))p Ga(;)1853 1406 y F9(\()1881 1418 +y Ga(y)1929 1406 y F9(\))1956 1418 y Ga(U)g F4(\))26 +b F6(\021)f Ga(N)549 1543 y Gg(\(1\))100 b Ga(M)p 754 +1558 99 4 v 36 w F4(=)25 b(\()p Ga(S)p 1009 1558 61 4 +v 25 w F6(\001)1115 1557 y Gc(m)1202 1543 y Ga(?)p F4(\))p +F6(h)p Ga(U)p 1317 1558 72 4 v 11 w F6(i)1425 1557 y +Gc(n)1521 1543 y Gg(and)49 b Ga(N)p 1700 1558 83 4 v +35 w F4(=)25 b Ga(S)p 1904 1558 61 4 v 5 w F6(h)p Ga(U)p +2000 1558 72 4 v 10 w F6(i)2107 1557 y Gc(r)2166 1543 +y F6(\001)2191 1557 y Gc(s)2248 1543 y Ga(U)p 2248 1558 +V 504 w Gg(by)f(De\002nition)g(2.6.17)549 1667 y(\(2\))100 +b Ga(n)25 b F6(\025)g Ga(s;)15 b(r)1692 b Gg(by)24 b(Lemma)e +(2.6.19\(i,ii\))549 1791 y(\(3\))p 756 1791 28 4 v 774 +1791 V 791 1791 V 165 w F6(h)p 856 1791 V 874 1791 V +891 1791 V 65 w(i)954 1805 y Gc(n)1026 1791 y F6(\035)p +1144 1791 V 1162 1791 V 1180 1791 V 110 w(\001)1252 1805 +y Gc(s)p 1311 1791 V 1329 1791 V 1347 1791 V 2531 1791 +a Gg(by)i(\(2\))g(and)g(De\002nition)g(2.6.14)549 1915 +y(\(4\))100 b F4(\()p Ga(S)p 789 1930 61 4 v 26 w F6(\001)896 +1929 y Gc(m)983 1915 y Ga(?)p F4(\))p F6(h)p Ga(U)p 1098 +1930 72 4 v 11 w F6(i)1206 1929 y Gc(n)1278 1915 y Ga(>)1349 +1882 y Gc(r)r(po)1482 1915 y Ga(S)p 1482 1930 61 4 v +53 w Gg(and)49 b F4(\()p Ga(S)p 1805 1930 V 26 w F6(\001)1912 +1929 y Gc(m)1999 1915 y Ga(?)p F4(\))p F6(h)p Ga(U)p +2114 1930 72 4 v 11 w F6(i)2222 1929 y Gc(n)2295 1915 +y Ga(>)2366 1882 y Gc(r)r(po)2498 1915 y Ga(U)p 2498 +1930 V 666 w Gg(by)23 b(rpo\(i\))549 2040 y(\(5\))100 +b F6(f)-24 b(j)p F4(\()p Ga(S)p 835 2055 61 4 v 27 w +F6(\001)943 2054 y Gc(m)1030 2040 y Ga(?)p F4(\))p Ga(;)15 +b(U)p 1150 2055 72 4 v 11 w F6(j)-24 b(g)26 b Ga(>)1366 +1995 y Gc(r)r(po)1366 2069 y(mul)q(t)1546 2040 y F6(f)-24 +b(j)p Ga(S)p 1592 2055 61 4 v 6 w(;)15 b(U)p 1694 2055 +72 4 v 11 w F6(j)-24 b(g)1413 b Gg(by)23 b(rpo\(i\))549 +2164 y(\(6\))100 b F4(\()p Ga(S)p 789 2179 61 4 v 26 +w F6(\001)896 2178 y Gc(m)983 2164 y Ga(?)p F4(\))p F6(h)p +Ga(U)p 1098 2179 72 4 v 11 w F6(i)1206 2178 y Gc(n)1278 +2164 y Ga(>)1349 2131 y Gc(r)r(po)1482 2164 y Ga(S)p +1482 2179 61 4 v 5 w F6(h)p Ga(U)p 1578 2179 72 4 v 10 +w F6(i)1685 2178 y Gc(r)2370 2164 y Gg(if)23 b Ga(n)i +F4(=)g Ga(r)s Gg(,)d(then)i(by)g(\(5\))g(and)g(rpo\(iii\))2395 +2288 y(if)g Ga(n)g(>)h(r)s Gg(,)d(then)j(by)e(\(4\))h(and)g(rpo\(ii\)) +549 2412 y(\(7\))100 b Ga(M)p 754 2427 99 4 v 36 w(>)949 +2379 y Gc(r)r(po)1081 2412 y Ga(N)p 1081 2427 83 4 v +1627 w Gg(by)24 b(\(3,4,6\))g(and)g(rpo\(ii\))549 2702 +y Ga(M)35 b F6(\021)25 b FL(Cut)847 2654 y FC( )908 2702 +y F4(\()943 2690 y FX(h)970 2702 y Ga(a)1018 2690 y FX(i)1046 +2702 y FL(Ax)o F4(\()p Ga(x;)15 b(a)p F4(\))r Ga(;)1400 +2690 y F9(\()1427 2702 y Ga(y)1475 2690 y F9(\))1503 +2702 y Ga(S)5 b F4(\))1690 2664 y Gc(x)1624 2702 y F6(\000)-31 +b(\000)g(!)25 b FL(Cut)p F4(\()1993 2690 y FX(h)2020 +2702 y Ga(a)2068 2690 y FX(i)2096 2702 y FL(Ax)o F4(\()p +Ga(x;)15 b(a)p F4(\))r Ga(;)2450 2690 y F9(\()2477 2702 +y Ga(y)2525 2690 y F9(\))2553 2702 y Ga(S)5 b F4(\))25 +b F6(\021)g Ga(N)549 2826 y Gg(\(1\))100 b Ga(M)p 754 +2841 99 4 v 36 w F4(=)25 b Ga(?)15 b F6(h)p Ga(S)p 1069 +2841 61 4 v 5 w F6(i)1165 2840 y Gc(m)1280 2826 y Gg(and)50 +b Ga(N)p 1460 2841 83 4 v 35 w F4(=)25 b Ga(?)20 b F6(\001)1754 +2840 y Gc(n)1822 2826 y Ga(S)p 1822 2841 61 4 v 936 w +Gg(by)k(De\002nition)g(2.6.17)549 2950 y(\(2\))100 b +Ga(m)25 b F6(\025)g Ga(n)1809 b Gg(by)24 b(Lemma)e(2.6.19\(i\))549 +3074 y(\(3\))p 756 3074 28 4 v 774 3074 V 791 3074 V +165 w F6(h)p 856 3074 V 874 3074 V 891 3074 V 65 w(i)954 +3088 y Gc(m)1046 3074 y F6(\035)p 1164 3074 V 1182 3074 +V 1199 3074 V 110 w(\001)1272 3088 y Gc(n)p 1341 3074 +V 1359 3074 V 1376 3074 V 2531 3074 a Gg(by)i(\(2\))g(and)g +(De\002nition)g(2.6.14)549 3198 y(\(4\))100 b Ga(?)15 +b F6(h)p Ga(S)p 849 3213 61 4 v 6 w F6(i)946 3212 y Gc(m)1038 +3198 y Ga(>)1109 3165 y Gc(r)r(po)1242 3198 y Ga(?)48 +b Gg(and)i Ga(?)15 b F6(h)p Ga(S)p 1610 3213 V 6 w F6(i)1707 +3212 y Gc(m)1799 3198 y Ga(>)1870 3165 y Gc(r)r(po)2002 +3198 y Ga(S)p 2002 3213 V 1168 w Gg(by)23 b(rpo\(i\))549 +3323 y(\(5\))100 b Ga(M)p 754 3338 99 4 v 36 w(>)949 +3290 y Gc(r)r(po)1081 3323 y Ga(N)p 1081 3338 83 4 v +1696 w Gg(by)23 b(\(3,4\))h(and)g(rpo\(ii\))p Black 321 +3603 a Gb(Commuting)f(Reduction:)p Black 45 w Gg(One)h(case)g(is)f(as)h +(follo)n(ws.)549 3803 y Ga(M)35 b F6(\021)25 b FL(Cut)p +F4(\()941 3791 y FX(h)969 3803 y Ga(a)1017 3791 y FX(i)1044 +3803 y Ga(S)5 b(;)1145 3791 y 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Gc(l)1622 4905 y F6(\000)-31 b(\000)g(!)25 b Ga(S)5 +b F4([)p Ga(y)13 b F6(7!)d Ga(x)p F4(])26 b F6(\021)f +Ga(N)549 5029 y Gg(\(1\))100 b Ga(M)p 754 5044 99 4 v +36 w F4(=)25 b Ga(?)20 b F6(\001)1064 5043 y Gc(n)1132 +5029 y Ga(S)p 1132 5044 61 4 v 53 w Gg(and)49 b Ga(N)p +1420 5044 83 4 v 35 w F4(=)25 b Ga(S)p 1624 5044 61 4 +v 1134 w Gg(by)f(De\002nition)g(2.6.17)549 5153 y(\(2\))100 +b Ga(M)p 754 5168 99 4 v 36 w(>)949 5120 y Gc(r)r(po)1081 +5153 y Ga(N)p 1081 5168 83 4 v 1764 w Gg(by)23 b(\(1\))h(and)g +(rpo\(ii\))p Black Black eop end +%%Page: 155 167 +TeXDict begin 155 166 bop Black 277 51 a Gb(B.1)23 b(Pr)n(oofs)h(of)g +(Chapter)f(2)2639 b(155)p 277 88 3691 4 v Black 504 384 +a Ga(M)36 b F6(\021)25 b FL(Cut)p F4(\()897 372 y FX(h)924 +384 y Ga(c)963 372 y FX(i)991 384 y FL(And)1146 398 y +Gc(R)1203 384 y F4(\()1238 372 y FX(h)1266 384 y Ga(a)1314 +372 y FX(i)1342 384 y Ga(S)5 b(;)1443 372 y FX(h)1471 +384 y Ga(b)1510 372 y FX(i)1537 384 y Ga(T)13 b(;)i(c)p +F4(\))q Ga(;)1758 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+y(\(5\))101 b FB(L)p Ga(S)p 745 1876 V 5 w FB(M)21 b +F6(\001)887 1875 y Gc(m)974 1861 y FB(L)p Ga(T)p 1009 +1876 66 4 v 13 w(;)15 b(U)p 1115 1876 72 4 v 10 w FB(M)26 +b Ga(>)1319 1828 y Gc(r)r(po)1452 1861 y Ga(U)p 1452 +1876 V 1170 w Gg(by)e(De\002nition)g(2.6.12\(i\))504 +1985 y(\(6\))101 b Ga(M)p 710 2000 99 4 v 35 w(>)904 +1952 y Gc(r)r(po)1037 1985 y Ga(N)p 1037 2000 83 4 v +1627 w Gg(by)24 b(\(2,4,5\))g(and)g(rpo\(ii\))p Black +277 2157 a Gb(Garbage)g(Reduction:)p Black 46 w Gg(Finally)-6 +b(,)23 b(we)e(gi)n(v)o(e)h(one)h(case)g(where)f(a)g(garbage)h +(reduction)i(is)d(performed.)504 2303 y Ga(M)36 b F6(\021)25 +b FL(Cut)803 2256 y FC( )863 2303 y F4(\()898 2291 y +FX(h)926 2303 y Ga(a)974 2291 y FX(i)1002 2303 y Ga(S)5 +b(;)1103 2291 y F9(\()1131 2303 y Ga(x)1183 2291 y F9(\))1210 +2303 y Ga(T)13 b F4(\))1388 2266 y Gc(g)r(c)1336 2303 +y F6(\000)-31 b(\000)g(!)25 b Ga(S)30 b F6(\021)25 b +Ga(N)504 2427 y Gg(\(1\))101 b Ga(M)p 710 2442 99 4 v +35 w F4(=)25 b Ga(S)p 929 2442 61 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMBX9) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMBX9 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-58 -250 1195 750}readonly def +/UniqueID 5000767 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 +B1805DA88AE375A04D99598EADFC625BDC1F9C315B6CF28C9BD427F32C745C99 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTT9) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch true def +end readonly def +/FontName /CMTT9 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-6 -233 542 698}readonly def +/UniqueID 5000831 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5F00F963068B8232429ED8B7CF6A3D879A2D1E +2931CE5F5D18C658602059F07BE66E6EFC9239D7AB2FB8A4CBD41675B8ECF279 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR9) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR9 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-39 -250 1036 750}readonly def +/UniqueID 5000792 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 +87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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All Rights Reserved) readonly def +/FullName (CMR5) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR5 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 49 /one put +readonly def +/FontBBox{-341 -250 1304 965}readonly def +/UniqueID 5000788 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI5 +%!PS-AdobeFont-1.1: CMMI5 1.100 +%%CreationDate: 1996 Aug 02 08:21:10 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI5) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI5 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 59 /comma put +dup 88 /X put +readonly def +/FontBBox{37 -250 1349 750}readonly def +/UniqueID 5087380 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMBSY7 +%!PS-AdobeFont-1.1: CMBSY7 001.000 +%%CreationDate: 1992 Oct 22 12:18:11 +% Computer Modern fonts were designed by Donald E. 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All Rights Reserved) readonly def +/FullName (CMBSY7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMBSY7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 1 /periodcentered put +readonly def +/FontBBox{0 -927 1542 750}readonly def +/UniqueID 5032008 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMTT8 +%!PS-AdobeFont-1.1: CMTT8 1.0 +%%CreationDate: 1991 Aug 20 16:46:05 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTT8) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch true def +end readonly def +/FontName /CMTT8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 108 /l put +dup 118 /v put +readonly def +/FontBBox{-5 -232 545 699}readonly def +/UniqueID 5000830 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: MSBM7 +%!PS-AdobeFont-1.1: MSBM7 2.1 +%%CreationDate: 1992 Oct 17 08:30:50 +% Math Symbol fonts were designed by the American Mathematical Society. +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (2.1) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (MSBM7) readonly def +/FamilyName (Euler) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /MSBM7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 63 /emptyset put +readonly def +/FontBBox{0 -504 2615 1004}readonly def +/UniqueID 5032014 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMIB10 +%!PS-AdobeFont-1.1: CMMIB10 1.100 +%%CreationDate: 1996 Jul 23 07:54:00 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMIB10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMIB10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 25 /pi put +readonly def +/FontBBox{-15 -250 1216 750}readonly def +/UniqueID 5087392 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMSY5 +%!PS-AdobeFont-1.1: CMSY5 1.0 +%%CreationDate: 1991 Aug 15 07:21:16 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY5) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMSY5 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /minus put +dup 48 /prime put +dup 102 /braceleft put +dup 103 /braceright put +readonly def +/FontBBox{21 -944 1448 791}readonly def +/UniqueID 5000815 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: MSBM10 +%!PS-AdobeFont-1.1: MSBM10 2.1 +%%CreationDate: 1993 Sep 17 11:10:37 +% Math Symbol fonts were designed by the American Mathematical Society. +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (2.1) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (MSBM10) readonly def +/FamilyName (Euler) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /MSBM10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 63 /emptyset put +readonly def +/FontBBox{-55 -420 2343 920}readonly def +/UniqueID 5031982 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI6 +%!PS-AdobeFont-1.1: CMMI6 1.100 +%%CreationDate: 1996 Jul 23 07:53:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI6) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI6 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 25 /pi put +dup 58 /period put +dup 59 /comma put +dup 61 /slash put +dup 65 /A put +dup 68 /D put +dup 71 /G put +dup 76 /L put +dup 77 /M put +dup 82 /R put +dup 84 /T put +dup 88 /X put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 105 /i put +dup 112 /p put +dup 115 /s put +dup 116 /t put +dup 120 /x put +dup 121 /y put +dup 122 /z put +readonly def +/FontBBox{11 -250 1241 750}readonly def +/UniqueID 5087381 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMTI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 88 /X put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 115 /s put +dup 116 /t put +readonly def +/FontBBox{-163 -250 1146 969}readonly def +/UniqueID 5000828 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE +D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTI9) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMTI9 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 88 /X put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 115 /s put +readonly def +/FontBBox{-35 -250 1148 750}readonly def +/UniqueID 5000827 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE +D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMBSY10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMBSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 1 /periodcentered put +readonly def +/FontBBox{-27 -940 1332 825}readonly def +/UniqueID 5000762 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMSY7 +%!PS-AdobeFont-1.1: CMSY7 1.0 +%%CreationDate: 1991 Aug 15 07:21:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMSY7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /minus put +dup 48 /prime put +dup 66 /B put +dup 102 /braceleft put +dup 103 /braceright put +readonly def +/FontBBox{-15 -951 1252 782}readonly def +/UniqueID 5000817 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMTT10 +%!PS-AdobeFont-1.1: CMTT10 1.00B +%%CreationDate: 1992 Apr 26 10:42:42 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTT10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch true def +end readonly def +/FontName /CMTT10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 102 /f put +readonly def +/FontBBox{-4 -235 731 800}readonly def +/UniqueID 5000832 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMTT9 +%!PS-AdobeFont-1.1: CMTT9 1.0 +%%CreationDate: 1991 Aug 20 16:46:24 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTT9) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch true def +end readonly def +/FontName /CMTT9 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 97 /a put +dup 102 /f put +dup 108 /l put +dup 109 /m put +dup 114 /r put +dup 118 /v put +readonly def +/FontBBox{-6 -233 542 698}readonly def +/UniqueID 5000831 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI7 +%!PS-AdobeFont-1.1: CMMI7 1.100 +%%CreationDate: 1996 Jul 23 07:53:53 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 25 /pi put +dup 59 /comma put +dup 65 /A put +dup 68 /D put +dup 76 /L put +dup 88 /X put +dup 97 /a put +dup 105 /i put +dup 110 /n put +dup 112 /p put +dup 116 /t put +readonly def +/FontBBox{0 -250 1171 750}readonly def +/UniqueID 5087382 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /minus put +dup 1 /periodcentered put +dup 14 /openbullet put +dup 15 /bullet put +dup 25 /approxequal put +dup 27 /propersuperset put +dup 33 /arrowright put +dup 41 /arrowdblright put +dup 50 /element put +dup 54 /negationslash put +dup 56 /universal put +dup 62 /latticetop put +dup 66 /B put +dup 94 /logicaland put +dup 95 /logicalor put +dup 96 /turnstileleft put +dup 102 /braceleft put +dup 103 /braceright put +dup 104 /angbracketleft put +dup 105 /angbracketright put +dup 106 /bar put +dup 110 /backslash put +dup 114 /nabla put +dup 116 /unionsq put +dup 117 /intersectionsq put +readonly def 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /Gamma put +dup 11 /alpha put +dup 21 /lambda put +dup 22 /mu put +dup 25 /pi put +dup 27 /sigma put +dup 58 /period put +dup 59 /comma put +dup 61 /slash put +dup 63 /star put +dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 70 /F put +dup 71 /G put +dup 77 /M put +dup 81 /Q put +dup 84 /T put +dup 86 /V put +dup 88 /X put +dup 89 /Y put +dup 97 /a put +dup 98 /b put +dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 105 /i put +dup 108 /l put +dup 109 /m put +dup 110 /n put +dup 112 /p put +dup 115 /s put +dup 116 /t put +dup 120 /x put +dup 121 /y put +dup 122 /z put +readonly def 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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FI(\))36 b FK(G)3260 4538 +y Fs(bs)5 b FC(;)p Fs(ts)523 4625 y FT(by)28 b(Corollary)f(1)h(that)h +FI(r)1275 4595 y Fv(00)1275 4649 y Fs(bs)1343 4625 y +FK(;)14 b FI(r)1449 4595 y Fv(0)1473 4625 y FH(;)g FK(\000)49 +b FI(\))38 b FK(\031)s Fu(\001)p FK(G)1873 4637 y Fs(bs)5 +b FC(;)p Fs(ts)2046 4625 y FT(is)30 b(deri)n(v)n(able)c(\(this)j +(deduction)d(does)i(not)g(in-)523 4725 y(troduce)33 b(an)o(y)h(ne)n(w)h +FK(\031)s FT(-rules\).)f(In)h(\(8\))f(we)h(can)f(pull)h(out)f(the)h +(permutation)e FK(\031)2905 4695 y Fv(0)2964 4725 y FT(and)h(we)h(ha)n +(v)o(e)523 4825 y FK(\031)s Fu(\001)p FK(\033)28 b FI(\016)d +FK(\033)792 4795 y Fv(0)816 4825 y FH(\()p FK(\031)898 +4795 y Fv(0)922 4825 y Fu(\001)o FK(G)1013 4837 y Fs(cs)5 +b FC(;)p Fs(Xs)1185 4825 y FH(\))40 b(=)f FK(\031)s FH(@)p +FK(\031)1526 4795 y Fv(0)1550 4825 y Fu(\001)o FH(\()p +FK(\033)29 b FI(\016)c FK(\033)1801 4795 y Fv(0)1825 +4825 y FH(\()p FK(G)1922 4837 y Fs(cs)5 b FC(;)p Fs(Xs)2094 +4825 y FH(\)\))p FT(.)30 b(Therefore)d(applying)g(the)i(substitution) +523 4924 y(to)22 b FK(G)675 4936 y Fs(cs)5 b FC(;)p Fs(Xs)869 +4924 y FT(gi)n(v)o(es)21 b FK(\031)s FH(@)p FK(\031)1228 +4894 y Fv(0)1252 4924 y Fu(\001)o FH(\()p FK(\033)j FI(\016)19 +b FK(\033)1492 4894 y Fv(0)1516 4924 y FH(\()p FK(G)1613 +4936 y Fs(cs)5 b FC(;)p Fs(Xs)1785 4924 y FH(\)\))26 +b(=)g FK(\031)s FH(@)p FK(\031)2131 4894 y Fv(0)2154 +4924 y Fu(\001)p FK(G)2246 4936 y Fs(cs)5 b FC(;)p Fs(ts)2386 +4920 y Fl(0)2435 4924 y FT(\(taking)21 b(the)h Fr(ts)2885 +4894 y Fv(0)2931 4924 y FT(we)g(introduced)p eop end +%%Page: 14 14 +TeXDict begin 14 13 bop 523 448 a FT(for)21 b FK(s)681 +460 y Fs(cs)t FC(;)p Fs(ts)820 444 y Fl(0)869 448 y FT(earlier\).)f +(Thus)h(by)f(Lemma)h(3)g(we)h(can)f(sho)n(w)f(that)i +FI(r)2448 418 y Fv(00)2448 469 y Fs(cs)2516 448 y FK(;)14 +b FI(r)2622 418 y Fv(0)2646 448 y FH(;)g FK(\000)36 b +FI(\))25 b FK(G)2943 460 y Fs(cs)5 b FC(;)p Fs(ts)3083 +444 y Fl(0)3132 448 y FT(is)22 b(deri)n(v-)523 548 y(able.)648 +651 y(Each)16 b(transformation)f(decreases)i(the)g(number)e(of)i +FK(\031)s FT(-rules)g(in)h(a)f(deduction)e(by)i(one)g(and)g(thus)523 +751 y(by)j(repeated)f(application)f(we)j(will)g(e)n(v)o(entually)d(end) +i(up)g(with)g(a)h FK(\031)s FT(-free)e(proof.)500 b FI(u)-55 +b(t)523 940 y FT(W)-7 b(e)28 b(ha)n(v)o(e)e(sho)n(wn)g(that)h(when)f +(all)i(the)f(formulas)e(in)i FK(\000)39 b FT(are)27 b(well-formed,)d(e) +n(v)o(ery)i(deduction)f(of)523 1039 y FK(\000)57 b FI(\))45 +b FK(G)33 b FT(containing)d FK(\031)s FT(-rules)i(can)g(be)g(replaced)f +(by)h(one)g(without)f FK(\031)s FT(-rules.)h(Consequently)-5 +b(,)523 1139 y(nominal)19 b(uni\002cation)g(is)i(suf)n(\002cient)f(for) +f(e)o(x)o(ecuting)f(well-formed)g FK(\013)p FT(Prolog)o(-programs.)523 +1423 y FL(4)99 b(V)-10 b(eri\002cation)26 b(of)f(W)-6 +b(ell-F)n(ormedness)24 b(Using)g(Nominal)h(Matching)523 +1632 y FT(In)19 b(this)h(section)f(we)g(consider)f(the)h(question)f(of) 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b FG(#)22 b Ft(Xs)6 b FN(;)13 +b FF(r)2443 1995 y Ff(as)t Fn(;)p Ff(Xs)2617 1987 y FF(`)21 +b FN(\033)s FG(\()p FN(\031)s Fz(\001)o FN(G)2893 1996 +y Ff(bs)t Fn(;)p Ff(Xs)3043 1987 y FG(\))g FF(\031)g +FN(G)3235 1995 y Ff(as)t Fn(;)p Ff(Xs)523 2164 y FT(hold.)f(F)o(or)h +(the)g(\002rst)h(judgement,)d FK(\033)25 b FT(can)c(be)g(found)f(by)h +(nominal)e(matching.)h(But)i(for)e(the)h(second)523 2264 +y(judgement,)j(\002nding)i(both)f(substitution)h FK(\033)k +FT(and)c(permutation)e FK(\031)30 b FT(requires)c(solving)f +(\(NP-hard\))523 2363 y(equi)n(v)n(ariant)13 b(matching)h(problems.)g +(This)h(seemingly)f(ne)o(gati)n(v)o(e)f(result)j(should,)e(ho)n(we)n(v) +o(er)m(,)e(be)j(seen)523 2463 y(in)29 b(the)f(conte)o(xt)g(that)g +(well-formedness)f(only)g(needs)h(to)h(be)g(v)o(eri\002ed)e(once)h(per) +g(clause,)g(rather)523 2563 y(than)20 b(repeatedly)e(during)h +(proof-search.)e(Thus,)i(the)h(one-time)f(cost)i(of)e(performing)f +(equi)n(v)n(ariant)523 2662 y(uni\002cation)h(in)i(checking)e 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All Rights Reserved) readonly def +/FullName (CMSY7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMSY7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-15 -951 1252 782}readonly def +/UniqueID 5000817 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMSY10 +%!PS-AdobeFont-1.1: CMSY10 1.0 +%%CreationDate: 1991 Aug 15 07:20:57 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR6) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR6 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-20 -250 1193 750}readonly def +/UniqueID 5000789 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMR7 +%!PS-AdobeFont-1.1: CMR7 1.0 +%%CreationDate: 1991 Aug 20 16:39:21 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-27 -250 1122 750}readonly def +/UniqueID 5000790 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMR10 +%!PS-AdobeFont-1.1: CMR10 1.00B +%%CreationDate: 1992 Feb 19 19:54:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-251 -250 1009 969}readonly def +/UniqueID 5000793 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 +87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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All Rights Reserved) readonly def +/FullName (CMSY9) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMSY9 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-30 -958 1146 777}readonly def +/UniqueID 5000819 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI7 +%!PS-AdobeFont-1.1: CMMI7 1.100 +%%CreationDate: 1996 Jul 23 07:53:53 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{0 -250 1171 750}readonly def +/UniqueID 5087382 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMTI10 +%!PS-AdobeFont-1.1: CMTI10 1.00B +%%CreationDate: 1992 Feb 19 19:56:16 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMTI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-163 -250 1146 969}readonly def +/UniqueID 5000828 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE +D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 +9E3948FFB0B4E70F212EC976D65099D84E0D37A7A771C3101D6AD26A0513378F 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI9) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI9 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-29 -250 1075 750}readonly def +/UniqueID 5087384 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE +D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 +9E394A533A081C36D6F5CA5FED4F9AC9ADE41E04F9FC52E758C9F45A92BED935 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMBX9) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMBX9 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-58 -250 1195 750}readonly def +/UniqueID 5000767 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 +B1805DA88AE375A04D99598EADFC625BDC1F9C315B6CF28C9BD427F32C745C99 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR6) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR6 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-20 -250 1193 750}readonly def +/UniqueID 5000789 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMR7 +%!PS-AdobeFont-1.1: CMR7 1.0 +%%CreationDate: 1991 Aug 20 16:39:21 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-27 -250 1122 750}readonly def +/UniqueID 5000790 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMR10 +%!PS-AdobeFont-1.1: CMR10 1.00B +%%CreationDate: 1992 Feb 19 19:54:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-251 -250 1009 969}readonly def +/UniqueID 5000793 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 +87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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+/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul +neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add +def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 +div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def + n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: 8r.enc 0 0 +% File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 +% +% @@psencodingfile@{ +% author = "S. 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if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1385 5382 a 1385 5382 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 1385 5382 a 1385 5382 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 16.11903 +8.2 0.0 NAngle 90 add Uput exch pop add a PtoC h1 add exch w1 add +exch } PutCoor PutBegin end + 1385 +5382 a 1339 5417 a Fq(A)1412 5380 y Fl(\003)1385 5382 +y + tx@Dict begin PutEnd end + 1385 5382 a 1385 5382 a + tx@Dict begin PutEnd end + 1385 5382 a 1385 5382 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@C /N@D InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1385 +5382 a 1385 5382 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 1385 5382 a 1385 5382 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 8.80824 +8.2 0.0 NAngle 90 add Uput exch pop add a PtoC h1 add exch w1 add +exch } PutCoor PutBegin end + 1385 5382 +a 1348 5417 a Fq(A)1385 5382 y + tx@Dict begin PutEnd end + 1385 5382 a 1385 5382 +a + tx@Dict begin PutEnd end + 1385 5382 a 1462 5288 a Fm(in)1999 5382 y @beginspecial +@setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 8.5359 +5.69046 19.91682 22.76227 .5 Frame gsave 0.85358 SLW 0 setgray 0 +setlinecap stroke grestore end + +@endspecial 1975 5215 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@A +16 {InitRnode } NewNode end end + 1975 5215 a 2070 +5215 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@B +16 {InitRnode } NewNode end end + 2070 5215 a 1975 5314 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@C +16 {InitRnode } NewNode end end + 1975 5314 a 2070 5314 +a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@D +16 {InitRnode } NewNode end end + 2070 5314 a 1999 5382 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@B InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1999 5382 a 1999 5382 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 1999 +5382 a 1999 5382 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 13.5583 +8.2 0.0 NAngle 90 add Uput exch pop add a PtoC h1 add exch w1 add +exch } PutCoor PutBegin end + 1999 5382 a 1943 5417 a Fq(A)2016 +5380 y Fl(\003)1999 5382 y + tx@Dict begin PutEnd end + 1999 5382 a 1999 5382 a + tx@Dict begin PutEnd end + 1999 +5382 a 1999 5382 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@C /N@D InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1999 5382 a 1999 5382 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 1999 5382 +a 1999 5382 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 8.80824 +8.2 0.0 NAngle 90 add Uput exch pop add a PtoC h1 add exch w1 add +exch } PutCoor PutBegin end + 1999 5382 a 1962 5417 a Fq(A)1999 5382 +y + tx@Dict begin PutEnd end + 1999 5382 a 1999 5382 a + tx@Dict begin PutEnd end + 1999 5382 a 2069 5288 a Fm(ev)p +0 TeXcolorgray 1773 5712 a Fr(4)p 0 TeXcolorgray eop +end +%%Page: 5 5 +TeXDict begin 5 4 bop 0 TeXcolorgray 0 TeXcolorgray 0 +TeXcolorgray 83 83 a Fr(W)-8 b(e)32 b(note)g(that)f(the)g(operation)g +(taking)g(a)h(polymap)f Fq(f)51 b Fm(:)40 b(\000)g Fn(!)g +Fm(\001)p Fq(;)17 b(B)37 b Fr(to)31 b Fq(f)2740 47 y +Fl(\003)2820 83 y Fm(:)40 b Fq(B)2966 47 y Fl(\003)3006 +83 y Fq(;)17 b Fm(\000)40 b Fn(!)g Fm(\001)32 b Fr(say)83 +203 y(is)26 b(implemented)f(by)h(composition:)e(one)i(has)h +Fq(f)1785 167 y Fl(\003)1855 203 y Fm(=)j Fq(f)11 b Fm(;)17 +b(in)o Fr(.)26 b(Similarly)g(for)g(the)h(operation)e(taking)83 +324 y Fq(g)36 b 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tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@B +16 {InitRnode } NewNode end end + 1629 796 a 1535 702 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@C +16 {InitRnode } NewNode end end + 1535 702 a 1629 +702 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@D +16 {InitRnode } NewNode end end + 1629 702 a 1535 607 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@E +16 {InitRnode } NewNode end end + 1535 607 a 1629 607 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@F +16 {InitRnode } NewNode end end + 1629 +607 a 1369 772 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@B InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1369 772 a 1369 772 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@C /N@D InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1369 772 a 1369 +772 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@E /N@F InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1369 772 a 1447 678 a Fm(in)1628 772 y(ev)1892 +765 y Fr(=)2014 820 y @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 8.5359 +5.69046 19.91682 22.76227 .5 Frame gsave 0.85358 SLW 0 setgray 0 +setlinecap stroke grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def [ 8.5359 14.22636 0.0 14.22636 /Lineto /lineto +load def false Line gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial @beginspecial +@setspecial + 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setlinecap stroke + grestore end + +@endspecial +Fn(^)1025 362 y + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@B +16 {InitRnode } NewNode end end + 1025 362 a 1025 457 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@C +16 {InitRnode } NewNode end end + 1025 457 a 978 +528 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@B InitNC { /AngleA 10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 978 528 a 978 528 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@C InitNC { /AngleA -10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 978 528 a 623 410 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@D +16 {InitRnode } NewNode end end + 623 410 +a 978 528 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@D InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 978 528 a 978 528 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 978 528 a 978 528 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 33.67334 +8.2 0.0 NAngle 90 sub Uput exch pop add a PtoC h1 add exch w1 add +exch } PutCoor PutBegin end + 978 +528 a 838 562 a Fq(A)d Fn(^)h Fq(B)978 528 y + tx@Dict begin PutEnd end + 978 528 +a 978 528 a + tx@Dict begin PutEnd end + 978 528 a 1280 410 a @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 11.38092 +5.69046 22.76227 22.76227 .5 Frame gsave 0.85358 SLW 0 setgray 0 +setlinecap stroke grestore end + + +@endspecial 1393 320 a Fq(f)1280 410 y @beginspecial +@setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 11.38092 +-5.69046 22.76227 -22.76227 .5 Frame gsave 0.85358 SLW 0 setgray +0 setlinecap stroke grestore end + +@endspecial 1397 556 a(g)1534 437 y + tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334 +} false /N@A 16 {InitRnode } NewNode end end + 1534 +437 a 20 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial Fn(^)1469 +292 y + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@B +16 {InitRnode } NewNode end end + 1469 292 a 1469 528 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@C +16 {InitRnode } NewNode end end + 1469 528 a 1280 410 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@B InitNC { /AngleA 170. def /AngleB 0. def 0.67 +0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 1280 +410 a 1280 410 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@C InitNC { /AngleA 190. def /AngleB 0. def 0.67 +0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 1280 410 a 1871 410 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@D +16 {InitRnode } NewNode end end + 1871 410 a 1280 +410 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@D InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1280 410 a 1280 410 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 1280 410 a 1280 410 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 34.68361 +8.2 0.0 NAngle 90 add Uput exch pop add a PtoC h1 add exch w1 add +exch } PutCoor PutBegin end + 1280 +410 a 1153 444 a Fq(C)29 b Fn(^)23 b Fq(D)1280 410 y + tx@Dict begin PutEnd end + +1280 410 a 1280 410 a + tx@Dict begin PutEnd end + 1280 410 a 2136 551 a @beginspecial +@setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 8.5359 +5.69046 19.91682 22.76227 .5 Frame gsave 0.85358 SLW 0 setgray 0 +setlinecap stroke grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath 0.42677 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def [ 8.5359 19.91682 2.84544 19.91682 /Lineto /lineto +load def false Line gsave 0.42677 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial +@beginspecial @setspecial + tx@Dict begin STP newpath 0.42677 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def [ 25.60728 19.91682 19.91682 19.91682 /Lineto +/lineto load def false Line gsave 0.42677 SLW 0 setgray 0 setlinecap +stroke grestore end + +@endspecial @beginspecial +@setspecial + tx@Dict begin STP newpath 0.42677 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def [ 8.5359 8.5359 2.84544 8.5359 /Lineto /lineto +load def false Line gsave 0.42677 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial @beginspecial @setspecial + tx@Dict begin STP newpath 0.42677 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def [ 25.60728 8.5359 19.91682 8.5359 /Lineto /lineto +load def false Line gsave 0.42677 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial +2106 462 a Fm(\000)165 b(\001)-186 b Fq(h)2255 362 y + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@A +16 {InitRnode } NewNode end end + +2255 362 a 2255 292 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@B +16 {InitRnode } NewNode end end + 2255 292 a 2136 292 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@C +16 {InitRnode } NewNode end end + 2136 292 +a 2136 551 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@B InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 2136 551 a 2136 551 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@B /N@C InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 2136 551 a 2136 551 +a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 2136 551 a 2136 551 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 9.33336 +8.33333 0.0 NAngle 90 sub Uput exch pop add a PtoC h1 add exch w1 +add exch } PutCoor PutBegin end + 2136 551 a 2097 586 a Fn(>)2136 +551 y + tx@Dict begin PutEnd end + 2136 551 a 2136 551 a + tx@Dict begin PutEnd 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1763 1342 a 1692 1413 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@B InitNC { /AngleA 10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 1692 1413 a 1692 +1413 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@C InitNC { /AngleA -10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 1692 1413 a 1337 1295 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@D +16 {InitRnode } NewNode end end + 1337 1295 a 1692 1413 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@D InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1692 1413 a 1692 1413 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 1692 1413 a 1692 1413 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 31.67337 +8.2 0.0 NAngle 90 sub Uput exch pop add a PtoC h1 add exch w1 add +exch } PutCoor PutBegin end + 1692 +1413 a 1560 1447 a Fq(A)e Fn(^)f Fq(B)1692 1413 y + tx@Dict begin PutEnd end + 1692 +1413 a 1692 1413 a + tx@Dict begin PutEnd end + 1692 1413 a 1898 1323 a + tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334 +} false /N@E 16 {InitRnode } NewNode end end + 1898 1323 +a 20 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial Fn(_)1857 +1248 y + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@F +16 {InitRnode } NewNode end end + 1857 1248 a 1857 1342 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@G +16 {InitRnode } NewNode end end + 1857 1342 a 1692 1413 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@E /N@F InitNC { /AngleA 170. def /AngleB 0. def 0.67 +0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 1692 1413 a 1692 1413 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@E /N@G InitNC { /AngleA 190. def /AngleB 0. def 0.67 +0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 1692 1413 a 2282 1295 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@H +16 {InitRnode } NewNode end end + 2282 +1295 a 1692 1413 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@E /N@H InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1692 1413 a 1692 1413 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 1692 1413 +a 1692 1413 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 32.68364 +8.2 0.0 NAngle 90 add Uput exch pop add a PtoC h1 add exch w1 add +exch } PutCoor PutBegin end + 1692 1413 a 1556 1447 a Fq(C)29 b Fn(_)23 +b Fq(D)1692 1413 y + tx@Dict begin PutEnd end + 1692 1413 a 1692 1413 a + tx@Dict begin PutEnd end + 1692 1413 +a 83 1584 a Fr(So)j(f)o(ar)g(we)g(ha)n(v)o(e)f(only)g(considered)g(the) +g(binary)g(operators.)g(There)h(are)g(man)o(y)e(similar)h(e)o(xamples) +83 1704 y(in)l(v)n(olving)e(also)i(the)f(rules)h(for)g +Fn(>)g Fr(which)g(we)g(merely)f(list.)763 1931 y Fq(f)822 +1890 y Fw(+)903 1931 y Fn(\001)e Fq(g)31 b Fm(=)d(\()p +Fq(f)k Fn(\001)22 b Fq(g)t 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tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial Fn(^)2093 3914 y + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@B +16 {InitRnode } NewNode end end + 2093 3914 a +2093 4009 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@C +16 {InitRnode } NewNode end end + 2093 4009 a 2046 4079 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@B InitNC { /AngleA 10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 2046 4079 a 2046 +4079 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@C InitNC { /AngleA -10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 2046 4079 a 1621 3961 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@D +16 {InitRnode } NewNode end end + 1621 3961 a 2046 4079 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@D InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 2046 4079 a 2046 4079 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 2046 4079 a 2046 4079 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 30.94975 +8.2 0.0 NAngle 90 sub Uput exch pop add a PtoC h1 add exch w1 add +exch } PutCoor PutBegin end + 2046 +4079 a 1918 4114 a Fq(A)f Fn(^)g Fq(A)2046 4079 y + tx@Dict begin PutEnd end + 2046 +4079 a 2046 4079 a + tx@Dict begin PutEnd end + 2046 4079 a 1548 3990 a Fq(d)2046 +4079 y @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true -62.59595 +5.69046 -51.21501 22.76227 .5 Frame gsave 0.85358 SLW 0 setgray 0 +setlinecap stroke grestore end + +@endspecial 1526 3961 +a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@E +16 {InitRnode } NewNode end end + 1526 3961 a 1385 3961 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@F +16 {InitRnode } NewNode end end + 1385 3961 a 2046 4079 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@E /N@F InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 2046 +4079 a 2046 4079 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 2046 4079 a 2046 4079 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 8.80824 +8.2 0.0 NAngle 90 sub Uput exch pop add a PtoC h1 add exch w1 add 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3.33334 +} false /N@A 16 {InitRnode } NewNode end end + 1969 1140 a 20 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial +Fn(^)1544 1140 y + tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334 +} false /N@AA 16 {InitRnode } NewNode end end + 1544 1140 a 20 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + + +@endspecial Fn(^)1881 995 y + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@B +16 {InitRnode } NewNode end end + 1881 995 a 1881 1231 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@C +16 {InitRnode } NewNode end end + 1881 +1231 a 1739 995 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@BB +16 {InitRnode } NewNode end end + 1739 995 a 1739 1231 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@CC +16 {InitRnode } NewNode end end + 1739 1231 a +1692 1113 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg -1.13809 +-1.13809 0 0 /N@A /N@B InitNC { /AngleA 230. def /AngleB 0. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 1692 1113 a 1692 1113 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg -1.13809 +-1.13809 0 0 /N@A /N@C InitNC { /AngleA 130. def /AngleB 0. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 1692 1113 a 1692 +1113 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@AA /N@BB InitNC { /AngleA 10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 1692 1113 a 1692 1113 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@AA /N@CC InitNC { /AngleA -10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 1692 1113 a 2282 1113 +a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@D +16 {InitRnode } NewNode end end + 2282 1113 a 1337 1113 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@DD +16 {InitRnode } NewNode end end + 1337 1113 a 1692 1113 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@AA /N@DD InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1692 +1113 a 1692 1113 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 1692 1113 a 1692 1113 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 35.00665 +8.2 0.0 NAngle 90 sub Uput exch pop add a PtoC h1 add exch w1 add +exch } PutCoor PutBegin end + 1692 1113 +a 1546 1147 a Fq(A)e Fn(^)f Fq(B)1692 1113 y + tx@Dict begin PutEnd end + 1692 1113 +a 1692 1113 a + tx@Dict begin PutEnd end + 1692 1113 a 1692 1113 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@D InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 1692 1113 a 1692 +1113 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 1692 1113 a 1692 1113 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { 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Fm(\))28 b(:)g(\()p Fq(A)22 b +Fn(_)g Fq(B)5 b Fm(\))23 b Fn(^)f Fq(C)35 b Fn(\000)-16 +b(!)27 b Fq(A)22 b Fn(_)h Fm(\()p Fq(B)k Fn(^)22 b Fq(C)7 +b Fm(\))p 0 TeXcolorgray 1748 5712 a Fr(16)p 0 TeXcolorgray +eop end +%%Page: 17 17 +TeXDict begin 17 16 bop 0 TeXcolorgray 0 TeXcolorgray +0 TeXcolorgray 83 83 a Fr(where)26 b(the)e(man)o(y)g(commuting)f(con)l +(v)o(ersions)g(are)j(indicated)e(in)g(the)h(follo)n(wing)e(pictures.) +771 691 y @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 3.9833 +1.99179 15.93352 17.92503 .5 Frame gsave 0.85358 SLW 0 setgray 0 +setlinecap stroke grestore end + +@endspecial 809 +628 a Fd(id)850 639 y Fc(C)771 691 y @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 3.9833 +21.90863 15.93352 37.84187 .5 Frame gsave 0.85358 SLW 0 setgray 0 +setlinecap stroke grestore end + + +@endspecial 808 463 a Fd(id)849 474 y Fc(B)771 691 y +@beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 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/N@BR +16 {InitRnode } NewNode end end + 903 443 a 903 278 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@CR +16 {InitRnode } NewNode end end + +903 278 a 651 553 a + tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334 +} false /N@A 16 {InitRnode } NewNode end end + 651 553 a 20 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + + +@endspecial Fn(_)949 388 y + tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334 +} false /N@B 16 {InitRnode } NewNode end end + 949 388 a 20 w @beginspecial +@setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial Fn(^)502 429 y + tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334 +} false /N@C 16 {InitRnode } NewNode end end + 502 429 a 20 +w @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial Fn(^)1098 512 +y + tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334 +} false /N@D 16 {InitRnode } NewNode end end + 1098 512 a 20 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial +Fn(_)771 691 y + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@AL InitNC { /AngleA -10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 771 691 a 771 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@BL InitNC { /AngleA 10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 771 691 a 771 691 +a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@B /N@CR InitNC { /AngleA 170. def /AngleB 0. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 771 691 a 771 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@B /N@BR InitNC { /AngleA 190. def /AngleB 0. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 771 691 a 771 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@C /N@CLL InitNC { /AngleA 10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 771 691 a 771 +691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@C /N@A InitNC { /AngleA -10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 771 691 a 771 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@CL /N@CLL InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 771 691 a 771 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@D /N@B InitNC { /AngleA 170. def /AngleB 0. def 0.67 +0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 771 691 +a 771 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@D /N@ARR InitNC { /AngleA 190. def /AngleB 0. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 771 691 a 771 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@AR /N@ARR InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 771 691 a 1515 484 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@E +16 {InitRnode } NewNode end end + +1515 484 a 192 402 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@F +16 {InitRnode } NewNode end end + 192 402 a 771 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@D /N@E InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 771 691 a 771 +691 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 771 691 a 771 691 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 51.22697 +8.2125 2.73749 NAngle 90 add Uput exch pop add a PtoC h1 add exch +w1 add exch } PutCoor PutBegin end + 771 691 a 558 714 a Fi(\()p +Fj(A)5 b Fh(^)g Fj(B)g Fi(\))g Fh(_)g Fj(C)771 691 y + tx@Dict begin PutEnd end + +771 691 a 771 691 a + tx@Dict begin PutEnd end + 771 691 a 771 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@C /N@F InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 771 691 a 771 +691 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 771 691 a 771 691 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 51.22697 +8.2125 2.73749 NAngle 90 sub Uput exch pop add a PtoC h1 add exch +w1 add exch } PutCoor PutBegin end + 771 691 a 558 714 a Fj(A)g +Fh(^)g Fi(\()p Fj(B)10 b Fh(_)5 b Fj(C)i Fi(\))771 691 +y + tx@Dict begin PutEnd end + 771 691 a 771 691 a + tx@Dict begin PutEnd end + 771 691 a 1488 w @beginspecial +@setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 3.9833 +1.99179 15.93352 17.92503 .5 Frame gsave 0.85358 SLW 0 setgray 0 +setlinecap stroke grestore end + +@endspecial 2297 628 a Fd(id)2338 639 y +Fc(C)2259 691 y @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 3.9833 +21.90863 15.93352 37.84187 .5 Frame gsave 0.85358 SLW 0 setgray 0 +setlinecap stroke grestore end + +@endspecial +2296 463 a Fd(id)2337 474 y Fc(B)2259 691 y @beginspecial +@setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 0.1 true 3.9833 +41.82547 15.93352 57.75871 .5 Frame gsave 0.85358 SLW 0 setgray 0 +setlinecap stroke grestore end + +@endspecial 2297 298 a Fd(id)2338 309 y +Fc(A)2292 278 y + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@AL +16 {InitRnode } NewNode end end + 2292 278 a 2292 443 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@BL +16 {InitRnode } NewNode end end + 2292 443 a 2292 +608 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@CL +16 {InitRnode } NewNode end end + 2292 608 a 2159 608 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@CLL +16 {InitRnode } NewNode end end + 2159 608 a 2391 278 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@AR +16 {InitRnode } NewNode end end + 2391 +278 a 2523 278 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@ARR +16 {InitRnode } NewNode end end + 2523 278 a 2391 443 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@BR +16 {InitRnode } NewNode end end + 2391 443 a 2391 +608 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@CR +16 {InitRnode } NewNode end end + 2391 608 a 2139 388 a + tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334 +} false /N@A 16 {InitRnode } NewNode end end + 2139 388 a 20 w @beginspecial +@setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial Fn(_)2437 553 y + tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334 +} false /N@B 16 {InitRnode } NewNode end end + 2437 553 a 20 +w @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial Fn(^)1991 512 +y + tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334 +} false /N@C 16 {InitRnode } NewNode end end + 1991 512 a 20 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + +@endspecial +Fn(^)2586 429 y + tx@Dict begin tx@NodeDict begin {9.74438 3.0777 12.82208 6.41104 3.33334 +} false /N@D 16 {InitRnode } NewNode end end + 2586 429 a 20 w @beginspecial @setspecial + tx@Dict begin STP newpath 0.85358 SLW 0 setgray 8.00002 2 div 6.66669 +0.0 add 2 div 2 copy 0.0 sub 4 2 roll Pyth 0.28453 add CLW 2 div add +0 360 arc closepath gsave 0.85358 SLW 0 setgray 0 setlinecap stroke + grestore end + + +@endspecial Fn(_)2259 691 y + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@AL InitNC { /AngleA 10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 2259 691 a 2259 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@A /N@BL InitNC { /AngleA -10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 2259 +691 a 2259 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@B /N@CR InitNC { /AngleA 190. def /AngleB 0. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 2259 691 a 2259 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@B /N@BR InitNC { /AngleA 170. def /AngleB 0. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 2259 691 a 2259 +691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@C /N@CLL InitNC { /AngleA -10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 2259 691 a 2259 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@C /N@A InitNC { /AngleA 10. def /AngleB 180. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 2259 691 a 2259 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@CL /N@CLL InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 2259 +691 a 2259 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@D /N@B InitNC { /AngleA 190. def /AngleB 0. def 0.67 +0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 2259 691 a 2259 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@D /N@ARR InitNC { /AngleA 170. def /AngleB 0. def 0.67 + 0.67 NCCurve } if end gsave 0.8 SLW 0 setgray 0 setlinecap stroke + grestore grestore end + 2259 691 a 2259 +691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@AR /N@ARR InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 2259 691 a 3003 402 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@E +16 {InitRnode } NewNode end end + 3003 402 a 1680 484 a + tx@Dict begin tx@NodeDict begin {0.0 0.0 0.0 0.0 0.0 } false /N@F +16 {InitRnode } NewNode end end + 1680 +484 a 2259 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@C /N@F InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 2259 691 a 2259 691 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 2259 691 a 2259 +691 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 51.22697 +8.2125 2.73749 NAngle 90 sub Uput exch pop add a PtoC h1 add exch +w1 add exch } PutCoor PutBegin end + 2259 691 a 2046 714 a Fi(\()p Fj(A)e Fh(_)g Fj(B)g +Fi(\))g Fh(^)g Fj(C)2259 691 y + tx@Dict begin PutEnd end + 2259 691 a 2259 691 a + tx@Dict begin PutEnd end + +2259 691 a 2259 691 a + tx@Dict begin gsave STV newpath 0.8 SLW 0 setgray /ArrowA { moveto +} def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 +0.0 0 0 /N@D /N@E InitNC { NCLine } if end gsave 0.8 SLW 0 setgray +0 setlinecap stroke grestore grestore end + 2259 691 a 2259 691 a + tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin end + 2259 691 +a 2259 691 a + tx@Dict begin { 0.85358 tx@Dict /NCLW known { NCLW add } if 51.22697 +8.2125 2.73749 NAngle 90 add Uput exch pop add a PtoC h1 add exch +w1 add exch } PutCoor PutBegin end + 2259 691 a 2046 714 a Fj(A)g Fh(_)g Fi(\()p +Fj(B)10 b Fh(^)5 b Fj(C)i Fi(\))2259 691 y + tx@Dict begin PutEnd end + 2259 691 a +2259 691 a + tx@Dict begin PutEnd end + 2259 691 a 83 927 a Fr(Note)25 b(that)f(these)h(maps)f(are)i +(linear)-5 b(.)83 1105 y(There)33 b(are)g(tw)o(o)f(distinct)e(kinds)h +(of)i(symmetry)e(at)h(play)g(here.)g(On)g(the)g(one)g(hand)g(we)h(ha)n +(v)o(e)f(the)83 1226 y(follo)n(wing.)p 0 TeXcolorgray +83 1404 a Fs(Pr)n(oposition)25 b(3.15.)p 0 TeXcolorgray +41 w Fq(w)i Fo(and)45 b Fm(~)-69 b Fq(w)27 b Fo(ar)l(e)e(self-dual:)f +(that)g(is,)g(we)h(have)707 1630 y Fm(\()p Fq(w)815 1645 +y Fk(A;B)s(;C)1023 1630 y Fm(\))1061 1589 y Fl(\003)1128 +1630 y Fm(=)i Fq(w)1301 1645 y Fk(C)1356 1626 y Fg(\003)1392 +1645 y Fk(;B)1468 1626 y Fg(\003)1504 1645 y Fk(;A)1577 +1626 y Fg(\003)1716 1630 y Fr(and)100 b Fm(\()19 b(~)-68 +b Fq(w)2068 1645 y Fk(A;B)s(;C)2275 1630 y Fm(\))2313 +1589 y Fl(\003)2380 1630 y Fm(=)47 b(~)-68 b Fq(w)2554 +1645 y Fk(C)2609 1626 y Fg(\003)2644 1645 y Fk(;B)2720 +1626 y Fg(\003)2756 1645 y Fk(;A)2829 1626 y Fg(\003)2886 +1630 y Fq(:)83 1914 y Fr(Essentially)34 b(this)f(follo)n(ws)h(from)g 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/n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def 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def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to 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886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: pst-text.pro 0 0 +%! +% PostScript header file pst-text.pro +% Version 97, 94/04/20; patched MV 10-09-99 00:36 +% For distribution, see pstricks.tex. + +/tx@TextPathDict 40 dict def +tx@TextPathDict begin + +% Syntax: PathPosition - +% Function: Searches for position of currentpath distance from +% beginning. Sets (X,Y)=position, and Angle=tangent. +/PathPosition +{ /targetdist exch def + /pathdist 0 def + /continue true def + /X { newx } def /Y { newy } def /Angle 0 def + gsave + flattenpath + { movetoproc } { linetoproc } { } { firstx firsty linetoproc } + /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if + grestore +} def + +/movetoproc { continue { @movetoproc } { pop pop } ifelse } def + +/@movetoproc +{ /newy exch def /newx exch def + /firstx newx def /firsty newy def +} def + +/linetoproc { continue { @linetoproc } { pop pop } ifelse } def + +/@linetoproc +{ + /oldx newx def /oldy newy def + /newy exch def /newx exch def + /dx newx oldx sub def + /dy newy oldy sub def + /dist dx dup mul dy dup mul add sqrt def + /pathdist pathdist dist add def + pathdist targetdist ge + { pathdist targetdist sub dist div dup + dy mul neg newy add /Y exch def + dx mul neg newx add /X exch def + /Angle dy dx atan def + /continue false def + } if +} def + +/TextPathShow +{ /String exch def + /CharCount 0 def + String length + { String CharCount 1 getinterval ShowChar + /CharCount CharCount 1 add def + } repeat +} def + +% Syntax: InitTextPath - +/InitTextPath +{ gsave + currentpoint /Y exch def /X exch def + exch X Hoffset sub sub mul + Voffset Hoffset sub add + neg X add /Hoffset exch def + /Voffset Y def + grestore +} def + +/Transform +{ PathPosition + dup + Angle cos mul Y add exch + Angle sin mul neg X add exch + translate + Angle rotate +} def + +/ShowChar +{ /Char exch def + gsave + Char end stringwidth + tx@TextPathDict begin + 2 div /Sy exch def 2 div /Sx exch def + +%%% MV 10-09-99 00:36 + /sc?currentpoint where {pop sc?currentpoint} {currentpoint} ifelse +% currentpoint + + Voffset sub Sy add exch + Hoffset sub Sx add + Transform + Sx neg Sy neg moveto + Char end tx@TextPathSavedShow + tx@TextPathDict begin + grestore + Sx 2 mul Sy 2 mul rmoveto +} def + +end +% END pst-text.pro + +%%EndProcSet +%%BeginProcSet: special.pro 0 0 +%! +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 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b(\(T)-8 b(otalit)m(y\).)33 b +Fs(Pr)l(ovide)l(d)g Fn(f)1796 3961 y Fr(1)1833 3949 y +Fs(,)e Fn(f)1930 3961 y Fr(2)1998 3949 y Fs(and)g Fn(f)2201 +3961 y Fr(3)2269 3949 y Fs(have)h(\014nite)e(supp)l(ort,)i(then)e(for)i +(al)t(l)523 4048 y Fn(t)e Fs(ther)l(e)g(exists)f(an)h +Fn(r)i Fs(such)e(that)g Fy(\()p Fn(t;)14 b(r)r Fy(\))24 +b Fk(2)f Fs(r)l(e)l(c)1944 4060 y Fg(f)1976 4068 y Fc(1)2009 +4060 y Fg(f)2041 4068 y Fc(2)2074 4060 y Fg(f)2106 4068 +y Fc(3)2143 4048 y Fs(.)523 4208 y(Pr)l(o)l(of.)43 b +Fy(By)24 b(the)g(strong)e(induction)i(principle,)g(where)f(w)n(e)g(tak) +n(e)g Fn(S)29 b Fy(to)23 b(b)r(e)h Fs(supp)6 b Fy(\()p +Fn(f)3083 4220 y Fr(1)3120 4208 y Fn(;)14 b(f)3198 4220 +y Fr(2)3235 4208 y Fn(;)g(f)3313 4220 y Fr(3)3350 4208 +y Fy(\),)523 4307 y(whic)n(h)25 b(w)n(e)g(kno)n(w)g(b)n(y)g(assumption) +g(is)g(\014nite.)h(Then)g(in)f(the)h(lam)n(b)r(da-case)e(w)n(e)h(can)g +(assume)523 4407 y(that)30 b Fn(a)25 b Fk(62)h Fs(supp)6 +b Fy(\()p Fn(f)1097 4419 y Fr(1)1134 4407 y Fn(;)14 b(f)1212 +4419 y Fr(2)1249 4407 y Fn(;)g(f)1327 4419 y Fr(3)1364 +4407 y Fy(\))29 b(holds,)g(whic)n(h)h(is)f(de\014ned)g(to)h(b)r(e)f +Fn(a)d Fy(#)g(\()p Fn(f)2735 4419 y Fr(1)2772 4407 y +Fn(;)14 b(f)2850 4419 y Fr(2)2887 4407 y Fn(;)g(f)2965 +4419 y Fr(3)3002 4407 y Fy(\).)29 b(All)h(cases)523 4506 +y(are)d(then)h(routine)f(applying)g(the)h(rules)f(in)h(\(12\).)523 +4666 y(Next)g(w)n(e)f(establish)g(that)h(all)g Fn(r)i +Fy(in)e(the)g(relation)f Fs(r)l(e)l(c)2205 4678 y Fg(f)2237 +4686 y Fc(1)2270 4678 y Fg(f)2302 4686 y Fc(2)2335 4678 +y Fg(f)2367 4686 y Fc(3)2431 4666 y Fy(ha)n(v)n(e)g(\014nite)h(supp)r +(ort.)523 4825 y Fd(Lemma)i(5)41 b(\(Finite)25 b(Supp)s(ort\).)h +Fs(If)g Fn(f)1814 4837 y Fr(1)1851 4825 y Fs(,)f Fn(f)1942 +4837 y Fr(2)2004 4825 y Fs(and)h Fn(f)2202 4837 y Fr(3)2264 +4825 y Fs(have)h(\014nite)d(supp)l(ort,)i(then)f Fy(\()p +Fn(t;)14 b(r)r Fy(\))25 b Fk(2)523 4924 y Fs(r)l(e)l(c)631 +4936 y Fg(f)663 4944 y Fc(1)695 4936 y Fg(f)727 4944 +y Fc(2)760 4936 y Fg(f)792 4944 y Fc(3)859 4924 y Fs(implies)31 +b(that)f Fn(r)i Fs(has)f(\014nite)e(supp)l(ort.)p eop +end +%%Page: 11 11 +TeXDict begin 11 10 bop 523 448 a Fs(Pr)l(o)l(of.)43 +b Fy(By)32 b(the)g(induction)g(principle)g(giv)n(e)f(in)h(\(13\).)f(In) +h(the)h(v)-5 b(ariable-case)29 b(w)n(e)j(ha)n(v)n(e)e(to)523 +548 y(sho)n(w)37 b(that)g Fn(f)969 560 y Fr(1)1020 548 +y Fn(a)g Fy(has)g(\014nite)h(supp)r(ort,)f(whic)n(h)h(w)n(e)f(inferred) +g(in)g(Example)g(1)g(using)g(our)523 648 y(heuristic.)27 +b(The)h(application-)f(and)g(lam)n(b)r(da-case)f(are)h(similar.)799 +b Fk(u)-55 b(t)523 825 y Fy(In)32 b(order)f(to)h(establish)f(the)h +(\\uniqueness")f(part)h(of)f(Theorem)h(1,)f(w)n(e)h(need)g(the)g(follo) +n(w-)523 924 y(ing)j(t)n(w)n(o)f(lemmas)h(establishing)f(that)i +Fs(r)l(e)l(c)1896 936 y Fg(f)1928 944 y Fc(1)1961 936 +y Fg(f)1993 944 y Fc(2)2026 936 y Fg(f)2058 944 y Fc(3)2130 +924 y Fy(is)f Fs(e)l(quivariant)44 b Fy(\(see)35 b([7]\))g(and)g(that)h +(it)523 1024 y(preserv)n(es)26 b(freshness.)523 1202 +y Fd(Lemma)k(6)41 b(\(Equiv)-5 b(ariance\).)29 b Fs(If)e +Fy(\()p Fn(t;)14 b(r)r Fy(\))25 b Fk(2)e Fs(r)l(e)l(c)2081 +1214 y Fg(f)2113 1222 y Fc(1)2145 1214 y Fg(f)2177 1222 +y Fc(2)2210 1214 y Fg(f)2242 1222 y Fc(3)2306 1202 y +Fs(then)k(for)h(al)t(l)g Fn(\031)i Fs(also)e Fy(\()p +Fn(\031)3060 1211 y Ff(\001)3099 1202 y Fn(t;)14 b(\031)3216 +1211 y Ff(\001)3254 1202 y Fn(r)r Fy(\))25 b Fk(2)523 +1301 y Fn(r)r(ec)637 1320 y Fr(\()p Fg(\031)704 1329 +y Ff(\001)742 1320 y Fg(f)774 1328 y Fc(1)807 1320 y +Fr(\)\()p Fg(\031)900 1329 y Ff(\001)938 1320 y Fg(f)970 +1328 y Fc(2)1003 1320 y Fr(\)\()p Fg(\031)1096 1329 y +Ff(\001)1134 1320 y Fg(f)1166 1328 y Fc(3)1199 1320 y +Fr(\))1229 1301 y Fs(.)523 1478 y(Pr)l(o)l(of.)43 b Fy(By)24 +b(the)h(induction)f(principle)g(giv)n(en)g(in)g(\(13\).)g(All)h(cases)e +(are)g(routine)h(b)n(y)g(pushing)523 1578 y(the)36 b(p)r(erm)n(utation) +f Fn(\031)k Fy(in)n(to)c Fn(t)g Fy(and)g Fn(r)r Fy(,)i(except)e(in)h 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Fg(f)1975 1974 y Fc(3)2042 1954 y Fs(and)30 b Fn(a)23 +b Fy(#)g(\()p Fn(f)2435 1966 y Fr(1)2472 1954 y Fn(;)14 +b(f)2550 1966 y Fr(2)2587 1954 y Fn(;)g(f)2665 1966 y +Fr(3)2702 1954 y Fn(;)g(t)p Fy(\))30 b Fs(implies)h Fn(a)23 +b Fy(#)g Fn(r)r Fs(.)523 2131 y(Pr)l(o)l(of.)43 b Fy(By)26 +b(the)h(induction)f(principle)g(giv)n(en)g(in)g(\(13\);)g(non-routine)f +(is)h(the)h(lam)n(b)r(da-case.)523 2231 y(In)f(this)g(case,)f(sa)n(y)g +(with)h(the)g(instan)n(tiations)f(\()p Fp(Lam)13 b Fn(a)2191 +2201 y Fj(0)2228 2231 y Fn(t)p Fy(\),)26 b(w)n(e)g(ha)n(v)n(e)e(that)i +Fn(a)2871 2201 y Fj(0)2918 2231 y Fy(#)d(\()p Fn(f)3083 +2243 y Fr(1)3120 2231 y Fn(;)14 b(f)3198 2243 y Fr(2)3235 +2231 y Fn(;)g(f)3313 2243 y Fr(3)3350 2231 y Fy(\).)523 +2331 y(W)-7 b(e)24 b(further)f(ha)n(v)n(e)f(that)i Fn(a)f +Fy(#)g(\()p Fn(f)1532 2343 y Fr(1)1569 2331 y Fn(;)14 +b(f)1647 2343 y Fr(2)1684 2331 y Fn(;)g(f)1762 2343 y +Fr(3)1799 2331 y Fn(;)g Fp(Lam)f Fn(a)2025 2301 y Fj(0)2062 +2331 y Fn(t)p Fy(\))23 b(and)h(ha)n(v)n(e)e(to)h(sho)n(w)g(that)g +Fn(a)g Fy(#)h Fn(f)3167 2343 y Fr(3)3217 2331 y Fn(a)3261 +2301 y Fj(0)3298 2331 y Fn(t)14 b(r)r Fy(.)523 2430 y(In)23 +b(case)g(that)g Fn(a)g Fy(=)g Fn(a)1168 2400 y Fj(0)1191 +2430 y Fy(,)g(w)n(e)g(kno)n(w)f(from)h(the)g(F)n(CB,)g(there)g(exists)g +(an)g Fn(a)2702 2400 y Fj(00)2767 2430 y Fy(suc)n(h)g(that)g +Fn(a)3169 2400 y Fj(00)3235 2430 y Fy(#)g Fn(f)3368 2442 +y Fr(3)523 2530 y Fy(and)g Fk(8)14 b Fn(t)g(r)n(:)g(a)901 +2500 y Fj(00)966 2530 y Fy(#)23 b Fn(f)1099 2542 y Fr(3)1150 +2530 y Fn(a)1194 2500 y Fj(00)1250 2530 y Fn(t)14 b(r)r +Fy(.)24 b(Using)g(\(10\))f(w)n(e)g(apply)g(the)h(sw)n(apping)f(\()p +Fn(a)14 b(a)2755 2500 y Fj(00)2797 2530 y Fy(\))24 b(to)g(b)r(oth)g +(sides)f(of)523 2630 y(our)30 b(goal)f(whic)n(h)i(giv)n(es)e +Fn(a)1343 2599 y Fj(00)1413 2630 y Fy(#)f(\(\()p Fn(a)14 +b(a)1676 2599 y Fj(00)1719 2630 y Fy(\))1751 2639 y Ff(\001)1790 +2630 y Fn(f)1831 2642 y Fr(3)1867 2630 y Fy(\))g Fn(a)1957 +2599 y Fj(00)2014 2630 y Fy(\(\()p Fn(a)g(a)2180 2599 +y Fj(00)2222 2630 y Fy(\))2254 2639 y Ff(\001)2293 2630 +y Fn(t)p Fy(\))g(\(\()p Fn(a)g(a)2535 2599 y Fj(00)2578 +2630 y Fy(\))2610 2639 y Ff(\001)2648 2630 y Fn(r)r Fy(\).)32 +b(Since)f Fn(a)c Fy(#)i Fn(f)3204 2642 y Fr(3)3271 2630 +y Fy(and)523 2729 y Fn(a)567 2699 y Fj(00)643 2729 y +Fy(#)34 b Fn(f)787 2741 y Fr(3)857 2729 y Fy(w)n(e)g(ha)n(v)n(e)f(b)n +(y)g(\(11\))h(that)g(\()p Fn(a)14 b(a)1807 2699 y Fj(00)1849 +2729 y Fy(\))1881 2738 y Ff(\001)1920 2729 y Fn(f)1961 +2741 y Fr(3)2031 2729 y Fy(=)33 b Fn(f)2170 2741 y Fr(3)2241 +2729 y Fy(and)h(hence)g(w)n(e)f(are)g(done.)h(In)g(case)523 +2829 y Fn(a)23 b Fk(6)p Fy(=)g Fn(a)722 2799 y Fj(0)768 +2829 y Fy(w)n(e)g(can)g(infer)h(from)f Fn(a)g Fy(#)g(\()p +Fn(f)1646 2841 y Fr(1)1683 2829 y Fn(;)14 b(f)1761 2841 +y Fr(2)1798 2829 y Fn(;)g(f)1876 2841 y Fr(3)1913 2829 +y Fn(;)g Fp(Lam)e Fn(a)2138 2799 y Fj(0)2175 2829 y Fn(t)p +Fy(\))24 b(that)g Fn(a)f Fy(#)g(\()p Fn(f)2669 2841 y +Fr(1)2706 2829 y Fn(;)14 b(f)2784 2841 y Fr(2)2821 2829 +y Fn(;)g(f)2899 2841 y Fr(3)2936 2829 y Fn(;)g(t)p Fy(\))23 +b(holds)g(and)523 2928 y(th)n(us)28 b(apply)f(the)h(induction)g(h)n(yp) +r(othesis.)1499 b Fk(u)-55 b(t)523 3106 y Fy(No)n(w)27 +b(w)n(e)g(can)h(sho)n(w)e(the)i(crucial)f(lemma)h(ab)r(out)f +Fs(r)l(e)l(c)2216 3118 y Fg(f)2248 3126 y Fc(1)2280 3118 +y Fg(f)2312 3126 y Fc(2)2345 3118 y Fg(f)2377 3126 y +Fc(3)2442 3106 y Fy(b)r(eing)h(a)f(\\function".)523 3283 +y Fd(Lemma)j(8)41 b(\(Uniqueness\).)31 b Fs(If)f Fn(f)1684 +3295 y Fr(1)1721 3283 y Fs(,)h Fn(f)1818 3295 y Fr(2)1884 +3283 y Fs(and)g Fn(f)2087 3295 y Fr(3)2154 3283 y Fs(have)g(\014nite)e +(supp)l(ort)h(and)h Fn(f)3056 3295 y Fr(3)3123 3283 y +Fs(satis\014es)523 3383 y(the)f(F)n(CB,)h(then)f Fy(\()p +Fn(t;)14 b(r)r Fy(\))24 b Fk(2)f Fs(r)l(e)l(c)1451 3395 +y Fg(f)1483 3403 y Fc(1)1516 3395 y Fg(f)1548 3403 y +Fc(2)1580 3395 y Fg(f)1612 3403 y Fc(3)1679 3383 y Fs(and)30 +b Fy(\()p Fn(t;)14 b(r)1978 3353 y Fj(0)2003 3383 y Fy(\))23 +b Fk(2)g Fs(r)l(e)l(c)2244 3395 y Fg(f)2276 3403 y Fc(1)2309 +3395 y Fg(f)2341 3403 y Fc(2)2373 3395 y Fg(f)2405 3403 +y Fc(3)2472 3383 y Fs(implies)31 b(that)f Fn(r)c Fy(=)d +Fn(r)3116 3353 y Fj(0)3140 3383 y Fs(.)523 3560 y(Pr)l(o)l(of.)43 +b Fy(By)26 b(the)g(induction)h(principle)f(giv)n(en)f(in)i(\(13\);)f +(again)f(the)h(only)g(non-routine)f(case)523 3660 y(is)36 +b(the)h(lam)n(b)r(da-case.)e(By)h(assumption)f(w)n(e)h(kno)n(w)g(that)h +(\()p Fp(Lam)12 b Fn(a)i(t;)g(f)2744 3672 y Fr(3)2795 +3660 y Fn(a)g(t)g(r)r Fy(\))38 b Fk(2)g Fs(r)l(e)l(c)3206 +3672 y Fg(f)3238 3680 y Fc(1)3271 3672 y Fg(f)3303 3680 +y Fc(2)3336 3672 y Fg(f)3368 3680 y Fc(3)523 3759 y Fy(from)24 +b(whic)n(h)g(w)n(e)g(can)g(infer)h(that)g Fn(a)e Fy(#)g(\()p +Fn(f)1816 3771 y Fr(1)1853 3759 y Fn(;)14 b(f)1931 3771 +y Fr(2)1968 3759 y Fn(;)g(f)2046 3771 y Fr(3)2083 3759 +y Fy(\))24 b(and)h(\()p Fn(t;)14 b(r)r Fy(\))24 b Fk(2)f +Fs(r)l(e)l(c)2678 3771 y Fg(f)2710 3779 y Fc(1)2743 3771 +y Fg(f)2775 3779 y Fc(2)2807 3771 y Fg(f)2839 3779 y +Fc(3)2876 3759 y Fy(;)i(the)g(induction)523 3859 y(h)n(yp)r(othesis)19 +b(states)g(that)g(for)g(all)g Fn(r)1588 3829 y Fj(0)1612 +3859 y Fy(,)g(\()p Fn(t;)14 b(r)1792 3829 y Fj(0)1816 +3859 y Fy(\))24 b Fk(2)f Fs(r)l(e)l(c)2058 3871 y Fg(f)2090 +3879 y Fc(1)2123 3871 y Fg(f)2155 3879 y Fc(2)2187 3871 +y Fg(f)2219 3879 y Fc(3)2276 3859 y Fy(implies)c Fn(r)26 +b Fy(=)d Fn(r)2739 3829 y Fj(0)2763 3859 y Fy(.)c(Using)g(the)h(second) +523 3959 y(assumption)g(\()p Fp(Lam)13 b Fn(b)h(t)1212 +3928 y Fj(0)1235 3959 y Fn(;)28 b(r)1325 3928 y Fj(0)1349 +3959 y Fy(\))23 b Fk(2)h Fs(r)l(e)l(c)1590 3971 y Fg(f)1622 +3979 y Fc(1)1655 3971 y Fg(f)1687 3979 y Fc(2)1720 3971 +y Fg(f)1752 3979 y Fc(3)1810 3959 y Fy(w)n(e)c(need)h(to)g(sho)n(w)f +(that)h Fn(f)2620 3971 y Fr(3)2671 3959 y Fn(a)14 b(t)g(r)25 +b Fy(=)e Fn(f)2964 3971 y Fr(3)3015 3959 y Fn(b)14 b(t)3095 +3928 y Fj(0)3131 3959 y Fn(r)3170 3928 y Fj(0)3215 3959 +y Fy(holds)523 4058 y(for)26 b(all)h Fp(Lam)13 b 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begin [ /View [/XYZ H.V] /Dest (cite.Wenzel06) cvn H.B /DEST +pdfmark end + 291 +3436 a Black 131 x Fw([17])p Black 26 w(W)-7 b(enzel,)54 +b(M.,)e Fy(Structur)m(ed)57 b(Induction)f(Pr)l(oofs)e(in)g +(Isabelle/Isar)p Fw(,)j(in:)d Fy(Pr)l(oc.)f(of)h(the)g(5th)467 +3680 y(International)38 b(Confer)m(ence)d(on)f(Mathematical)i(Knowledg) +o(e)f(Mana)o(g)o(ement)g(\(MKM\))p Fw(,)d(LN)m(AI)467 +3793 y Fx(4108)p Fw(,)24 b(2006.)p Black 1872 5513 a +Fu(15)p Black eop end +%%Trailer + +userdict /end-hook known{end-hook}if +%%EOF diff -r 0b4a5595cbe4 -r 680070975206 Publications/lfmtp-07.pdf Binary file Publications/lfmtp-07.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/lftechreport.pdf Binary file Publications/lftechreport.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/lics-08.pdf Binary file Publications/lics-08.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/lmcs.pdf Binary file Publications/lmcs.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/ln.pdf Binary file Publications/ln.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/merlin-05.pdf Binary file Publications/merlin-05.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/merlin-05.ps --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Publications/merlin-05.ps Sat Oct 22 12:11:38 2011 +0100 @@ -0,0 +1,3710 @@ +%!PS-Adobe-2.0 +%%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software +%%Title: a04-urban.dvi +%%Pages: 8 +%%PageOrder: Ascend +%%BoundingBox: 0 0 595 842 +%%DocumentFonts: Times-Bold Times-Roman Times-BoldItalic Times-Italic +%%DocumentPaperSizes: a4 +%%EndComments +%DVIPSWebPage: (www.radicaleye.com) +%DVIPSCommandLine: dvips a04-urban.dvi -o a04-urban.ps +%DVIPSParameters: dpi=600 +%DVIPSSource: TeX output 2007.02.24:0557 +%%BeginProcSet: tex.pro 0 0 +%! +/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S +N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 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pop 1 } if +] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1 +setlinecap stroke } def +/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch +2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +% DG/SR modification end +Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +% def +a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +pop pop } def +% DG/SR modification end +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def 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newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul +neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add +def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 +div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def + n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop 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closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: 8r.enc 0 0 +% File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 +% +% @@psencodingfile@{ +% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, +% W. Schmidt, P. Lehman", +% version = "2.0", +% date = "30 October 2002", +% filename = "8r.enc", +% email = "tex-fonts@@tug.org", +% docstring = "This is the encoding vector for Type1 and TrueType +% fonts to be used with TeX. This file is part of the +% PSNFSS bundle, version 9" +% @} +% +% The idea is to have all the characters normally included in Type 1 fonts +% available for typesetting. This is effectively the characters in Adobe +% Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol, +% MacRoman, and some extra characters from Lucida. +% +% Character code assignments were made as follows: +% +% (1) the Windows ANSI characters are almost all in their Windows ANSI +% positions, because some Windows users cannot easily reencode the +% fonts, and it makes no difference on other systems. The only Windows +% ANSI characters not available are those that make no sense for +% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen +% (173). quotesingle and grave are moved just because it's such an +% irritation not having them in TeX positions. +% +% (2) Remaining characters are assigned arbitrarily to the lower part +% of the range, avoiding 0, 10 and 13 in case we meet dumb software. +% +% (3) Y&Y Lucida Bright includes some extra text characters; in the +% hopes that other PostScript fonts, perhaps created for public +% consumption, will include them, they are included starting at 0x12. +% These are /dotlessj /ff /ffi /ffl. +% +% (4) hyphen appears twice for compatibility with both ASCII and Windows. +% +% (5) /Euro was assigned to 128, as in Windows ANSI +% +% (6) Missing characters from MacRoman encoding incorporated as follows: +% +% PostScript MacRoman TeXBase1 +% -------------- -------------- -------------- +% /notequal 173 0x16 +% /infinity 176 0x17 +% /lessequal 178 0x18 +% /greaterequal 179 0x19 +% /partialdiff 182 0x1A +% /summation 183 0x1B +% /product 184 0x1C +% /pi 185 0x1D +% /integral 186 0x81 +% /Omega 189 0x8D +% /radical 195 0x8E +% /approxequal 197 0x8F +% /Delta 198 0x9D +% /lozenge 215 0x9E +% +/TeXBase1Encoding [ +% 0x00 + /.notdef /dotaccent /fi /fl + /fraction /hungarumlaut /Lslash /lslash + /ogonek /ring /.notdef /breve + /minus /.notdef /Zcaron /zcaron +% 0x10 + /caron /dotlessi /dotlessj /ff + /ffi /ffl /notequal /infinity + /lessequal /greaterequal /partialdiff /summation + /product /pi /grave /quotesingle +% 0x20 + /space /exclam /quotedbl /numbersign + /dollar /percent /ampersand /quoteright + /parenleft /parenright /asterisk /plus + /comma /hyphen /period /slash +% 0x30 + /zero /one /two /three + /four /five /six /seven + /eight /nine /colon /semicolon + /less /equal /greater /question +% 0x40 + /at /A /B /C + /D /E /F /G + /H /I /J /K + /L /M /N /O +% 0x50 + /P /Q /R /S + /T /U /V /W + /X /Y /Z /bracketleft 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prologue for pstricks.tex. +% Version 97 patch 4, 04/05/10 +% For distribution, see pstricks.tex. +% +/tx@Dict 200 dict def tx@Dict begin +/ADict 25 dict def +/CM { matrix currentmatrix } bind def +/SLW /setlinewidth load def +/CLW /currentlinewidth load def +/CP /currentpoint load def +/ED { exch def } bind def +/L /lineto load def +/T /translate load def +/TMatrix { } def +/RAngle { 0 } def +/Atan { /atan load stopped { pop pop 0 } if } def +/Div { dup 0 eq { pop } { div } ifelse } def +/NET { neg exch neg exch T } def +/Pyth { dup mul exch dup mul add sqrt } def +/PtoC { 2 copy cos mul 3 1 roll sin mul } def +/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } +def +/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def +} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } +/pathforall load stopped { pop pop pop pop } if z } def +/STP { .996264 dup scale } def +/STV { SDict begin normalscale end STP } def +% +%%-------------- DG begin patch 15 ---------------%% +%/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def +%PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y +%mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul +%/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] +%0 } ifelse setdash stroke } def +/DashLine { + dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse + /b ED /x1 ED /y1 ED /x ED /y ED + /z y x add y1 add x1 add def + /Coef b a .5 sub 2 mul y mul sub z Div round + z mul a .5 sub 2 mul y mul add b exch Div def + /y y Coef mul def /x x Coef mul def /y1 y1 Coef mul def /x1 x1 Coef mul def + x1 0 gt y1 0 gt x 0 gt y 0 gt and { [ y x y1 x1 ] 1 a sub y mul} + { [ 1 0] 0 } ifelse setdash stroke +} def +%%-------------- DG end patch 15 ---------------%% +/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt +{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add +def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if +] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1 +setlinecap stroke } def +/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch +2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 +% DG/SR modification begin - Dec. 12, 1997 - Patch 2 +%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a +% DG/SR modification end +Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict +/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } +% def +a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore +pop pop } def +% DG/SR modification end +/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg +exch 3 index sub exch Atan rotate newpath } def +/EndArrow { @mtrx setmatrix CP grestore end } def +/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 +scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill +grestore } def +/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 +CLW moveto } def +/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2 +div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0 +CLW moveto } def +/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW +2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0 +curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto } +def +/SD { 0 360 arc fill } def +/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS +CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def +/Shadow { [ { /moveto load } { /lineto load } { /curveto load } { +/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto +load } if ] cvx newpath 3 1 roll T exec } def +/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch +cvi def } def +/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if +f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub +def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def +/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } +ifelse { pop } repeat a } def +/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq +and { pop pop /n n 1 sub def } if } def +/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } +repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 +ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 +moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto +Lineto pop pop closepath } ifelse } def +/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul +neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add +def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 +div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +setmatrix } def +% DG modification begin - Jan. 15, 1997 +%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { +%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 +%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +%setmatrix } def +/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup +CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 +div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 +d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx +% DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) +% setmatrix } def +setmatrix pop } def +% DG/SR modification end +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth +def } def +/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 +def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp +mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos +abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def +/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul +m mul neg def } def +/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } +ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } +def +/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def +/NC { CC x1 y1 x2 y2 x y curveto } def +/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def +/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def +/NAC { x2 y2 x y curveto CC x1 y1 } def +/EAC { x2 y2 x y ArrowB curveto pop pop } def +/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def + n { NC } repeat EOC } ifelse } def +/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload +/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop +pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def +/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { +CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } +repeat closepath pop pop } ifelse } def +/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def +/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def +/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } +def +/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix +rotate matrix concatmatrix exch findfont exch makefont setfont } def +/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto +x1 y1 lineto closepath } def +/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 +y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div +exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse +/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto +x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } +ifelse } def +/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add +/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { +pop pop Rect } { OvalFrame } ifelse } def +/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop +} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] +aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def +/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 +2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } +ifelse } def +/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { +6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def +/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 +sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } +def +/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 +sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA +x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 +y0 x0 2 mul x1 sub y1 ] def } def +/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } +if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if +/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div +round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div +round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub +0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def +/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } +if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } +{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add +exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n +div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 +dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { +dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { +pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup +stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} +{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i +w add def } repeat grestore gsave n 0 gt +% DG/SR modification begin - Nov. 7, 1997 - Patch 1 +%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } +{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } +% DG/SR modification end +{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul +n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n +div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop +1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs +dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt +{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g +exch t L stroke /i i h add def } repeat grestore } def +/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 +1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add +exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c +mul neg d } def +/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def +/Rot { CP CP translate 3 -1 roll neg rotate NET } def +/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } +def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle +dup a add ] cvx def } def +/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] +cvx def } def +/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def +/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def +/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def +/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s +abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b +div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { +h1 abs h sub dup s mul abs } ifelse } def +/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s +mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q +{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add +exch } def +/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible +/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def +} if } ifelse } def +/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def +/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit +neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def +/IfVisible true def } def +end +% END pstricks.pro + +%%EndProcSet +%%BeginProcSet: pst-dots.pro 0 0 +%!PS-Adobe-2.0 +%%Title: Dot Font for PSTricks +%%Creator: Timothy Van Zandt +%%Creation Date: May 7, 1993 +%% Version 97 patch 1, 99/12/16 +%% Modified by Etienne Riga - Dec. 16, 1999 +%% to add /Diamond, /SolidDiamond and /BoldDiamond +10 dict dup begin + /FontType 3 def + /FontMatrix [ .001 0 0 .001 0 0 ] def + /FontBBox [ 0 0 0 0 ] def + /Encoding 256 array def + 0 1 255 { Encoding exch /.notdef put } for + Encoding + dup (b) 0 get /Bullet put + dup (c) 0 get /Circle put + dup (C) 0 get /BoldCircle put + dup (u) 0 get /SolidTriangle put + dup (t) 0 get /Triangle put + dup (T) 0 get /BoldTriangle put + dup (r) 0 get /SolidSquare put + dup (s) 0 get /Square put + dup (S) 0 get /BoldSquare put + dup (q) 0 get /SolidPentagon put + dup (p) 0 get /Pentagon put + dup (P) 0 get /BoldPentagon put +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + dup (l) 0 get /SolidDiamond put + dup (d) 0 get /Diamond put + (D) 0 get /BoldDiamond put +% DG/SR modification end + /Metrics 13 dict def + Metrics begin + /Bullet 1000 def + /Circle 1000 def + /BoldCircle 1000 def + /SolidTriangle 1344 def + /Triangle 1344 def + /BoldTriangle 1344 def + /SolidSquare 886 def + /Square 886 def + /BoldSquare 886 def + /SolidPentagon 1093.2 def + /Pentagon 1093.2 def + /BoldPentagon 1093.2 def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /SolidDiamond 1008 def + /Diamond 1008 def + /BoldDiamond 1008 def +% DG/SR modification end + /.notdef 0 def + end + /BBoxes 13 dict def + BBoxes begin + /Circle { -550 -550 550 550 } def + /BoldCircle /Circle load def + /Bullet /Circle load def + /Triangle { -571.5 -330 571.5 660 } def + /BoldTriangle /Triangle load def + /SolidTriangle /Triangle load def + /Square { -450 -450 450 450 } def + /BoldSquare /Square load def + /SolidSquare /Square load def + /Pentagon { -546.6 -465 546.6 574.7 } def + /BoldPentagon /Pentagon load def + /SolidPentagon /Pentagon load def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /Diamond { -428.5 -742.5 428.5 742.5 } def + /BoldDiamond /Diamond load def + /SolidDiamond /Diamond load def +% DG/SR modification end + /.notdef { 0 0 0 0 } def + end + /CharProcs 20 dict def + CharProcs begin + /Adjust { + 2 copy dtransform floor .5 add exch floor .5 add exch idtransform + 3 -1 roll div 3 1 roll exch div exch scale + } def + /CirclePath { 0 0 500 0 360 arc closepath } def + /Bullet { 500 500 Adjust CirclePath fill } def + /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath + eofill } def + /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath + eofill } def + /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def + /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto + closepath } def + /SolidTriangle { TrianglePath fill } def + /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def + /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def + /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto + -450 -450 lineto closepath } def + /SolidSquare { SquarePath fill } def + /Square { SquarePath .89 .89 scale SquarePath eofill } def + /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def + /PentagonPath { + -337.8 -465 moveto + 337.8 -465 lineto + 546.6 177.6 lineto + 0 574.7 lineto + -546.6 177.6 lineto + closepath + } def + /SolidPentagon { PentagonPath fill } def + /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def + /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def +% DG/SR modification begin - Dec. 16, 1999 - From Etienne Riga + /DiamondPath { 0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto + 428.5 0 lineto closepath } def + /SolidDiamond { DiamondPath fill } def + /Diamond { DiamondPath .85 .85 scale DiamondPath eofill } def + /BoldDiamond { DiamondPath .7 .7 scale DiamondPath eofill } def +% DG/SR modification end + /.notdef { } def + end + /BuildGlyph { + exch + begin + Metrics 1 index get exec 0 + BBoxes 3 index get exec + setcachedevice + CharProcs begin load exec end + end + } def + /BuildChar { + 1 index /Encoding get exch get + 1 index /BuildGlyph get exec + } bind def +end +/PSTricksDotFont exch definefont pop +%END pst-dots.pro + +%%EndProcSet +%%BeginProcSet: pst-node.pro 0 0 +%! +% PostScript prologue for pst-node.tex. +% Version 97 patch 1, 97/05/09. +% For distribution, see pstricks.tex. +% +/tx@NodeDict 400 dict def tx@NodeDict begin +tx@Dict begin /T /translate load def end +/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } +if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end +grestore } def +/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def +} def +/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch +Sin mul } def } def +/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def +} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } +ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx +dup Sin mul Cos Div } ifelse } def +/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub +/u ED /NodePos { GetRnodePos } def } def +/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup +Cos mul exch Sin mul } def +/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h +mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul +} ifelse } def +/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d +ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d +sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan +sin def /NodePos { TriNodePos } def } def +/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos +hh mul Atan dup cos ww mul exch sin hh mul } def +/GetCenter { begin X Y NodeMtrx transform CM itransform end } def +/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist +Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } +{ 0 Dist Sin mul } ifelse } ifelse Do } def +/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform +exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx +dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop +XYPos } ifelse } def +/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 +roll sin mul sub exch } ifelse } def +/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA +AddOffset yA add /yA1 ED xA add /xA1 ED } def +/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB +AddOffset yB add /yB1 ED xB add /xB1 ED } def +/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA +AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED +ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED +} ifelse } def +/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB +AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED +ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED +} ifelse } def +/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED +/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b +known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA +ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def +/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub +mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def +/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt +{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop +} repeat LPutLine cleartomark } def +/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED +/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 +mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx +sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul +add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add +y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul +mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def +/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def +} def +/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def +/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit +} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd +} def +/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def +} def +/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def +/NAngle yyB yyA sub xxB xxA sub Atan def } def +/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def +/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def +} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { +exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark +VPosEnd } def +/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 +roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx +def grestore exec /LPutVar /SaveLPutVar load def } def +/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def +GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { +LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { +LPutVar VPutLine } def LPutVar } def +/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop +end } def +/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub +Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan +/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 +yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +ifelse } def +/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 +roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA +GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict +begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] +cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines +} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def +/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx +itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 +yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 +yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def +/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def +/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 +yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform +/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 +tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def +xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx +transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } +{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB +0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict +begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx +def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if +xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end +/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED +GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin +false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { +LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } +def +/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate +def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 +mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 +mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 +xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false +Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] +cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { +VPutLines } def } def +% DG/SR modification begin - May 9, 1997 - Patch 1 +%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r +%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r +r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add +exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 +mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED +% DG/SR modification end +} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add +AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r +Div def /y ED /x ED } def +/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB +180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos +mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def +/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy +add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos +{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar +tx@Dict begin false Polygon end } def +/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan +def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 +mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def +/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div +def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def +GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul +sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 +eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } +{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def +0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 +0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 +roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } +ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos +{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { +r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } +{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add +add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub +mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t +sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse +y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { +LPutPos } def } def +/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB +sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 +ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB +w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos +{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } +{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } +def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin +/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def +/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg +exch X sub neg exch moveto setmatrix CP grestore } def +/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 +def } ifelse LPutCoor } def +/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } +if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } +def +/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if +r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } +ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } +def +end +% END pst-node.pro + +%%EndProcSet +%%BeginProcSet: 8r.enc 0 0 +% File 8r.enc TeX Base 1 Encoding Revision 2.0 2002-10-30 +% +% @@psencodingfile@{ +% author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, +% W. Schmidt, P. Lehman", +% version = "2.0", +% date = "30 October 2002", +% filename = "8r.enc", +% email = "tex-fonts@@tug.org", +% docstring = "This is the encoding vector for Type1 and TrueType +% fonts to be used with TeX. This file is part of the +% PSNFSS bundle, version 9" +% @} +% +% The idea is to have all the characters normally included in Type 1 fonts +% available for typesetting. This is effectively the characters in Adobe +% Standard encoding, ISO Latin 1, Windows ANSI including the euro symbol, +% MacRoman, and some extra characters from Lucida. +% +% Character code assignments were made as follows: +% +% (1) the Windows ANSI characters are almost all in their Windows ANSI +% positions, because some Windows users cannot easily reencode the +% fonts, and it makes no difference on other systems. 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begin gsave STV newpath 0.56905 SLW 0 setgray /ArrowA { +moveto } def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 +neg 0.0 0.0 0 0 /N@@@A /N@@@B InitNC { NCLine } if end gsave 0.56905 +SLW 0 setgray 0 setlinecap stroke grestore grestore end + 436 3252 a 436 3252 a + tx@Dict begin tx@NodeDict begin {62.59595 25.60728 } false /N@@@A +10 {InitPnode } NewNode end end + 436 3252 a 436 3252 +a + tx@Dict begin tx@NodeDict begin {170.71646 25.60728 } false /N@@@B +10 {InitPnode } NewNode end end + 436 3252 a 436 3252 a + tx@Dict begin gsave STV newpath 0.56905 SLW 0 setgray /ArrowA { +moveto } def /ArrowB { } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 +neg 0.0 0.0 0 0 /N@@@A /N@@@B InitNC { NCLine } if end gsave 0.56905 +SLW 0 setgray 0 setlinecap stroke grestore grestore end + 436 3252 a 2102 2747 a Fs(phi)1771 +2916 y(lam)1889 2924 y Fp(\013)2282 2758 y FI(e)o(xisting)2282 +2815 y(type)534 2887 y(ne)n(w)534 2945 y(type)1707 3124 +y(non-empty)1707 3181 y(subset)756 2916 y 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Knuth. +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (001.000) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMBSY7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMBSY7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 1 /periodcentered put +readonly def +/FontBBox{0 -927 1542 750}readonly def +/UniqueID 5032008 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMTT8 +%!PS-AdobeFont-1.1: CMTT8 1.0 +%%CreationDate: 1991 Aug 20 16:46:05 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTT8) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch true def +end readonly def +/FontName /CMTT8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-5 -232 545 699}readonly def +/UniqueID 5000830 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMSY6 +%!PS-AdobeFont-1.1: CMSY6 1.0 +%%CreationDate: 1991 Aug 15 07:21:34 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY6) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMSY6 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-4 -948 1329 786}readonly def +/UniqueID 5000816 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI6 +%!PS-AdobeFont-1.1: CMMI6 1.100 +%%CreationDate: 1996 Jul 23 07:53:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI6) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI6 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{11 -250 1241 750}readonly def +/UniqueID 5087381 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE +D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 +5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (2.1) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMIB10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMIB10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-15 -250 1216 750}readonly def +/UniqueID 5087392 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMTI10 +%!PS-AdobeFont-1.1: CMTI10 1.00B +%%CreationDate: 1992 Feb 19 19:56:16 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMTI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-163 -250 1146 969}readonly def +/UniqueID 5000828 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMR10 +%!PS-AdobeFont-1.1: CMR10 1.00B +%%CreationDate: 1992 Feb 19 19:54:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-251 -250 1009 969}readonly def +/UniqueID 5000793 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 +87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-29 -960 1116 775}readonly def +/UniqueID 5000820 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 +7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 +A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 +E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A +221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A +27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF +5B78EC1D88228725F1C453A678F58A7E1B7BD7CA700717D288EB8DA1F57C4F09 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMBSY10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMBSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-27 -940 1332 825}readonly def +/UniqueID 5000762 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMEX10 +%!PS-AdobeFont-1.1: CMEX10 1.00 +%%CreationDate: 1992 Jul 23 21:22:48 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMEX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMEX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 56 /bracelefttp put +dup 57 /bracerighttp put +dup 58 /braceleftbt put +dup 59 /bracerightbt put +dup 60 /braceleftmid put +dup 61 /bracerightmid put +dup 62 /braceex put +dup 88 /summationdisplay put +readonly def +/FontBBox{-24 -2960 1454 772}readonly def +/UniqueID 5000774 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (2.1) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (2.1) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (MSBM10) readonly def +/FamilyName (Euler) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /MSBM10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 63 /emptyset put +readonly def +/FontBBox{-55 -420 2343 920}readonly def +/UniqueID 5031982 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI5 +%!PS-AdobeFont-1.1: CMMI5 1.100 +%%CreationDate: 1996 Aug 02 08:21:10 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI5) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI5 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{37 -250 1349 750}readonly def +/UniqueID 5087380 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMR5 +%!PS-AdobeFont-1.1: CMR5 1.00B +%%CreationDate: 1992 Feb 19 19:55:02 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR5) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR5 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-341 -250 1304 965}readonly def +/UniqueID 5000788 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMMI6 +%!PS-AdobeFont-1.1: CMMI6 1.100 +%%CreationDate: 1996 Jul 23 07:53:52 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI6) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI6 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{11 -250 1241 750}readonly def +/UniqueID 5087381 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE +D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 +5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC +4391C9DF440285B8FC159D0E98D4258FC57892DDF0342CA1080743A076089583 +6AD6FB2DC4C13F077F17789476E48402796E685107AF60A63FB0DE0266D55CF1 +8D0AD65B9342CB686E564758C96164FFA711B11C1CE8C726F3C7BB1044BBD283 +9AA4675747DF61E130A55E297CA5F0182A3F12F9085AF2F503481071724077A9 +387E27879A9649AD5F186F33500FAC8F7FA26634BDCE1221EC0ED0E359E5EA5E +6166526FEB90C30D30099FBDC1BC2F9B62EFEEC48345160804AA98F8D0AA54B7 +A480E715426651865C8E444EDB798C7E11040AF6E5A7ED1888653C6DBF5E6169 +70BCD9C063B63B561EF165BF3AF11F8E519F37C6FDA2827685739DE2C48B5ADE +EE84F067D704D4511DBFA49E166D543CFD9ECD7417055D8A827F51E087CD2927 +BAFC7E6CFBD70B0FE969F890A11149D3D44D422C3370495DA9951AEE7253A49F +3A9444C8CD9158D84117299F7F2332FEB0F94E6ED8BC7AA789A3219BC2F227D3 +3B5BC75FB53B55D72AF4A6A7BB613FA235B11BB37D059FD87127CEF73D5B3FBF +9F91ABAD78BD9240BD9525EBA78095EA0BDB25D1A19E876F292882EAD5619D46 +D20317A345D931F4FF4EAE6216C27044CBA525E3B917CEA25A04C120466C4B93 +FC720E6BA832A06CCA0A3916CEF0968D49085AEBD243C41A448289A6F05CE3F5 +79148DC112A3CC7E8FF810B8C1A09E05F496C0F1EBA334E42E05C376C98F5F69 +C06C71BFC0A2F3AC9951CFBB143C66FB84F9C4ED27DF70869352D61BD5E11508 +0797B87C709E3C151EB44E478CA576D257DF226C00BEF712425856AF0377038F +7A17D416F208B7718C27CE7D4CB4DA2755D80DD0B9BA847D5EFC18A0985F26B0 +D383A2BB84CA8D0ACABE15ADE0A4E16A21C67B63701C22EAB3D4965FAD4B4013 +1DB24106B490D120406A76942E3D22E6239729C22475CB74A740F737E532440E +ED93D7DC7E66828533B1E89492378286A329DD59517B9AA2AA50BA846F47514F +31499C288FED7E87012280F97AD60D2DD3A7D88EA4326FA258DC8FB0FBEAD3E4 +0593A58F2B958009E288C7EBDF997E48FBA5304879386FE51CEB9C33DA3935FB +F5E66146FEA53F33D7F98EFCAFA2B74E40BEA16A9956004AB554A50FED460D4D +34806CB786909E74C75514489104E16B9DB406398D43855D9D868FFAF17236E9 +E18065C5FBEC0A5A22C6AD7764BAB978E5190881A388DF7BFBC664129B099686 +A17652E7EB5DDBDF557CFC0A93F8B703EA7962D8F1343158359FB63C893F8E7C +D32BFA93B63A9FF4CA03CFAA0CAD0F1A113A4626B5DA09148349C90F68DD0D3D +749B258484F6E383A21C2DBA7278685C29026D43E9B76FBA07A1B448627A489D +3500A4217A45F355845308382219E5C66F39518405354F4A32B3237878BB73B6 +614CE0A2276709B17605BE8DADF01E261141E18C807F5426DA9857EBAD9F36C4 +077C32E5495F7B004917FDC05135E1C066F1618621DD643B190CC07EFCE250DA +6C48 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +%%EndFont +%%BeginFont: CMMIB10 +%!PS-AdobeFont-1.1: CMMIB10 1.100 +%%CreationDate: 1996 Jul 23 07:54:00 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMIB10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMIB10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-15 -250 1216 750}readonly def +/UniqueID 5087392 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMBX10 +%!PS-AdobeFont-1.1: CMBX10 1.00B +%%CreationDate: 1992 Feb 19 19:54:06 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMBX10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMBX10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-301 -250 1164 946}readonly def +/UniqueID 5000768 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMBXTI10 +%!PS-AdobeFont-1.1: CMBXTI10 1.0 +%%CreationDate: 1991 Aug 18 17:46:30 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMBXTI10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Bold) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMBXTI10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-29 -250 1274 754}readonly def +/UniqueID 5000771 def +currentdict end +currentfile eexec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cleartomark +%%EndFont +%%BeginFont: CMR8 +%!PS-AdobeFont-1.1: CMR8 1.0 +%%CreationDate: 1991 Aug 20 16:39:40 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR8) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-36 -250 1070 750}readonly def +/UniqueID 5000791 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C +68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY8) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMSY8 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-30 -955 1185 779}readonly def +/UniqueID 5000818 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 +7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 +A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 +E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A +221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFBB2A7C1B5D8E7E8AA0 +5B10EA43D6A8ED61AF5B23D49920D8F79DAB6A59062134D84AC0100187A6CD1F +80F5DDD9D222ACB1C23326A7656A635C4A241CCD32CBFDF8363206B8AA36E107 +1477F5496111E055C7491002AFF272E46ECC46422F0380D093284870022523FB +DA1716CC4F2E2CCAD5F173FCBE6EDDB874AD255CD5E5C0F86214393FCB5F5C20 +9C3C2BB5886E36FC3CCC21483C3AC193485A46E9D22BD7201894E4D45ADD9BF1 +CC5CF6A5010B5654AC0BE0DA903DB563B13840BA3015F72E51E3BC80156388BA +F83C7D393392BCBC227771CDCB976E9330253ACACB1811D98821C8EAA6108C84 +166B3851634883E1DFD97D1819EEC112FEE6AB74138AA57C32C40B53238142B0 +FFD1C3CEF6429A695FA14A644342233A08FF35F7AAF790722003E849BEEC4488 +3479B4E1149C8E3A67F8A9B81A6E11D007E9D721B1B0C2B21234C7A4A4BFDED4 +07DCA44310553284009E5A6B8283D275CA9504B1295AA2CFDA1E4AD96C96ECC8 +863BFF85AEC30DB31819103878F12028B2BCC4DF7107F0F2BE4BA911E97E8ABF +201E0D9CB730EA4F4C2419B9EEC4A5EDF821F2CF7AEE08EACF1417C946D93404 +765CEBC79E85742E9A8BB21A01032D4E4A7DB663F7872B1AEE63E66FE0A9EE2D +DAB71E938EB532F8DA4BE950F8D54A778B2ADA262279A64E6BC6BF2DEE05A03D +0EDB2759743BD5BBD8A66A5A714F046B8B946C0A2C3A6AC855CF820E0DEC4594 +BB0E8AB3ABABA56BB5D5D400551A86DA941E823C86A5D1BBA9110A78652189C8 +7035B78DAD18ACB5713C30B0CF1662DC8D4BC67F108783717CE2DF4BF6043F2B +7E5147CAE9E13BE2DE6FA346337D925B10D11ACD206C1ED1A608BF197FDF471C +4FA1621B03853209B0B17236F88F73BB2DE7F282A9846E24C4BAD4CFF9630BFA +877B8E2199094C3C3410950025CDD49BFA1CCCE20A14B9F111B776673AE9D60E +4189385F91501C15F52124A66C6BD79681CFDD97361827AC7FB23E374A934BEC +2466EFC46A640D4646ACE3C0AF3D1438A135673895BBFDCDD9D452C6C35F0CD0 +72019DBDEFAEA873DBCB1402CA1F6739D49BC3F951B8CAEDC2FE1C5E13DF7DA2 +2411C041B782436AC96FA309EEA8E3E7724272EE5D277C76099045986B835E0D +5101ECA2CF42E56FC1EB7326E81FC2BC24449AD2F554C74FB8E7EC83D33A2976 +7AE44A57C617628810EF8DED0DCCF628D5DC20C0584946A8A3E1634D0AEE5063 +D2118C760AC05B138ECF6D862EC73EE558EF80E9E25C12EACD5C0B07E06DE0A6 +97B32514A170D7D7A253D09FF665C536C9B628F2428305FD4AF5F38395CEB664 +4484A320C6C779FC1EF8D9D6D5F25E78A59B520AF7B49705072BBA07B3FC94C5 +57C306C697F3258BF17D17E794C5A023F6B4BA203F8F303ACFDA31A4BC2B8626 +9AEC1F2DDC90BF45588425DED6589E59E41CCE53E3F3C92854BC8B72E62603D0 +931D9FD867A7556E09CF5E61FC6AE4E1E589B2CBD912A71EF10A6AB0F554D058 +00F73501F1A95CEBAA75269CF87A6BCC32162BFB44B4EB0D4B058EAAFA38E6B2 +EC9D0707264BEF9044AFF0C7A65CDE973759E1E53C5BBB2272C3CB63731A6D7B +C0FB5370136A2AAD9E1C7A7D521F683ECB4560A85B559167688812B6D1E4CD2E +0E3DE6D110E0CCAD3A1A716CA6B49909A32607F9978A7FA913A6E8F30930E7FF +C127E28B36098B6347DAD6B3F82908BA26356451F9A49B82739F80DCD2792383 +B9593B64B1C42B840DE962AF3452BECF040D8031761ABCD1B943603E3E285102 +779906BAD4613BD0FB80079A098E42F682824FCBFFDAB3D4DBC9CB7A599CA704 +57F6EC1603B9105DA837C7EF52EC545027D613A0F67D08708FB018852AABDB1A +37D245521036881E8FB39A88E38E57FB01D179924DE9339910AFA525EE495679 +268D80CD9B0D5F6F37890636D31B43220E9129B9C46607F9D01273580D7E3717 +C8C5D2974B4D0947F12FA31CEBB2BD7250718CF75D94F4D498436B79C73495AD +F9F30BE7481C9BE301EB539B0E2371A20C9EF6B573F6B8A235657EED50D47369 +AC0DEBBB87A35187C750AE04BAFE3B85810800003FC6540AF5648C2FE73BFF27 +679A091269F71592511FF9702D60550F970A9965F9B0CFA0ED486565C7A46D03 +46244FD6828C65013BB22945BD0712B97B5804092F86FEEE1E5C476C2177A898 +EE3137E6790F5189A35C2314D445AF35DCF6F8543D266B44BB8FC728E7BB0326 +9A47B3B78B769CC9AE80E81EBAD96AC8182E1CEB0E +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +%%EndFont +%%BeginFont: CMSY6 +%!PS-AdobeFont-1.1: CMSY6 1.0 +%%CreationDate: 1991 Aug 15 07:21:34 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY6) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /CMSY6 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-4 -948 1329 786}readonly def +/UniqueID 5000816 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 +7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 +A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 +E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A +221A37D9A807DD01161779DDE7D5FC1B2109839E5B52DFB7605D7BA557CC35D6 +49F6EB651B83771034BA0C39DB8D426A24543EF4529E2D939125B5157482688E +9045C2242F4AFA4C489D975C029177CD6497EACD181FF151A45F521A4C4043C2 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. 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American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR9) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR9 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-39 -250 1036 750}readonly def +/UniqueID 5000792 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 +87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR6) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR6 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-20 -250 1193 750}readonly def +/UniqueID 5000789 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C +68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /CMMI7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{0 -250 1171 750}readonly def +/UniqueID 5087382 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE +3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B +532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 +B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B +986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE +D919C2DDD26BDC0D99398B9F4D03D77639DF1232A4D6233A9CAF69B151DFD33F +C0962EAC6E3EBFB8AD256A3C654EAAF9A50C51BC6FA90B61B60401C235AFAB7B 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMR10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch false def +end readonly def +/FontName /CMR10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-251 -250 1009 969}readonly def +/UniqueID 5000793 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 +87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.00B) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMTT10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle 0 def +/isFixedPitch true def +end readonly def +/FontName /CMTT10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /.notdef put +readonly def +/FontBBox{-4 -235 731 800}readonly def +/UniqueID 5000832 def +currentdict end +currentfile eexec +D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 +016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 +9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F +D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 +469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 +2BDBF16FBC7512FAA308A093FE5F00F963068B8232429ED8B7CF6A3D879A2D19 +38DD5C4467F9DD8C5D1A2000B3A6BF2F25629BAEC199AE8BD4BA6ED9BBF7DABF 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Fv(-abstraction-1\))1951 +1325 y FS(a)g FB(6)p FF(=)g FS(a)2135 1294 y Fw(0)2231 +1325 y FB(r)h(`)f FS(a)g FF(#)g FS(t)p 1951 1360 610 +4 v 2049 1436 a FB(r)g(`)g FS(a)g FF(#)h FS(a)2391 1404 +y Fw(0)2413 1436 y FS(:t)2582 1376 y Fv(\()p Ft(#)p Fv +(-abstraction-2\))1112 1552 y FS(a)f FB(6)p FF(=)g FS(a)1296 +1520 y Fw(0)p 1033 1587 364 4 v 1033 1663 a FB(r)g(`)g +FS(a)g FF(#)h FS(a)1375 1631 y Fw(0)1419 1603 y Fv(\()p +Ft(#)p Fv(-atom\))1869 1556 y FF(\()p FS(\031)1946 1524 +y Fw(\000)p FG(1)2028 1556 y Fz(\001)o FS(a)f FF(#)h +FS(X)6 b FF(\))21 b FB(2)h(r)p 1869 1594 588 4 v 1942 +1663 a(r)f(`)h FS(a)f FF(#)g FS(\031)s Fz(\001)o FS(X)2478 +1610 y Fv(\()p Ft(#)p Fv(-suspension\))p 3402 1702 4 +1334 v 523 1705 2882 4 v 1374 1849 a FU(Fig)o(.)12 b(2.)18 +b FV(Inducti)n(v)o(e)i(de\002nition)f(of)g FB(\031)g +FV(and)g FF(#)p FV(.)523 2139 y FP(suspension\))g(in)h(F)l(ig)o(.)g +(2\))g(is)h(de\002ned)e(by)1442 2351 y FA(ds)8 b FM(\()p +FQ(\031)s(;)14 b(\031)1695 2316 y FL(0)1719 2351 y FM(\))1774 +2299 y Fs(def)1777 2351 y FM(=)26 b FO(f)p FQ(a)c FO(j)i +FQ(\031)s FK(\001)o FQ(a)f FO(6)p FM(=)g FQ(\031)2304 +2316 y FL(0)2328 2351 y FK(\001)o FQ(a)p FO(g)g FQ(:)822 +b FW(\(7\))523 2538 y(Note)17 b(that)g(e)n(v)o(ery)f(disagreement)f +(set)j(of)f(the)g(lists)i FQ(\031)i FW(and)16 b FQ(\031)2226 +2508 y FL(0)2267 2538 y FW(is)i(a)g(subset)f(of)g(the)g +FP(\002nite)g FW(set)h(of)f(atoms)523 2638 y(occurring)e(in)i(either)f +(of)h(the)f(lists,)i(because)f(if)g FQ(a)g FW(does)f(not)h(occur)f(in)h +(those)f(lists,)i(then)f(from)f(Fig.)g(1)523 2737 y(we)21 +b(get)f FQ(\031)s FK(\001)p FQ(a)j FM(=)f FQ(a)h FM(=)g +FQ(\031)1199 2707 y FL(0)1222 2737 y FK(\001)p FQ(a)p +FW(.)d(T)-7 b(o)21 b(illustrate)f(the)g(use)h(of)f(disagreement)e +(sets,)j(consider)1235 2923 y FO(f)p FQ(a)h FM(#)i FQ(X)6 +b(;)14 b(c)23 b FM(#)g FQ(X)6 b FO(g)23 b(`)g FM(\()p +FQ(a)14 b(c)p FM(\)\()p FQ(a)g(b)p FM(\))p FK(\001)o +FQ(X)30 b FO(\031)22 b FM(\()p FQ(b)14 b(c)p FM(\))p +FK(\001)p FQ(X)523 3109 y FW(which)h(holds)f(by)h(\()p +FO(\031)p FW(-suspension\),)e(since)i(the)g(disagreement)f(set)i(of)8 +b FM(\()p FQ(a)14 b(c)p FM(\))-8 b(\()p FQ(a)14 b(b)p +FM(\))8 b FW(and)g FM(\()p FQ(b)14 b(c)p FM(\))8 b FW(is)g +FO(f)p FQ(a;c)p FO(g)p FW(.)523 3292 y FH(Lemma)21 b(1.)41 +b FO(r)30 b(`)f(\000)g(\031)h(\000)24 b FP(is)g(an)g(equivalence)e(r)m +(elation;)h(it)h(is)h(pr)m(eserved)f(by)f(all)h(of)g(the)g(term-)523 +3391 y(forming)g(oper)o(ations)f(in)h(Def)o(.)h(2;)f(and)f(it)i(r)m +(espects)g(the)g(fr)m(eshness)g(r)m(elation)f(\(i.e)o(.)f(if)j +FO(r)31 b(`)f FQ(a)h FM(#)g FQ(t)523 3491 y FP(and)24 +b FO(r)32 b(`)f FQ(t)h FO(\031)f FQ(t)1044 3461 y FL(0)1067 +3491 y FP(,)26 b(then)e FO(r)32 b(`)f FQ(a)h FM(#)g FQ(t)1672 +3461 y FL(0)1695 3491 y FP(\).)25 b(Both)f FO(\031)h +FP(and)f FM(#)i FP(ar)m(e)f(pr)m(eserved)f(by)h(the)g(permutation)523 +3591 y(action)c(given)h(in)g(F)l(ig)o(.)g(1)g(in)g(the)g(following)g +(sense:)g(if)35 b FO(r)26 b(`)h FQ(t)f FO(\031)g FQ(t)2470 +3560 y FL(0)2494 3591 y FP(,)c(then)g FO(r)k(`)h FQ(\031)s +FK(\001)o FQ(t)g FO(\031)f FQ(\031)s FK(\001)p FQ(t)3207 +3560 y FL(0)3230 3591 y FP(;)c(and)523 3690 y(if)33 b +FO(r)23 b(`)g FQ(a)g FM(#)g FQ(t)p FP(,)e(then)f FO(r)j(`)g +FQ(\031)s FK(\001)o FQ(a)g FM(#)h FQ(\031)s FK(\001)o +FQ(t)p FP(.)523 3790 y(Pr)l(oof)o(.)e FW(Although)i(reasoning)h(about)g +FO(\031)h FW(and)g FM(#)h FW(is)g(rather)e(pleasant)h(once)f(the)h(abo) +o(v)o(e)f(f)o(acts)i(are)523 3889 y(pro)o(v)o(ed,)g(establishing)i +(them)h(\002rst)g(is)h(rather)e(trick)o(y\227mainly)f(because)h(of)h +(the)f(lar)o(ge)g(number)523 3989 y(of)21 b(cases,)i(b)n(ut)e(also)h +(because)f(the)h(f)o(acts)g(in)g(the)f(lemma)g(are)h(inter)n +(-dependent;)d(in)i(addition)g(some)523 4089 y(further)14 +b(properties)g(of)h(the)h(permutation)d(action)i(and)g(disagreement)f +(sets)j(need)e(to)g(be)h(established)523 4188 y(\002rst)21 +b(\(statements)f(omitted\).)1376 4158 y Fy(1)3350 4188 +y FO(u)-55 b(t)648 4369 y FW(The)22 b(main)g(reason)f(for)h(using)g +(suspensions)g(in)h(the)f(syntax)g(of)g(terms)h(is)g(to)g(enable)e(a)i +(de\002ni-)523 4469 y(tion)e(of)g FP(substitution)f(of)i(terms)g(for)g +(variables)f FW(which)g(allo)n(ws)g(capture)f(of)h(free)g(atoms)g(by)g +(atom-)523 4568 y(abstractions)c(while)h(still)h(respecting)d +FQ(\013)p FW(-equi)n(v)n(alence.)f(The)j(follo)n(wing)e(lemma)h +(establishes)h(this.)523 4668 y(First)j(we)g(gi)n(v)o(e)e(some)h +(terminology)e(and)h(notation)g(for)h(term-substitution.)p +523 4746 473 4 v 558 4801 a Fr(1)606 4833 y FV(A)h(machine-check)o(ed)j +(proof)d(of)g(all)g(the)g(results)g(using)h(the)f(theorem)g(pro)o(v)o +(er)h(Isabelle)f(can)h(be)f(found)h(at)606 4924 y FC(http)g +FF(:)g FS(==)p FC(www)p FS(:)p FC(cl)p FS(:)p FC(cam)p +FS(:)p FC(ac)p FS(:)p FC(uk)p FS(=)1480 4916 y Fw(\030)1538 +4924 y FC(cu200)p FS(=)p FC(Unification)t FV(.)p eop +end +%%Page: 8 8 +TeXDict begin 8 7 bop 523 448 a FH(De\002nition)20 b(4.)41 +b FP(A)32 b FE(substitution)h FQ(\033)j FP(is)d(a)f(sort-r)m(especting) +f(function)f(fr)l(om)j(variables)e(to)h(terms)523 548 +y(with)22 b(the)g(pr)l(operty)g(that)f FQ(\033)s FM(\()p +FQ(X)7 b FM(\))27 b(=)e FQ(X)k FP(for)22 b(all)g(b)n(ut)g(\002nitely)g +(many)f(variables)g FQ(X)7 b FP(.)22 b(W)-8 b(e)22 b(shall)g(write)523 +648 y Fq(dom)8 b Fp(\()p Fo(\033)s Fp(\))23 b FP(for)f(the)f(\002nite)g +(set)h(of)g(variables)f FQ(X)28 b FP(satisfying)21 b +FQ(\033)s FM(\()p FQ(X)7 b FM(\))26 b FO(6)p FM(=)f FQ(X)7 +b FP(.)21 b(If)g FA(dom)7 b FM(\()p FQ(\033)s FM(\))23 +b FP(consists)f(of)523 747 y(variables)e FQ(X)922 759 +y FJ(1)959 747 y FQ(;)14 b(:)g(:)g(:)f(;)h(X)1212 759 +y FI(n)1278 747 y FP(and)19 b FQ(\033)s FM(\()p FQ(X)1574 +759 y FI(i)1602 747 y FM(\))24 b(=)e FQ(t)1775 759 y +FI(i)1824 747 y FP(for)e FQ(i)j FM(=)g(1)p FQ(::n)p FP(,)d(we)h(shall)f +(sometimes)h(write)g FQ(\033)j FP(as)1442 896 y FQ(\033)i +FM(=)d([)p FQ(X)1695 908 y FJ(1)1755 896 y FM(:=)g FQ(t)1896 +908 y FJ(1)1933 896 y FQ(;)14 b(:)g(:)g(:)f(;)h(X)2186 +908 y FI(n)2254 896 y FM(:=)23 b FQ(t)2395 908 y FI(n)2440 +896 y FM(])p FQ(:)822 b FW(\(8\))523 1044 y FP(W)-8 b(e)27 +b(write)h FQ(\033)s FM(\()p FQ(t)p FM(\))g FP(for)f(the)f(r)m(esult)h +(of)g FE(applying)e(a)h(substitution)i FQ(\033)i FP(to)d(a)f(term)h +FQ(t)p FP(;)g(this)g(is)g(the)g(term)523 1144 y(obtained)19 +b(fr)l(om)i FQ(t)h FP(by)f(r)m(eplacing)e(eac)o(h)h(suspension)g +FQ(\031)s FK(\001)p FQ(X)27 b FP(in)21 b FQ(t)h FP(\(as)e +FQ(X)28 b FP(r)o(ang)o(es)20 b(o)o(ver)h FA(dom)8 b FM(\()p +FQ(\033)s FM(\))p FP(\))22 b(by)523 1244 y(the)17 b(term)h +FQ(\031)s FK(\001)p FQ(\033)s FM(\()p FQ(X)7 b FM(\))18 +b FP(got)e(by)h(letting)g FQ(\031)k FP(act)c(on)g(the)g(term)h +FQ(\033)s FM(\()p FQ(X)7 b FM(\))17 b FP(using)g(the)g(de\002nition)e +(in)j(F)l(ig)o(.)e(1.)h(F)-9 b(or)523 1343 y(e)n(xample)o(,)25 +b(if)h FQ(\033)35 b FM(=)d([)p FQ(X)25 b FM(:=)18 b FO(h)p +FQ(b;)c(Y)19 b FO(i)p FM(])26 b FP(and)e FQ(t)33 b FM(=)f +FQ(a:)p FM(\()p FQ(a)14 b(b)p FM(\))p FK(\001)o FQ(X)7 +b FP(,)25 b(then)f FQ(\033)s FM(\()p FQ(t)p FM(\))34 +b(=)e FQ(a:)p FO(h)p FQ(a;)14 b FM(\()p FQ(a)g(b)p FM(\))p +FK(\001)o FQ(Y)19 b FO(i)p FP(.)26 b(Given)523 1443 y(substitutions)20 +b FQ(\033)k FP(and)19 b FQ(\033)1230 1413 y FL(0)1254 +1443 y FP(,)h(and)g(fr)m(eshness)g(en)m(vir)l(onments)f +FO(r)i FP(and)f FO(r)2533 1413 y FL(0)2556 1443 y FP(,)h(we)g(write) +1161 1592 y FM(\()p FQ(a)p FM(\))84 b FO(r)1422 1557 +y FL(0)1468 1592 y FO(`)23 b FQ(\033)s FM(\()p FO(r)p +FM(\))167 b FP(and)e FM(\()p FQ(b)p FM(\))83 b FO(r)23 +b(`)g FQ(\033)j FO(\031)d FQ(\033)2743 1557 y FL(0)3308 +1592 y FW(\(9\))523 1740 y FP(to)32 b(mean)f(that)g(\(for)h(a\))f +FO(r)1320 1710 y FL(0)1388 1740 y FO(`)44 b FQ(a)g FM(#)g +FQ(\033)s FM(\()p FQ(X)7 b FM(\))33 b FP(holds)e(for)h(eac)o(h)f +FM(\()p FQ(a)44 b FM(#)h FQ(X)7 b FM(\))43 b FO(2)i(r)32 +b FP(and)f(\(for)h(b\))523 1840 y FO(r)23 b(`)g FQ(\033)s +FM(\()p FQ(X)7 b FM(\))23 b FO(\031)g FQ(\033)1040 1810 +y FL(0)1064 1840 y FM(\()p FQ(X)7 b FM(\))20 b FP(holds)g(for)h(all)f +FQ(X)29 b FO(2)24 b FA(dom)7 b FM(\()p FQ(\033)s FM(\))19 +b FO([)g FA(dom)7 b FM(\()p FQ(\033)2435 1810 y FL(0)2459 +1840 y FM(\))p FP(.)523 1980 y FH(Lemma)21 b(2)41 b(\(Substitution\).) +14 b FP(Substitution)g(commutes)h(with)h(the)f(permutation)e(action:)h +FQ(\033)s FM(\()p FQ(\031)s FK(\001)q FQ(t)p FM(\))23 +b(=)523 2080 y FQ(\031)s FK(\001)p FM(\()p FQ(\033)s +FM(\()p FQ(t)p FM(\)\))p FP(.)f(Substitution)c(pr)m(eserves)j +FO(\031)g FP(and)e FM(#)i FP(in)f(the)g(following)g(sense:)581 +2196 y FO(\017)41 b FP(if)21 b FO(r)800 2166 y FL(0)847 +2196 y FO(`)h FQ(\033)s FM(\()p FO(r)p FM(\))g FP(and)e +FO(r)j(`)g FQ(t)g FO(\031)f FQ(t)1607 2166 y FL(0)1631 +2196 y FP(,)e(then)g FO(r)1905 2166 y FL(0)1951 2196 +y FO(`)j FQ(\033)s FM(\()p FQ(t)p FM(\))h FO(\031)f FQ(\033)s +FM(\()p FQ(t)2393 2166 y FL(0)2417 2196 y FM(\))p FP(;)581 +2289 y FO(\017)41 b FP(if)21 b FO(r)800 2259 y FL(0)847 +2289 y FO(`)h FQ(\033)s FM(\()p FO(r)p FM(\))g FP(and)e +FO(r)j(`)g FQ(a)g FM(#)g FQ(t)p FP(,)d(then)g FO(r)1900 +2259 y FL(0)1947 2289 y FO(`)i FQ(a)h FM(#)h FQ(\033)s +FM(\()p FQ(t)p FM(\))p FP(.)523 2411 y(Pr)l(oof)o(.)e +FW(The)d(\002rst)i(sentence)e(follo)n(ws)h(by)f(induction)f(on)h(the)h +(structure)f(of)g FQ(t)p FW(.)i(The)e(second)g(follo)n(ws)523 +2511 y(by)h(induction)f(on)h(the)h(proofs)e(of)h FO(r)k(`)f +FQ(t)h FO(\031)f FQ(t)1851 2481 y FL(0)1896 2511 y FW(and)d +FO(r)k(`)f FQ(a)h FM(#)g FQ(t)d FW(from)e(the)i(rules)f(in)h(Fig.)g(2,) +f(using)523 2611 y(the)g(\002rst)h(sentence)f(and)f(the)i(\(proof)d +(of\))h(Lemma)h(1.)1302 b FO(u)-55 b(t)648 2751 y FW(W)-7 +b(e)27 b(claim)f(that)g(the)h(relation)e FO(\031)h FW(de\002ned)f(in)i +(Fig.)f(2)g(gi)n(v)o(es)g(the)g(correct)f(notion)g(of)h +FQ(\013)p FW(-equi-)523 2851 y(v)n(alence)19 b(for)h(terms)h(o)o(v)o +(er)e(a)i(nominal)e(signature.)g(This)h(is)i(reasonable,)c(gi)n(v)o(en) +i(Lemma)f(1)i(and)e(the)523 2950 y(f)o(act)e(that,)g(by)f 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FP(\))f(not)h(occurring)f(at)g(all)h(in)g +FQ(t)p FP(.)523 3589 y(Her)m(e)g FM([)p FQ(a)p FL(7!)p +FQ(b)p FM(])p FQ(t)f FP(indicates)g(the)g(r)m(esult)h(of)f(r)m +(eplacing)f(all)h(fr)m(ee)h(occurr)m(ences)f(of)g FQ(a)h +FP(with)f FQ(b)h FP(in)f FQ(t)p FP(.)523 3729 y FH(Theor)o(em)g(1)41 +b(\(Adequacy\).)17 b FP(If)h FQ(t)g FP(and)f FQ(t)1688 +3699 y FL(0)1729 3729 y FP(ar)m(e)h FH(gr)o(ound)g(terms)g +FW(\(i.e.)f(terms)h(with)g(no)f(v)n(ariables)g(and)523 +3829 y(hence)e(no)h(suspensions\))f FP(o)o(ver)h(a)g(nominal)f +(signatur)m(e)o(,)g(then)h(the)g(r)m(elation)g FQ(t)23 +b FM(=)2804 3841 y FI(\013)2860 3829 y FQ(t)2890 3799 +y FL(0)2930 3829 y FP(of)16 b(Def)o(.)g(5)g(holds)523 +3928 y(if)23 b(and)e(only)h(if)h Fn(?)j FO(`)g FQ(t)h +FO(\031)f FQ(t)1320 3898 y FL(0)1366 3928 y FP(is)d(pr)l(o)o(vable)e +(fr)l(om)i(the)f(rules)h(in)f(F)l(ig)o(.)g(2.)g(Furthermor)m(e)o(,)f +Fn(?)26 b FO(`)h FQ(a)f FM(#)h FQ(t)523 4028 y FP(is)21 +b(pr)l(o)o(vable)e(if)i(and)f(only)f(if)i FQ(a)g 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FT(Pr)m(oc.)f(of)h(T)l(A)n(CS)658 +1818 y(2001)p FV(,)d(v)o(olume)f(2215)h(of)f FT(LNCS)p +FV(,)f(pages)i(243\226262.)h(Springer)o(-V)-8 b(erlag,)18 +b(2001.)523 1910 y(14.)42 b(M.)24 b(Hamana.)45 b(Simple)24 +b FS(\014)1358 1918 y FG(0)1393 1910 y FV(-uni\002cation)h(for)f(terms) +h(with)f(conte)o(xt)h(holes.)45 b(In)24 b FT(Pr)m(oc.)g(of)g(UNIF)g +(2002)p FV(,)658 2001 y(2002.)k(Unpublished)21 b(proceedings.)523 +2092 y(15.)42 b(M.)19 b(Hashimoto)g(and)h(A.)e(Ohori.)27 +b(A)19 b(typed)g(conte)o(xt)h(calculus.)27 b FT(TCS)p +FV(,)19 b(266:249\226271,)i(2001.)523 2183 y(16.)42 b(F)-6 +b(.)17 b(Honsell,)h(M.)g(Miculan,)g(and)h(I.)e(Scagnetto.)25 +b(An)18 b(axiomatic)h(approach)g(to)f(metareasoning)i(on)e(nom-)658 +2275 y(inal)25 b(algebras)h(in)f(HO)m(AS.)46 b(In)25 +b FT(Pr)m(oc.)f(of)h(ICALP)f(2001)p FV(,)i(v)o(olume)f(2076)i(of)e +FT(LNCS)p FV(,)f(pages)i(963\226978.)658 2366 y(Springer)o(-V)-8 +b(erlag,)18 b(2001.)523 2457 y(17.)42 b(J.)19 b(W)-7 +b(.)18 b(Klop.)27 b(T)-5 b(erm)19 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b(D.)21 b(Miller)l(.)34 b(A)21 b(logic)h(programming)h +(language)g(with)e(lambda-abstraction,)h(function)g(v)n(ariables,)g +(and)658 3188 y(simple)d(uni\002cation.)27 b FT(J)n(ournal)20 +b(of)f(Lo)o(gic)g(and)h(Computation)p FV(,)g(1:497\226536,)h(1991.)523 +3279 y(21.)42 b(R.)20 b(Milner)m(,)h(J.)f(P)o(arro)n(w)-5 +b(,)20 b(and)h(D.)g(W)-6 b(alk)o(er)l(.)32 b(A)21 b(calculus)g(of)g +(mobile)g(processes)h(\(parts)e(I)h(and)g(II\).)32 b +FT(Infor)o(-)658 3371 y(mation)19 b(and)h(Computation)p +FV(,)g(100:1\22677,)g(1992.)523 3462 y(22.)42 b(F)-6 +b(.)13 b(Pfenning)i(and)h(C.)d(Elliott.)j(Higher)o(-order)f(abstract)f +(syntax.)19 b(In)14 b FT(Pr)m(oc.)g(A)n(CM-SIGPLAN)e(Confer)m(ence)658 +3553 y(on)19 b(Pr)m(o)o(gr)o(amming)h(Langua)o(g)o(e)h(Design)e(and)h +(Implementation)p FV(,)g(pages)f(199\226208.)i(A)m(CM)e(Press,)f(1988.) +523 3645 y(23.)42 b(A.)24 b(M.)g(Pitts.)44 b(Nominal)25 +b(logic:)f(A)g(\002rst)g(order)h(theory)g(of)f(names)i(and)f(binding.) +46 b(In)24 b FT(Pr)m(oc.)g(of)h(T)l(A)n(CS)658 3736 y(2001)p +FV(,)20 b(v)o(olume)f(2215)h(of)f FT(LNCS)p FV(,)f(pages)i(219\226242.) +h(Springer)o(-V)-8 b(erlag,)18 b(2001.)523 3827 y(24.)42 +b(A.)18 b(M.)h(Pitts)e(and)j(M.)e(J.)h(Gabbay)-5 b(.)27 +b(A)19 b(metalanguage)h(for)f(programming)h(with)f(bound)h(names)g +(modulo)658 3919 y(renaming.)40 b(In)22 b FT(Pr)m(oc.)g(of)h(MPC2000)p +FV(,)g(v)o(olume)g(1837)h(of)f FT(LNCS)p FV(,)e(pages)j(230\226255.)h +(Springer)o(-V)-8 b(erlag,)658 4010 y(2000.)523 4101 +y(25.)42 b(G.)27 b(D.)h(Plotkin.)56 b(An)28 b(illati)n(v)o(e)f(theory)i +(of)f(relations.)57 b(In)28 b FT(Situation)h(Theory)f(and)h(its)e +(Applications)p FV(,)658 4193 y(v)o(olume)19 b(22)h(of)f +FT(CSLI)f(Lecur)m(e)h(Notes)p FV(,)g(pages)h(133\226146.)h(Stanford)e +(Uni)n(v)o(ersity)-5 b(,)19 b(1990.)523 4284 y(26.)42 +b(M.)27 b(Sato,)f(T)-6 b(.)26 b(Sakurai,)g(and)i(Y)-10 +b(.)26 b(Kame)o(yama.)53 b(A)26 b(simply)h(typed)h(conte)o(xt)f +(calculus)g(with)g(\002rst-class)658 4375 y(en)m(vironments.)h +FT(J)n(ournal)21 b(of)d(Functional)i(and)g(Lo)o(gic)f(Pr)m(o)o(gr)o +(amming)p FV(,)g(2002\(4\),)h(2002.)523 4467 y(27.)42 +b(M.)20 b(R.)f(Shinwell,)g(A.)h(M.)g(Pitts,)e(and)j(M.)f(J.)f(Gabbay)-5 +b(.)32 b(FreshML:)20 b(Programming)h(with)e(binders)i(made)658 +4558 y(simple.)27 b(In)19 b FT(Pr)m(oc.)f(of)h(ICFP)e(2003)p +FV(.)j(A)m(CM)f(Press,)f(2003.)p eop end +%%Trailer + +userdict /end-hook known{end-hook}if +%%EOF diff -r 0b4a5595cbe4 -r 680070975206 Publications/proposal-2007.pdf Binary file Publications/proposal-2007.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/rexp.pdf Binary file Publications/rexp.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/rta-08.pdf Binary file Publications/rta-08.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/sac-11.pdf Binary file Publications/sac-11.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/tableaux-01.pdf Binary file Publications/tableaux-01.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/tableaux-01.ps.gz Binary file Publications/tableaux-01.ps.gz has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/tableaux-98.bib --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Publications/tableaux-98.bib Sat Oct 22 12:11:38 2011 +0100 @@ -0,0 +1,15 @@ + +@INPROCEEDINGS{Urban98, + AUTHOR = {C.~Urban}, + TITLE = {{I}mplementation of {P}roof {S}earch in the + {I}mperative {P}rogramming {L}anguage {P}izza}, + BOOKTITLE = {Automated Reasoning with Analytic Tableaux and + Related Methods}, + EDITOR = {H.~de Swart}, + PUBLISHER = {Springer-Verlag}, + SERIES = {LNAI}, + VOLUME = 1397, + PAGES = {313--319}, + YEAR = 1998 +} + diff -r 0b4a5595cbe4 -r 680070975206 Publications/tableaux-98.ps.gz Binary file Publications/tableaux-98.ps.gz has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/tlca-99.bib --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Publications/tlca-99.bib Sat Oct 22 12:11:38 2011 +0100 @@ -0,0 +1,15 @@ + + +@INPROCEEDINGS{UrbanBierman99, + AUTHOR = {C.~Urban and G.M.~Bierman}, + TITLE = {{S}trong {N}ormalisation of {C}ut-{E}limination + in {C}lassical {L}ogic}, + BOOKTITLE = {Typed Lambda Calculi and Applications}, + EDITOR = {J.-Y.~Girard}, + PAGES = {365--380}, + SERIES = {LNCS}, + VOLUME = 1581, + PUBLISHER = {Springer Verlag}, + YEAR = 1999 +} + diff -r 0b4a5595cbe4 -r 680070975206 Publications/tlca-99.pdf Binary file Publications/tlca-99.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/tlca-99.ps.gz Binary file Publications/tlca-99.ps.gz has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/tphols-08.pdf Binary file Publications/tphols-08.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/univ-10.pdf Binary file Publications/univ-10.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/variable.pdf Binary file Publications/variable.pdf has changed diff -r 0b4a5595cbe4 -r 680070975206 Publications/w-07.pdf Binary file 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