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% $Id: pstricks.pro 902 2014-03-30 16:23:33Z herbert $
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%% PostScript prologue for pstricks.tex.
%% Version 1.22, 2014/02/20
%%
%% This program can be redistributed and/or modified under the terms
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%
%
% Define the follwing gs-functions if not known, eg when using distiller
%
systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if
systemdict /.setblendmode known not {/.setblendmode { pop } def } if
systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if
%
/tx@Dict 200 dict def 				% the main PSTricks dictionary
tx@Dict begin
/ADict 25 dict def				% The arrow dictionary
/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
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/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def  % return 0 for negative arguments 
/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known
/ATAN1 {neg -1 atan 180 sub } def		% atan(x) (only one parameter)
/Div { dup 0 eq { pop } { div } ifelse } def  	% control the division
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/tan { dup cos abs 1.e-10 lt
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/PtoC { 2 copy cos mul 3 1 roll sin mul } def 	% Polar to Cartesian
%/Rand { rand 4294967295 div } def		% a real random number
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%----------------- hv added 20050516 ---------------
/PiDiv2 1.57079632680 def
/Pi 3.14159265359 def 
/TwoPi 6.28318530718 def
/Euler 2.71828182846 def 
%/e Euler bind def
%
/RadtoDeg { 180 mul Pi div } bind def 		% convert from radian to degrees
/DegtoRad { Pi mul 180 div } bind def 		% viceversa
%
/startGlobal { true setglobal globaldict begin } bind def
/endGlobal { end false setglobal } bind def
/pssetRGBcolor /setrgbcolor load def
/pssetCMYKcolor /setcmykcolor load def
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%
%----------------- hv end---------------------------
/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def
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   {}
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   /pathforall load stopped { pop pop pop pop } if
   z 
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%
/STP { .996264 dup scale } def			% BP/PT scaling
/STV { SDict begin normalscale end STP  } def	% 
%
/DashLine {
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     { /a .5 def PathLength exch div }
     { pop /a 1 def PathLength } ifelse
     /b ED % pattern should fit evenly in b
     dup /X ED % pattern array
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%
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%
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   a 0 dtransform round exch round exch
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%
/PenroseFillA {%  on stack: scaling factor, border color, kite color, dart color
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   /dart_colour ED
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   Scale 1 lt { 1 Scale dup add div mul cvi } if %%%%   Number of iterations
   10					%%%%   Long side length in millimeters
   /border_width { L 0.06 mul }def		%%%%   Choose the scalefactor for the borders
   /L exch 25.4 div 72 mul def		%%%%   Conversion: mm -> inches -> points
   /f{-1 5 sqrt add 2 div}bind def		%%%%   The reciprocal of the golden ratio
   /l{L f mul}bind def			%%%%   Short side length l = L*f
   /Ll{L l add}bind def			%%%%   Ll =  L + l
   /c{36 cos L mul}bind def		%%%%   c  =  L*cos(36)
   /s{36 sin L mul}bind def		%%%%   s  =  L*sin(36)
   /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
 	     0 setlinewidth stroke grestore border_colour stroke } bind def
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   border_width setlinewidth  1 setlinejoin  1 setlinecap
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   dup f exch neg exp dup scale
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%
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/TruchetFill { %	 on stack: scaling factor
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   1 exch div round /penroseFactor ED
   a 0 dtransform round exch round exch
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       } for
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   } def
%
   /f 3 def
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%
/BeginArrow {
   ADict begin 			% hold it local, for end see EndArrow
   /@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 % end the ADict
%
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   2 div /w ED
   mul dup /h ED
   mul /a ED
   { 0 h T 1 -1 scale } if
   w neg h moveto
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   gsave fill grestore 
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%
/ArrowD { % the sides are drawn as curves (hv 20071211)
   CLW mul add dup
   2 div /w ED
   mul dup /h ED
   mul /Inset ED
   { 0 h T 1 -1 scale } if % changes the direction
% we use y=w/h^2 * x^2 as equation for the control points
% for the coordinates the arrow is seen from top to bottom
% the bottom (tip) is (0;0)
   w neg h moveto % lower left of >
   w 9 div 4 mul neg h 3 div 2 mul
   w 9 div neg       h 3 div
   0 0 curveto    % tip of >
   w 9 div        h 3 div
   w 9 div 4 mul  h 3 div 2 mul
   w h curveto % upper left of >
   w neg Inset neg rlineto % move to x=0 and inset
   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 { % DS is the dot size
   { /z DS def } { /z 0 def } ifelse  	% outer or inner dimen
   /b ED 				% the color definition
   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 { % holds the coordinates and on top of stack the showpoints boolean
   /showpoints ED
   counttomark 2 div dup cvi /n ED  	% n 2 div on stack
   n eq not { exch pop } if		% even numbers of points? delete one
   ] aload /Points ED
   showpoints not { Points aload pop } if
%    { ] aload /Points ED } 
%    { n 2 mul 1 add -1 roll pop } ifelse	% delete the mark symbol 
} 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
%
/LineToYAxis {
   /Ox ED		% Save the x origin value
   NArray            % all x-y pairs on stack
   n { 2 copy moveto % go to current point
     Ox exch Lineto   % line to y-axis
     pop             % delete old x-value
   } repeat
} def
%
/LineToXAxis{
   /Oy ED		% Save the y origin value
   NArray		% all x-y pairs on stack
   n 0 eq not
     { n 1 eq { 0 0 /n 2 def } if
       ArrowA
       /n n 2 sub def
       CP 2 copy moveto pop Oy Lineto
       n { 2 copy moveto pop Oy Lineto } repeat
       CP
       4 2 roll
       ArrowB
       2 copy moveto pop Oy
       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
%
/SymbolPolygon {   % on stack [ x y x y ...
   counttomark 					% number of elements
   2 add /m ED
   2 copy m 2 roll				% copy last two
   m 2 div cvi /n ED    				% n pairs
   /YA ED /XA ED					% the start point
   n 1 sub {
     /YB ED /XB ED
     /XLength XB XA sub def
     /YLength YB YA sub def
     /PAngle YLength XLength Atan def
     /XYLength XLength YLength Pyth def
     /nSym XYLength SymStep Div cvi def
     /Shift Symbol stringwidth pop 2 Div def
     /deltaX XLength nSym Div def
     /deltaY YLength nSym Div def
     XA Shift sub YA Shift sub moveto
     nSym {
       gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
       Symbol show
       grestore
       deltaX deltaY rmoveto
     } repeat
%    XB Shift sub YB Shift sub moveto Symbol show
     /YA YB def /XA XB def
   } repeat
   pop	% delete the mark symbol
} 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
%
/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
%
/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
%
/CurvePath {
   %% for negative SymStep we calculate the distance
   SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
   0.5 setflat
   flattenpath /z 0 def /z0 0 def
   { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
     x1 Shift sub y1 Shift sub moveto
     gsave
     curveticks
       { x1 y1 translate startAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       { startAngle rotate Symbol show }
     ifelse
     grestore /z0 z def }
   { /y ED /x ED PathLength@ z z0 sub SymStep ge {
       x Shift sub y Shift sub moveto
       gsave
       curveticks
         { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
           x y translate rotAngle rotate
           0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
           SymbolLinewidth setlinewidth stroke
         }
         {
           rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
           Symbol show
         }
       ifelse
       grestore /z0 z def } if
     /yOld y def /xOld x def }
   {} %% the lineto part
   { /y y2 def /x x2 def PathLength@
     x Shift sub y Shift sub moveto
     gsave
     curveticks
       { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
         x y translate rotAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       {
         x Shift sub y Shift sub moveto
         rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
         Symbol show
       }
     ifelse
     grestore
   }
   pathforall 
%  curveticks 
%   { gsave 
%     x y translate rotAngle rotate 
%     0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
%     SymbolLinewidth setlinewidth stroke grestore
%   } if
   z 
} def
%
/OpenSymbolCurve {
   OpenCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/AltOpenSymbolCurve {
   AltCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolCurve {
   ClosedCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} def
%
/CalcBezierSpline {%  Christoph Bersch
   10 dict begin
   /getX { Points exch 2 mul get } def
   /getY { Points exch 2 mul 1 add get } def
   /n Points length 1 sub 2 idiv def
   /GetFirstControlPoints {
     /x n array def
     /tmp n array def
     /b 2 def
     x 0 rhs 0 get b div put
     1 1 n 1 sub {
       /i exch def
       tmp i 1 b div dup 4 1 roll put
       i n 1 sub lt { 4 }{ 3.5 } ifelse exch sub /b exch def
       x i rhs i get x i 1 sub get sub b div put
     } for
     1 1 n 1 sub {
       n exch sub
       dup dup x exch 1 sub 2 copy 6 2 roll
       get 3 1 roll tmp exch get
       exch x exch get mul sub
       put
     } for
     x
   } def
   %
   n 1 eq {
     0 getX 2 mul 1 getX add 3 div
     0 getY 2 mul 1 getY add 3 div
     exch dup 3 1 roll 2 mul 0 getX sub
     exch dup 3 1 roll 2 mul 0 getY sub
     [ 0 getX 0 getY 7 3 roll 1 getX 1 getY ] /outPoints exch def
   } {
     /outPoints 6 n mul 2 add array def
     0 1 n {
       dup dup 6 mul dup 1 add
       outPoints exch 5 -1 roll getY put
       outPoints exch 3 -1 roll getX put
     } for
     /rhs n array def
     1 1 n 2 sub {
       rhs exch dup dup getX 4 mul exch 1 add getX 2 mul add put
     } for
     rhs 0 0 getX 1 getX 2 mul add put
     rhs n 1 sub dup getX 8 mul n getX add 2 div put
     GetFirstControlPoints
     1 1 n 2 sub {
       rhs exch dup dup getY 4 mul exch 1 add getY 2 mul add put
     } for
     rhs 0 0 getY 1 getY 2 mul add put
     rhs n 1 sub dup getY 8 mul n getY add 2 div put
     GetFirstControlPoints
     0 1 n 1 sub {
       /i exch def
       2 copy
       i get outPoints 6 i mul 3 add 3 -1 roll put
       i get outPoints 6 i mul 2 add 3 -1 roll put
       2 copy
       i n 1 sub lt {
         i 1 add get i 1 add getY 2 mul exch sub outPoints 6 i mul 5 add 3 -1 roll put
         i 1 add get i 1 add getX 2 mul exch sub outPoints 6 i mul 4 add 3 -1 roll put
       }{
         n 1 sub get n getY add 2 div outPoints 6 n 1 sub mul 5 add 3 -1 roll put
         n 1 sub get n getX add 2 div outPoints 6 n 1 sub mul 4 add 3 -1 roll put
       } ifelse
     } for
     pop pop
   } ifelse
   outPoints
   end
} def
/Spline {
   /showpoints ED
   counttomark 2 div dup cvi /n ED
   n eq not { exch pop } if
   ] /Points ED
   n 1 gt {
     CalcBezierSpline
     mark exch aload pop
     ArrowA
     n 2 sub {
       6 2 roll 4 2 roll curveto
     } repeat
     6 2 roll 4 2 roll ArrowB curveto
   } if
} def
/OpenSymbolSpline {
   Spline
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/OpenSymbolBezier {
   OpenBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolBezier {
   /f ED				 % save showpoints value
   2 copy /yEnd ED /xEnd ED
   counttomark -2 roll 2 copy /yStart ED /xStart ED
   counttomark 2 roll
   f
   ClosedBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath
   [ xEnd yEnd xStart yStart SymbolLine 
} 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 ED /x0 ED /y1 ED /x1 ED
   /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
%
/Parab1 { % 1 end  |  0 SP
   /ySP ED /xSP ED /y1 ED /x1 ED
   /dx xSP x1 sub 3 div def
   /dy ySP y1 sub 3 div def
   newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
                        x1 ySP lineto closepath clip
   currentpoint
   newpath moveto
   xSP dx sub ySP dy add x1 y1 ArrowA
   xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
   curveto
   /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def 
} def
%
/Grid {
   newpath
   /a 4 string def
   /b ED % 				psk@gridlabels in pt
   /c ED % 				{ \pst@usecolor\psgridlabelcolor }
   /n ED % 				psk@griddots
   cvi dup 1 lt { pop 1 } if
   /s ED % 				\psk@subgriddiv
   s div dup 0 eq { pop 1 } if
   /dy ED s div dup 0 eq { pop 1 } if %	\pst@number\psyunit abs
   /dx ED dy div round dy mul %		\pst@number\psxunit abs
   /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 {
   /rotAngle ED
   /mtrx CM def
   T
   rotAngle rotate
   scale 0 0 1 5 3 roll arc
   mtrx setmatrix 
} def
%
/ArcAdjust { %%%% Vincent Guirardel
% given a target length (targetLength) and an initial angle (angle0) [in the stack],
% let  M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
% This computes an angle t such that (x0,y0) is at distance 
% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
% contrary to TvZ's code.
% To achieve, this, one iterates the following process: start with some angle t,
% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
%
% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
% the value of d = add/sub is used to know on which side we have to move.
% It is only used in the initialisation of the angle before the iteration.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input stack:  1: target length 2: initial angle
% variables used : rx, ry, d (=add/sub)
%
   /targetLength ED /angle0 ED
   /x0 rx angle0 cos mul def
   /y0 ry angle0 sin mul def
% we are looking for an angle t such that (x0,y0) is at distance targetLength 
% from the point M(t)=(rx*cos(t),ry*sin(t)))
%initialisation of angle (using 1st order approx = TvZ's code)
   targetLength 57.2958 mul
   angle0 sin rx mul dup mul
   angle0 cos ry mul dup mul
   add sqrt div 
% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
% (if the ellipse is very curved at the point where we draw the arrow, %
% the value can be much more than 360 degrees !)
% this should avoid going on the wrong side (more than 180 degrees) or go near
% a bad attractive point (at 180 degrees)
   dup 90 ge { pop 90 } if
   angle0 exch d % add or sub
% maximum number of times to iterate the iterative procedure:
% iterative procedure: takes an angle t on top of stack, computes a 
% better angle (and put it on top of stack)
   30 { dup
% compute distance D between (x0,y0) and M(t)
     dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
% if D almost equals targetLength, we stop
     dup targetLength sub abs 1e-5 le { pop exit } if
% stack now contains D t
% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
     exch dup cos rx mul x0 sub  exch sin ry mul y0 sub
% stack contains:  y(t)-y0, x(t)-x0, d
     2 index Div targetLength mul y0 add ry Div exch
     2 index Div targetLength mul x0 add rx Div
% stack contains x(t')/rx , y(t')/ry , d
% now compute t', and remove D from stack
     atan exch pop
   } repeat
% we don't look at what happened... in particular, if targetLength is greater 
% than the diameter of the ellipse...
% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
% to give back the result as a an angle relative to angle0 we could add the following line:
% angle0 sub 0 exch d
%
% begin bug fix 2006-01-11
% we want to adjust the new angle t' by a multiple of 360 so that  | t'-angle0 | <= 180
%(we don't want to make the ellipse turn more or less than it should)...
dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
% end bug fix
} def
%
/EllipticArcArrow {
   /d ED      % is add or sub
   /b ED      % arrow procedure
   /a1 ED     % angle
   gsave
   newpath
   0 -1000 moveto
   clip                  % Set clippath far from arrow.
   newpath
   0 1 0 0 b             % Draw arrow to determine length.
   grestore
% Length of arrow is on top of stack. Next 3 numbers are junk.
%
   a1 exch ArcAdjust   % Angular position of base of arrow.
   /a2 ED
   pop pop pop
   a2 cos rx mul xOrig add % hv 2007-08-29   x->xOrig
   a2 sin ry mul yOrig add % hv 2007-08-29   y->yOrig
   a1 cos rx mul xOrig add %
   a1 sin ry mul yOrig add % 
% Now arrow tip coor and base coor are on stack.
   b pop pop pop pop       % Draw arrow, and discard coordinates.
   a2 CLW 8 div
% change value of d (test it by looking if  `` 1 1 d '' gives 2 or not )
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
   ArcAdjust
% resets original value of d
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse  % Adjust angle to give overlap.
} def
%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
%
/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 {
   5 dict begin
   /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
   end
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro

%%EndProcSet
%%BeginProcSet: pst-algparser.pro 0 0
% $Id: pst-algparser.pro 902 2014-03-30 16:23:33Z herbert $
%%
%% PostScript prologue for PSTricks algorithm parser
%% Version 0.05, 2014/03/30
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%%-----------------------------------------------------------------------------%
%
/AlgParser { tx@AlgToPs begin AlgToPs end } def  % Dominique Rodriguez
%
/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
%
% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
%
% 09/2011 DR factorial with ! added
%
% E->T|E+T
% T->FS|T*FS
% FS -> F | +FS | -FS
% F->P|F^SF|P!
% P->(E)|literal
% literal->number|var|var[E]|func(params)
% params->E|E,param
% number->TOBEFINISHED
%
%% E expression, T term, SF signed factor, F factor, P power
%
%% parser
%
%% str
%
%% C->E<condition_operators>E
%% STR index -> STR index+lenExpr
/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp  } def
%
%% analyze Expression List (separator , or | )
%% STR index -> STR index+lenExpr
%% /AnalyzeListOfE {
%%   { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
%%     NextNonBlankChar dup 0 eq { pop exit } if
%%     dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
%%     pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
%%   AnalyzeListOfEPostHook
%% } def
/AnalyzeListOfE {
   /NotFirst false def
   { NextNonBlankChar pop AnalyzeExpr
     NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
     dup Strlen eq { exit } if NextNonBlankChar
     dup 44 ne 1 index 124 ne and
     { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
     if  pop 1 add } loop
   AnalyzeListOfEPostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% E->T|E+T
%% STR index -> STR index+lenExpr
/AnalyzeExpr {
   AnalyzePreHook AnalyzeTerm IsEndingExpr
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% T->FS|T*FS
%% STR index
/AnalyzeTerm {
   AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% FS -> F | +FS | -FS
%% STR index
/AnalyzeSignedFactor {
   AnalyzePreHook 2 copy get dup IsUnaryOp
   { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
   { pop AnalyzeFactor }
   ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% F->P|F^P|P!
%% STR index
/AnalyzeFactor {
   AnalyzePreHook AnalyzePower IsEndingFactor
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { dup 33 eq%% is there a ! DR 09/2011
       { pop 1 add NextNonBlankChar pop EvalFactorial }
       { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
       ifelse
       IsEndingFactor { pop exit } if } loop }
   ifelse  AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% P->(E)|literal
%% STR index
/AnalyzePower {
   %% depending of first char either a number, or a literal
   2 copy get dup 40 eq%%an open par
   { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
   { AnalyzeLiteral }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index STR[index] -> STR index
%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% recognize + or -
%% chr -> T/F
/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadNumber {
   exch dup 3 -1 roll dup 3 1 roll
   %%read mantissa
   { 1 add  2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
   dup 101 eq exch 69 eq or
   %%% there is a "e" or "E" -> read exponant
   { 1 add 2 copy get dup IsUnaryOp
     { pop 1 add 2 copy get } if
     { IsNumber not { exit } if 1 add 2 copy get } loop }
   if
   dup 4 1 roll
   3 -1 roll exch 1 index sub getinterval
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadCondOp {
   NextNonBlankChar 1 index 4 1 roll
   { IsCondOp not { exit } if 1 add  2 copy get } loop
   2 copy 5 -1 roll
   exch 1 index sub getinterval 3 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can contain only : 0123456789.
%% chr -> T/F
/IsLiteral {%
   dup 48 ge exch dup  57 le 3 -1 roll and exch
   dup 65 ge exch dup  90 le 3 -1 roll and 3 -1 roll or exch
   dup 97 ge exch     122 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
%% STR index -> literal STR index' nextchr
/ReadLiteral {
   exch dup 3 -1 roll dup 3 1 roll
   %%read literal core
   { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
   4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a clpar
%% STR index -> STR index STR[index] T/F
/IsEndingExpr {%
   2 copy dup Strlen eq
   %% if end of str is reached -> end !
   { pop pop 0 true }
   %% ending chr -> clpar, comma, |, <, >, =, !,
   {get dup  dup  41 eq
        exch dup 124 eq
        exch dup  93 eq
        exch dup  44 eq
        exch dup  30 eq
        exch dup  60 ge exch 62 le and or or or or or}
   ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a +-
%% STR index -> STR index STR[index] T/F
/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or */
%% STR index -> STR index STR[index] T/F
/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or ^
%% STR index -> STR index STR[index] T/F
/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index STR[index]
/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
%%%%%%%%%%%%%%%%%%%%%%%%
%% DEBUG
/BRK {false} def
/BRKtrue {/BRK true def} def
/BRKStop {BRK {BRKtoto} if } def
/BRKEvalStop {BRK exch if } def
/BRKBRK2true {BRK {BRK2true} if } def
/BRK2 {false} def
/BRK2true {/BRK2 true def} def
/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
end
%
%-------------------------------------------------------------------------------%
%
/tx@AlgToPs 12 dict def tx@AlgToPs begin
%
%% algExpr -> PSVector
/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
/Strlen 0 def
/EvalListOfExpr {} def%
/EvalNumber {%
     ReadNumber  cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
     exch 1 add array astore def NextNonBlankChar pop } def
/EvalAddSub {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
} def
/EvalMulDiv {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
} def
/EvalPower {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   pop /exp cvx exch 1 add array astore def
} def
/EvalFactorial {% DR 09/2011
   /ExpressionVector ExpressionVector aload length
   /fact cvx exch 1 add array astore def
} def
/EvalLiteral {%
   ReadLiteral
   dup 40 eq%%% there is an open par -> function call
   { pop 2 index
     dup (Sum) eq { EvalSum }
     { dup (IfTE) eq { EvalCond }
       { dup (Derive) eq { pop EvalDerive }
 	{ pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
           /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
 	  exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
   { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
     dup 91 eq%%% there is an open bracket -> vector element
     { pop 1 add NextNonBlankChar pop AnalyzeExpr
       /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
     { pop NextNonBlankChar pop }
     ifelse}
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% the derive function : Derive(n,f(x))
%% firstparindex lastparindex ->
/EvalDerive {
   %% manage the function descripiton
   1 add ReadNumber 3 1 roll NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   1 add NextNonBlankChar pop
   3 -1 roll cvi
   dup 0 eq
   { pop AnalyzeExpr 3 -1 roll pop 1 add }
   { 1 sub 3 1 roll (x)  exch tx@Derive begin DeriveIndexed end 4 -1 roll
     { (x) tx@Derive begin Derive end } repeat
     ExpressionVector exch /ExpressionVector [] def
     AlgToPs aload length
     /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll  /l2 exch def /l1 exch def
     l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
     1 index length /Strlen exch def } ifelse
} def
/EvalSum {%
   pop 1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
   5 -1 roll 4 add array astore def
   %% keep ExpressionVector for later and create a new one for internal Sum computation
   ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
   1 add NextNonBlankChar pop AnalyzeExpr
   %% add each term
   /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
   /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
   array astore def 3 -1 roll pop 1 add
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
/EvalCond {%
   pop 1 add AnalyzeCond NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   ExpressionVector 3 1 roll /ExpressionVector [] def
   1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
   NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add AnalyzeExpr
   NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
   ExpressionVector
   /ExpressionVector 6 -1 roll aload length dup
   6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
   1 add 3 -1 roll pop
} def
%% CondOp STR index
/EvalCondOp {%
   3 -1 roll
   dup (=) eq  { /eq } {%
   dup (<) eq  { /lt } {%
   dup (>) eq  { /gt } {%
   dup (>=) eq { /ge } {%
   dup (<=) eq { /ge } {%
   dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
   ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
   cvx exch pop
   /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
/EvalUnaryOp {
   3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook {} bind def
/PreEvalHook {} bind def
/AnalyzeListOfEPostHook {} bind def
/AnalyzePostHook {} def
/RollOp { 3 1 roll } bind def
end   %tx@CoreAnalyzerDict
%
%--------------------------------------------------------------------%
%
/tx@Derive 41 dict def tx@Derive begin
%%increase ^^ for each function added
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable -> PSVector
/Derive {%
   10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
} def
/Strlen 0 def
/InitParser { dup length /Strlen exch def 0 } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable index -> PSVector
/DeriveIndexed {%
   3 1 roll 10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u,v)'=-(u',v')
/EvalListOfExpr {%
   4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
            2 copy 7 -1 roll dup length 4 1 roll putinterval add
   6 -2 roll pop pop
   2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (-u)'=-(u')
/EvalUnaryOp {
   4 -2 roll 4 index (0) eq
   { (0) StrConcat 7 -1 roll pop }
   { 7 -1 roll 45 eq
     { AddSub AddOpPar true } { false } ifelse
     3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (number)'=0
/EvalNumber { ReadNumber (0) 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u+v)'=u'+v'
/EvalAddSub {%
   7 index dup (0) eq
   { pop true }%% du=0 nothing added
   { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
   ifelse
   5 index dup (0) eq
   { pop { (0) } { 4 -2 roll 2 copy pop 0  6 2 roll GetIntervalNewStr } ifelse }%%dv=0
   { exch
     { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
     { 5 -2 roll 7 index 43 eq%%something yet added
       { AddAdd false } { AddSub AddOpPar true } ifelse }
     ifelse 11 1 roll
     3 -1 roll StrConcat 10 -1 roll { AddClPar } if
     2 copy pop 0 6 2 roll GetIntervalNewStr }
   ifelse
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)' or (u/v)'
/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)'=u'*v+u*v'
/EvalMul {%
   4 -2 roll 7 index dup (0) eq
   { pop false }%%du=0
   { (1) eq%%du=1
     { false }
     { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
     3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
     true }%%du!=0
   ifelse
   5 1 roll 5 index (0) eq
   { 5 -1 roll not { (0) StrConcat } if }%%dv=0
   { 5 -1 roll { AddAdd } if
     4 index (1) eq
     { 8 index StrConcat }
     { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
     ifelse
   }%%dv!=0
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u/v)'=(u'*v-u*v')/v^2
/EvalDiv {%
   4 -2 roll
   4 index (0) eq%%dv=0 -> u'/v
   { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
   { 7 index dup (0) eq
     { pop }%%du=0
     { (1) eq%%du=1
       { false }
       { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
       3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
     ifelse
       AddSub
       4 index (1) eq
       { 8 index StrConcat }
       { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
       ifelse
     %}%%dv!=0
     2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
     AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str1 index str2 -> str1 index
/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
/EvalPower {%
   4 -2 roll 7 index (0) eq
   {%%if du=0 then (u^v)'=v'ln(u)u^v
     4 index (0) eq
     { (0) StrConcat }%%if dv=0 then (u^v)'=0
     { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
       8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
       AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
   }
   {%%du!=0
     4 index (0) eq
     {%%if dv=0 then (u^v)'=vu'u^(v-1)
       5 index dup IsStrNumber
       { dup (0) eq
         { StrConcat }
         { dup dup (1) eq exch (1.0) eq or
           { StrConcat  }
 	  { StrConcat
 	    7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
 	    { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
             (*\() StrConcat 8 index StrConcat (\)) StrConcat
             5 index  dup dup (2) eq exch (2.0) eq or
 	    { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
       { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
         5 index StrConcat (-1\)) StrConcat } ifelse
     }
     {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
       7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
       AddOpPar 5 index StrConcat (\)*\() StrConcat
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (-1\)+\() StrConcat
       4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (\)*ln\() StrConcat
       8 index StrConcat AddClPar
     } ifelse
   } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for factorial ! only cst => null derivative
/EvalFactorial {% DR 09/2011
   4 index (0) eq
   { (0) mark 8 -2 roll  cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
   { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str -> true/false
/IsStrNumber {%
   true exch
   { dup 48 lt exch dup 57 gt 3 -1 roll or
     exch dup 46 ne%%.
     exch dup 43 ne%%+
     exch 45 ne%%-
     and and and { pop false } if } forall
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalLiteral {%
   ReadLiteral dup 40 eq%%% there is an open par -> function call
   { pop (EvalFunc_             ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
   { dup 91 eq%%% there is an open bracket -> vector element
     { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
     { pop EvalVariable }
     ifelse }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first last parpos Expr[first:parpos-1] ->
/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (f(u))'=u'f'(u)
/EvalFunc {
   4 2 roll 4 index (1) ne
   { AddOpPar 4 index StrConcat (\)*) StrConcat } if
   (Eval             ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Func derivative -> Eval<func>
/EvalFunc_sin {%
   PreCommonFunc
   { (cos\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_cos {%
   PreCommonFunc
   { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_tan {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_asin {%
   PreCommonFunc
   { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_acos {%
   PreCommonFunc
   { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_atg {%
   PreCommonFunc
   { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_floor {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ln {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_exp {%
   PreCommonFunc
   {  (exp\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_EXP {%
   PreCommonFunc
   {  (EXP\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_sqrt {%
   PreCommonFunc
   { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Fact {%
   PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
   PostCommonFunc } def
/EvalFunc_sh {%
   PreCommonFunc
   { (ch\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ch {%
   PreCommonFunc
   { (sh\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_th {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argsh {%
   PreCommonFunc
   { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argch {%
   PreCommonFunc
   { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argth {%
   PreCommonFunc
   { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/PreCommonFunc {
   1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
   4 2 roll 4 index (0) eq
   { (0) StrConcat false }
   { 4 index (1)  ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
} def
/PostCommonFunc {
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
/EvalFunc_Derive {%
   1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
   4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
   4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
   exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_Sum {%
   1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop 3 -1 roll pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
   1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
   4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_IfTE {%
   3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
   NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   1 add NextNonBlankChar pop dup 5 1 roll
   AnalyzeExpr NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add NextNonBlankChar pop
   AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
   6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% advance in str until a comma is found (no error detection!)
%% str index -> str index'
/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for condition....
/EvalCondOp { 3 -1 roll pop } bind def
/PutIntervalOneAdd {putinterval 1 add} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add close parenthesis in string at the given index
%% str index -> str index+1
/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add 0 in string at the given index
%% str index -> str index+1
/AddZero {2 copy (0) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddMul {2 copy (*) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a plus sign in string at the given index
%% str index -> str index+1
/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a minus sign in string at the given index
%% str index -> str index+1
/AddSub {2 copy (-) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a pipe sign in string at the given index
%% str index -> str index+1
/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook { dup 5 1 roll } bind def
/PreEvalHook {} def
/AnalyzePostHook { 7 -1 roll pop } bind def
/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
/RollOp { 5 1 roll } bind def
end%%%tx@CoreAnalyzerDict
/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NEW FUNC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
%% x -> theta
/asin {%
   dup abs 1 gt { EQDFasinrangeerror  } if
   dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
} def
%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
%% x -> theta
/acos {%
   dup abs 1 gt { EQDFacosrangeerror  } if
   dup dup mul 1 exch sub sqrt exch atan DegtoRad
} def
%% function arctangent in radians
%% x -> theta
/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
%% HYPERBOLIC FUNCTIONS
/sh { dup Ex exch neg Ex sub 2 div } def
/ch { dup Ex exch neg Ex add 2 div } def
/th { dup sh exch ch div } def
/Argsh { dup dup mul 1 add sqrt add ln } def
/Argch { dup dup mul 1 sub sqrt add ln } def
/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
%% modified exponential funtion for 0
%% x n -> x^n
/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
%% modified exponential funtion for 0
%% x -> e^x
/Ex { Euler exch exp } bind def
%%
%% factorial function
%% n -> n!
/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
/fact { Fact } bind def
/! { Fact } bind def
end
%
% END pst-algparser.pro

%%EndProcSet
%%BeginProcSet: pst-tools.pro 0 0
% $Id: pst-tools.pro 842 2013-10-26 10:25:41Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.04, 2013/10/26
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
/Pi2 1.57079632679489661925640 def
/factorial { % n on stack, returns n!
   dup 0 eq { 1 }{
     dup 1 gt { dup 1 sub factorial mul } if }
   ifelse } def 
%
/MoverN { % m n on stack, returns the binomial coefficient m over n
   2 dict begin
   /n exch def /m exch def
   n 0 eq { 1 }{
     m n eq { 1 }{
       m factorial n factorial m n sub factorial mul div } ifelse } ifelse
   end
} def
%
/ps@ReverseOrderOfPoints { % on stack [P1 P2 P3 ...Pn]=>[Pn,Pn-1,...,P2,P1]
   5 dict begin       % all local
   aload length /n ED % number of coors
   n 2 div cvi /m ED  % number of Points
   /n1 n def
   m { n1 2 roll /n1 n1 2 sub def } repeat
   n array astore
   end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% subroutines for complex numbers, given as an array [a b] 
% which is a+bi = Real+i Imag
%
/cxadd {		% [a1 b1] [a2 b2] = [a1+a2 b1+b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   3 -1 roll		% [a2 b2] a2 [a1 b1]
   dup 0 get		% [a2 b2] a2 [a1 b1] a1
   3 -1 roll		% [a2 b2] [a1 b1] a1 a2
   add			% [a2 b2] [a1 b1] a1+a2
   3 1 roll		% a1+a2 [a2 b2] [a1 b1]
   1 get			% a1+a2 [a2 b2] b1
   exch 1 get		% a1+a2 b1 b2
   add 2 array astore
} def
%
/cxneg {		% [a b]
   dup 1 get		% [a b] b
   exch 0 get		% b a
   neg exch neg		% -a -b
   2 array astore
} def
%
/cxsub { cxneg cxadd } def  % same as negative addition
%
% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
/cxmul {		% [a1 b1] [a2 b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   exch 1 get		% [a1 b1] a2 b2
   3 -1 roll		% a2 b2 [a1 b1]
   dup 0 get		% a2 b2 [a1 b1] a1
   exch 1 get		% a2 b2 a1 b1
   dup			% a2 b2 a1 b1 b1
   5 -1 roll dup		% b2 a1 b1 b1 a2 a2
   3 1 roll mul		% b2 a1 b1 a2 b1a2
   5 -2 roll dup		% b1 a2 b1a2 b2 a1 a1
   3 -1 roll dup		% b1 a2 b1a2 a1 a1 b2 b2
   3 1 roll mul		% b1 a2 b1a2 a1 b2 a1b2
   4 -1 roll add		% b1 a2 a1 b2 b3
   4 2 roll mul		% b1 b2 b3 a1a2
   4 2 roll mul sub	% b3 a3
   exch 2 array astore
} def
%
% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
/cxsqr {		% [a b]   square root
   dup 0 get exch 1 get	% a b
   dup dup mul		% a b b^2
   3 -1 roll		% b b^2 a
   dup dup mul 		% b b^2 a a^2
   3 -1 roll sub		% b a a2
   3 1 roll mul 2 mul	% a2 b2
   2 array astore
} def
%
/cxsqrt {		% [a b]
%  dup cxnorm sqrt /r exch def
%  cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
   cxlog 		% log[a b]
   2 cxrdiv 		% log[a b]/2
   aload pop exch	% b a
   2.781 exch exp	% b exp(a)
   exch cxconv exch	% [Re +iIm] exp(a)
   cxrmul		%
} def
%
/cxarg { 		% [a b]
   aload pop 		% a b
   exch atan 		% arctan b/a
   DegtoRad 		% arg(z)=atan(b/a)
} def
%
% log[a b] = [a^2-b^2 2ab] = [a2 b2]
/cxlog {		% [a b]
   dup 			% [a b][a b]
   cxnorm 		% [a b] |z|
   log 			% [a b] log|z|
   exch 			% log|z|[a b]
   cxarg 		% log|z| Theta
   cxmake2 		% [log|z| Theta]
} def
%
% square of magnitude of complex number
/cxnorm2 {		% [a b]
   dup 0 get exch 1 get	% a b
   dup mul			% a b^2
   exch dup mul add	% a^2+b^2
} def
%
/cxnorm {		% [a b]
   cxnorm2 sqrt
} def
%
/cxconj {		% conjugent complex
   dup 0 get exch 1 get	% a b
   neg 2 array astore	% [a -b]
} def
%
/cxre { 0 get } def	% real value
/cxim { 1 get } def	% imag value
%
% 1/[a b] = ([a -b]/(a^2+b^2)
/cxrecip {		% [a b]
   dup cxnorm2 exch	% n2 [a b]
   dup 0 get exch 1 get	% n2 a b
   3 -1 roll		% a b n2
   dup			% a b n2 n2
   4 -1 roll exch div	% b n2 a/n2
   3 1 roll div		% a/n2 b/n2
   neg 2 array astore
} def
%
/cxmake1 { 0 2 array astore } def % make a complex number, real given
/cxmake2 { 2 array astore } def	  % dito, both given
%
/cxdiv { cxrecip cxmul } def
%
% multiplikation by a real number
/cxrmul {		% [a b] r
   exch aload pop	% r a b
   3 -1 roll dup		% a b r r
   3 1 roll mul		% a r b*r
   3 1 roll mul		% b*r a*r
   exch 2 array astore   % [a*r b*r]
} def
%
% division by a real number
/cxrdiv {		% [a b] r
   1 exch div		% [a b] 1/r
   cxrmul
} def
%
% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
/cxconv {		% theta
   RadtoDeg dup sin exch cos cxmake2
} def

%%%%% ### bubblesort ###
%% syntax : array bubblesort --> array2 trie par ordre croissant
%% code de Bill Casselman
%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
/bubblesort { % on stack must be an array [ ... ]
4 dict begin
    /a exch def
    /n a length 1 sub def
    n 0 gt {
       % at this point only the n+1 items in the bottom of a remain to
       % the sorted largest item in that blocks is to be moved up into
       % position n
       n {
          0 1 n 1 sub {
             /i exch def
             a i get a i 1 add get gt {
                % if a[i] > a[i+1] swap a[i] and a[i+1]
                a i 1 add
                a i get
                a i a i 1 add get
                % set new a[i] = old a[i+1]
                put
                % set new a[i+1] = old a[i]
                put
             } if
          } for
          /n n 1 sub def
       } repeat
    } if
    a % return the sorted array
end
} def
%
/concatstringarray{  %  [(a) (b) ... (z)] --> (ab...z)  20100422
   0 1 index { length add } forall
   string
   0 3 2 roll
   { 3 copy putinterval length add }forall
   pop 
} bind def
%
/dot2comma {% on stack a string (...)
   2 dict begin
   /Output exch def
   0 1 Output length 1 sub {
     /Index exch def
     Output Index get 46 eq { Output Index 44 put } if
   } for
   Output
   end
} def
%
/rightTrim { % on stack the string and the character number to be stripped
   /charNo exch def
   dup
   length 1 sub -1 0 {
     /i exch def dup i get charNo ne { exit } if
   } for
   0 i 1 add getinterval
   dup length string copy
} bind def  % leaves the stripped string on the stack

/psStringwidth /stringwidth load def
/psShow /show load def

%/stringwidth{ 32 rightTrim psStringwidth } bind def

%/show { 32 rightTrim psShow } bind def
%-----------------------------------------------------------------------------%

/pgffunctions {
     /pgfsc{}bind def% stroke color is empty by default
     /pgffc{}bind def% fill color is empty by default
     /pgfstr{stroke}bind def%
     /pgffill{fill}bind def%
     /pgfeofill{eofill}bind def%
     /pgfe{a dup 0 rlineto exch 0 exch rlineto neg 0 rlineto closepath}bind def% rectangle
     /pgfw{setlinewidth}bind def% setlinewidth
     /pgfs{save pgfpd 72 Resolution div 72 VResolution div neg scale
       magscale{1 DVImag div dup scale}if
       pgfx neg pgfy neg translate pgffoa .setopacityalpha}bind def% save
     /pgfr{pgfsd restore}bind def %restore
     userdict begin%
     /pgfo{pgfsd /pgfx currentpoint /pgfy exch def def @beginspecial}bind def %open
     /pgfc{newpath @endspecial pgfpd}bind def %close
     /pgfsd{globaldict /pgfdelta /delta where {pop delta} {0} ifelse put}bind def% save delta
     /pgfpd{/delta globaldict /pgfdelta get def}bind def % put delta
     /.setopacityalpha where {pop} {/.setopacityalpha{pop}def} ifelse % install .setopacityalpha
     /.pgfsetfillopacityalpha{/pgffoa exch def
       /pgffill{gsave pgffoa .setopacityalpha fill 1 .setopacityalpha newpath fill grestore newpath}bind def
       /pgfeofill{gsave pgffoa .setopacityalpha eofill 1 .setopacityalpha newpath eofill grestore newpath}bind def}bind def
     /.pgfsetstrokeopacityalpha{/pgfsoa exch def /pgfstr{gsave pgfsoa .setopacityalpha stroke grestore newpath}bind def}bind def
     /pgffoa 1 def
     /pgfsoa 1 def
     end
} def
%-----------------------------------------------------------------------------%
% END pst-tools.pro

%%EndProcSet
%%BeginProcSet: pst-dots.pro 0 0
% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02,  2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt <tvz@Princeton.EDU>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga  - Dec. 16, 1999
%% Modified by Etienne Riga  - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17 
%
10 dict dup begin			% hold local
   /FontType 3 def
   /FontMatrix [.001 0 0 .001 0 0] def
%  /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
   /FontBBox [-1000 -1000 1000 1000] def  % See end of file in /BuildGlyph
   /Encoding 256 array def
   0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
   Encoding				   % replace with given dot names
     dup (b) 0 get /Bullet put		   % get the numerical position of b in ASCII
%					   % and save /Bullet at this place in Encoding
     dup (c) 0 get /Circle put
     dup (C) 0 get /BoldCircle put	% 67
     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
%%%
     dup (k) 0 get /Asterisk put
     dup (K) 0 get /BoldAsterisk put
     dup (J) 0 get /SolidAsterisk put
     dup (h) 0 get /Hexagon put
     dup (H) 0 get /BoldHexagon put
     dup (G) 0 get /SolidHexagon put
     dup (f) 0 get /Octogon put		% 2008-04-18 hv
     dup (F) 0 get /BoldOctogon put	% 2008-04-18 hv
     dup (g) 0 get /SolidOctogon put	% 2008-04-18 hv
     dup (a) 0 get /Add put
     dup (A) 0 get /BoldAdd put 		% 65
     dup (x) 0 get /Mul put
     dup (X) 0 get /BoldMul put
     dup (m) 0 get /Oplus put
     dup (M) 0 get /BOplus put
     dup (e) 0 get /SolidOplus put
     dup (n) 0 get /Otimes put
     dup (N) 0 get /BOtimes put
     dup (E) 0 get /SolidOtimes put
     dup (i) 0 get /Bar put
     dup (I) 0 get /BoldBar put
     dup (l) 0 get /SolidDiamond put
     dup (d) 0 get /Diamond put
         (D) 0 get /BoldDiamond put
%%% 
/CharProcs 47 dict def
CharProcs begin
   /CirclePath {0 0 500 0 360 arc closepath} def
   /Bullet {CirclePath fill} def
   /Circle {CirclePath .9 .9 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
%-------------- hv begin 2004/07/25   from: er 2003/03/24
   /HexagonPath {
     0 550 moveto -476 275 lineto -476 -275 lineto
     0 -550 lineto 476 -275 lineto 476 275 lineto closepath
   } def
   /SolidHexagon {HexagonPath fill} def
   /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
   /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
%					2008-04-18 hv
   /OctogonPath {
      550 dup 22.5 tan mul dup neg dup add /xMove exch def
      exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
   /SolidOctogon { OctogonPath fill                             } def
   /Octogon {      OctogonPath .89 .89 scale OctogonPath eofill } def
   /BoldOctogon {  OctogonPath .79 .79 scale OctogonPath eofill } def
%
   /AsteriskPath {
     20 0 moveto 10 250 180 500 0 500 curveto
     -180 500 -10 250 -20 0 curveto closepath
   } def
   /Asterisk {
     AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
     60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
   } def
%
   /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
   /BoldAsteriskPath {
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%      BBoxes 3 index get exec
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%     -571.5 -742.5 571.5 742.5
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%%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      = "27nov06",
%   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
%
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% 0x00
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  /ogonek /ring /.notdef /breve
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% 0x10
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  /lessequal /greaterequal /partialdiff /summation
  /product /pi /grave /quotesingle
% 0x20
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  /parenleft /parenright /asterisk /plus
  /comma /hyphen /period /slash
% 0x30
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  /four /five /six /seven
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% 0x40
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% 0x50
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  /T /U /V /W
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% 0x60
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% 0x70
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  /x /y /z /braceleft
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% 0x80
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  /quotedblbase /ellipsis /dagger /daggerdbl
  /circumflex /perthousand /Scaron /guilsinglleft
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% 0x90
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  /quotedblright /bullet /endash /emdash
  /tilde /trademark /scaron /guilsinglright
  /oe /Delta /lozenge /Ydieresis
% 0xA0
  /.notdef /exclamdown /cent /sterling
  /currency /yen /brokenbar /section
  /dieresis /copyright /ordfeminine /guillemotleft
  /logicalnot /hyphen /registered /macron
% 0xB0
  /degree /plusminus /twosuperior /threesuperior
  /acute /mu /paragraph /periodcentered
  /cedilla /onesuperior /ordmasculine /guillemotright
  /onequarter /onehalf /threequarters /questiondown
% 0xC0
  /Agrave /Aacute /Acircumflex /Atilde
  /Adieresis /Aring /AE /Ccedilla
  /Egrave /Eacute /Ecircumflex /Edieresis
  /Igrave /Iacute /Icircumflex /Idieresis
% 0xD0
  /Eth /Ntilde /Ograve /Oacute
  /Ocircumflex /Otilde /Odieresis /multiply
  /Oslash /Ugrave /Uacute /Ucircumflex
  /Udieresis /Yacute /Thorn /germandbls
% 0xE0
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  /adieresis /aring /ae /ccedilla
  /egrave /eacute /ecircumflex /edieresis
  /igrave /iacute /icircumflex /idieresis
% 0xF0
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cleartomark
%%EndFont 
%%BeginFont: rtxsc
%!PS-AdobeFont-1.0: rtxsc 3.0a
%%CreationDate: 03/26/2008 at 12:00 PM
%%VMusage: 1024 16650
20 dict begin
/FontInfo 16 dict dup begin
/version (3.0a) readonly def
/FullName (rtxsc) readonly def
/FamilyName (rtxsc) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 3.0a, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /rtxsc def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 97 /a put
dup 98 /b put
dup 104 /h put
dup 107 /k put
dup 109 /m put
dup 116 /t put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-35 -163 750 681}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: rtxi
%!PS-AdobeFont-1.0: rtxi 3.0
%%CreationDate: 12/14/2000 at 12:00 PM
%%VMusage: 1024 12681
20 dict begin
/FontInfo 16 dict dup begin
/version (3.0) readonly def
/FullName (rtxi) readonly def
/FamilyName (rtxi) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 3.0, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /rtxi def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /ff put
dup 14 /ffi put
dup 38 /ampersand put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-141 -207 808 682}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: NimbusRomNo9L-ReguItal
%!PS-AdobeFont-1.0: NimbusRomNo9L-ReguItal 1.05
%%CreationDate: Wed Dec 22 1999
% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% (URW)++,Copyright 1999 by (URW)++ Design & Development
% See the file COPYING (GNU General Public License) for license conditions.
% As a special exception, permission is granted to include this font
% program in a Postscript or PDF file that consists of a document that
% contains text to be displayed or printed using this font, regardless
% of the conditions or license applying to the document itself.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.05) readonly def
/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def
/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def
/FullName (Nimbus Roman No9 L Regular Italic) readonly def
/FamilyName (Nimbus Roman No9 L) readonly def
/Weight (Regular) readonly def
/ItalicAngle -15.5 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/FontName /NimbusRomNo9L-ReguItal def
/PaintType 0 def
/WMode 0 def
/FontBBox {-169 -270 1010 924} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding StandardEncoding def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: txsyb
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%%CreationDate: 12/14/2000 at 12:00 PM
%%VMusage: 1024 28332
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/FontInfo 16 dict dup begin
/version (3.0) readonly def
/FullName (txsyb) readonly def
/FamilyName (txsyb) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 3.0, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /txsyb def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 90 /Z put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-45 -187 2238 794}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: rtxmi
%!PS-AdobeFont-1.0: rtxmi 3.1
%%CreationDate: 12/15/2000 at 12:00 PM
%%VMusage: 1024 18707
20 dict begin
/FontInfo 16 dict dup begin
/version (3.1) readonly def
/FullName (rtxmi) readonly def
/FamilyName (rtxmi) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 3.1, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /rtxmi def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 17 /eta put
dup 20 /kappa put
dup 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 24 /xi put
dup 25 /pi put
dup 27 /sigma put
dup 28 /tau put
dup 33 /omega put
dup 34 /epsilon put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 64 /partialdiff put
dup 96 /lscript put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-124 -214 902 762}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: txsyc
%!PS-AdobeFont-1.0: txsyc 3.0
%%CreationDate: 12/14/2000 at 12:00 PM
%%VMusage: 1024 31202
20 dict begin
/FontInfo 16 dict dup begin
/version (3.0) readonly def
/FullName (txsyc) readonly def
/FamilyName (txsyc) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 3.0, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /txsyc def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 27 /simequal put
dup 44 /nequal put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-170 -330 1336 843}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: NimbusRomNo9L-Regu
%!PS-AdobeFont-1.0: NimbusRomNo9L-Regu 1.05
%%CreationDate: Wed Dec 22 1999
% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% (URW)++,Copyright 1999 by (URW)++ Design & Development
% See the file COPYING (GNU General Public License) for license conditions.
% As a special exception, permission is granted to include this font
% program in a Postscript or PDF file that consists of a document that
% contains text to be displayed or printed using this font, regardless
% of the conditions or license applying to the document itself.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.05) readonly def
/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def
/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def
/FullName (Nimbus Roman No9 L Regular) readonly def
/FamilyName (Nimbus Roman No9 L) readonly def
/Weight (Regular) readonly def
/ItalicAngle 0.0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/FontName /NimbusRomNo9L-Regu def
/PaintType 0 def
/WMode 0 def
/FontBBox {-168 -281 1000 924} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding StandardEncoding def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: txsy
%!PS-AdobeFont-1.0: txsy 3.0
%%CreationDate: 12/14/2000 at 12:00 PM
%%VMusage: 1024 24296
20 dict begin
/FontInfo 16 dict dup begin
/version (3.0) readonly def
/FullName (txsy) readonly def
/FamilyName (txsy) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 3.0, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /txsy def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 1 /periodcentered put
dup 2 /multiply put
dup 3 /asteriskmath put
dup 6 /plusminus put
dup 14 /openbullet put
dup 18 /reflexsubset put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 24 /similar put
dup 28 /lessmuch put
dup 29 /greatermuch put
dup 33 /arrowright put
dup 35 /arrowdown put
dup 48 /prime put
dup 49 /infinity put
dup 50 /element put
dup 55 /mapsto put
dup 70 /F put
dup 78 /N put
dup 81 /Q put
dup 92 /intersection put
dup 94 /logicaland 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 112 /radical put
dup 120 /section put
dup 121 /dagger put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-22 -944 1227 866}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: txex
%!PS-AdobeFont-1.0: txex 3.0
%%CreationDate: 12/14/2000 at 12:00 PM
%%VMusage: 1024 21483
20 dict begin
/FontInfo 16 dict dup begin
/version (3.0) readonly def
/FullName (txex) readonly def
/FamilyName (txex) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 3.0, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /txex def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /parenleftbig put
dup 1 /parenrightbig put
dup 56 /bracelefttp put
dup 58 /braceleftbt put
dup 60 /braceleftmid put
dup 62 /braceex put
dup 80 /summationtext put
dup 88 /summationdisplay put
dup 90 /integraldisplay put
dup 112 /radicalbig put
dup 113 /radicalBig put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-5 -2960 1609 752}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: NimbusRomNo9L-Medi
%!PS-AdobeFont-1.0: NimbusRomNo9L-Medi 1.05
%%CreationDate: Wed Dec 22 1999
% Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development
% (URW)++,Copyright 1999 by (URW)++ Design & Development
% See the file COPYING (GNU General Public License) for license conditions.
% As a special exception, permission is granted to include this font
% program in a Postscript or PDF file that consists of a document that
% contains text to be displayed or printed using this font, regardless
% of the conditions or license applying to the document itself.
12 dict begin
/FontInfo 10 dict dup begin
/version (1.05) readonly def
/Notice ((URW)++,Copyright 1999 by (URW)++ Design & Development. See the file COPYING (GNU General Public License) for license conditions. As a special exception, permission is granted to include this font program in a Postscript or PDF file that consists of a document that contains text to be displayed or printed using this font, regardless of the conditions or license applying to the document itself.) readonly def
/Copyright (Copyright (URW)++,Copyright 1999 by (URW)++ Design & Development) readonly def
/FullName (Nimbus Roman No9 L Medium) readonly def
/FamilyName (Nimbus Roman No9 L) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0.0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/FontName /NimbusRomNo9L-Medi def
/PaintType 0 def
/WMode 0 def
/FontBBox {-168 -341 1000 960} readonly def
/FontType 1 def
/FontMatrix [0.001 0.0 0.0 0.001 0.0 0.0] readonly def
/Encoding StandardEncoding def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: rtxr
%!PS-AdobeFont-1.0: rtxr 3.0
%%CreationDate: 12/14/2000 at 12:00 PM
%%VMusage: 1024 12232
20 dict begin
/FontInfo 16 dict dup begin
/version (3.0) readonly def
/FullName (rtxr) readonly def
/FamilyName (rtxr) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/Notice (Version 3.0, GPL) readonly def
/em 1000 def
/ascent 800 def
/descent 200 def
end readonly def
/FontName /rtxr def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 3 /Lambda put
dup 5 /Pi put
dup 8 /Phi put
dup 10 /Omega put
dup 11 /ff put
dup 14 /ffi put
dup 43 /plus put
dup 47 /slash put
dup 61 /equal put
readonly def
/PaintType 0 def
/FontType 1 def
/StrokeWidth 0 def
/FontMatrix[0.001 0 0 0.001 0 0]readonly def
/FontBBox{-70 -218 792 683}readonly def
currentdict end
currentfile eexec
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/getrepl islev2 {{ globaldict /PSfrags get aload length }}
                 {{ PSfrags aload length }} ifelse B
/convert {
    /src X src length string
    /c 0 def src length {
       dup c src c get dup 32 lt { pop 32 } if put /c c 1 add def
    } repeat
} B
/Begin {
     /saver save def
     srcFM exch 3 exch put
     0 ne /debugMode X 0 setrepl
     dup /S exch dict def { S 3 1 roll exch convert exch put } repeat
     srcM CM dup invertmatrix pop
     mark { currentdict { end } stopped { pop exit } if } loop
     PSfragDict counttomark { begin } repeat pop
} B
/End {
     mark { currentdict end dup PSfragDict eq { pop exit } if } loop
     counttomark { begin } repeat pop
     getrepl saver restore
     7 idiv dup /S exch dict def {
         6 array astore /mtrx X tstr cvs /K X
         S K [ S K known { S K get aload pop } if mtrx ] put
     } repeat
} B
/Place {
     tstr cvs /K X
     S K known {
         bind /proc X tM CM pop
         CP /cY X /cX X
         0 0 transform idtransform neg /aY X neg /aX X
         S K get dup length /maxiter X
         /iter 1 def {
             iter maxiter ne { /saver save def } if
             tM setmatrix aX aY translate
             [ exch aload pop idtransform ] concat
             cX neg cY neg translate cX cY moveto
             /proc load OE
             iter maxiter ne { saver restore /iter iter 1 add def } if
         } forall
         /noXY { CP /cY X /cX X } stopped def
         tM setmatrix noXY { newpath } { cX cY moveto } ifelse
     } {
         Hide OE Unhide
     } ifelse
} B
/normalize {
     2 index dup mul 2 index dup mul add sqrt div
     dup 4 -1 roll exch mul 3 1 roll mul
} B
/replace {
     aload pop MD
     CP /bY X /lX X gsave sM setmatrix
     str stringwidth abs exch abs add dup 0 eq
         { pop } { 360 exch div dup scale } ifelse
     lX neg bY neg translate newpath lX bY moveto
     str { /ch X ( ) dup 0 ch put false charpath ch Kproc } forall
     flattenpath pathbbox [ /uY /uX /lY /lX ] MD
     CP grestore moveto
     currentfont /FontMatrix get dstFM copy dup
     0 get 0 lt { uX lX /uX X /lX X } if
     3 get 0 lt { uY lY /uY X /lY X } if
     /cX uX lX add 0.5 mul def
     /cY uY lY add 0.5 mul def
     debugMode { gsave 0 setgray 1 setlinewidth
         lX lY moveto lX uY lineto uX uY lineto uX lY lineto closepath
         lX bY moveto uX bY lineto lX cY moveto uX cY lineto
         cX lY moveto cX uY lineto stroke
     grestore } if
     dstFM dup invertmatrix dstM CM srcM
     2 { dstM concatmatrix } repeat pop
     getrepl /temp X
         S str convert get {
             aload pop [ /rot /scl /loc /K ] MD
             /aX cX def /aY cY def
             loc {
                 dup 66  eq { /aY bY def } { % B
                 dup 98  eq { /aY lY def } { % b
                 dup 108 eq { /aX lX def } { % l
                 dup 114 eq { /aX uX def } { % r
                 dup 116 eq { /aY uY def }   % t
                 if } ifelse } ifelse } ifelse } ifelse pop
             } forall
             K srcFM rot tM rotate dstM
             2 { tM concatmatrix } repeat aload pop pop pop
             2 { scl normalize 4 2 roll } repeat
             aX aY transform
             /temp temp 7 add def
         } forall
     temp setrepl
} B
/Rif {
     S 3 index convert known { pop replace } { exch pop OE } ifelse
} B
/XA { bind [ /Kproc /str } B /XC { ] 2 array astore def } B
/xs   { pop } XA XC
/xks  { /kern load OE } XA /kern XC
/xas  { pop ax ay rmoveto } XA /ay /ax XC
/xws  { c eq { cx cy rmoveto } if } XA /c /cy /cx XC
/xaws { ax ay rmoveto c eq { cx cy rmoveto } if }
     XA /ay /ax /c /cy /cx XC
/raws { xaws { awidthshow } Rif } B
/rws  { xws { widthshow } Rif } B
/rks  { xks { kshow } Rif } B
/ras  { xas { ashow } Rif } B
/rs   { xs { show } Rif } B
/rrs { getrepl dup 2 add -1 roll //restore exec setrepl } B
PSfragDict begin
islev2 not { /restore { /rrs PSfrag } B } if
/show       { /rs   PSfrag } B
/kshow      { /rks  PSfrag } B
/ashow      { /ras  PSfrag } B
/widthshow  { /rws  PSfrag } B
/awidthshow { /raws PSfrag } B
end PSfragDict RO pop
end

%%EndProcSet
%%BeginProcSet: pstricks.pro 0 0
% $Id: pstricks.pro 902 2014-03-30 16:23:33Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 1.22, 2014/02/20
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
% Define the follwing gs-functions if not known, eg when using distiller
%
systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if
systemdict /.setblendmode known not {/.setblendmode { pop } def } if
systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if
%
/tx@Dict 200 dict def 				% the main PSTricks dictionary
tx@Dict begin
/ADict 25 dict def				% The arrow dictionary
/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
/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def  % return 0 for negative arguments 
/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known
/ATAN1 {neg -1 atan 180 sub } def		% atan(x) (only one parameter)
/Div { dup 0 eq { pop } { div } ifelse } def  	% control the division
/Log { dup 1e-20 lt { pop -1e30 }{ log } ifelse } def % control the log
/tan { dup cos abs 1.e-10 lt
   { pop 1.e10 } 				% return 1.e10 as infinit
   { dup sin exch cos div } ifelse 		% default sin/cos
} def
/Tan { dup sin exch cos Div } def 		% sin(x)/cos(x) x in degrees
/Acos {dup dup mul neg 1 add dup 0 lt {		% arc cos, returns 0 when negative root
   pop pop 0 }{ sqrt exch atan} ifelse } def
/Acos2 { 2 dict begin
   /x ED /y ED
   y abs 1.0e-20 lt { 1.0e30 } if
   x y div
   dup dup mul neg 1 add dup 0 lt {		% arc cos needs two values x,y
   pop pop 0 }{ sqrt exch atan} ifelse
   y 0 lt { 180 add } if
} def
/NET { neg exch neg exch T } def	      	% change coordinate system to the negative one 
/Pyth { dup mul exch dup mul add sqrt } def   	% Pythagoras, expects 2 parameter
/Pyth2 {					% Pythagoras, xA yA xB yB
   3 -1 roll 		% xA xB yB yA
   sub			% xA xB yB-yA
   3 1 roll 		% yB-yA xA xB
   sub			% yB-yA xA-xB
   Pyth } def
/PtoC { 2 copy cos mul 3 1 roll sin mul } def 	% Polar to Cartesian
%/Rand { rand 4294967295 div } def		% a real random number
/Rand { rand 2147483447 div } def		% a real random number between 0 and 1
%----------------- hv added 20050516 ---------------
/PiDiv2 1.57079632680 def
/Pi 3.14159265359 def 
/TwoPi 6.28318530718 def
/Euler 2.71828182846 def 
%/e Euler bind def
%
/RadtoDeg { 180 mul Pi div } bind def 		% convert from radian to degrees
/DegtoRad { Pi mul 180 div } bind def 		% viceversa
%
/startGlobal { true setglobal globaldict begin } bind def
/endGlobal { end false setglobal } bind def
/pssetRGBcolor /setrgbcolor load def
/pssetCMYKcolor /setcmykcolor load def
/pssetGraycolor /setgray load def
%
%----------------- hv end---------------------------
/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			% BP/PT scaling
/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 % pattern should fit evenly in b
     dup /X ED % pattern array
     0 get /y ED % length of first black segment
     /z 0 X {add} forall def % length of the full pattern
     %% Computation of the scaling factor as described by van Zandt:
     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
     %%%% scaling factor on stack.
     /z ED %% now, z is the scaling factor
     false % for the length test below
     X { z mul } forall X astore %% modification TN 04-08-07
     %%% Checking whether at least one dash in X has positive length:
     {0 gt or} forall
     { 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
%
/SymbolLine {   % on stack [ x y x y ...
   counttomark 					% number of elements
   2 div cvi /n ED     				% n pairs
   /YA ED /XA ED					% the start point
   n 1 sub {
     /YB ED /XB ED
     /XLength XB XA sub def
     /YLength YB YA sub def
     /PAngle YLength XLength Atan def
     /XYLength XLength YLength Pyth def
     %% for negative SymStep we calculate the distance
     SymStep 0 lt
       { %XYLength SymStep div abs cvi
         /nSym SymStep abs cvi def }
       { /nSym XYLength SymStep div cvi def }
     ifelse
     0.5 setflat
     /Shift Symbol stringwidth pop 2 div def
     /deltaX XLength nSym div def
     /deltaY YLength nSym div def
     curveticks
       { XA YA moveto }
       { XA Shift sub YA Shift sub moveto }
     ifelse
     nSym {
       gsave
       curveticks
         { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
           currentpoint translate rotAngle rotate
           0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
           SymbolLinewidth setlinewidth stroke
         }
         {
           rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
           Symbol show
         }
       ifelse
       grestore
       deltaX deltaY rmoveto
     } repeat
     /YA YB def /XA XB def
   } repeat
   curveticks
     { XA YA moveto }
     { XA Shift sub YA Shift sub moveto }
   ifelse
   gsave
   curveticks
     { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
       XA YA translate rotAngle rotate
       0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
       SymbolLinewidth setlinewidth stroke
     }
     {
       rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
       Symbol show
     }
   ifelse
   grestore
   pop 				% delete the mark symbol
} def
%
/LineFill { % hv ------------ patch 7 -------------
   gsave
   abs /hatchWidthInc ED
   abs /hatchSepInc ED
   abs CLW add /a ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform pathbbox
   /y2 ED
   a Div ceiling cvi /x2 ED /y1 ED
   a Div cvi /x1 ED /y2 y2 y1 sub def
   clipType   % must be defined in pstricks.tex: clip -- eoclip
   newpath
   2 setlinecap
   systemdict
   /setstrokeadjust known { true setstrokeadjust } if
   x2 x1 sub 1 add {
     x1 a mul y1 moveto 0 y2 rlineto stroke
     /x1 x1 1 add
       hatchWidthInc 0 gt { CLW add } if
     def
     hatchSepInc 0 gt hatchWidthInc 0 gt or {
       /a a hatchSepInc add def
       CLW hatchWidthInc add SLW
     } if
   } repeat
   grestore
   pop pop } def
%
/DotFill {%	 on stack: dot radius
   /dotRadius ED
   abs CLW add /a ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform
   pathbbox % llx lly urx ury of smallest bounding box
   /y2 ED /x2 ED /y1 ED /x1 ED
   y2 y1 sub a div 2 add cvi /Ny ED
   x2 x1 sub a div 2 add cvi /Nx ED
   clipType   % must be defined in pstricks.tex: clip -- eoclip
   newpath
   /yA y1 dotRadius add CLW add def
   /xA0 x1 dotRadius add CLW add def
   Ny {
      /xA xA0 def
      Nx {
        newpath
        xA yA dotRadius 0 360 arc
        SolidDot { gsave fill grestore } if
        stroke
        xA a add /xA ED
      } repeat
      yA a add /yA ED
   } repeat
   grestore
} def
%
/PenroseFill {%	 on stack: scaling factor
   /Scale ED
%  1 exch div round /penroseFactor ED 
%  a 0 dtransform round exch round exch
%  2 copy idtransform 
%  exch Atan rotate 
%  idtransform pop /a ED 
%  .25 .25 itransform pathbbox 
%  /y2 ED 
%  a Div ceiling cvi /x2 ED /y1 ED 
%  a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath 
gsave
   220 150 translate
   Scale dup scale
   systemdict /setstrokeadjust known { true setstrokeadjust } if
   /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
  { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
   [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
   i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
   mul j l + S rmoveto}F i L j L stroke }F}F}F}F
   grestore 
%  pop pop 
} def
%
/PenroseFillA {%  on stack: scaling factor, border color, kite color, dart color
   /Scale ED
   Scale dup scale
   /border_colour ED
   /kite_colour ED
   /dart_colour ED
   clip
   newpath
   gsave
   100 100 translate
   6
   Scale 1 lt { 1 Scale dup add div mul cvi } if %%%%   Number of iterations
   10					%%%%   Long side length in millimeters
   /border_width { L 0.06 mul }def		%%%%   Choose the scalefactor for the borders
   /L exch 25.4 div 72 mul def		%%%%   Conversion: mm -> inches -> points
   /f{-1 5 sqrt add 2 div}bind def		%%%%   The reciprocal of the golden ratio
   /l{L f mul}bind def			%%%%   Short side length l = L*f
   /Ll{L l add}bind def			%%%%   Ll =  L + l
   /c{36 cos L mul}bind def		%%%%   c  =  L*cos(36)
   /s{36 sin L mul}bind def		%%%%   s  =  L*sin(36)
   /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
 	     0 setlinewidth stroke grestore border_colour stroke } bind def
   /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
 			   Ll 0 translate 144 rotate kite grestore }
 	      		 { kite_colour L draw_tile }ifelse
 	     pop } bind def
   /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
 			   -144 rotate Ll neg 0 translate half_dart grestore }
 	      		 { dart_colour l draw_tile }ifelse
   	     pop } bind def
   /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
   border_width setlinewidth  1 setlinejoin  1 setlinecap
%  450 0 translate
   dup f exch neg exp dup scale
   5 {kite 72 rotate } repeat stroke
   grestore
} def
%
%
/TruchetFill { %	 on stack: scaling factor
   10 dict begin
   dup dup scale
   1 exch div round /penroseFactor ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform pathbbox
   /y2 ED
   a Div ceiling cvi /x2 ED /y1 ED
   a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath
   systemdict
   /setstrokeadjust known { true setstrokeadjust } if
   /ma a neg def
   /ha a 2 div def
   /mha ha neg def
   /tile {
     rand dup 2 idiv 2 mul eq { 90 rotate } if
     mha mha moveto ha mha lineto
     ha ha lineto mha ha lineto
%    closepath .1 setlinewidth stroke
     contents
   } def
   /contents{
     0 ha moveto ha 0 lineto
     0 mha moveto mha 0 lineto
%    1 setlinewidth stroke
   } def
   /dotiling {
     f ma mul a f a mul {
       /i exch def
       f ma mul a f a mul {
         /j exch def
         gsave i j translate
         tile stroke grestore
       } for
     } for
   } def
%
   /f 3 def
   5 srand dotiling
   end % local user dict
} def
%
/BeginArrow {
   ADict begin 			% hold it local, for end see EndArrow
   /@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 % end the ADict
%
/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
%
/ArrowD { % the sides are drawn as curves (hv 20071211)
   CLW mul add dup
   2 div /w ED
   mul dup /h ED
   mul /Inset ED
   { 0 h T 1 -1 scale } if % changes the direction
% we use y=w/h^2 * x^2 as equation for the control points
% for the coordinates the arrow is seen from top to bottom
% the bottom (tip) is (0;0)
   w neg h moveto % lower left of >
   w 9 div 4 mul neg h 3 div 2 mul
   w 9 div neg       h 3 div
   0 0 curveto    % tip of >
   w 9 div        h 3 div
   w 9 div 4 mul  h 3 div 2 mul
   w h curveto % upper left of >
   w neg Inset neg rlineto % move to x=0 and inset
   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 { % DS is the dot size
   { /z DS def } { /z 0 def } ifelse  	% outer or inner dimen
   /b ED 				% the color definition
   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 { % holds the coordinates and on top of stack the showpoints boolean
   /showpoints ED
   counttomark 2 div dup cvi /n ED  	% n 2 div on stack
   n eq not { exch pop } if		% even numbers of points? delete one
   ] aload /Points ED
   showpoints not { Points aload pop } if
%    { ] aload /Points ED } 
%    { n 2 mul 1 add -1 roll pop } ifelse	% delete the mark symbol 
} 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
%
/LineToYAxis {
   /Ox ED		% Save the x origin value
   NArray            % all x-y pairs on stack
   n { 2 copy moveto % go to current point
     Ox exch Lineto   % line to y-axis
     pop             % delete old x-value
   } repeat
} def
%
/LineToXAxis{
   /Oy ED		% Save the y origin value
   NArray		% all x-y pairs on stack
   n 0 eq not
     { n 1 eq { 0 0 /n 2 def } if
       ArrowA
       /n n 2 sub def
       CP 2 copy moveto pop Oy Lineto
       n { 2 copy moveto pop Oy Lineto } repeat
       CP
       4 2 roll
       ArrowB
       2 copy moveto pop Oy
       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
%
/SymbolPolygon {   % on stack [ x y x y ...
   counttomark 					% number of elements
   2 add /m ED
   2 copy m 2 roll				% copy last two
   m 2 div cvi /n ED    				% n pairs
   /YA ED /XA ED					% the start point
   n 1 sub {
     /YB ED /XB ED
     /XLength XB XA sub def
     /YLength YB YA sub def
     /PAngle YLength XLength Atan def
     /XYLength XLength YLength Pyth def
     /nSym XYLength SymStep Div cvi def
     /Shift Symbol stringwidth pop 2 Div def
     /deltaX XLength nSym Div def
     /deltaY YLength nSym Div def
     XA Shift sub YA Shift sub moveto
     nSym {
       gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
       Symbol show
       grestore
       deltaX deltaY rmoveto
     } repeat
%    XB Shift sub YB Shift sub moveto Symbol show
     /YA YB def /XA XB def
   } repeat
   pop	% delete the mark symbol
} 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
%
/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
%
/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
%
/CurvePath {
   %% for negative SymStep we calculate the distance
   SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
   0.5 setflat
   flattenpath /z 0 def /z0 0 def
   { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
     x1 Shift sub y1 Shift sub moveto
     gsave
     curveticks
       { x1 y1 translate startAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       { startAngle rotate Symbol show }
     ifelse
     grestore /z0 z def }
   { /y ED /x ED PathLength@ z z0 sub SymStep ge {
       x Shift sub y Shift sub moveto
       gsave
       curveticks
         { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
           x y translate rotAngle rotate
           0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
           SymbolLinewidth setlinewidth stroke
         }
         {
           rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
           Symbol show
         }
       ifelse
       grestore /z0 z def } if
     /yOld y def /xOld x def }
   {} %% the lineto part
   { /y y2 def /x x2 def PathLength@
     x Shift sub y Shift sub moveto
     gsave
     curveticks
       { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
         x y translate rotAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       {
         x Shift sub y Shift sub moveto
         rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
         Symbol show
       }
     ifelse
     grestore
   }
   pathforall 
%  curveticks 
%   { gsave 
%     x y translate rotAngle rotate 
%     0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
%     SymbolLinewidth setlinewidth stroke grestore
%   } if
   z 
} def
%
/OpenSymbolCurve {
   OpenCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/AltOpenSymbolCurve {
   AltCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolCurve {
   ClosedCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} def
%
/CalcBezierSpline {%  Christoph Bersch
   10 dict begin
   /getX { Points exch 2 mul get } def
   /getY { Points exch 2 mul 1 add get } def
   /n Points length 1 sub 2 idiv def
   /GetFirstControlPoints {
     /x n array def
     /tmp n array def
     /b 2 def
     x 0 rhs 0 get b div put
     1 1 n 1 sub {
       /i exch def
       tmp i 1 b div dup 4 1 roll put
       i n 1 sub lt { 4 }{ 3.5 } ifelse exch sub /b exch def
       x i rhs i get x i 1 sub get sub b div put
     } for
     1 1 n 1 sub {
       n exch sub
       dup dup x exch 1 sub 2 copy 6 2 roll
       get 3 1 roll tmp exch get
       exch x exch get mul sub
       put
     } for
     x
   } def
   %
   n 1 eq {
     0 getX 2 mul 1 getX add 3 div
     0 getY 2 mul 1 getY add 3 div
     exch dup 3 1 roll 2 mul 0 getX sub
     exch dup 3 1 roll 2 mul 0 getY sub
     [ 0 getX 0 getY 7 3 roll 1 getX 1 getY ] /outPoints exch def
   } {
     /outPoints 6 n mul 2 add array def
     0 1 n {
       dup dup 6 mul dup 1 add
       outPoints exch 5 -1 roll getY put
       outPoints exch 3 -1 roll getX put
     } for
     /rhs n array def
     1 1 n 2 sub {
       rhs exch dup dup getX 4 mul exch 1 add getX 2 mul add put
     } for
     rhs 0 0 getX 1 getX 2 mul add put
     rhs n 1 sub dup getX 8 mul n getX add 2 div put
     GetFirstControlPoints
     1 1 n 2 sub {
       rhs exch dup dup getY 4 mul exch 1 add getY 2 mul add put
     } for
     rhs 0 0 getY 1 getY 2 mul add put
     rhs n 1 sub dup getY 8 mul n getY add 2 div put
     GetFirstControlPoints
     0 1 n 1 sub {
       /i exch def
       2 copy
       i get outPoints 6 i mul 3 add 3 -1 roll put
       i get outPoints 6 i mul 2 add 3 -1 roll put
       2 copy
       i n 1 sub lt {
         i 1 add get i 1 add getY 2 mul exch sub outPoints 6 i mul 5 add 3 -1 roll put
         i 1 add get i 1 add getX 2 mul exch sub outPoints 6 i mul 4 add 3 -1 roll put
       }{
         n 1 sub get n getY add 2 div outPoints 6 n 1 sub mul 5 add 3 -1 roll put
         n 1 sub get n getX add 2 div outPoints 6 n 1 sub mul 4 add 3 -1 roll put
       } ifelse
     } for
     pop pop
   } ifelse
   outPoints
   end
} def
/Spline {
   /showpoints ED
   counttomark 2 div dup cvi /n ED
   n eq not { exch pop } if
   ] /Points ED
   n 1 gt {
     CalcBezierSpline
     mark exch aload pop
     ArrowA
     n 2 sub {
       6 2 roll 4 2 roll curveto
     } repeat
     6 2 roll 4 2 roll ArrowB curveto
   } if
} def
/OpenSymbolSpline {
   Spline
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/OpenSymbolBezier {
   OpenBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolBezier {
   /f ED				 % save showpoints value
   2 copy /yEnd ED /xEnd ED
   counttomark -2 roll 2 copy /yStart ED /xStart ED
   counttomark 2 roll
   f
   ClosedBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath
   [ xEnd yEnd xStart yStart SymbolLine 
} 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 ED /x0 ED /y1 ED /x1 ED
   /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
%
/Parab1 { % 1 end  |  0 SP
   /ySP ED /xSP ED /y1 ED /x1 ED
   /dx xSP x1 sub 3 div def
   /dy ySP y1 sub 3 div def
   newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
                        x1 ySP lineto closepath clip
   currentpoint
   newpath moveto
   xSP dx sub ySP dy add x1 y1 ArrowA
   xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
   curveto
   /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def 
} def
%
/Grid {
   newpath
   /a 4 string def
   /b ED % 				psk@gridlabels in pt
   /c ED % 				{ \pst@usecolor\psgridlabelcolor }
   /n ED % 				psk@griddots
   cvi dup 1 lt { pop 1 } if
   /s ED % 				\psk@subgriddiv
   s div dup 0 eq { pop 1 } if
   /dy ED s div dup 0 eq { pop 1 } if %	\pst@number\psyunit abs
   /dx ED dy div round dy mul %		\pst@number\psxunit abs
   /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 {
   /rotAngle ED
   /mtrx CM def
   T
   rotAngle rotate
   scale 0 0 1 5 3 roll arc
   mtrx setmatrix 
} def
%
/ArcAdjust { %%%% Vincent Guirardel
% given a target length (targetLength) and an initial angle (angle0) [in the stack],
% let  M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
% This computes an angle t such that (x0,y0) is at distance 
% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
% contrary to TvZ's code.
% To achieve, this, one iterates the following process: start with some angle t,
% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
%
% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
% the value of d = add/sub is used to know on which side we have to move.
% It is only used in the initialisation of the angle before the iteration.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input stack:  1: target length 2: initial angle
% variables used : rx, ry, d (=add/sub)
%
   /targetLength ED /angle0 ED
   /x0 rx angle0 cos mul def
   /y0 ry angle0 sin mul def
% we are looking for an angle t such that (x0,y0) is at distance targetLength 
% from the point M(t)=(rx*cos(t),ry*sin(t)))
%initialisation of angle (using 1st order approx = TvZ's code)
   targetLength 57.2958 mul
   angle0 sin rx mul dup mul
   angle0 cos ry mul dup mul
   add sqrt div 
% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
% (if the ellipse is very curved at the point where we draw the arrow, %
% the value can be much more than 360 degrees !)
% this should avoid going on the wrong side (more than 180 degrees) or go near
% a bad attractive point (at 180 degrees)
   dup 90 ge { pop 90 } if
   angle0 exch d % add or sub
% maximum number of times to iterate the iterative procedure:
% iterative procedure: takes an angle t on top of stack, computes a 
% better angle (and put it on top of stack)
   30 { dup
% compute distance D between (x0,y0) and M(t)
     dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
% if D almost equals targetLength, we stop
     dup targetLength sub abs 1e-5 le { pop exit } if
% stack now contains D t
% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
     exch dup cos rx mul x0 sub  exch sin ry mul y0 sub
% stack contains:  y(t)-y0, x(t)-x0, d
     2 index Div targetLength mul y0 add ry Div exch
     2 index Div targetLength mul x0 add rx Div
% stack contains x(t')/rx , y(t')/ry , d
% now compute t', and remove D from stack
     atan exch pop
   } repeat
% we don't look at what happened... in particular, if targetLength is greater 
% than the diameter of the ellipse...
% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
% to give back the result as a an angle relative to angle0 we could add the following line:
% angle0 sub 0 exch d
%
% begin bug fix 2006-01-11
% we want to adjust the new angle t' by a multiple of 360 so that  | t'-angle0 | <= 180
%(we don't want to make the ellipse turn more or less than it should)...
dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
% end bug fix
} def
%
/EllipticArcArrow {
   /d ED      % is add or sub
   /b ED      % arrow procedure
   /a1 ED     % angle
   gsave
   newpath
   0 -1000 moveto
   clip                  % Set clippath far from arrow.
   newpath
   0 1 0 0 b             % Draw arrow to determine length.
   grestore
% Length of arrow is on top of stack. Next 3 numbers are junk.
%
   a1 exch ArcAdjust   % Angular position of base of arrow.
   /a2 ED
   pop pop pop
   a2 cos rx mul xOrig add % hv 2007-08-29   x->xOrig
   a2 sin ry mul yOrig add % hv 2007-08-29   y->yOrig
   a1 cos rx mul xOrig add %
   a1 sin ry mul yOrig add % 
% Now arrow tip coor and base coor are on stack.
   b pop pop pop pop       % Draw arrow, and discard coordinates.
   a2 CLW 8 div
% change value of d (test it by looking if  `` 1 1 d '' gives 2 or not )
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
   ArcAdjust
% resets original value of d
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse  % Adjust angle to give overlap.
} def
%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
%
/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 {
   5 dict begin
   /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
   end
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro

%%EndProcSet
%%BeginProcSet: pst-algparser.pro 0 0
% $Id: pst-algparser.pro 902 2014-03-30 16:23:33Z herbert $
%%
%% PostScript prologue for PSTricks algorithm parser
%% Version 0.05, 2014/03/30
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%%-----------------------------------------------------------------------------%
%
/AlgParser { tx@AlgToPs begin AlgToPs end } def  % Dominique Rodriguez
%
/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
%
% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
%
% 09/2011 DR factorial with ! added
%
% E->T|E+T
% T->FS|T*FS
% FS -> F | +FS | -FS
% F->P|F^SF|P!
% P->(E)|literal
% literal->number|var|var[E]|func(params)
% params->E|E,param
% number->TOBEFINISHED
%
%% E expression, T term, SF signed factor, F factor, P power
%
%% parser
%
%% str
%
%% C->E<condition_operators>E
%% STR index -> STR index+lenExpr
/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp  } def
%
%% analyze Expression List (separator , or | )
%% STR index -> STR index+lenExpr
%% /AnalyzeListOfE {
%%   { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
%%     NextNonBlankChar dup 0 eq { pop exit } if
%%     dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
%%     pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
%%   AnalyzeListOfEPostHook
%% } def
/AnalyzeListOfE {
   /NotFirst false def
   { NextNonBlankChar pop AnalyzeExpr
     NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
     dup Strlen eq { exit } if NextNonBlankChar
     dup 44 ne 1 index 124 ne and
     { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
     if  pop 1 add } loop
   AnalyzeListOfEPostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% E->T|E+T
%% STR index -> STR index+lenExpr
/AnalyzeExpr {
   AnalyzePreHook AnalyzeTerm IsEndingExpr
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% T->FS|T*FS
%% STR index
/AnalyzeTerm {
   AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% FS -> F | +FS | -FS
%% STR index
/AnalyzeSignedFactor {
   AnalyzePreHook 2 copy get dup IsUnaryOp
   { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
   { pop AnalyzeFactor }
   ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% F->P|F^P|P!
%% STR index
/AnalyzeFactor {
   AnalyzePreHook AnalyzePower IsEndingFactor
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { dup 33 eq%% is there a ! DR 09/2011
       { pop 1 add NextNonBlankChar pop EvalFactorial }
       { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
       ifelse
       IsEndingFactor { pop exit } if } loop }
   ifelse  AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% P->(E)|literal
%% STR index
/AnalyzePower {
   %% depending of first char either a number, or a literal
   2 copy get dup 40 eq%%an open par
   { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
   { AnalyzeLiteral }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index STR[index] -> STR index
%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% recognize + or -
%% chr -> T/F
/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadNumber {
   exch dup 3 -1 roll dup 3 1 roll
   %%read mantissa
   { 1 add  2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
   dup 101 eq exch 69 eq or
   %%% there is a "e" or "E" -> read exponant
   { 1 add 2 copy get dup IsUnaryOp
     { pop 1 add 2 copy get } if
     { IsNumber not { exit } if 1 add 2 copy get } loop }
   if
   dup 4 1 roll
   3 -1 roll exch 1 index sub getinterval
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadCondOp {
   NextNonBlankChar 1 index 4 1 roll
   { IsCondOp not { exit } if 1 add  2 copy get } loop
   2 copy 5 -1 roll
   exch 1 index sub getinterval 3 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can contain only : 0123456789.
%% chr -> T/F
/IsLiteral {%
   dup 48 ge exch dup  57 le 3 -1 roll and exch
   dup 65 ge exch dup  90 le 3 -1 roll and 3 -1 roll or exch
   dup 97 ge exch     122 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
%% STR index -> literal STR index' nextchr
/ReadLiteral {
   exch dup 3 -1 roll dup 3 1 roll
   %%read literal core
   { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
   4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a clpar
%% STR index -> STR index STR[index] T/F
/IsEndingExpr {%
   2 copy dup Strlen eq
   %% if end of str is reached -> end !
   { pop pop 0 true }
   %% ending chr -> clpar, comma, |, <, >, =, !,
   {get dup  dup  41 eq
        exch dup 124 eq
        exch dup  93 eq
        exch dup  44 eq
        exch dup  30 eq
        exch dup  60 ge exch 62 le and or or or or or}
   ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a +-
%% STR index -> STR index STR[index] T/F
/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or */
%% STR index -> STR index STR[index] T/F
/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or ^
%% STR index -> STR index STR[index] T/F
/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index STR[index]
/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
%%%%%%%%%%%%%%%%%%%%%%%%
%% DEBUG
/BRK {false} def
/BRKtrue {/BRK true def} def
/BRKStop {BRK {BRKtoto} if } def
/BRKEvalStop {BRK exch if } def
/BRKBRK2true {BRK {BRK2true} if } def
/BRK2 {false} def
/BRK2true {/BRK2 true def} def
/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
end
%
%-------------------------------------------------------------------------------%
%
/tx@AlgToPs 12 dict def tx@AlgToPs begin
%
%% algExpr -> PSVector
/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
/Strlen 0 def
/EvalListOfExpr {} def%
/EvalNumber {%
     ReadNumber  cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
     exch 1 add array astore def NextNonBlankChar pop } def
/EvalAddSub {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
} def
/EvalMulDiv {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
} def
/EvalPower {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   pop /exp cvx exch 1 add array astore def
} def
/EvalFactorial {% DR 09/2011
   /ExpressionVector ExpressionVector aload length
   /fact cvx exch 1 add array astore def
} def
/EvalLiteral {%
   ReadLiteral
   dup 40 eq%%% there is an open par -> function call
   { pop 2 index
     dup (Sum) eq { EvalSum }
     { dup (IfTE) eq { EvalCond }
       { dup (Derive) eq { pop EvalDerive }
 	{ pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
           /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
 	  exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
   { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
     dup 91 eq%%% there is an open bracket -> vector element
     { pop 1 add NextNonBlankChar pop AnalyzeExpr
       /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
     { pop NextNonBlankChar pop }
     ifelse}
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% the derive function : Derive(n,f(x))
%% firstparindex lastparindex ->
/EvalDerive {
   %% manage the function descripiton
   1 add ReadNumber 3 1 roll NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   1 add NextNonBlankChar pop
   3 -1 roll cvi
   dup 0 eq
   { pop AnalyzeExpr 3 -1 roll pop 1 add }
   { 1 sub 3 1 roll (x)  exch tx@Derive begin DeriveIndexed end 4 -1 roll
     { (x) tx@Derive begin Derive end } repeat
     ExpressionVector exch /ExpressionVector [] def
     AlgToPs aload length
     /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll  /l2 exch def /l1 exch def
     l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
     1 index length /Strlen exch def } ifelse
} def
/EvalSum {%
   pop 1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
   5 -1 roll 4 add array astore def
   %% keep ExpressionVector for later and create a new one for internal Sum computation
   ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
   1 add NextNonBlankChar pop AnalyzeExpr
   %% add each term
   /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
   /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
   array astore def 3 -1 roll pop 1 add
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
/EvalCond {%
   pop 1 add AnalyzeCond NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   ExpressionVector 3 1 roll /ExpressionVector [] def
   1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
   NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add AnalyzeExpr
   NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
   ExpressionVector
   /ExpressionVector 6 -1 roll aload length dup
   6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
   1 add 3 -1 roll pop
} def
%% CondOp STR index
/EvalCondOp {%
   3 -1 roll
   dup (=) eq  { /eq } {%
   dup (<) eq  { /lt } {%
   dup (>) eq  { /gt } {%
   dup (>=) eq { /ge } {%
   dup (<=) eq { /ge } {%
   dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
   ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
   cvx exch pop
   /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
/EvalUnaryOp {
   3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook {} bind def
/PreEvalHook {} bind def
/AnalyzeListOfEPostHook {} bind def
/AnalyzePostHook {} def
/RollOp { 3 1 roll } bind def
end   %tx@CoreAnalyzerDict
%
%--------------------------------------------------------------------%
%
/tx@Derive 41 dict def tx@Derive begin
%%increase ^^ for each function added
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable -> PSVector
/Derive {%
   10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
} def
/Strlen 0 def
/InitParser { dup length /Strlen exch def 0 } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable index -> PSVector
/DeriveIndexed {%
   3 1 roll 10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u,v)'=-(u',v')
/EvalListOfExpr {%
   4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
            2 copy 7 -1 roll dup length 4 1 roll putinterval add
   6 -2 roll pop pop
   2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (-u)'=-(u')
/EvalUnaryOp {
   4 -2 roll 4 index (0) eq
   { (0) StrConcat 7 -1 roll pop }
   { 7 -1 roll 45 eq
     { AddSub AddOpPar true } { false } ifelse
     3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (number)'=0
/EvalNumber { ReadNumber (0) 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u+v)'=u'+v'
/EvalAddSub {%
   7 index dup (0) eq
   { pop true }%% du=0 nothing added
   { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
   ifelse
   5 index dup (0) eq
   { pop { (0) } { 4 -2 roll 2 copy pop 0  6 2 roll GetIntervalNewStr } ifelse }%%dv=0
   { exch
     { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
     { 5 -2 roll 7 index 43 eq%%something yet added
       { AddAdd false } { AddSub AddOpPar true } ifelse }
     ifelse 11 1 roll
     3 -1 roll StrConcat 10 -1 roll { AddClPar } if
     2 copy pop 0 6 2 roll GetIntervalNewStr }
   ifelse
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)' or (u/v)'
/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)'=u'*v+u*v'
/EvalMul {%
   4 -2 roll 7 index dup (0) eq
   { pop false }%%du=0
   { (1) eq%%du=1
     { false }
     { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
     3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
     true }%%du!=0
   ifelse
   5 1 roll 5 index (0) eq
   { 5 -1 roll not { (0) StrConcat } if }%%dv=0
   { 5 -1 roll { AddAdd } if
     4 index (1) eq
     { 8 index StrConcat }
     { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
     ifelse
   }%%dv!=0
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u/v)'=(u'*v-u*v')/v^2
/EvalDiv {%
   4 -2 roll
   4 index (0) eq%%dv=0 -> u'/v
   { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
   { 7 index dup (0) eq
     { pop }%%du=0
     { (1) eq%%du=1
       { false }
       { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
       3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
     ifelse
       AddSub
       4 index (1) eq
       { 8 index StrConcat }
       { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
       ifelse
     %}%%dv!=0
     2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
     AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str1 index str2 -> str1 index
/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
/EvalPower {%
   4 -2 roll 7 index (0) eq
   {%%if du=0 then (u^v)'=v'ln(u)u^v
     4 index (0) eq
     { (0) StrConcat }%%if dv=0 then (u^v)'=0
     { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
       8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
       AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
   }
   {%%du!=0
     4 index (0) eq
     {%%if dv=0 then (u^v)'=vu'u^(v-1)
       5 index dup IsStrNumber
       { dup (0) eq
         { StrConcat }
         { dup dup (1) eq exch (1.0) eq or
           { StrConcat  }
 	  { StrConcat
 	    7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
 	    { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
             (*\() StrConcat 8 index StrConcat (\)) StrConcat
             5 index  dup dup (2) eq exch (2.0) eq or
 	    { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
       { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
         5 index StrConcat (-1\)) StrConcat } ifelse
     }
     {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
       7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
       AddOpPar 5 index StrConcat (\)*\() StrConcat
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (-1\)+\() StrConcat
       4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (\)*ln\() StrConcat
       8 index StrConcat AddClPar
     } ifelse
   } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for factorial ! only cst => null derivative
/EvalFactorial {% DR 09/2011
   4 index (0) eq
   { (0) mark 8 -2 roll  cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
   { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str -> true/false
/IsStrNumber {%
   true exch
   { dup 48 lt exch dup 57 gt 3 -1 roll or
     exch dup 46 ne%%.
     exch dup 43 ne%%+
     exch 45 ne%%-
     and and and { pop false } if } forall
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalLiteral {%
   ReadLiteral dup 40 eq%%% there is an open par -> function call
   { pop (EvalFunc_             ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
   { dup 91 eq%%% there is an open bracket -> vector element
     { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
     { pop EvalVariable }
     ifelse }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first last parpos Expr[first:parpos-1] ->
/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (f(u))'=u'f'(u)
/EvalFunc {
   4 2 roll 4 index (1) ne
   { AddOpPar 4 index StrConcat (\)*) StrConcat } if
   (Eval             ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Func derivative -> Eval<func>
/EvalFunc_sin {%
   PreCommonFunc
   { (cos\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_cos {%
   PreCommonFunc
   { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_tan {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_asin {%
   PreCommonFunc
   { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_acos {%
   PreCommonFunc
   { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_atg {%
   PreCommonFunc
   { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_floor {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ln {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_exp {%
   PreCommonFunc
   {  (exp\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_EXP {%
   PreCommonFunc
   {  (EXP\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_sqrt {%
   PreCommonFunc
   { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Fact {%
   PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
   PostCommonFunc } def
/EvalFunc_sh {%
   PreCommonFunc
   { (ch\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ch {%
   PreCommonFunc
   { (sh\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_th {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argsh {%
   PreCommonFunc
   { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argch {%
   PreCommonFunc
   { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argth {%
   PreCommonFunc
   { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/PreCommonFunc {
   1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
   4 2 roll 4 index (0) eq
   { (0) StrConcat false }
   { 4 index (1)  ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
} def
/PostCommonFunc {
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
/EvalFunc_Derive {%
   1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
   4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
   4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
   exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_Sum {%
   1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop 3 -1 roll pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
   1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
   4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_IfTE {%
   3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
   NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   1 add NextNonBlankChar pop dup 5 1 roll
   AnalyzeExpr NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add NextNonBlankChar pop
   AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
   6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% advance in str until a comma is found (no error detection!)
%% str index -> str index'
/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for condition....
/EvalCondOp { 3 -1 roll pop } bind def
/PutIntervalOneAdd {putinterval 1 add} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add close parenthesis in string at the given index
%% str index -> str index+1
/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add 0 in string at the given index
%% str index -> str index+1
/AddZero {2 copy (0) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddMul {2 copy (*) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a plus sign in string at the given index
%% str index -> str index+1
/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a minus sign in string at the given index
%% str index -> str index+1
/AddSub {2 copy (-) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a pipe sign in string at the given index
%% str index -> str index+1
/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook { dup 5 1 roll } bind def
/PreEvalHook {} def
/AnalyzePostHook { 7 -1 roll pop } bind def
/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
/RollOp { 5 1 roll } bind def
end%%%tx@CoreAnalyzerDict
/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NEW FUNC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
%% x -> theta
/asin {%
   dup abs 1 gt { EQDFasinrangeerror  } if
   dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
} def
%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
%% x -> theta
/acos {%
   dup abs 1 gt { EQDFacosrangeerror  } if
   dup dup mul 1 exch sub sqrt exch atan DegtoRad
} def
%% function arctangent in radians
%% x -> theta
/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
%% HYPERBOLIC FUNCTIONS
/sh { dup Ex exch neg Ex sub 2 div } def
/ch { dup Ex exch neg Ex add 2 div } def
/th { dup sh exch ch div } def
/Argsh { dup dup mul 1 add sqrt add ln } def
/Argch { dup dup mul 1 sub sqrt add ln } def
/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
%% modified exponential funtion for 0
%% x n -> x^n
/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
%% modified exponential funtion for 0
%% x -> e^x
/Ex { Euler exch exp } bind def
%%
%% factorial function
%% n -> n!
/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
/fact { Fact } bind def
/! { Fact } bind def
end
%
% END pst-algparser.pro

%%EndProcSet
%%BeginProcSet: pst-tools.pro 0 0
% $Id: pst-tools.pro 842 2013-10-26 10:25:41Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.04, 2013/10/26
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
/Pi2 1.57079632679489661925640 def
/factorial { % n on stack, returns n!
   dup 0 eq { 1 }{
     dup 1 gt { dup 1 sub factorial mul } if }
   ifelse } def 
%
/MoverN { % m n on stack, returns the binomial coefficient m over n
   2 dict begin
   /n exch def /m exch def
   n 0 eq { 1 }{
     m n eq { 1 }{
       m factorial n factorial m n sub factorial mul div } ifelse } ifelse
   end
} def
%
/ps@ReverseOrderOfPoints { % on stack [P1 P2 P3 ...Pn]=>[Pn,Pn-1,...,P2,P1]
   5 dict begin       % all local
   aload length /n ED % number of coors
   n 2 div cvi /m ED  % number of Points
   /n1 n def
   m { n1 2 roll /n1 n1 2 sub def } repeat
   n array astore
   end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% subroutines for complex numbers, given as an array [a b] 
% which is a+bi = Real+i Imag
%
/cxadd {		% [a1 b1] [a2 b2] = [a1+a2 b1+b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   3 -1 roll		% [a2 b2] a2 [a1 b1]
   dup 0 get		% [a2 b2] a2 [a1 b1] a1
   3 -1 roll		% [a2 b2] [a1 b1] a1 a2
   add			% [a2 b2] [a1 b1] a1+a2
   3 1 roll		% a1+a2 [a2 b2] [a1 b1]
   1 get			% a1+a2 [a2 b2] b1
   exch 1 get		% a1+a2 b1 b2
   add 2 array astore
} def
%
/cxneg {		% [a b]
   dup 1 get		% [a b] b
   exch 0 get		% b a
   neg exch neg		% -a -b
   2 array astore
} def
%
/cxsub { cxneg cxadd } def  % same as negative addition
%
% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
/cxmul {		% [a1 b1] [a2 b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   exch 1 get		% [a1 b1] a2 b2
   3 -1 roll		% a2 b2 [a1 b1]
   dup 0 get		% a2 b2 [a1 b1] a1
   exch 1 get		% a2 b2 a1 b1
   dup			% a2 b2 a1 b1 b1
   5 -1 roll dup		% b2 a1 b1 b1 a2 a2
   3 1 roll mul		% b2 a1 b1 a2 b1a2
   5 -2 roll dup		% b1 a2 b1a2 b2 a1 a1
   3 -1 roll dup		% b1 a2 b1a2 a1 a1 b2 b2
   3 1 roll mul		% b1 a2 b1a2 a1 b2 a1b2
   4 -1 roll add		% b1 a2 a1 b2 b3
   4 2 roll mul		% b1 b2 b3 a1a2
   4 2 roll mul sub	% b3 a3
   exch 2 array astore
} def
%
% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
/cxsqr {		% [a b]   square root
   dup 0 get exch 1 get	% a b
   dup dup mul		% a b b^2
   3 -1 roll		% b b^2 a
   dup dup mul 		% b b^2 a a^2
   3 -1 roll sub		% b a a2
   3 1 roll mul 2 mul	% a2 b2
   2 array astore
} def
%
/cxsqrt {		% [a b]
%  dup cxnorm sqrt /r exch def
%  cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
   cxlog 		% log[a b]
   2 cxrdiv 		% log[a b]/2
   aload pop exch	% b a
   2.781 exch exp	% b exp(a)
   exch cxconv exch	% [Re +iIm] exp(a)
   cxrmul		%
} def
%
/cxarg { 		% [a b]
   aload pop 		% a b
   exch atan 		% arctan b/a
   DegtoRad 		% arg(z)=atan(b/a)
} def
%
% log[a b] = [a^2-b^2 2ab] = [a2 b2]
/cxlog {		% [a b]
   dup 			% [a b][a b]
   cxnorm 		% [a b] |z|
   log 			% [a b] log|z|
   exch 			% log|z|[a b]
   cxarg 		% log|z| Theta
   cxmake2 		% [log|z| Theta]
} def
%
% square of magnitude of complex number
/cxnorm2 {		% [a b]
   dup 0 get exch 1 get	% a b
   dup mul			% a b^2
   exch dup mul add	% a^2+b^2
} def
%
/cxnorm {		% [a b]
   cxnorm2 sqrt
} def
%
/cxconj {		% conjugent complex
   dup 0 get exch 1 get	% a b
   neg 2 array astore	% [a -b]
} def
%
/cxre { 0 get } def	% real value
/cxim { 1 get } def	% imag value
%
% 1/[a b] = ([a -b]/(a^2+b^2)
/cxrecip {		% [a b]
   dup cxnorm2 exch	% n2 [a b]
   dup 0 get exch 1 get	% n2 a b
   3 -1 roll		% a b n2
   dup			% a b n2 n2
   4 -1 roll exch div	% b n2 a/n2
   3 1 roll div		% a/n2 b/n2
   neg 2 array astore
} def
%
/cxmake1 { 0 2 array astore } def % make a complex number, real given
/cxmake2 { 2 array astore } def	  % dito, both given
%
/cxdiv { cxrecip cxmul } def
%
% multiplikation by a real number
/cxrmul {		% [a b] r
   exch aload pop	% r a b
   3 -1 roll dup		% a b r r
   3 1 roll mul		% a r b*r
   3 1 roll mul		% b*r a*r
   exch 2 array astore   % [a*r b*r]
} def
%
% division by a real number
/cxrdiv {		% [a b] r
   1 exch div		% [a b] 1/r
   cxrmul
} def
%
% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
/cxconv {		% theta
   RadtoDeg dup sin exch cos cxmake2
} def

%%%%% ### bubblesort ###
%% syntax : array bubblesort --> array2 trie par ordre croissant
%% code de Bill Casselman
%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
/bubblesort { % on stack must be an array [ ... ]
4 dict begin
    /a exch def
    /n a length 1 sub def
    n 0 gt {
       % at this point only the n+1 items in the bottom of a remain to
       % the sorted largest item in that blocks is to be moved up into
       % position n
       n {
          0 1 n 1 sub {
             /i exch def
             a i get a i 1 add get gt {
                % if a[i] > a[i+1] swap a[i] and a[i+1]
                a i 1 add
                a i get
                a i a i 1 add get
                % set new a[i] = old a[i+1]
                put
                % set new a[i+1] = old a[i]
                put
             } if
          } for
          /n n 1 sub def
       } repeat
    } if
    a % return the sorted array
end
} def
%
/concatstringarray{  %  [(a) (b) ... (z)] --> (ab...z)  20100422
   0 1 index { length add } forall
   string
   0 3 2 roll
   { 3 copy putinterval length add }forall
   pop 
} bind def
%
/dot2comma {% on stack a string (...)
   2 dict begin
   /Output exch def
   0 1 Output length 1 sub {
     /Index exch def
     Output Index get 46 eq { Output Index 44 put } if
   } for
   Output
   end
} def
%
/rightTrim { % on stack the string and the character number to be stripped
   /charNo exch def
   dup
   length 1 sub -1 0 {
     /i exch def dup i get charNo ne { exit } if
   } for
   0 i 1 add getinterval
   dup length string copy
} bind def  % leaves the stripped string on the stack

/psStringwidth /stringwidth load def
/psShow /show load def

%/stringwidth{ 32 rightTrim psStringwidth } bind def

%/show { 32 rightTrim psShow } bind def
%-----------------------------------------------------------------------------%

/pgffunctions {
     /pgfsc{}bind def% stroke color is empty by default
     /pgffc{}bind def% fill color is empty by default
     /pgfstr{stroke}bind def%
     /pgffill{fill}bind def%
     /pgfeofill{eofill}bind def%
     /pgfe{a dup 0 rlineto exch 0 exch rlineto neg 0 rlineto closepath}bind def% rectangle
     /pgfw{setlinewidth}bind def% setlinewidth
     /pgfs{save pgfpd 72 Resolution div 72 VResolution div neg scale
       magscale{1 DVImag div dup scale}if
       pgfx neg pgfy neg translate pgffoa .setopacityalpha}bind def% save
     /pgfr{pgfsd restore}bind def %restore
     userdict begin%
     /pgfo{pgfsd /pgfx currentpoint /pgfy exch def def @beginspecial}bind def %open
     /pgfc{newpath @endspecial pgfpd}bind def %close
     /pgfsd{globaldict /pgfdelta /delta where {pop delta} {0} ifelse put}bind def% save delta
     /pgfpd{/delta globaldict /pgfdelta get def}bind def % put delta
     /.setopacityalpha where {pop} {/.setopacityalpha{pop}def} ifelse % install .setopacityalpha
     /.pgfsetfillopacityalpha{/pgffoa exch def
       /pgffill{gsave pgffoa .setopacityalpha fill 1 .setopacityalpha newpath fill grestore newpath}bind def
       /pgfeofill{gsave pgffoa .setopacityalpha eofill 1 .setopacityalpha newpath eofill grestore newpath}bind def}bind def
     /.pgfsetstrokeopacityalpha{/pgfsoa exch def /pgfstr{gsave pgfsoa .setopacityalpha stroke grestore newpath}bind def}bind def
     /pgffoa 1 def
     /pgfsoa 1 def
     end
} def
%-----------------------------------------------------------------------------%
% END pst-tools.pro

%%EndProcSet
%%BeginProcSet: pst-dots.pro 0 0
% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02,  2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt <tvz@Princeton.EDU>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga  - Dec. 16, 1999
%% Modified by Etienne Riga  - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17 
%
10 dict dup begin			% hold local
   /FontType 3 def
   /FontMatrix [.001 0 0 .001 0 0] def
%  /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
   /FontBBox [-1000 -1000 1000 1000] def  % See end of file in /BuildGlyph
   /Encoding 256 array def
   0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
   Encoding				   % replace with given dot names
     dup (b) 0 get /Bullet put		   % get the numerical position of b in ASCII
%					   % and save /Bullet at this place in Encoding
     dup (c) 0 get /Circle put
     dup (C) 0 get /BoldCircle put	% 67
     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
%%%
     dup (k) 0 get /Asterisk put
     dup (K) 0 get /BoldAsterisk put
     dup (J) 0 get /SolidAsterisk put
     dup (h) 0 get /Hexagon put
     dup (H) 0 get /BoldHexagon put
     dup (G) 0 get /SolidHexagon put
     dup (f) 0 get /Octogon put		% 2008-04-18 hv
     dup (F) 0 get /BoldOctogon put	% 2008-04-18 hv
     dup (g) 0 get /SolidOctogon put	% 2008-04-18 hv
     dup (a) 0 get /Add put
     dup (A) 0 get /BoldAdd put 		% 65
     dup (x) 0 get /Mul put
     dup (X) 0 get /BoldMul put
     dup (m) 0 get /Oplus put
     dup (M) 0 get /BOplus put
     dup (e) 0 get /SolidOplus put
     dup (n) 0 get /Otimes put
     dup (N) 0 get /BOtimes put
     dup (E) 0 get /SolidOtimes put
     dup (i) 0 get /Bar put
     dup (I) 0 get /BoldBar put
     dup (l) 0 get /SolidDiamond put
     dup (d) 0 get /Diamond put
         (D) 0 get /BoldDiamond put
%%% 
/CharProcs 47 dict def
CharProcs begin
   /CirclePath {0 0 500 0 360 arc closepath} def
   /Bullet {CirclePath fill} def
   /Circle {CirclePath .9 .9 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
%-------------- hv begin 2004/07/25   from: er 2003/03/24
   /HexagonPath {
     0 550 moveto -476 275 lineto -476 -275 lineto
     0 -550 lineto 476 -275 lineto 476 275 lineto closepath
   } def
   /SolidHexagon {HexagonPath fill} def
   /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
   /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
%					2008-04-18 hv
   /OctogonPath {
      550 dup 22.5 tan mul dup neg dup add /xMove exch def
      exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
   /SolidOctogon { OctogonPath fill                             } def
   /Octogon {      OctogonPath .89 .89 scale OctogonPath eofill } def
   /BoldOctogon {  OctogonPath .79 .79 scale OctogonPath eofill } def
%
   /AsteriskPath {
     20 0 moveto 10 250 180 500 0 500 curveto
     -180 500 -10 250 -20 0 curveto closepath
   } def
   /Asterisk {
     AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
     60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
   } def
%
   /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
   /BoldAsteriskPath {
     50 30 cos 100 mul moveto  Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp closepath
   } def
   /BoldAsterisk {BoldAsteriskPath fill} def
   /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
   /CrossPath {
     40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
     -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
     40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
   } def
   /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
     -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
     80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
   } def
   /Add {CrossPath fill} def
   /Mul {45 rotate CrossPath fill} def
   /BoldAdd {BoldCrossPath fill} def
   /BoldMul {45 rotate BoldCrossPath fill} def
   /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
   /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
   /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
   /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
   /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
   /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
   /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
   /Bar {BarPath fill} def
   /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
   /BoldBar {BoldBarPath fill} def
   /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 .865 .865 scale DiamondPath eofill} def
   /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
%%%
   /.notdef { } def
end
%
/BuildGlyph {
   exch
   begin 
%  Metrics 1 index get exec 0
     0 0
%      BBoxes 3 index get exec
     -1000 -1000 1000 1000
%     -571.5 -742.5 571.5 742.5
     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

%%EndProcSet
%%BeginProcSet: cmmi10.pfb 0 0
%!PS-AdobeFont-1.0: CMMI10 003.002
%%Title: CMMI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMMI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup
/UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI10 def
/FontBBox {-32 -250 1048 750 }readonly def
/UniqueID 5087385 def
/PaintType 0 def
/FontInfo 10 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI10.) readonly def
  /FullName (CMMI10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle -14.04 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
  /ascent 750 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 15 /epsilon1 put
dup 16 /zeta put
dup 17 /eta put
dup 18 /theta put
dup 19 /iota put
dup 20 /kappa put
dup 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 24 /xi put
dup 25 /pi put
dup 26 /rho put
dup 27 /sigma put
dup 28 /tau put
dup 29 /upsilon put
dup 30 /phi put
dup 31 /chi put
dup 32 /psi put
dup 33 /omega put
dup 34 /epsilon put
dup 35 /theta1 put
dup 36 /pi1 put
dup 37 /rho1 put
dup 38 /sigma1 put
dup 39 /phi1 put
dup 40 /arrowlefttophalf put
dup 41 /arrowleftbothalf put
dup 42 /arrowrighttophalf put
dup 43 /arrowrightbothalf put
dup 44 /arrowhookleft put
dup 45 /arrowhookright put
dup 46 /triangleright put
dup 47 /triangleleft put
dup 48 /zerooldstyle put
dup 49 /oneoldstyle put
dup 50 /twooldstyle put
dup 51 /threeoldstyle put
dup 52 /fouroldstyle put
dup 53 /fiveoldstyle put
dup 54 /sixoldstyle put
dup 55 /sevenoldstyle put
dup 56 /eightoldstyle put
dup 57 /nineoldstyle put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 63 /star put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /flat put
dup 92 /natural put
dup 93 /sharp put
dup 94 /slurbelow put
dup 95 /slurabove put
dup 96 /lscript put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /dotlessi put
dup 124 /dotlessj put
dup 125 /weierstrass put
dup 126 /vector put
dup 127 /tie put
dup 128 /psi put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 173 /Omega put
dup 174 /alpha put
dup 175 /beta put
dup 176 /gamma put
dup 177 /delta put
dup 178 /epsilon1 put
dup 179 /zeta put
dup 180 /eta put
dup 181 /theta put
dup 182 /iota put
dup 183 /kappa put
dup 184 /lambda put
dup 185 /mu put
dup 186 /nu put
dup 187 /xi put
dup 188 /pi put
dup 189 /rho put
dup 190 /sigma put
dup 191 /tau put
dup 192 /upsilon put
dup 193 /phi put
dup 194 /chi put
dup 195 /psi put
dup 196 /tie put
readonly def
currentdict end
currentfile eexec

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cleartomark
{restore}if


%%EndProcSet
%%BeginProcSet: cmr10.pfb 0 0
%!PS-AdobeFont-1.0: CMR10 003.002
%%Title: CMR10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMR10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR10 def
/FontBBox {-40 -250 1009 750 }readonly def
/UniqueID 5000793 def
/PaintType 0 def
/FontInfo 9 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
  /FullName (CMR10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle 0 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 15 /ffl put
dup 16 /dotlessi put
dup 17 /dotlessj put
dup 18 /grave put
dup 19 /acute put
dup 20 /caron put
dup 21 /breve put
dup 22 /macron put
dup 23 /ring put
dup 24 /cedilla put
dup 25 /germandbls put
dup 26 /ae put
dup 27 /oe put
dup 28 /oslash put
dup 29 /AE put
dup 30 /OE put
dup 31 /Oslash put
dup 32 /suppress put
dup 33 /exclam put
dup 34 /quotedblright put
dup 35 /numbersign put
dup 36 /dollar put
dup 37 /percent put
dup 38 /ampersand put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 42 /asterisk put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 60 /exclamdown put
dup 61 /equal put
dup 62 /questiondown put
dup 63 /question put
dup 64 /at put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 94 /circumflex put
dup 95 /dotaccent put
dup 96 /quoteleft put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 124 /emdash put
dup 125 /hungarumlaut put
dup 126 /tilde put
dup 127 /dieresis put
dup 128 /suppress put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 171 /sfthyphen put
dup 172 /nbspace put
dup 173 /Omega put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 178 /ffl put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 187 /cedilla put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 196 /dieresis put
readonly def
currentdict end
currentfile eexec

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   .25 .25 itransform
   pathbbox % llx lly urx ury of smallest bounding box
   /y2 ED /x2 ED /y1 ED /x1 ED
   y2 y1 sub a div 2 add cvi /Ny ED
   x2 x1 sub a div 2 add cvi /Nx ED
   clipType   % must be defined in pstricks.tex: clip -- eoclip
   newpath
   /yA y1 dotRadius add CLW add def
   /xA0 x1 dotRadius add CLW add def
   Ny {
      /xA xA0 def
      Nx {
        newpath
        xA yA dotRadius 0 360 arc
        SolidDot { gsave fill grestore } if
        stroke
        xA a add /xA ED
      } repeat
      yA a add /yA ED
   } repeat
   grestore
} def
%
/PenroseFill {%	 on stack: scaling factor
   /Scale ED
%  1 exch div round /penroseFactor ED 
%  a 0 dtransform round exch round exch
%  2 copy idtransform 
%  exch Atan rotate 
%  idtransform pop /a ED 
%  .25 .25 itransform pathbbox 
%  /y2 ED 
%  a Div ceiling cvi /x2 ED /y1 ED 
%  a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath 
gsave
   220 150 translate
   Scale dup scale
   systemdict /setstrokeadjust known { true setstrokeadjust } if
   /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
  { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
   [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
   i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
   mul j l + S rmoveto}F i L j L stroke }F}F}F}F
   grestore 
%  pop pop 
} def
%
/PenroseFillA {%  on stack: scaling factor, border color, kite color, dart color
   /Scale ED
   Scale dup scale
   /border_colour ED
   /kite_colour ED
   /dart_colour ED
   clip
   newpath
   gsave
   100 100 translate
   6
   Scale 1 lt { 1 Scale dup add div mul cvi } if %%%%   Number of iterations
   10					%%%%   Long side length in millimeters
   /border_width { L 0.06 mul }def		%%%%   Choose the scalefactor for the borders
   /L exch 25.4 div 72 mul def		%%%%   Conversion: mm -> inches -> points
   /f{-1 5 sqrt add 2 div}bind def		%%%%   The reciprocal of the golden ratio
   /l{L f mul}bind def			%%%%   Short side length l = L*f
   /Ll{L l add}bind def			%%%%   Ll =  L + l
   /c{36 cos L mul}bind def		%%%%   c  =  L*cos(36)
   /s{36 sin L mul}bind def		%%%%   s  =  L*sin(36)
   /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
 	     0 setlinewidth stroke grestore border_colour stroke } bind def
   /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
 			   Ll 0 translate 144 rotate kite grestore }
 	      		 { kite_colour L draw_tile }ifelse
 	     pop } bind def
   /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
 			   -144 rotate Ll neg 0 translate half_dart grestore }
 	      		 { dart_colour l draw_tile }ifelse
   	     pop } bind def
   /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
   border_width setlinewidth  1 setlinejoin  1 setlinecap
%  450 0 translate
   dup f exch neg exp dup scale
   5 {kite 72 rotate } repeat stroke
   grestore
} def
%
%
/TruchetFill { %	 on stack: scaling factor
   10 dict begin
   dup dup scale
   1 exch div round /penroseFactor ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform pathbbox
   /y2 ED
   a Div ceiling cvi /x2 ED /y1 ED
   a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath
   systemdict
   /setstrokeadjust known { true setstrokeadjust } if
   /ma a neg def
   /ha a 2 div def
   /mha ha neg def
   /tile {
     rand dup 2 idiv 2 mul eq { 90 rotate } if
     mha mha moveto ha mha lineto
     ha ha lineto mha ha lineto
%    closepath .1 setlinewidth stroke
     contents
   } def
   /contents{
     0 ha moveto ha 0 lineto
     0 mha moveto mha 0 lineto
%    1 setlinewidth stroke
   } def
   /dotiling {
     f ma mul a f a mul {
       /i exch def
       f ma mul a f a mul {
         /j exch def
         gsave i j translate
         tile stroke grestore
       } for
     } for
   } def
%
   /f 3 def
   5 srand dotiling
   end % local user dict
} def
%
/BeginArrow {
   ADict begin 			% hold it local, for end see EndArrow
   /@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 % end the ADict
%
/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
%
/ArrowD { % the sides are drawn as curves (hv 20071211)
   CLW mul add dup
   2 div /w ED
   mul dup /h ED
   mul /Inset ED
   { 0 h T 1 -1 scale } if % changes the direction
% we use y=w/h^2 * x^2 as equation for the control points
% for the coordinates the arrow is seen from top to bottom
% the bottom (tip) is (0;0)
   w neg h moveto % lower left of >
   w 9 div 4 mul neg h 3 div 2 mul
   w 9 div neg       h 3 div
   0 0 curveto    % tip of >
   w 9 div        h 3 div
   w 9 div 4 mul  h 3 div 2 mul
   w h curveto % upper left of >
   w neg Inset neg rlineto % move to x=0 and inset
   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 { % DS is the dot size
   { /z DS def } { /z 0 def } ifelse  	% outer or inner dimen
   /b ED 				% the color definition
   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 { % holds the coordinates and on top of stack the showpoints boolean
   /showpoints ED
   counttomark 2 div dup cvi /n ED  	% n 2 div on stack
   n eq not { exch pop } if		% even numbers of points? delete one
   ] aload /Points ED
   showpoints not { Points aload pop } if
%    { ] aload /Points ED } 
%    { n 2 mul 1 add -1 roll pop } ifelse	% delete the mark symbol 
} 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
%
/LineToYAxis {
   /Ox ED		% Save the x origin value
   NArray            % all x-y pairs on stack
   n { 2 copy moveto % go to current point
     Ox exch Lineto   % line to y-axis
     pop             % delete old x-value
   } repeat
} def
%
/LineToXAxis{
   /Oy ED		% Save the y origin value
   NArray		% all x-y pairs on stack
   n 0 eq not
     { n 1 eq { 0 0 /n 2 def } if
       ArrowA
       /n n 2 sub def
       CP 2 copy moveto pop Oy Lineto
       n { 2 copy moveto pop Oy Lineto } repeat
       CP
       4 2 roll
       ArrowB
       2 copy moveto pop Oy
       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
%
/SymbolPolygon {   % on stack [ x y x y ...
   counttomark 					% number of elements
   2 add /m ED
   2 copy m 2 roll				% copy last two
   m 2 div cvi /n ED    				% n pairs
   /YA ED /XA ED					% the start point
   n 1 sub {
     /YB ED /XB ED
     /XLength XB XA sub def
     /YLength YB YA sub def
     /PAngle YLength XLength Atan def
     /XYLength XLength YLength Pyth def
     /nSym XYLength SymStep Div cvi def
     /Shift Symbol stringwidth pop 2 Div def
     /deltaX XLength nSym Div def
     /deltaY YLength nSym Div def
     XA Shift sub YA Shift sub moveto
     nSym {
       gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
       Symbol show
       grestore
       deltaX deltaY rmoveto
     } repeat
%    XB Shift sub YB Shift sub moveto Symbol show
     /YA YB def /XA XB def
   } repeat
   pop	% delete the mark symbol
} 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
%
/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
%
/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
%
/CurvePath {
   %% for negative SymStep we calculate the distance
   SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
   0.5 setflat
   flattenpath /z 0 def /z0 0 def
   { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
     x1 Shift sub y1 Shift sub moveto
     gsave
     curveticks
       { x1 y1 translate startAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       { startAngle rotate Symbol show }
     ifelse
     grestore /z0 z def }
   { /y ED /x ED PathLength@ z z0 sub SymStep ge {
       x Shift sub y Shift sub moveto
       gsave
       curveticks
         { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
           x y translate rotAngle rotate
           0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
           SymbolLinewidth setlinewidth stroke
         }
         {
           rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
           Symbol show
         }
       ifelse
       grestore /z0 z def } if
     /yOld y def /xOld x def }
   {} %% the lineto part
   { /y y2 def /x x2 def PathLength@
     x Shift sub y Shift sub moveto
     gsave
     curveticks
       { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
         x y translate rotAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       {
         x Shift sub y Shift sub moveto
         rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
         Symbol show
       }
     ifelse
     grestore
   }
   pathforall 
%  curveticks 
%   { gsave 
%     x y translate rotAngle rotate 
%     0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
%     SymbolLinewidth setlinewidth stroke grestore
%   } if
   z 
} def
%
/OpenSymbolCurve {
   OpenCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/AltOpenSymbolCurve {
   AltCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolCurve {
   ClosedCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} def
%
/CalcBezierSpline {%  Christoph Bersch
   10 dict begin
   /getX { Points exch 2 mul get } def
   /getY { Points exch 2 mul 1 add get } def
   /n Points length 1 sub 2 idiv def
   /GetFirstControlPoints {
     /x n array def
     /tmp n array def
     /b 2 def
     x 0 rhs 0 get b div put
     1 1 n 1 sub {
       /i exch def
       tmp i 1 b div dup 4 1 roll put
       i n 1 sub lt { 4 }{ 3.5 } ifelse exch sub /b exch def
       x i rhs i get x i 1 sub get sub b div put
     } for
     1 1 n 1 sub {
       n exch sub
       dup dup x exch 1 sub 2 copy 6 2 roll
       get 3 1 roll tmp exch get
       exch x exch get mul sub
       put
     } for
     x
   } def
   %
   n 1 eq {
     0 getX 2 mul 1 getX add 3 div
     0 getY 2 mul 1 getY add 3 div
     exch dup 3 1 roll 2 mul 0 getX sub
     exch dup 3 1 roll 2 mul 0 getY sub
     [ 0 getX 0 getY 7 3 roll 1 getX 1 getY ] /outPoints exch def
   } {
     /outPoints 6 n mul 2 add array def
     0 1 n {
       dup dup 6 mul dup 1 add
       outPoints exch 5 -1 roll getY put
       outPoints exch 3 -1 roll getX put
     } for
     /rhs n array def
     1 1 n 2 sub {
       rhs exch dup dup getX 4 mul exch 1 add getX 2 mul add put
     } for
     rhs 0 0 getX 1 getX 2 mul add put
     rhs n 1 sub dup getX 8 mul n getX add 2 div put
     GetFirstControlPoints
     1 1 n 2 sub {
       rhs exch dup dup getY 4 mul exch 1 add getY 2 mul add put
     } for
     rhs 0 0 getY 1 getY 2 mul add put
     rhs n 1 sub dup getY 8 mul n getY add 2 div put
     GetFirstControlPoints
     0 1 n 1 sub {
       /i exch def
       2 copy
       i get outPoints 6 i mul 3 add 3 -1 roll put
       i get outPoints 6 i mul 2 add 3 -1 roll put
       2 copy
       i n 1 sub lt {
         i 1 add get i 1 add getY 2 mul exch sub outPoints 6 i mul 5 add 3 -1 roll put
         i 1 add get i 1 add getX 2 mul exch sub outPoints 6 i mul 4 add 3 -1 roll put
       }{
         n 1 sub get n getY add 2 div outPoints 6 n 1 sub mul 5 add 3 -1 roll put
         n 1 sub get n getX add 2 div outPoints 6 n 1 sub mul 4 add 3 -1 roll put
       } ifelse
     } for
     pop pop
   } ifelse
   outPoints
   end
} def
/Spline {
   /showpoints ED
   counttomark 2 div dup cvi /n ED
   n eq not { exch pop } if
   ] /Points ED
   n 1 gt {
     CalcBezierSpline
     mark exch aload pop
     ArrowA
     n 2 sub {
       6 2 roll 4 2 roll curveto
     } repeat
     6 2 roll 4 2 roll ArrowB curveto
   } if
} def
/OpenSymbolSpline {
   Spline
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/OpenSymbolBezier {
   OpenBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolBezier {
   /f ED				 % save showpoints value
   2 copy /yEnd ED /xEnd ED
   counttomark -2 roll 2 copy /yStart ED /xStart ED
   counttomark 2 roll
   f
   ClosedBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath
   [ xEnd yEnd xStart yStart SymbolLine 
} 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 ED /x0 ED /y1 ED /x1 ED
   /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
%
/Parab1 { % 1 end  |  0 SP
   /ySP ED /xSP ED /y1 ED /x1 ED
   /dx xSP x1 sub 3 div def
   /dy ySP y1 sub 3 div def
   newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
                        x1 ySP lineto closepath clip
   currentpoint
   newpath moveto
   xSP dx sub ySP dy add x1 y1 ArrowA
   xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
   curveto
   /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def 
} def
%
/Grid {
   newpath
   /a 4 string def
   /b ED % 				psk@gridlabels in pt
   /c ED % 				{ \pst@usecolor\psgridlabelcolor }
   /n ED % 				psk@griddots
   cvi dup 1 lt { pop 1 } if
   /s ED % 				\psk@subgriddiv
   s div dup 0 eq { pop 1 } if
   /dy ED s div dup 0 eq { pop 1 } if %	\pst@number\psyunit abs
   /dx ED dy div round dy mul %		\pst@number\psxunit abs
   /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 {
   /rotAngle ED
   /mtrx CM def
   T
   rotAngle rotate
   scale 0 0 1 5 3 roll arc
   mtrx setmatrix 
} def
%
/ArcAdjust { %%%% Vincent Guirardel
% given a target length (targetLength) and an initial angle (angle0) [in the stack],
% let  M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
% This computes an angle t such that (x0,y0) is at distance 
% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
% contrary to TvZ's code.
% To achieve, this, one iterates the following process: start with some angle t,
% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
%
% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
% the value of d = add/sub is used to know on which side we have to move.
% It is only used in the initialisation of the angle before the iteration.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input stack:  1: target length 2: initial angle
% variables used : rx, ry, d (=add/sub)
%
   /targetLength ED /angle0 ED
   /x0 rx angle0 cos mul def
   /y0 ry angle0 sin mul def
% we are looking for an angle t such that (x0,y0) is at distance targetLength 
% from the point M(t)=(rx*cos(t),ry*sin(t)))
%initialisation of angle (using 1st order approx = TvZ's code)
   targetLength 57.2958 mul
   angle0 sin rx mul dup mul
   angle0 cos ry mul dup mul
   add sqrt div 
% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
% (if the ellipse is very curved at the point where we draw the arrow, %
% the value can be much more than 360 degrees !)
% this should avoid going on the wrong side (more than 180 degrees) or go near
% a bad attractive point (at 180 degrees)
   dup 90 ge { pop 90 } if
   angle0 exch d % add or sub
% maximum number of times to iterate the iterative procedure:
% iterative procedure: takes an angle t on top of stack, computes a 
% better angle (and put it on top of stack)
   30 { dup
% compute distance D between (x0,y0) and M(t)
     dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
% if D almost equals targetLength, we stop
     dup targetLength sub abs 1e-5 le { pop exit } if
% stack now contains D t
% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
     exch dup cos rx mul x0 sub  exch sin ry mul y0 sub
% stack contains:  y(t)-y0, x(t)-x0, d
     2 index Div targetLength mul y0 add ry Div exch
     2 index Div targetLength mul x0 add rx Div
% stack contains x(t')/rx , y(t')/ry , d
% now compute t', and remove D from stack
     atan exch pop
   } repeat
% we don't look at what happened... in particular, if targetLength is greater 
% than the diameter of the ellipse...
% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
% to give back the result as a an angle relative to angle0 we could add the following line:
% angle0 sub 0 exch d
%
% begin bug fix 2006-01-11
% we want to adjust the new angle t' by a multiple of 360 so that  | t'-angle0 | <= 180
%(we don't want to make the ellipse turn more or less than it should)...
dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
% end bug fix
} def
%
/EllipticArcArrow {
   /d ED      % is add or sub
   /b ED      % arrow procedure
   /a1 ED     % angle
   gsave
   newpath
   0 -1000 moveto
   clip                  % Set clippath far from arrow.
   newpath
   0 1 0 0 b             % Draw arrow to determine length.
   grestore
% Length of arrow is on top of stack. Next 3 numbers are junk.
%
   a1 exch ArcAdjust   % Angular position of base of arrow.
   /a2 ED
   pop pop pop
   a2 cos rx mul xOrig add % hv 2007-08-29   x->xOrig
   a2 sin ry mul yOrig add % hv 2007-08-29   y->yOrig
   a1 cos rx mul xOrig add %
   a1 sin ry mul yOrig add % 
% Now arrow tip coor and base coor are on stack.
   b pop pop pop pop       % Draw arrow, and discard coordinates.
   a2 CLW 8 div
% change value of d (test it by looking if  `` 1 1 d '' gives 2 or not )
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
   ArcAdjust
% resets original value of d
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse  % Adjust angle to give overlap.
} def
%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
%
/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 {
   5 dict begin
   /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
   end
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro

%%EndProcSet
%%BeginProcSet: pst-algparser.pro 0 0
% $Id: pst-algparser.pro 902 2014-03-30 16:23:33Z herbert $
%%
%% PostScript prologue for PSTricks algorithm parser
%% Version 0.05, 2014/03/30
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%%-----------------------------------------------------------------------------%
%
/AlgParser { tx@AlgToPs begin AlgToPs end } def  % Dominique Rodriguez
%
/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
%
% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
%
% 09/2011 DR factorial with ! added
%
% E->T|E+T
% T->FS|T*FS
% FS -> F | +FS | -FS
% F->P|F^SF|P!
% P->(E)|literal
% literal->number|var|var[E]|func(params)
% params->E|E,param
% number->TOBEFINISHED
%
%% E expression, T term, SF signed factor, F factor, P power
%
%% parser
%
%% str
%
%% C->E<condition_operators>E
%% STR index -> STR index+lenExpr
/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp  } def
%
%% analyze Expression List (separator , or | )
%% STR index -> STR index+lenExpr
%% /AnalyzeListOfE {
%%   { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
%%     NextNonBlankChar dup 0 eq { pop exit } if
%%     dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
%%     pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
%%   AnalyzeListOfEPostHook
%% } def
/AnalyzeListOfE {
   /NotFirst false def
   { NextNonBlankChar pop AnalyzeExpr
     NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
     dup Strlen eq { exit } if NextNonBlankChar
     dup 44 ne 1 index 124 ne and
     { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
     if  pop 1 add } loop
   AnalyzeListOfEPostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% E->T|E+T
%% STR index -> STR index+lenExpr
/AnalyzeExpr {
   AnalyzePreHook AnalyzeTerm IsEndingExpr
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% T->FS|T*FS
%% STR index
/AnalyzeTerm {
   AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% FS -> F | +FS | -FS
%% STR index
/AnalyzeSignedFactor {
   AnalyzePreHook 2 copy get dup IsUnaryOp
   { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
   { pop AnalyzeFactor }
   ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% F->P|F^P|P!
%% STR index
/AnalyzeFactor {
   AnalyzePreHook AnalyzePower IsEndingFactor
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { dup 33 eq%% is there a ! DR 09/2011
       { pop 1 add NextNonBlankChar pop EvalFactorial }
       { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
       ifelse
       IsEndingFactor { pop exit } if } loop }
   ifelse  AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% P->(E)|literal
%% STR index
/AnalyzePower {
   %% depending of first char either a number, or a literal
   2 copy get dup 40 eq%%an open par
   { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
   { AnalyzeLiteral }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index STR[index] -> STR index
%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% recognize + or -
%% chr -> T/F
/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadNumber {
   exch dup 3 -1 roll dup 3 1 roll
   %%read mantissa
   { 1 add  2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
   dup 101 eq exch 69 eq or
   %%% there is a "e" or "E" -> read exponant
   { 1 add 2 copy get dup IsUnaryOp
     { pop 1 add 2 copy get } if
     { IsNumber not { exit } if 1 add 2 copy get } loop }
   if
   dup 4 1 roll
   3 -1 roll exch 1 index sub getinterval
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadCondOp {
   NextNonBlankChar 1 index 4 1 roll
   { IsCondOp not { exit } if 1 add  2 copy get } loop
   2 copy 5 -1 roll
   exch 1 index sub getinterval 3 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can contain only : 0123456789.
%% chr -> T/F
/IsLiteral {%
   dup 48 ge exch dup  57 le 3 -1 roll and exch
   dup 65 ge exch dup  90 le 3 -1 roll and 3 -1 roll or exch
   dup 97 ge exch     122 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
%% STR index -> literal STR index' nextchr
/ReadLiteral {
   exch dup 3 -1 roll dup 3 1 roll
   %%read literal core
   { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
   4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a clpar
%% STR index -> STR index STR[index] T/F
/IsEndingExpr {%
   2 copy dup Strlen eq
   %% if end of str is reached -> end !
   { pop pop 0 true }
   %% ending chr -> clpar, comma, |, <, >, =, !,
   {get dup  dup  41 eq
        exch dup 124 eq
        exch dup  93 eq
        exch dup  44 eq
        exch dup  30 eq
        exch dup  60 ge exch 62 le and or or or or or}
   ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a +-
%% STR index -> STR index STR[index] T/F
/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or */
%% STR index -> STR index STR[index] T/F
/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or ^
%% STR index -> STR index STR[index] T/F
/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index STR[index]
/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
%%%%%%%%%%%%%%%%%%%%%%%%
%% DEBUG
/BRK {false} def
/BRKtrue {/BRK true def} def
/BRKStop {BRK {BRKtoto} if } def
/BRKEvalStop {BRK exch if } def
/BRKBRK2true {BRK {BRK2true} if } def
/BRK2 {false} def
/BRK2true {/BRK2 true def} def
/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
end
%
%-------------------------------------------------------------------------------%
%
/tx@AlgToPs 12 dict def tx@AlgToPs begin
%
%% algExpr -> PSVector
/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
/Strlen 0 def
/EvalListOfExpr {} def%
/EvalNumber {%
     ReadNumber  cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
     exch 1 add array astore def NextNonBlankChar pop } def
/EvalAddSub {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
} def
/EvalMulDiv {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
} def
/EvalPower {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   pop /exp cvx exch 1 add array astore def
} def
/EvalFactorial {% DR 09/2011
   /ExpressionVector ExpressionVector aload length
   /fact cvx exch 1 add array astore def
} def
/EvalLiteral {%
   ReadLiteral
   dup 40 eq%%% there is an open par -> function call
   { pop 2 index
     dup (Sum) eq { EvalSum }
     { dup (IfTE) eq { EvalCond }
       { dup (Derive) eq { pop EvalDerive }
 	{ pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
           /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
 	  exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
   { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
     dup 91 eq%%% there is an open bracket -> vector element
     { pop 1 add NextNonBlankChar pop AnalyzeExpr
       /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
     { pop NextNonBlankChar pop }
     ifelse}
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% the derive function : Derive(n,f(x))
%% firstparindex lastparindex ->
/EvalDerive {
   %% manage the function descripiton
   1 add ReadNumber 3 1 roll NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   1 add NextNonBlankChar pop
   3 -1 roll cvi
   dup 0 eq
   { pop AnalyzeExpr 3 -1 roll pop 1 add }
   { 1 sub 3 1 roll (x)  exch tx@Derive begin DeriveIndexed end 4 -1 roll
     { (x) tx@Derive begin Derive end } repeat
     ExpressionVector exch /ExpressionVector [] def
     AlgToPs aload length
     /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll  /l2 exch def /l1 exch def
     l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
     1 index length /Strlen exch def } ifelse
} def
/EvalSum {%
   pop 1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
   5 -1 roll 4 add array astore def
   %% keep ExpressionVector for later and create a new one for internal Sum computation
   ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
   1 add NextNonBlankChar pop AnalyzeExpr
   %% add each term
   /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
   /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
   array astore def 3 -1 roll pop 1 add
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
/EvalCond {%
   pop 1 add AnalyzeCond NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   ExpressionVector 3 1 roll /ExpressionVector [] def
   1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
   NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add AnalyzeExpr
   NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
   ExpressionVector
   /ExpressionVector 6 -1 roll aload length dup
   6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
   1 add 3 -1 roll pop
} def
%% CondOp STR index
/EvalCondOp {%
   3 -1 roll
   dup (=) eq  { /eq } {%
   dup (<) eq  { /lt } {%
   dup (>) eq  { /gt } {%
   dup (>=) eq { /ge } {%
   dup (<=) eq { /ge } {%
   dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
   ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
   cvx exch pop
   /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
/EvalUnaryOp {
   3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook {} bind def
/PreEvalHook {} bind def
/AnalyzeListOfEPostHook {} bind def
/AnalyzePostHook {} def
/RollOp { 3 1 roll } bind def
end   %tx@CoreAnalyzerDict
%
%--------------------------------------------------------------------%
%
/tx@Derive 41 dict def tx@Derive begin
%%increase ^^ for each function added
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable -> PSVector
/Derive {%
   10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
} def
/Strlen 0 def
/InitParser { dup length /Strlen exch def 0 } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable index -> PSVector
/DeriveIndexed {%
   3 1 roll 10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u,v)'=-(u',v')
/EvalListOfExpr {%
   4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
            2 copy 7 -1 roll dup length 4 1 roll putinterval add
   6 -2 roll pop pop
   2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (-u)'=-(u')
/EvalUnaryOp {
   4 -2 roll 4 index (0) eq
   { (0) StrConcat 7 -1 roll pop }
   { 7 -1 roll 45 eq
     { AddSub AddOpPar true } { false } ifelse
     3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (number)'=0
/EvalNumber { ReadNumber (0) 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u+v)'=u'+v'
/EvalAddSub {%
   7 index dup (0) eq
   { pop true }%% du=0 nothing added
   { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
   ifelse
   5 index dup (0) eq
   { pop { (0) } { 4 -2 roll 2 copy pop 0  6 2 roll GetIntervalNewStr } ifelse }%%dv=0
   { exch
     { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
     { 5 -2 roll 7 index 43 eq%%something yet added
       { AddAdd false } { AddSub AddOpPar true } ifelse }
     ifelse 11 1 roll
     3 -1 roll StrConcat 10 -1 roll { AddClPar } if
     2 copy pop 0 6 2 roll GetIntervalNewStr }
   ifelse
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)' or (u/v)'
/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)'=u'*v+u*v'
/EvalMul {%
   4 -2 roll 7 index dup (0) eq
   { pop false }%%du=0
   { (1) eq%%du=1
     { false }
     { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
     3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
     true }%%du!=0
   ifelse
   5 1 roll 5 index (0) eq
   { 5 -1 roll not { (0) StrConcat } if }%%dv=0
   { 5 -1 roll { AddAdd } if
     4 index (1) eq
     { 8 index StrConcat }
     { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
     ifelse
   }%%dv!=0
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u/v)'=(u'*v-u*v')/v^2
/EvalDiv {%
   4 -2 roll
   4 index (0) eq%%dv=0 -> u'/v
   { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
   { 7 index dup (0) eq
     { pop }%%du=0
     { (1) eq%%du=1
       { false }
       { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
       3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
     ifelse
       AddSub
       4 index (1) eq
       { 8 index StrConcat }
       { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
       ifelse
     %}%%dv!=0
     2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
     AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str1 index str2 -> str1 index
/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
/EvalPower {%
   4 -2 roll 7 index (0) eq
   {%%if du=0 then (u^v)'=v'ln(u)u^v
     4 index (0) eq
     { (0) StrConcat }%%if dv=0 then (u^v)'=0
     { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
       8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
       AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
   }
   {%%du!=0
     4 index (0) eq
     {%%if dv=0 then (u^v)'=vu'u^(v-1)
       5 index dup IsStrNumber
       { dup (0) eq
         { StrConcat }
         { dup dup (1) eq exch (1.0) eq or
           { StrConcat  }
 	  { StrConcat
 	    7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
 	    { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
             (*\() StrConcat 8 index StrConcat (\)) StrConcat
             5 index  dup dup (2) eq exch (2.0) eq or
 	    { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
       { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
         5 index StrConcat (-1\)) StrConcat } ifelse
     }
     {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
       7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
       AddOpPar 5 index StrConcat (\)*\() StrConcat
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (-1\)+\() StrConcat
       4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (\)*ln\() StrConcat
       8 index StrConcat AddClPar
     } ifelse
   } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for factorial ! only cst => null derivative
/EvalFactorial {% DR 09/2011
   4 index (0) eq
   { (0) mark 8 -2 roll  cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
   { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str -> true/false
/IsStrNumber {%
   true exch
   { dup 48 lt exch dup 57 gt 3 -1 roll or
     exch dup 46 ne%%.
     exch dup 43 ne%%+
     exch 45 ne%%-
     and and and { pop false } if } forall
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalLiteral {%
   ReadLiteral dup 40 eq%%% there is an open par -> function call
   { pop (EvalFunc_             ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
   { dup 91 eq%%% there is an open bracket -> vector element
     { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
     { pop EvalVariable }
     ifelse }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first last parpos Expr[first:parpos-1] ->
/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (f(u))'=u'f'(u)
/EvalFunc {
   4 2 roll 4 index (1) ne
   { AddOpPar 4 index StrConcat (\)*) StrConcat } if
   (Eval             ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Func derivative -> Eval<func>
/EvalFunc_sin {%
   PreCommonFunc
   { (cos\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_cos {%
   PreCommonFunc
   { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_tan {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_asin {%
   PreCommonFunc
   { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_acos {%
   PreCommonFunc
   { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_atg {%
   PreCommonFunc
   { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_floor {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ln {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_exp {%
   PreCommonFunc
   {  (exp\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_EXP {%
   PreCommonFunc
   {  (EXP\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_sqrt {%
   PreCommonFunc
   { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Fact {%
   PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
   PostCommonFunc } def
/EvalFunc_sh {%
   PreCommonFunc
   { (ch\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ch {%
   PreCommonFunc
   { (sh\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_th {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argsh {%
   PreCommonFunc
   { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argch {%
   PreCommonFunc
   { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argth {%
   PreCommonFunc
   { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/PreCommonFunc {
   1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
   4 2 roll 4 index (0) eq
   { (0) StrConcat false }
   { 4 index (1)  ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
} def
/PostCommonFunc {
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
/EvalFunc_Derive {%
   1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
   4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
   4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
   exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_Sum {%
   1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop 3 -1 roll pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
   1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
   4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_IfTE {%
   3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
   NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   1 add NextNonBlankChar pop dup 5 1 roll
   AnalyzeExpr NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add NextNonBlankChar pop
   AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
   6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% advance in str until a comma is found (no error detection!)
%% str index -> str index'
/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for condition....
/EvalCondOp { 3 -1 roll pop } bind def
/PutIntervalOneAdd {putinterval 1 add} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add close parenthesis in string at the given index
%% str index -> str index+1
/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add 0 in string at the given index
%% str index -> str index+1
/AddZero {2 copy (0) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddMul {2 copy (*) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a plus sign in string at the given index
%% str index -> str index+1
/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a minus sign in string at the given index
%% str index -> str index+1
/AddSub {2 copy (-) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a pipe sign in string at the given index
%% str index -> str index+1
/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook { dup 5 1 roll } bind def
/PreEvalHook {} def
/AnalyzePostHook { 7 -1 roll pop } bind def
/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
/RollOp { 5 1 roll } bind def
end%%%tx@CoreAnalyzerDict
/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NEW FUNC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
%% x -> theta
/asin {%
   dup abs 1 gt { EQDFasinrangeerror  } if
   dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
} def
%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
%% x -> theta
/acos {%
   dup abs 1 gt { EQDFacosrangeerror  } if
   dup dup mul 1 exch sub sqrt exch atan DegtoRad
} def
%% function arctangent in radians
%% x -> theta
/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
%% HYPERBOLIC FUNCTIONS
/sh { dup Ex exch neg Ex sub 2 div } def
/ch { dup Ex exch neg Ex add 2 div } def
/th { dup sh exch ch div } def
/Argsh { dup dup mul 1 add sqrt add ln } def
/Argch { dup dup mul 1 sub sqrt add ln } def
/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
%% modified exponential funtion for 0
%% x n -> x^n
/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
%% modified exponential funtion for 0
%% x -> e^x
/Ex { Euler exch exp } bind def
%%
%% factorial function
%% n -> n!
/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
/fact { Fact } bind def
/! { Fact } bind def
end
%
% END pst-algparser.pro

%%EndProcSet
%%BeginProcSet: pst-tools.pro 0 0
% $Id: pst-tools.pro 842 2013-10-26 10:25:41Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.04, 2013/10/26
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
/Pi2 1.57079632679489661925640 def
/factorial { % n on stack, returns n!
   dup 0 eq { 1 }{
     dup 1 gt { dup 1 sub factorial mul } if }
   ifelse } def 
%
/MoverN { % m n on stack, returns the binomial coefficient m over n
   2 dict begin
   /n exch def /m exch def
   n 0 eq { 1 }{
     m n eq { 1 }{
       m factorial n factorial m n sub factorial mul div } ifelse } ifelse
   end
} def
%
/ps@ReverseOrderOfPoints { % on stack [P1 P2 P3 ...Pn]=>[Pn,Pn-1,...,P2,P1]
   5 dict begin       % all local
   aload length /n ED % number of coors
   n 2 div cvi /m ED  % number of Points
   /n1 n def
   m { n1 2 roll /n1 n1 2 sub def } repeat
   n array astore
   end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% subroutines for complex numbers, given as an array [a b] 
% which is a+bi = Real+i Imag
%
/cxadd {		% [a1 b1] [a2 b2] = [a1+a2 b1+b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   3 -1 roll		% [a2 b2] a2 [a1 b1]
   dup 0 get		% [a2 b2] a2 [a1 b1] a1
   3 -1 roll		% [a2 b2] [a1 b1] a1 a2
   add			% [a2 b2] [a1 b1] a1+a2
   3 1 roll		% a1+a2 [a2 b2] [a1 b1]
   1 get			% a1+a2 [a2 b2] b1
   exch 1 get		% a1+a2 b1 b2
   add 2 array astore
} def
%
/cxneg {		% [a b]
   dup 1 get		% [a b] b
   exch 0 get		% b a
   neg exch neg		% -a -b
   2 array astore
} def
%
/cxsub { cxneg cxadd } def  % same as negative addition
%
% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
/cxmul {		% [a1 b1] [a2 b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   exch 1 get		% [a1 b1] a2 b2
   3 -1 roll		% a2 b2 [a1 b1]
   dup 0 get		% a2 b2 [a1 b1] a1
   exch 1 get		% a2 b2 a1 b1
   dup			% a2 b2 a1 b1 b1
   5 -1 roll dup		% b2 a1 b1 b1 a2 a2
   3 1 roll mul		% b2 a1 b1 a2 b1a2
   5 -2 roll dup		% b1 a2 b1a2 b2 a1 a1
   3 -1 roll dup		% b1 a2 b1a2 a1 a1 b2 b2
   3 1 roll mul		% b1 a2 b1a2 a1 b2 a1b2
   4 -1 roll add		% b1 a2 a1 b2 b3
   4 2 roll mul		% b1 b2 b3 a1a2
   4 2 roll mul sub	% b3 a3
   exch 2 array astore
} def
%
% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
/cxsqr {		% [a b]   square root
   dup 0 get exch 1 get	% a b
   dup dup mul		% a b b^2
   3 -1 roll		% b b^2 a
   dup dup mul 		% b b^2 a a^2
   3 -1 roll sub		% b a a2
   3 1 roll mul 2 mul	% a2 b2
   2 array astore
} def
%
/cxsqrt {		% [a b]
%  dup cxnorm sqrt /r exch def
%  cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
   cxlog 		% log[a b]
   2 cxrdiv 		% log[a b]/2
   aload pop exch	% b a
   2.781 exch exp	% b exp(a)
   exch cxconv exch	% [Re +iIm] exp(a)
   cxrmul		%
} def
%
/cxarg { 		% [a b]
   aload pop 		% a b
   exch atan 		% arctan b/a
   DegtoRad 		% arg(z)=atan(b/a)
} def
%
% log[a b] = [a^2-b^2 2ab] = [a2 b2]
/cxlog {		% [a b]
   dup 			% [a b][a b]
   cxnorm 		% [a b] |z|
   log 			% [a b] log|z|
   exch 			% log|z|[a b]
   cxarg 		% log|z| Theta
   cxmake2 		% [log|z| Theta]
} def
%
% square of magnitude of complex number
/cxnorm2 {		% [a b]
   dup 0 get exch 1 get	% a b
   dup mul			% a b^2
   exch dup mul add	% a^2+b^2
} def
%
/cxnorm {		% [a b]
   cxnorm2 sqrt
} def
%
/cxconj {		% conjugent complex
   dup 0 get exch 1 get	% a b
   neg 2 array astore	% [a -b]
} def
%
/cxre { 0 get } def	% real value
/cxim { 1 get } def	% imag value
%
% 1/[a b] = ([a -b]/(a^2+b^2)
/cxrecip {		% [a b]
   dup cxnorm2 exch	% n2 [a b]
   dup 0 get exch 1 get	% n2 a b
   3 -1 roll		% a b n2
   dup			% a b n2 n2
   4 -1 roll exch div	% b n2 a/n2
   3 1 roll div		% a/n2 b/n2
   neg 2 array astore
} def
%
/cxmake1 { 0 2 array astore } def % make a complex number, real given
/cxmake2 { 2 array astore } def	  % dito, both given
%
/cxdiv { cxrecip cxmul } def
%
% multiplikation by a real number
/cxrmul {		% [a b] r
   exch aload pop	% r a b
   3 -1 roll dup		% a b r r
   3 1 roll mul		% a r b*r
   3 1 roll mul		% b*r a*r
   exch 2 array astore   % [a*r b*r]
} def
%
% division by a real number
/cxrdiv {		% [a b] r
   1 exch div		% [a b] 1/r
   cxrmul
} def
%
% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
/cxconv {		% theta
   RadtoDeg dup sin exch cos cxmake2
} def

%%%%% ### bubblesort ###
%% syntax : array bubblesort --> array2 trie par ordre croissant
%% code de Bill Casselman
%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
/bubblesort { % on stack must be an array [ ... ]
4 dict begin
    /a exch def
    /n a length 1 sub def
    n 0 gt {
       % at this point only the n+1 items in the bottom of a remain to
       % the sorted largest item in that blocks is to be moved up into
       % position n
       n {
          0 1 n 1 sub {
             /i exch def
             a i get a i 1 add get gt {
                % if a[i] > a[i+1] swap a[i] and a[i+1]
                a i 1 add
                a i get
                a i a i 1 add get
                % set new a[i] = old a[i+1]
                put
                % set new a[i+1] = old a[i]
                put
             } if
          } for
          /n n 1 sub def
       } repeat
    } if
    a % return the sorted array
end
} def
%
/concatstringarray{  %  [(a) (b) ... (z)] --> (ab...z)  20100422
   0 1 index { length add } forall
   string
   0 3 2 roll
   { 3 copy putinterval length add }forall
   pop 
} bind def
%
/dot2comma {% on stack a string (...)
   2 dict begin
   /Output exch def
   0 1 Output length 1 sub {
     /Index exch def
     Output Index get 46 eq { Output Index 44 put } if
   } for
   Output
   end
} def
%
/rightTrim { % on stack the string and the character number to be stripped
   /charNo exch def
   dup
   length 1 sub -1 0 {
     /i exch def dup i get charNo ne { exit } if
   } for
   0 i 1 add getinterval
   dup length string copy
} bind def  % leaves the stripped string on the stack

/psStringwidth /stringwidth load def
/psShow /show load def

%/stringwidth{ 32 rightTrim psStringwidth } bind def

%/show { 32 rightTrim psShow } bind def
%-----------------------------------------------------------------------------%

/pgffunctions {
     /pgfsc{}bind def% stroke color is empty by default
     /pgffc{}bind def% fill color is empty by default
     /pgfstr{stroke}bind def%
     /pgffill{fill}bind def%
     /pgfeofill{eofill}bind def%
     /pgfe{a dup 0 rlineto exch 0 exch rlineto neg 0 rlineto closepath}bind def% rectangle
     /pgfw{setlinewidth}bind def% setlinewidth
     /pgfs{save pgfpd 72 Resolution div 72 VResolution div neg scale
       magscale{1 DVImag div dup scale}if
       pgfx neg pgfy neg translate pgffoa .setopacityalpha}bind def% save
     /pgfr{pgfsd restore}bind def %restore
     userdict begin%
     /pgfo{pgfsd /pgfx currentpoint /pgfy exch def def @beginspecial}bind def %open
     /pgfc{newpath @endspecial pgfpd}bind def %close
     /pgfsd{globaldict /pgfdelta /delta where {pop delta} {0} ifelse put}bind def% save delta
     /pgfpd{/delta globaldict /pgfdelta get def}bind def % put delta
     /.setopacityalpha where {pop} {/.setopacityalpha{pop}def} ifelse % install .setopacityalpha
     /.pgfsetfillopacityalpha{/pgffoa exch def
       /pgffill{gsave pgffoa .setopacityalpha fill 1 .setopacityalpha newpath fill grestore newpath}bind def
       /pgfeofill{gsave pgffoa .setopacityalpha eofill 1 .setopacityalpha newpath eofill grestore newpath}bind def}bind def
     /.pgfsetstrokeopacityalpha{/pgfsoa exch def /pgfstr{gsave pgfsoa .setopacityalpha stroke grestore newpath}bind def}bind def
     /pgffoa 1 def
     /pgfsoa 1 def
     end
} def
%-----------------------------------------------------------------------------%
% END pst-tools.pro

%%EndProcSet
%%BeginProcSet: pst-dots.pro 0 0
% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02,  2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt <tvz@Princeton.EDU>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga  - Dec. 16, 1999
%% Modified by Etienne Riga  - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17 
%
10 dict dup begin			% hold local
   /FontType 3 def
   /FontMatrix [.001 0 0 .001 0 0] def
%  /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
   /FontBBox [-1000 -1000 1000 1000] def  % See end of file in /BuildGlyph
   /Encoding 256 array def
   0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
   Encoding				   % replace with given dot names
     dup (b) 0 get /Bullet put		   % get the numerical position of b in ASCII
%					   % and save /Bullet at this place in Encoding
     dup (c) 0 get /Circle put
     dup (C) 0 get /BoldCircle put	% 67
     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
%%%
     dup (k) 0 get /Asterisk put
     dup (K) 0 get /BoldAsterisk put
     dup (J) 0 get /SolidAsterisk put
     dup (h) 0 get /Hexagon put
     dup (H) 0 get /BoldHexagon put
     dup (G) 0 get /SolidHexagon put
     dup (f) 0 get /Octogon put		% 2008-04-18 hv
     dup (F) 0 get /BoldOctogon put	% 2008-04-18 hv
     dup (g) 0 get /SolidOctogon put	% 2008-04-18 hv
     dup (a) 0 get /Add put
     dup (A) 0 get /BoldAdd put 		% 65
     dup (x) 0 get /Mul put
     dup (X) 0 get /BoldMul put
     dup (m) 0 get /Oplus put
     dup (M) 0 get /BOplus put
     dup (e) 0 get /SolidOplus put
     dup (n) 0 get /Otimes put
     dup (N) 0 get /BOtimes put
     dup (E) 0 get /SolidOtimes put
     dup (i) 0 get /Bar put
     dup (I) 0 get /BoldBar put
     dup (l) 0 get /SolidDiamond put
     dup (d) 0 get /Diamond put
         (D) 0 get /BoldDiamond put
%%% 
/CharProcs 47 dict def
CharProcs begin
   /CirclePath {0 0 500 0 360 arc closepath} def
   /Bullet {CirclePath fill} def
   /Circle {CirclePath .9 .9 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
%-------------- hv begin 2004/07/25   from: er 2003/03/24
   /HexagonPath {
     0 550 moveto -476 275 lineto -476 -275 lineto
     0 -550 lineto 476 -275 lineto 476 275 lineto closepath
   } def
   /SolidHexagon {HexagonPath fill} def
   /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
   /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
%					2008-04-18 hv
   /OctogonPath {
      550 dup 22.5 tan mul dup neg dup add /xMove exch def
      exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
   /SolidOctogon { OctogonPath fill                             } def
   /Octogon {      OctogonPath .89 .89 scale OctogonPath eofill } def
   /BoldOctogon {  OctogonPath .79 .79 scale OctogonPath eofill } def
%
   /AsteriskPath {
     20 0 moveto 10 250 180 500 0 500 curveto
     -180 500 -10 250 -20 0 curveto closepath
   } def
   /Asterisk {
     AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
     60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
   } def
%
   /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
   /BoldAsteriskPath {
     50 30 cos 100 mul moveto  Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp closepath
   } def
   /BoldAsterisk {BoldAsteriskPath fill} def
   /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
   /CrossPath {
     40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
     -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
     40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
   } def
   /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
     -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
     80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
   } def
   /Add {CrossPath fill} def
   /Mul {45 rotate CrossPath fill} def
   /BoldAdd {BoldCrossPath fill} def
   /BoldMul {45 rotate BoldCrossPath fill} def
   /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
   /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
   /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
   /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
   /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
   /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
   /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
   /Bar {BarPath fill} def
   /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
   /BoldBar {BoldBarPath fill} def
   /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 .865 .865 scale DiamondPath eofill} def
   /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
%%%
   /.notdef { } def
end
%
/BuildGlyph {
   exch
   begin 
%  Metrics 1 index get exec 0
     0 0
%      BBoxes 3 index get exec
     -1000 -1000 1000 1000
%     -571.5 -742.5 571.5 742.5
     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

%%EndProcSet
%%BeginProcSet: cmmi10.pfb 0 0
%!PS-AdobeFont-1.0: CMMI10 003.002
%%Title: CMMI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMMI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup
/UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI10 def
/FontBBox {-32 -250 1048 750 }readonly def
/UniqueID 5087385 def
/PaintType 0 def
/FontInfo 10 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI10.) readonly def
  /FullName (CMMI10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle -14.04 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
  /ascent 750 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 15 /epsilon1 put
dup 16 /zeta put
dup 17 /eta put
dup 18 /theta put
dup 19 /iota put
dup 20 /kappa put
dup 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 24 /xi put
dup 25 /pi put
dup 26 /rho put
dup 27 /sigma put
dup 28 /tau put
dup 29 /upsilon put
dup 30 /phi put
dup 31 /chi put
dup 32 /psi put
dup 33 /omega put
dup 34 /epsilon put
dup 35 /theta1 put
dup 36 /pi1 put
dup 37 /rho1 put
dup 38 /sigma1 put
dup 39 /phi1 put
dup 40 /arrowlefttophalf put
dup 41 /arrowleftbothalf put
dup 42 /arrowrighttophalf put
dup 43 /arrowrightbothalf put
dup 44 /arrowhookleft put
dup 45 /arrowhookright put
dup 46 /triangleright put
dup 47 /triangleleft put
dup 48 /zerooldstyle put
dup 49 /oneoldstyle put
dup 50 /twooldstyle put
dup 51 /threeoldstyle put
dup 52 /fouroldstyle put
dup 53 /fiveoldstyle put
dup 54 /sixoldstyle put
dup 55 /sevenoldstyle put
dup 56 /eightoldstyle put
dup 57 /nineoldstyle put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 63 /star put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /flat put
dup 92 /natural put
dup 93 /sharp put
dup 94 /slurbelow put
dup 95 /slurabove put
dup 96 /lscript put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /dotlessi put
dup 124 /dotlessj put
dup 125 /weierstrass put
dup 126 /vector put
dup 127 /tie put
dup 128 /psi put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 173 /Omega put
dup 174 /alpha put
dup 175 /beta put
dup 176 /gamma put
dup 177 /delta put
dup 178 /epsilon1 put
dup 179 /zeta put
dup 180 /eta put
dup 181 /theta put
dup 182 /iota put
dup 183 /kappa put
dup 184 /lambda put
dup 185 /mu put
dup 186 /nu put
dup 187 /xi put
dup 188 /pi put
dup 189 /rho put
dup 190 /sigma put
dup 191 /tau put
dup 192 /upsilon put
dup 193 /phi put
dup 194 /chi put
dup 195 /psi put
dup 196 /tie put
readonly def
currentdict end
currentfile eexec

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cleartomark
{restore}if


%%EndProcSet
%%BeginProcSet: cmr10.pfb 0 0
%!PS-AdobeFont-1.0: CMR10 003.002
%%Title: CMR10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMR10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR10 def
/FontBBox {-40 -250 1009 750 }readonly def
/UniqueID 5000793 def
/PaintType 0 def
/FontInfo 9 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
  /FullName (CMR10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle 0 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 15 /ffl put
dup 16 /dotlessi put
dup 17 /dotlessj put
dup 18 /grave put
dup 19 /acute put
dup 20 /caron put
dup 21 /breve put
dup 22 /macron put
dup 23 /ring put
dup 24 /cedilla put
dup 25 /germandbls put
dup 26 /ae put
dup 27 /oe put
dup 28 /oslash put
dup 29 /AE put
dup 30 /OE put
dup 31 /Oslash put
dup 32 /suppress put
dup 33 /exclam put
dup 34 /quotedblright put
dup 35 /numbersign put
dup 36 /dollar put
dup 37 /percent put
dup 38 /ampersand put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 42 /asterisk put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 60 /exclamdown put
dup 61 /equal put
dup 62 /questiondown put
dup 63 /question put
dup 64 /at put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 94 /circumflex put
dup 95 /dotaccent put
dup 96 /quoteleft put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 124 /emdash put
dup 125 /hungarumlaut put
dup 126 /tilde put
dup 127 /dieresis put
dup 128 /suppress put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 171 /sfthyphen put
dup 172 /nbspace put
dup 173 /Omega put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 178 /ffl put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 187 /cedilla put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 196 /dieresis put
readonly def
currentdict end
currentfile eexec

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   /color_packet colormap offset 3 getinterval def
   color_packet 0 get 0.299 mul
   color_packet 1 get 0.587 mul add
   color_packet 2 get 0.114 mul add
   cvi
   /gray_packet exch def
   compression 0 eq
   {
     /number_pixels 1 def
   }
   {
     currentfile byte readhexstring pop 0 get
     /number_pixels exch 1 add def
   } ifelse
   0 1 number_pixels 1 sub
   {
     pixels exch gray_packet put
   } for
   pixels 0 number_pixels getinterval
} bind def

/PseudoClassPacket
{
   %
   % Get a PseudoClass packet.
   %
   % Parameters:
   %   index: index into the colormap.
   %   length: number of pixels minus one of this color (optional).
   %
   currentfile byte readhexstring pop 0 get
   /offset exch 3 mul def
   /color_packet colormap offset 3 getinterval def
   compression 0 eq
   {
     /number_pixels 3 def
   }
   {
     currentfile byte readhexstring pop 0 get
     /number_pixels exch 1 add 3 mul def
   } ifelse
   0 3 number_pixels 1 sub
   {
     pixels exch color_packet putinterval
   } for
   pixels 0 number_pixels getinterval
} bind def

/PseudoClassImage
{
   %
   % Display a PseudoClass image.
   %
   % Parameters:
   %   class: 0-PseudoClass or 1-Grayscale.
   %
   currentfile buffer readline pop
   token pop /class exch def pop
   class 0 gt
   {
     currentfile buffer readline pop
     token pop /depth exch def pop
     /grays columns 8 add depth sub depth mul 8 idiv string def
     columns rows depth
     [
       columns 0 0
       rows neg 0 rows
     ]
     { currentfile grays readhexstring pop } image
   }
   {
     %
     % Parameters:
     %   colors: number of colors in the colormap.
     %   colormap: red, green, blue color packets.
     %
     currentfile buffer readline pop
     token pop /colors exch def pop
     /colors colors 3 mul def
     /colormap colors string def
     currentfile colormap readhexstring pop pop
     systemdict /colorimage known
     {
       columns rows 8
       [
         columns 0 0
         rows neg 0 rows
       ]
       { PseudoClassPacket } false 3 colorimage
     }
     {
       %
       % No colorimage operator;  convert to grayscale.
       %
       columns rows 8
       [
         columns 0 0
         rows neg 0 rows
       ]
       { GrayPseudoClassPacket } image
     } ifelse
   } ifelse
} bind def

/DisplayImage
{
   %
   % Display a DirectClass or PseudoClass image.
   %
   % Parameters:
   %   x & y translation.
   %   x & y scale.
   %   label pointsize.
   %   image label.
   %   image columns & rows.
   %   class: 0-DirectClass or 1-PseudoClass.
   %   compression: 0-none or 1-RunlengthEncoded.
   %   hex color packets.
   %
   gsave
   /buffer 512 string def
   /byte 1 string def
   /color_packet 3 string def
   /pixels 768 string def

   currentfile buffer readline pop
   token pop /x exch def
   token pop /y exch def pop
   x y translate
   currentfile buffer readline pop
   token pop /x exch def
   token pop /y exch def pop
   currentfile buffer readline pop
   token pop /pointsize exch def pop
   /Times-Roman findfont pointsize scalefont setfont
   x y scale
   currentfile buffer readline pop
   token pop /columns exch def
   token pop /rows exch def pop
   currentfile buffer readline pop
   token pop /class exch def pop
   currentfile buffer readline pop
   token pop /compression exch def pop
   class 0 gt { PseudoClassImage } { DirectClassImage } ifelse
   grestore
   showpage
} bind def
%%EndProlog
%%Page:  1 1
%%PageBoundingBox: 0 0 400 533
DisplayImage
0 0
400 533
12.000000
400 533
0
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%%PageTrailer
%%Trailer
%%EOF

%%EndDocument
  @endspecial 0 TeXcolorgray 0 TeXcolorgray 2111 1733
a @beginspecial 0 @llx 0 @lly 268 @urx 326 @ury 1709
@rwi @setspecial
%%BeginDocument: figures/sitter.eps
%!PS-Adobe-3.0 EPSF-3.0
%%Creator: (ImageMagick)
%%Title: (sitter.eps)
%%CreationDate: (2015-11-02T11:32:16+01:00)
%%BoundingBox: -0 -0 268 326
%%HiResBoundingBox: 0 0 268 326
%%DocumentData: Clean7Bit
%%LanguageLevel: 1
%%Pages: 1
%%EndComments

%%BeginDefaults
%%EndDefaults

%%BeginProlog
%
% Display a color image.  The image is displayed in color on
% Postscript viewers or printers that support color, otherwise
% it is displayed as grayscale.
%
/DirectClassPacket
{
   %
   % Get a DirectClass packet.
   %
   % Parameters:
   %   red.
   %   green.
   %   blue.
   %   length: number of pixels minus one of this color (optional).
   %
   currentfile color_packet readhexstring pop pop
   compression 0 eq
   {
     /number_pixels 3 def
   }
   {
     currentfile byte readhexstring pop 0 get
     /number_pixels exch 1 add 3 mul def
   } ifelse
   0 3 number_pixels 1 sub
   {
     pixels exch color_packet putinterval
   } for
   pixels 0 number_pixels getinterval
} bind def

/DirectClassImage
{
   %
   % Display a DirectClass image.
   %
   systemdict /colorimage known
   {
     columns rows 8
     [
       columns 0 0
       rows neg 0 rows
     ]
     { DirectClassPacket } false 3 colorimage
   }
   {
     %
     % No colorimage operator;  convert to grayscale.
     %
     columns rows 8
     [
       columns 0 0
       rows neg 0 rows
     ]
     { GrayDirectClassPacket } image
   } ifelse
} bind def

/GrayDirectClassPacket
{
   %
   % Get a DirectClass packet;  convert to grayscale.
   %
   % Parameters:
   %   red
   %   green
   %   blue
   %   length: number of pixels minus one of this color (optional).
   %
   currentfile color_packet readhexstring pop pop
   color_packet 0 get 0.299 mul
   color_packet 1 get 0.587 mul add
   color_packet 2 get 0.114 mul add
   cvi
   /gray_packet exch def
   compression 0 eq
   {
     /number_pixels 1 def
   }
   {
     currentfile byte readhexstring pop 0 get
     /number_pixels exch 1 add def
   } ifelse
   0 1 number_pixels 1 sub
   {
     pixels exch gray_packet put
   } for
   pixels 0 number_pixels getinterval
} bind def

/GrayPseudoClassPacket
{
   %
   % Get a PseudoClass packet;  convert to grayscale.
   %
   % Parameters:
   %   index: index into the colormap.
   %   length: number of pixels minus one of this color (optional).
   %
   currentfile byte readhexstring pop 0 get
   /offset exch 3 mul def
   /color_packet colormap offset 3 getinterval def
   color_packet 0 get 0.299 mul
   color_packet 1 get 0.587 mul add
   color_packet 2 get 0.114 mul add
   cvi
   /gray_packet exch def
   compression 0 eq
   {
     /number_pixels 1 def
   }
   {
     currentfile byte readhexstring pop 0 get
     /number_pixels exch 1 add def
   } ifelse
   0 1 number_pixels 1 sub
   {
     pixels exch gray_packet put
   } for
   pixels 0 number_pixels getinterval
} bind def

/PseudoClassPacket
{
   %
   % Get a PseudoClass packet.
   %
   % Parameters:
   %   index: index into the colormap.
   %   length: number of pixels minus one of this color (optional).
   %
   currentfile byte readhexstring pop 0 get
   /offset exch 3 mul def
   /color_packet colormap offset 3 getinterval def
   compression 0 eq
   {
     /number_pixels 3 def
   }
   {
     currentfile byte readhexstring pop 0 get
     /number_pixels exch 1 add 3 mul def
   } ifelse
   0 3 number_pixels 1 sub
   {
     pixels exch color_packet putinterval
   } for
   pixels 0 number_pixels getinterval
} bind def

/PseudoClassImage
{
   %
   % Display a PseudoClass image.
   %
   % Parameters:
   %   class: 0-PseudoClass or 1-Grayscale.
   %
   currentfile buffer readline pop
   token pop /class exch def pop
   class 0 gt
   {
     currentfile buffer readline pop
     token pop /depth exch def pop
     /grays columns 8 add depth sub depth mul 8 idiv string def
     columns rows depth
     [
       columns 0 0
       rows neg 0 rows
     ]
     { currentfile grays readhexstring pop } image
   }
   {
     %
     % Parameters:
     %   colors: number of colors in the colormap.
     %   colormap: red, green, blue color packets.
     %
     currentfile buffer readline pop
     token pop /colors exch def pop
     /colors colors 3 mul def
     /colormap colors string def
     currentfile colormap readhexstring pop pop
     systemdict /colorimage known
     {
       columns rows 8
       [
         columns 0 0
         rows neg 0 rows
       ]
       { PseudoClassPacket } false 3 colorimage
     }
     {
       %
       % No colorimage operator;  convert to grayscale.
       %
       columns rows 8
       [
         columns 0 0
         rows neg 0 rows
       ]
       { GrayPseudoClassPacket } image
     } ifelse
   } ifelse
} bind def

/DisplayImage
{
   %
   % Display a DirectClass or PseudoClass image.
   %
   % Parameters:
   %   x & y translation.
   %   x & y scale.
   %   label pointsize.
   %   image label.
   %   image columns & rows.
   %   class: 0-DirectClass or 1-PseudoClass.
   %   compression: 0-none or 1-RunlengthEncoded.
   %   hex color packets.
   %
   gsave
   /buffer 512 string def
   /byte 1 string def
   /color_packet 3 string def
   /pixels 768 string def

   currentfile buffer readline pop
   token pop /x exch def
   token pop /y exch def pop
   x y translate
   currentfile buffer readline pop
   token pop /x exch def
   token pop /y exch def pop
   currentfile buffer readline pop
   token pop /pointsize exch def pop
   /Times-Roman findfont pointsize scalefont setfont
   x y scale
   currentfile buffer readline pop
   token pop /columns exch def
   token pop /rows exch def pop
   currentfile buffer readline pop
   token pop /class exch def pop
   currentfile buffer readline pop
   token pop /compression exch def pop
   class 0 gt { PseudoClassImage } { DirectClassImage } ifelse
   grestore
} bind def
%%EndProlog
%%Page:  1 1
%%PageBoundingBox: 0 0 268 326
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       dup c src c get dup 32 lt { pop 32 } if put /c c 1 add def
    } repeat
} B
/Begin {
     /saver save def
     srcFM exch 3 exch put
     0 ne /debugMode X 0 setrepl
     dup /S exch dict def { S 3 1 roll exch convert exch put } repeat
     srcM CM dup invertmatrix pop
     mark { currentdict { end } stopped { pop exit } if } loop
     PSfragDict counttomark { begin } repeat pop
} B
/End {
     mark { currentdict end dup PSfragDict eq { pop exit } if } loop
     counttomark { begin } repeat pop
     getrepl saver restore
     7 idiv dup /S exch dict def {
         6 array astore /mtrx X tstr cvs /K X
         S K [ S K known { S K get aload pop } if mtrx ] put
     } repeat
} B
/Place {
     tstr cvs /K X
     S K known {
         bind /proc X tM CM pop
         CP /cY X /cX X
         0 0 transform idtransform neg /aY X neg /aX X
         S K get dup length /maxiter X
         /iter 1 def {
             iter maxiter ne { /saver save def } if
             tM setmatrix aX aY translate
             [ exch aload pop idtransform ] concat
             cX neg cY neg translate cX cY moveto
             /proc load OE
             iter maxiter ne { saver restore /iter iter 1 add def } if
         } forall
         /noXY { CP /cY X /cX X } stopped def
         tM setmatrix noXY { newpath } { cX cY moveto } ifelse
     } {
         Hide OE Unhide
     } ifelse
} B
/normalize {
     2 index dup mul 2 index dup mul add sqrt div
     dup 4 -1 roll exch mul 3 1 roll mul
} B
/replace {
     aload pop MD
     CP /bY X /lX X gsave sM setmatrix
     str stringwidth abs exch abs add dup 0 eq
         { pop } { 360 exch div dup scale } ifelse
     lX neg bY neg translate newpath lX bY moveto
     str { /ch X ( ) dup 0 ch put false charpath ch Kproc } forall
     flattenpath pathbbox [ /uY /uX /lY /lX ] MD
     CP grestore moveto
     currentfont /FontMatrix get dstFM copy dup
     0 get 0 lt { uX lX /uX X /lX X } if
     3 get 0 lt { uY lY /uY X /lY X } if
     /cX uX lX add 0.5 mul def
     /cY uY lY add 0.5 mul def
     debugMode { gsave 0 setgray 1 setlinewidth
         lX lY moveto lX uY lineto uX uY lineto uX lY lineto closepath
         lX bY moveto uX bY lineto lX cY moveto uX cY lineto
         cX lY moveto cX uY lineto stroke
     grestore } if
     dstFM dup invertmatrix dstM CM srcM
     2 { dstM concatmatrix } repeat pop
     getrepl /temp X
         S str convert get {
             aload pop [ /rot /scl /loc /K ] MD
             /aX cX def /aY cY def
             loc {
                 dup 66  eq { /aY bY def } { % B
                 dup 98  eq { /aY lY def } { % b
                 dup 108 eq { /aX lX def } { % l
                 dup 114 eq { /aX uX def } { % r
                 dup 116 eq { /aY uY def }   % t
                 if } ifelse } ifelse } ifelse } ifelse pop
             } forall
             K srcFM rot tM rotate dstM
             2 { tM concatmatrix } repeat aload pop pop pop
             2 { scl normalize 4 2 roll } repeat
             aX aY transform
             /temp temp 7 add def
         } forall
     temp setrepl
} B
/Rif {
     S 3 index convert known { pop replace } { exch pop OE } ifelse
} B
/XA { bind [ /Kproc /str } B /XC { ] 2 array astore def } B
/xs   { pop } XA XC
/xks  { /kern load OE } XA /kern XC
/xas  { pop ax ay rmoveto } XA /ay /ax XC
/xws  { c eq { cx cy rmoveto } if } XA /c /cy /cx XC
/xaws { ax ay rmoveto c eq { cx cy rmoveto } if }
     XA /ay /ax /c /cy /cx XC
/raws { xaws { awidthshow } Rif } B
/rws  { xws { widthshow } Rif } B
/rks  { xks { kshow } Rif } B
/ras  { xas { ashow } Rif } B
/rs   { xs { show } Rif } B
/rrs { getrepl dup 2 add -1 roll //restore exec setrepl } B
PSfragDict begin
islev2 not { /restore { /rrs PSfrag } B } if
/show       { /rs   PSfrag } B
/kshow      { /rks  PSfrag } B
/ashow      { /ras  PSfrag } B
/widthshow  { /rws  PSfrag } B
/awidthshow { /raws PSfrag } B
end PSfragDict RO pop
end

%%EndProcSet
%%BeginProcSet: pstricks.pro 0 0
% $Id: pstricks.pro 902 2014-03-30 16:23:33Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 1.22, 2014/02/20
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
% Define the follwing gs-functions if not known, eg when using distiller
%
systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if
systemdict /.setblendmode known not {/.setblendmode { pop } def } if
systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if
%
/tx@Dict 200 dict def 				% the main PSTricks dictionary
tx@Dict begin
/ADict 25 dict def				% The arrow dictionary
/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
/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def  % return 0 for negative arguments 
/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known
/ATAN1 {neg -1 atan 180 sub } def		% atan(x) (only one parameter)
/Div { dup 0 eq { pop } { div } ifelse } def  	% control the division
/Log { dup 1e-20 lt { pop -1e30 }{ log } ifelse } def % control the log
/tan { dup cos abs 1.e-10 lt
   { pop 1.e10 } 				% return 1.e10 as infinit
   { dup sin exch cos div } ifelse 		% default sin/cos
} def
/Tan { dup sin exch cos Div } def 		% sin(x)/cos(x) x in degrees
/Acos {dup dup mul neg 1 add dup 0 lt {		% arc cos, returns 0 when negative root
   pop pop 0 }{ sqrt exch atan} ifelse } def
/Acos2 { 2 dict begin
   /x ED /y ED
   y abs 1.0e-20 lt { 1.0e30 } if
   x y div
   dup dup mul neg 1 add dup 0 lt {		% arc cos needs two values x,y
   pop pop 0 }{ sqrt exch atan} ifelse
   y 0 lt { 180 add } if
} def
/NET { neg exch neg exch T } def	      	% change coordinate system to the negative one 
/Pyth { dup mul exch dup mul add sqrt } def   	% Pythagoras, expects 2 parameter
/Pyth2 {					% Pythagoras, xA yA xB yB
   3 -1 roll 		% xA xB yB yA
   sub			% xA xB yB-yA
   3 1 roll 		% yB-yA xA xB
   sub			% yB-yA xA-xB
   Pyth } def
/PtoC { 2 copy cos mul 3 1 roll sin mul } def 	% Polar to Cartesian
%/Rand { rand 4294967295 div } def		% a real random number
/Rand { rand 2147483447 div } def		% a real random number between 0 and 1
%----------------- hv added 20050516 ---------------
/PiDiv2 1.57079632680 def
/Pi 3.14159265359 def 
/TwoPi 6.28318530718 def
/Euler 2.71828182846 def 
%/e Euler bind def
%
/RadtoDeg { 180 mul Pi div } bind def 		% convert from radian to degrees
/DegtoRad { Pi mul 180 div } bind def 		% viceversa
%
/startGlobal { true setglobal globaldict begin } bind def
/endGlobal { end false setglobal } bind def
/pssetRGBcolor /setrgbcolor load def
/pssetCMYKcolor /setcmykcolor load def
/pssetGraycolor /setgray load def
%
%----------------- hv end---------------------------
/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			% BP/PT scaling
/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 % pattern should fit evenly in b
     dup /X ED % pattern array
     0 get /y ED % length of first black segment
     /z 0 X {add} forall def % length of the full pattern
     %% Computation of the scaling factor as described by van Zandt:
     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
     %%%% scaling factor on stack.
     /z ED %% now, z is the scaling factor
     false % for the length test below
     X { z mul } forall X astore %% modification TN 04-08-07
     %%% Checking whether at least one dash in X has positive length:
     {0 gt or} forall
     { 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
%
/SymbolLine {   % on stack [ x y x y ...
   counttomark 					% number of elements
   2 div cvi /n ED     				% n pairs
   /YA ED /XA ED					% the start point
   n 1 sub {
     /YB ED /XB ED
     /XLength XB XA sub def
     /YLength YB YA sub def
     /PAngle YLength XLength Atan def
     /XYLength XLength YLength Pyth def
     %% for negative SymStep we calculate the distance
     SymStep 0 lt
       { %XYLength SymStep div abs cvi
         /nSym SymStep abs cvi def }
       { /nSym XYLength SymStep div cvi def }
     ifelse
     0.5 setflat
     /Shift Symbol stringwidth pop 2 div def
     /deltaX XLength nSym div def
     /deltaY YLength nSym div def
     curveticks
       { XA YA moveto }
       { XA Shift sub YA Shift sub moveto }
     ifelse
     nSym {
       gsave
       curveticks
         { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
           currentpoint translate rotAngle rotate
           0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
           SymbolLinewidth setlinewidth stroke
         }
         {
           rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
           Symbol show
         }
       ifelse
       grestore
       deltaX deltaY rmoveto
     } repeat
     /YA YB def /XA XB def
   } repeat
   curveticks
     { XA YA moveto }
     { XA Shift sub YA Shift sub moveto }
   ifelse
   gsave
   curveticks
     { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
       XA YA translate rotAngle rotate
       0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
       SymbolLinewidth setlinewidth stroke
     }
     {
       rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
       Symbol show
     }
   ifelse
   grestore
   pop 				% delete the mark symbol
} def
%
/LineFill { % hv ------------ patch 7 -------------
   gsave
   abs /hatchWidthInc ED
   abs /hatchSepInc ED
   abs CLW add /a ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform pathbbox
   /y2 ED
   a Div ceiling cvi /x2 ED /y1 ED
   a Div cvi /x1 ED /y2 y2 y1 sub def
   clipType   % must be defined in pstricks.tex: clip -- eoclip
   newpath
   2 setlinecap
   systemdict
   /setstrokeadjust known { true setstrokeadjust } if
   x2 x1 sub 1 add {
     x1 a mul y1 moveto 0 y2 rlineto stroke
     /x1 x1 1 add
       hatchWidthInc 0 gt { CLW add } if
     def
     hatchSepInc 0 gt hatchWidthInc 0 gt or {
       /a a hatchSepInc add def
       CLW hatchWidthInc add SLW
     } if
   } repeat
   grestore
   pop pop } def
%
/DotFill {%	 on stack: dot radius
   /dotRadius ED
   abs CLW add /a ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform
   pathbbox % llx lly urx ury of smallest bounding box
   /y2 ED /x2 ED /y1 ED /x1 ED
   y2 y1 sub a div 2 add cvi /Ny ED
   x2 x1 sub a div 2 add cvi /Nx ED
   clipType   % must be defined in pstricks.tex: clip -- eoclip
   newpath
   /yA y1 dotRadius add CLW add def
   /xA0 x1 dotRadius add CLW add def
   Ny {
      /xA xA0 def
      Nx {
        newpath
        xA yA dotRadius 0 360 arc
        SolidDot { gsave fill grestore } if
        stroke
        xA a add /xA ED
      } repeat
      yA a add /yA ED
   } repeat
   grestore
} def
%
/PenroseFill {%	 on stack: scaling factor
   /Scale ED
%  1 exch div round /penroseFactor ED 
%  a 0 dtransform round exch round exch
%  2 copy idtransform 
%  exch Atan rotate 
%  idtransform pop /a ED 
%  .25 .25 itransform pathbbox 
%  /y2 ED 
%  a Div ceiling cvi /x2 ED /y1 ED 
%  a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath 
gsave
   220 150 translate
   Scale dup scale
   systemdict /setstrokeadjust known { true setstrokeadjust } if
   /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
  { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
   [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
   i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
   mul j l + S rmoveto}F i L j L stroke }F}F}F}F
   grestore 
%  pop pop 
} def
%
/PenroseFillA {%  on stack: scaling factor, border color, kite color, dart color
   /Scale ED
   Scale dup scale
   /border_colour ED
   /kite_colour ED
   /dart_colour ED
   clip
   newpath
   gsave
   100 100 translate
   6
   Scale 1 lt { 1 Scale dup add div mul cvi } if %%%%   Number of iterations
   10					%%%%   Long side length in millimeters
   /border_width { L 0.06 mul }def		%%%%   Choose the scalefactor for the borders
   /L exch 25.4 div 72 mul def		%%%%   Conversion: mm -> inches -> points
   /f{-1 5 sqrt add 2 div}bind def		%%%%   The reciprocal of the golden ratio
   /l{L f mul}bind def			%%%%   Short side length l = L*f
   /Ll{L l add}bind def			%%%%   Ll =  L + l
   /c{36 cos L mul}bind def		%%%%   c  =  L*cos(36)
   /s{36 sin L mul}bind def		%%%%   s  =  L*sin(36)
   /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
 	     0 setlinewidth stroke grestore border_colour stroke } bind def
   /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
 			   Ll 0 translate 144 rotate kite grestore }
 	      		 { kite_colour L draw_tile }ifelse
 	     pop } bind def
   /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
 			   -144 rotate Ll neg 0 translate half_dart grestore }
 	      		 { dart_colour l draw_tile }ifelse
   	     pop } bind def
   /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
   border_width setlinewidth  1 setlinejoin  1 setlinecap
%  450 0 translate
   dup f exch neg exp dup scale
   5 {kite 72 rotate } repeat stroke
   grestore
} def
%
%
/TruchetFill { %	 on stack: scaling factor
   10 dict begin
   dup dup scale
   1 exch div round /penroseFactor ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform pathbbox
   /y2 ED
   a Div ceiling cvi /x2 ED /y1 ED
   a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath
   systemdict
   /setstrokeadjust known { true setstrokeadjust } if
   /ma a neg def
   /ha a 2 div def
   /mha ha neg def
   /tile {
     rand dup 2 idiv 2 mul eq { 90 rotate } if
     mha mha moveto ha mha lineto
     ha ha lineto mha ha lineto
%    closepath .1 setlinewidth stroke
     contents
   } def
   /contents{
     0 ha moveto ha 0 lineto
     0 mha moveto mha 0 lineto
%    1 setlinewidth stroke
   } def
   /dotiling {
     f ma mul a f a mul {
       /i exch def
       f ma mul a f a mul {
         /j exch def
         gsave i j translate
         tile stroke grestore
       } for
     } for
   } def
%
   /f 3 def
   5 srand dotiling
   end % local user dict
} def
%
/BeginArrow {
   ADict begin 			% hold it local, for end see EndArrow
   /@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 % end the ADict
%
/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
%
/ArrowD { % the sides are drawn as curves (hv 20071211)
   CLW mul add dup
   2 div /w ED
   mul dup /h ED
   mul /Inset ED
   { 0 h T 1 -1 scale } if % changes the direction
% we use y=w/h^2 * x^2 as equation for the control points
% for the coordinates the arrow is seen from top to bottom
% the bottom (tip) is (0;0)
   w neg h moveto % lower left of >
   w 9 div 4 mul neg h 3 div 2 mul
   w 9 div neg       h 3 div
   0 0 curveto    % tip of >
   w 9 div        h 3 div
   w 9 div 4 mul  h 3 div 2 mul
   w h curveto % upper left of >
   w neg Inset neg rlineto % move to x=0 and inset
   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 { % DS is the dot size
   { /z DS def } { /z 0 def } ifelse  	% outer or inner dimen
   /b ED 				% the color definition
   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 { % holds the coordinates and on top of stack the showpoints boolean
   /showpoints ED
   counttomark 2 div dup cvi /n ED  	% n 2 div on stack
   n eq not { exch pop } if		% even numbers of points? delete one
   ] aload /Points ED
   showpoints not { Points aload pop } if
%    { ] aload /Points ED } 
%    { n 2 mul 1 add -1 roll pop } ifelse	% delete the mark symbol 
} 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
%
/LineToYAxis {
   /Ox ED		% Save the x origin value
   NArray            % all x-y pairs on stack
   n { 2 copy moveto % go to current point
     Ox exch Lineto   % line to y-axis
     pop             % delete old x-value
   } repeat
} def
%
/LineToXAxis{
   /Oy ED		% Save the y origin value
   NArray		% all x-y pairs on stack
   n 0 eq not
     { n 1 eq { 0 0 /n 2 def } if
       ArrowA
       /n n 2 sub def
       CP 2 copy moveto pop Oy Lineto
       n { 2 copy moveto pop Oy Lineto } repeat
       CP
       4 2 roll
       ArrowB
       2 copy moveto pop Oy
       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
%
/SymbolPolygon {   % on stack [ x y x y ...
   counttomark 					% number of elements
   2 add /m ED
   2 copy m 2 roll				% copy last two
   m 2 div cvi /n ED    				% n pairs
   /YA ED /XA ED					% the start point
   n 1 sub {
     /YB ED /XB ED
     /XLength XB XA sub def
     /YLength YB YA sub def
     /PAngle YLength XLength Atan def
     /XYLength XLength YLength Pyth def
     /nSym XYLength SymStep Div cvi def
     /Shift Symbol stringwidth pop 2 Div def
     /deltaX XLength nSym Div def
     /deltaY YLength nSym Div def
     XA Shift sub YA Shift sub moveto
     nSym {
       gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
       Symbol show
       grestore
       deltaX deltaY rmoveto
     } repeat
%    XB Shift sub YB Shift sub moveto Symbol show
     /YA YB def /XA XB def
   } repeat
   pop	% delete the mark symbol
} 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
%
/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
%
/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
%
/CurvePath {
   %% for negative SymStep we calculate the distance
   SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
   0.5 setflat
   flattenpath /z 0 def /z0 0 def
   { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
     x1 Shift sub y1 Shift sub moveto
     gsave
     curveticks
       { x1 y1 translate startAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       { startAngle rotate Symbol show }
     ifelse
     grestore /z0 z def }
   { /y ED /x ED PathLength@ z z0 sub SymStep ge {
       x Shift sub y Shift sub moveto
       gsave
       curveticks
         { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
           x y translate rotAngle rotate
           0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
           SymbolLinewidth setlinewidth stroke
         }
         {
           rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
           Symbol show
         }
       ifelse
       grestore /z0 z def } if
     /yOld y def /xOld x def }
   {} %% the lineto part
   { /y y2 def /x x2 def PathLength@
     x Shift sub y Shift sub moveto
     gsave
     curveticks
       { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
         x y translate rotAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       {
         x Shift sub y Shift sub moveto
         rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
         Symbol show
       }
     ifelse
     grestore
   }
   pathforall 
%  curveticks 
%   { gsave 
%     x y translate rotAngle rotate 
%     0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
%     SymbolLinewidth setlinewidth stroke grestore
%   } if
   z 
} def
%
/OpenSymbolCurve {
   OpenCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/AltOpenSymbolCurve {
   AltCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolCurve {
   ClosedCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} def
%
/CalcBezierSpline {%  Christoph Bersch
   10 dict begin
   /getX { Points exch 2 mul get } def
   /getY { Points exch 2 mul 1 add get } def
   /n Points length 1 sub 2 idiv def
   /GetFirstControlPoints {
     /x n array def
     /tmp n array def
     /b 2 def
     x 0 rhs 0 get b div put
     1 1 n 1 sub {
       /i exch def
       tmp i 1 b div dup 4 1 roll put
       i n 1 sub lt { 4 }{ 3.5 } ifelse exch sub /b exch def
       x i rhs i get x i 1 sub get sub b div put
     } for
     1 1 n 1 sub {
       n exch sub
       dup dup x exch 1 sub 2 copy 6 2 roll
       get 3 1 roll tmp exch get
       exch x exch get mul sub
       put
     } for
     x
   } def
   %
   n 1 eq {
     0 getX 2 mul 1 getX add 3 div
     0 getY 2 mul 1 getY add 3 div
     exch dup 3 1 roll 2 mul 0 getX sub
     exch dup 3 1 roll 2 mul 0 getY sub
     [ 0 getX 0 getY 7 3 roll 1 getX 1 getY ] /outPoints exch def
   } {
     /outPoints 6 n mul 2 add array def
     0 1 n {
       dup dup 6 mul dup 1 add
       outPoints exch 5 -1 roll getY put
       outPoints exch 3 -1 roll getX put
     } for
     /rhs n array def
     1 1 n 2 sub {
       rhs exch dup dup getX 4 mul exch 1 add getX 2 mul add put
     } for
     rhs 0 0 getX 1 getX 2 mul add put
     rhs n 1 sub dup getX 8 mul n getX add 2 div put
     GetFirstControlPoints
     1 1 n 2 sub {
       rhs exch dup dup getY 4 mul exch 1 add getY 2 mul add put
     } for
     rhs 0 0 getY 1 getY 2 mul add put
     rhs n 1 sub dup getY 8 mul n getY add 2 div put
     GetFirstControlPoints
     0 1 n 1 sub {
       /i exch def
       2 copy
       i get outPoints 6 i mul 3 add 3 -1 roll put
       i get outPoints 6 i mul 2 add 3 -1 roll put
       2 copy
       i n 1 sub lt {
         i 1 add get i 1 add getY 2 mul exch sub outPoints 6 i mul 5 add 3 -1 roll put
         i 1 add get i 1 add getX 2 mul exch sub outPoints 6 i mul 4 add 3 -1 roll put
       }{
         n 1 sub get n getY add 2 div outPoints 6 n 1 sub mul 5 add 3 -1 roll put
         n 1 sub get n getX add 2 div outPoints 6 n 1 sub mul 4 add 3 -1 roll put
       } ifelse
     } for
     pop pop
   } ifelse
   outPoints
   end
} def
/Spline {
   /showpoints ED
   counttomark 2 div dup cvi /n ED
   n eq not { exch pop } if
   ] /Points ED
   n 1 gt {
     CalcBezierSpline
     mark exch aload pop
     ArrowA
     n 2 sub {
       6 2 roll 4 2 roll curveto
     } repeat
     6 2 roll 4 2 roll ArrowB curveto
   } if
} def
/OpenSymbolSpline {
   Spline
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/OpenSymbolBezier {
   OpenBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolBezier {
   /f ED				 % save showpoints value
   2 copy /yEnd ED /xEnd ED
   counttomark -2 roll 2 copy /yStart ED /xStart ED
   counttomark 2 roll
   f
   ClosedBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath
   [ xEnd yEnd xStart yStart SymbolLine 
} 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 ED /x0 ED /y1 ED /x1 ED
   /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
%
/Parab1 { % 1 end  |  0 SP
   /ySP ED /xSP ED /y1 ED /x1 ED
   /dx xSP x1 sub 3 div def
   /dy ySP y1 sub 3 div def
   newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
                        x1 ySP lineto closepath clip
   currentpoint
   newpath moveto
   xSP dx sub ySP dy add x1 y1 ArrowA
   xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
   curveto
   /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def 
} def
%
/Grid {
   newpath
   /a 4 string def
   /b ED % 				psk@gridlabels in pt
   /c ED % 				{ \pst@usecolor\psgridlabelcolor }
   /n ED % 				psk@griddots
   cvi dup 1 lt { pop 1 } if
   /s ED % 				\psk@subgriddiv
   s div dup 0 eq { pop 1 } if
   /dy ED s div dup 0 eq { pop 1 } if %	\pst@number\psyunit abs
   /dx ED dy div round dy mul %		\pst@number\psxunit abs
   /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 {
   /rotAngle ED
   /mtrx CM def
   T
   rotAngle rotate
   scale 0 0 1 5 3 roll arc
   mtrx setmatrix 
} def
%
/ArcAdjust { %%%% Vincent Guirardel
% given a target length (targetLength) and an initial angle (angle0) [in the stack],
% let  M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
% This computes an angle t such that (x0,y0) is at distance 
% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
% contrary to TvZ's code.
% To achieve, this, one iterates the following process: start with some angle t,
% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
%
% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
% the value of d = add/sub is used to know on which side we have to move.
% It is only used in the initialisation of the angle before the iteration.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input stack:  1: target length 2: initial angle
% variables used : rx, ry, d (=add/sub)
%
   /targetLength ED /angle0 ED
   /x0 rx angle0 cos mul def
   /y0 ry angle0 sin mul def
% we are looking for an angle t such that (x0,y0) is at distance targetLength 
% from the point M(t)=(rx*cos(t),ry*sin(t)))
%initialisation of angle (using 1st order approx = TvZ's code)
   targetLength 57.2958 mul
   angle0 sin rx mul dup mul
   angle0 cos ry mul dup mul
   add sqrt div 
% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
% (if the ellipse is very curved at the point where we draw the arrow, %
% the value can be much more than 360 degrees !)
% this should avoid going on the wrong side (more than 180 degrees) or go near
% a bad attractive point (at 180 degrees)
   dup 90 ge { pop 90 } if
   angle0 exch d % add or sub
% maximum number of times to iterate the iterative procedure:
% iterative procedure: takes an angle t on top of stack, computes a 
% better angle (and put it on top of stack)
   30 { dup
% compute distance D between (x0,y0) and M(t)
     dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
% if D almost equals targetLength, we stop
     dup targetLength sub abs 1e-5 le { pop exit } if
% stack now contains D t
% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
     exch dup cos rx mul x0 sub  exch sin ry mul y0 sub
% stack contains:  y(t)-y0, x(t)-x0, d
     2 index Div targetLength mul y0 add ry Div exch
     2 index Div targetLength mul x0 add rx Div
% stack contains x(t')/rx , y(t')/ry , d
% now compute t', and remove D from stack
     atan exch pop
   } repeat
% we don't look at what happened... in particular, if targetLength is greater 
% than the diameter of the ellipse...
% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
% to give back the result as a an angle relative to angle0 we could add the following line:
% angle0 sub 0 exch d
%
% begin bug fix 2006-01-11
% we want to adjust the new angle t' by a multiple of 360 so that  | t'-angle0 | <= 180
%(we don't want to make the ellipse turn more or less than it should)...
dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
% end bug fix
} def
%
/EllipticArcArrow {
   /d ED      % is add or sub
   /b ED      % arrow procedure
   /a1 ED     % angle
   gsave
   newpath
   0 -1000 moveto
   clip                  % Set clippath far from arrow.
   newpath
   0 1 0 0 b             % Draw arrow to determine length.
   grestore
% Length of arrow is on top of stack. Next 3 numbers are junk.
%
   a1 exch ArcAdjust   % Angular position of base of arrow.
   /a2 ED
   pop pop pop
   a2 cos rx mul xOrig add % hv 2007-08-29   x->xOrig
   a2 sin ry mul yOrig add % hv 2007-08-29   y->yOrig
   a1 cos rx mul xOrig add %
   a1 sin ry mul yOrig add % 
% Now arrow tip coor and base coor are on stack.
   b pop pop pop pop       % Draw arrow, and discard coordinates.
   a2 CLW 8 div
% change value of d (test it by looking if  `` 1 1 d '' gives 2 or not )
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
   ArcAdjust
% resets original value of d
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse  % Adjust angle to give overlap.
} def
%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
%
/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 {
   5 dict begin
   /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
   end
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro

%%EndProcSet
%%BeginProcSet: pst-algparser.pro 0 0
% $Id: pst-algparser.pro 902 2014-03-30 16:23:33Z herbert $
%%
%% PostScript prologue for PSTricks algorithm parser
%% Version 0.05, 2014/03/30
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%%-----------------------------------------------------------------------------%
%
/AlgParser { tx@AlgToPs begin AlgToPs end } def  % Dominique Rodriguez
%
/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
%
% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
%
% 09/2011 DR factorial with ! added
%
% E->T|E+T
% T->FS|T*FS
% FS -> F | +FS | -FS
% F->P|F^SF|P!
% P->(E)|literal
% literal->number|var|var[E]|func(params)
% params->E|E,param
% number->TOBEFINISHED
%
%% E expression, T term, SF signed factor, F factor, P power
%
%% parser
%
%% str
%
%% C->E<condition_operators>E
%% STR index -> STR index+lenExpr
/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp  } def
%
%% analyze Expression List (separator , or | )
%% STR index -> STR index+lenExpr
%% /AnalyzeListOfE {
%%   { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
%%     NextNonBlankChar dup 0 eq { pop exit } if
%%     dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
%%     pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
%%   AnalyzeListOfEPostHook
%% } def
/AnalyzeListOfE {
   /NotFirst false def
   { NextNonBlankChar pop AnalyzeExpr
     NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
     dup Strlen eq { exit } if NextNonBlankChar
     dup 44 ne 1 index 124 ne and
     { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
     if  pop 1 add } loop
   AnalyzeListOfEPostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% E->T|E+T
%% STR index -> STR index+lenExpr
/AnalyzeExpr {
   AnalyzePreHook AnalyzeTerm IsEndingExpr
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% T->FS|T*FS
%% STR index
/AnalyzeTerm {
   AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% FS -> F | +FS | -FS
%% STR index
/AnalyzeSignedFactor {
   AnalyzePreHook 2 copy get dup IsUnaryOp
   { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
   { pop AnalyzeFactor }
   ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% F->P|F^P|P!
%% STR index
/AnalyzeFactor {
   AnalyzePreHook AnalyzePower IsEndingFactor
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { dup 33 eq%% is there a ! DR 09/2011
       { pop 1 add NextNonBlankChar pop EvalFactorial }
       { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
       ifelse
       IsEndingFactor { pop exit } if } loop }
   ifelse  AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% P->(E)|literal
%% STR index
/AnalyzePower {
   %% depending of first char either a number, or a literal
   2 copy get dup 40 eq%%an open par
   { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
   { AnalyzeLiteral }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index STR[index] -> STR index
%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% recognize + or -
%% chr -> T/F
/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadNumber {
   exch dup 3 -1 roll dup 3 1 roll
   %%read mantissa
   { 1 add  2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
   dup 101 eq exch 69 eq or
   %%% there is a "e" or "E" -> read exponant
   { 1 add 2 copy get dup IsUnaryOp
     { pop 1 add 2 copy get } if
     { IsNumber not { exit } if 1 add 2 copy get } loop }
   if
   dup 4 1 roll
   3 -1 roll exch 1 index sub getinterval
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadCondOp {
   NextNonBlankChar 1 index 4 1 roll
   { IsCondOp not { exit } if 1 add  2 copy get } loop
   2 copy 5 -1 roll
   exch 1 index sub getinterval 3 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can contain only : 0123456789.
%% chr -> T/F
/IsLiteral {%
   dup 48 ge exch dup  57 le 3 -1 roll and exch
   dup 65 ge exch dup  90 le 3 -1 roll and 3 -1 roll or exch
   dup 97 ge exch     122 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
%% STR index -> literal STR index' nextchr
/ReadLiteral {
   exch dup 3 -1 roll dup 3 1 roll
   %%read literal core
   { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
   4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a clpar
%% STR index -> STR index STR[index] T/F
/IsEndingExpr {%
   2 copy dup Strlen eq
   %% if end of str is reached -> end !
   { pop pop 0 true }
   %% ending chr -> clpar, comma, |, <, >, =, !,
   {get dup  dup  41 eq
        exch dup 124 eq
        exch dup  93 eq
        exch dup  44 eq
        exch dup  30 eq
        exch dup  60 ge exch 62 le and or or or or or}
   ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a +-
%% STR index -> STR index STR[index] T/F
/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or */
%% STR index -> STR index STR[index] T/F
/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or ^
%% STR index -> STR index STR[index] T/F
/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index STR[index]
/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
%%%%%%%%%%%%%%%%%%%%%%%%
%% DEBUG
/BRK {false} def
/BRKtrue {/BRK true def} def
/BRKStop {BRK {BRKtoto} if } def
/BRKEvalStop {BRK exch if } def
/BRKBRK2true {BRK {BRK2true} if } def
/BRK2 {false} def
/BRK2true {/BRK2 true def} def
/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
end
%
%-------------------------------------------------------------------------------%
%
/tx@AlgToPs 12 dict def tx@AlgToPs begin
%
%% algExpr -> PSVector
/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
/Strlen 0 def
/EvalListOfExpr {} def%
/EvalNumber {%
     ReadNumber  cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
     exch 1 add array astore def NextNonBlankChar pop } def
/EvalAddSub {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
} def
/EvalMulDiv {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
} def
/EvalPower {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   pop /exp cvx exch 1 add array astore def
} def
/EvalFactorial {% DR 09/2011
   /ExpressionVector ExpressionVector aload length
   /fact cvx exch 1 add array astore def
} def
/EvalLiteral {%
   ReadLiteral
   dup 40 eq%%% there is an open par -> function call
   { pop 2 index
     dup (Sum) eq { EvalSum }
     { dup (IfTE) eq { EvalCond }
       { dup (Derive) eq { pop EvalDerive }
 	{ pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
           /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
 	  exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
   { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
     dup 91 eq%%% there is an open bracket -> vector element
     { pop 1 add NextNonBlankChar pop AnalyzeExpr
       /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
     { pop NextNonBlankChar pop }
     ifelse}
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% the derive function : Derive(n,f(x))
%% firstparindex lastparindex ->
/EvalDerive {
   %% manage the function descripiton
   1 add ReadNumber 3 1 roll NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   1 add NextNonBlankChar pop
   3 -1 roll cvi
   dup 0 eq
   { pop AnalyzeExpr 3 -1 roll pop 1 add }
   { 1 sub 3 1 roll (x)  exch tx@Derive begin DeriveIndexed end 4 -1 roll
     { (x) tx@Derive begin Derive end } repeat
     ExpressionVector exch /ExpressionVector [] def
     AlgToPs aload length
     /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll  /l2 exch def /l1 exch def
     l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
     1 index length /Strlen exch def } ifelse
} def
/EvalSum {%
   pop 1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
   5 -1 roll 4 add array astore def
   %% keep ExpressionVector for later and create a new one for internal Sum computation
   ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
   1 add NextNonBlankChar pop AnalyzeExpr
   %% add each term
   /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
   /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
   array astore def 3 -1 roll pop 1 add
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
/EvalCond {%
   pop 1 add AnalyzeCond NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   ExpressionVector 3 1 roll /ExpressionVector [] def
   1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
   NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add AnalyzeExpr
   NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
   ExpressionVector
   /ExpressionVector 6 -1 roll aload length dup
   6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
   1 add 3 -1 roll pop
} def
%% CondOp STR index
/EvalCondOp {%
   3 -1 roll
   dup (=) eq  { /eq } {%
   dup (<) eq  { /lt } {%
   dup (>) eq  { /gt } {%
   dup (>=) eq { /ge } {%
   dup (<=) eq { /ge } {%
   dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
   ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
   cvx exch pop
   /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
/EvalUnaryOp {
   3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook {} bind def
/PreEvalHook {} bind def
/AnalyzeListOfEPostHook {} bind def
/AnalyzePostHook {} def
/RollOp { 3 1 roll } bind def
end   %tx@CoreAnalyzerDict
%
%--------------------------------------------------------------------%
%
/tx@Derive 41 dict def tx@Derive begin
%%increase ^^ for each function added
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable -> PSVector
/Derive {%
   10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
} def
/Strlen 0 def
/InitParser { dup length /Strlen exch def 0 } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable index -> PSVector
/DeriveIndexed {%
   3 1 roll 10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u,v)'=-(u',v')
/EvalListOfExpr {%
   4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
            2 copy 7 -1 roll dup length 4 1 roll putinterval add
   6 -2 roll pop pop
   2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (-u)'=-(u')
/EvalUnaryOp {
   4 -2 roll 4 index (0) eq
   { (0) StrConcat 7 -1 roll pop }
   { 7 -1 roll 45 eq
     { AddSub AddOpPar true } { false } ifelse
     3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (number)'=0
/EvalNumber { ReadNumber (0) 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u+v)'=u'+v'
/EvalAddSub {%
   7 index dup (0) eq
   { pop true }%% du=0 nothing added
   { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
   ifelse
   5 index dup (0) eq
   { pop { (0) } { 4 -2 roll 2 copy pop 0  6 2 roll GetIntervalNewStr } ifelse }%%dv=0
   { exch
     { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
     { 5 -2 roll 7 index 43 eq%%something yet added
       { AddAdd false } { AddSub AddOpPar true } ifelse }
     ifelse 11 1 roll
     3 -1 roll StrConcat 10 -1 roll { AddClPar } if
     2 copy pop 0 6 2 roll GetIntervalNewStr }
   ifelse
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)' or (u/v)'
/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)'=u'*v+u*v'
/EvalMul {%
   4 -2 roll 7 index dup (0) eq
   { pop false }%%du=0
   { (1) eq%%du=1
     { false }
     { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
     3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
     true }%%du!=0
   ifelse
   5 1 roll 5 index (0) eq
   { 5 -1 roll not { (0) StrConcat } if }%%dv=0
   { 5 -1 roll { AddAdd } if
     4 index (1) eq
     { 8 index StrConcat }
     { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
     ifelse
   }%%dv!=0
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u/v)'=(u'*v-u*v')/v^2
/EvalDiv {%
   4 -2 roll
   4 index (0) eq%%dv=0 -> u'/v
   { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
   { 7 index dup (0) eq
     { pop }%%du=0
     { (1) eq%%du=1
       { false }
       { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
       3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
     ifelse
       AddSub
       4 index (1) eq
       { 8 index StrConcat }
       { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
       ifelse
     %}%%dv!=0
     2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
     AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str1 index str2 -> str1 index
/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
/EvalPower {%
   4 -2 roll 7 index (0) eq
   {%%if du=0 then (u^v)'=v'ln(u)u^v
     4 index (0) eq
     { (0) StrConcat }%%if dv=0 then (u^v)'=0
     { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
       8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
       AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
   }
   {%%du!=0
     4 index (0) eq
     {%%if dv=0 then (u^v)'=vu'u^(v-1)
       5 index dup IsStrNumber
       { dup (0) eq
         { StrConcat }
         { dup dup (1) eq exch (1.0) eq or
           { StrConcat  }
 	  { StrConcat
 	    7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
 	    { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
             (*\() StrConcat 8 index StrConcat (\)) StrConcat
             5 index  dup dup (2) eq exch (2.0) eq or
 	    { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
       { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
         5 index StrConcat (-1\)) StrConcat } ifelse
     }
     {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
       7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
       AddOpPar 5 index StrConcat (\)*\() StrConcat
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (-1\)+\() StrConcat
       4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (\)*ln\() StrConcat
       8 index StrConcat AddClPar
     } ifelse
   } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for factorial ! only cst => null derivative
/EvalFactorial {% DR 09/2011
   4 index (0) eq
   { (0) mark 8 -2 roll  cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
   { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str -> true/false
/IsStrNumber {%
   true exch
   { dup 48 lt exch dup 57 gt 3 -1 roll or
     exch dup 46 ne%%.
     exch dup 43 ne%%+
     exch 45 ne%%-
     and and and { pop false } if } forall
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalLiteral {%
   ReadLiteral dup 40 eq%%% there is an open par -> function call
   { pop (EvalFunc_             ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
   { dup 91 eq%%% there is an open bracket -> vector element
     { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
     { pop EvalVariable }
     ifelse }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first last parpos Expr[first:parpos-1] ->
/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (f(u))'=u'f'(u)
/EvalFunc {
   4 2 roll 4 index (1) ne
   { AddOpPar 4 index StrConcat (\)*) StrConcat } if
   (Eval             ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Func derivative -> Eval<func>
/EvalFunc_sin {%
   PreCommonFunc
   { (cos\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_cos {%
   PreCommonFunc
   { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_tan {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_asin {%
   PreCommonFunc
   { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_acos {%
   PreCommonFunc
   { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_atg {%
   PreCommonFunc
   { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_floor {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ln {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_exp {%
   PreCommonFunc
   {  (exp\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_EXP {%
   PreCommonFunc
   {  (EXP\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_sqrt {%
   PreCommonFunc
   { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Fact {%
   PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
   PostCommonFunc } def
/EvalFunc_sh {%
   PreCommonFunc
   { (ch\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ch {%
   PreCommonFunc
   { (sh\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_th {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argsh {%
   PreCommonFunc
   { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argch {%
   PreCommonFunc
   { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argth {%
   PreCommonFunc
   { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/PreCommonFunc {
   1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
   4 2 roll 4 index (0) eq
   { (0) StrConcat false }
   { 4 index (1)  ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
} def
/PostCommonFunc {
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
/EvalFunc_Derive {%
   1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
   4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
   4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
   exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_Sum {%
   1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop 3 -1 roll pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
   1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
   4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_IfTE {%
   3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
   NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   1 add NextNonBlankChar pop dup 5 1 roll
   AnalyzeExpr NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add NextNonBlankChar pop
   AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
   6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% advance in str until a comma is found (no error detection!)
%% str index -> str index'
/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for condition....
/EvalCondOp { 3 -1 roll pop } bind def
/PutIntervalOneAdd {putinterval 1 add} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add close parenthesis in string at the given index
%% str index -> str index+1
/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add 0 in string at the given index
%% str index -> str index+1
/AddZero {2 copy (0) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddMul {2 copy (*) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a plus sign in string at the given index
%% str index -> str index+1
/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a minus sign in string at the given index
%% str index -> str index+1
/AddSub {2 copy (-) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a pipe sign in string at the given index
%% str index -> str index+1
/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook { dup 5 1 roll } bind def
/PreEvalHook {} def
/AnalyzePostHook { 7 -1 roll pop } bind def
/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
/RollOp { 5 1 roll } bind def
end%%%tx@CoreAnalyzerDict
/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NEW FUNC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
%% x -> theta
/asin {%
   dup abs 1 gt { EQDFasinrangeerror  } if
   dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
} def
%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
%% x -> theta
/acos {%
   dup abs 1 gt { EQDFacosrangeerror  } if
   dup dup mul 1 exch sub sqrt exch atan DegtoRad
} def
%% function arctangent in radians
%% x -> theta
/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
%% HYPERBOLIC FUNCTIONS
/sh { dup Ex exch neg Ex sub 2 div } def
/ch { dup Ex exch neg Ex add 2 div } def
/th { dup sh exch ch div } def
/Argsh { dup dup mul 1 add sqrt add ln } def
/Argch { dup dup mul 1 sub sqrt add ln } def
/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
%% modified exponential funtion for 0
%% x n -> x^n
/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
%% modified exponential funtion for 0
%% x -> e^x
/Ex { Euler exch exp } bind def
%%
%% factorial function
%% n -> n!
/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
/fact { Fact } bind def
/! { Fact } bind def
end
%
% END pst-algparser.pro

%%EndProcSet
%%BeginProcSet: pst-tools.pro 0 0
% $Id: pst-tools.pro 842 2013-10-26 10:25:41Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.04, 2013/10/26
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
/Pi2 1.57079632679489661925640 def
/factorial { % n on stack, returns n!
   dup 0 eq { 1 }{
     dup 1 gt { dup 1 sub factorial mul } if }
   ifelse } def 
%
/MoverN { % m n on stack, returns the binomial coefficient m over n
   2 dict begin
   /n exch def /m exch def
   n 0 eq { 1 }{
     m n eq { 1 }{
       m factorial n factorial m n sub factorial mul div } ifelse } ifelse
   end
} def
%
/ps@ReverseOrderOfPoints { % on stack [P1 P2 P3 ...Pn]=>[Pn,Pn-1,...,P2,P1]
   5 dict begin       % all local
   aload length /n ED % number of coors
   n 2 div cvi /m ED  % number of Points
   /n1 n def
   m { n1 2 roll /n1 n1 2 sub def } repeat
   n array astore
   end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% subroutines for complex numbers, given as an array [a b] 
% which is a+bi = Real+i Imag
%
/cxadd {		% [a1 b1] [a2 b2] = [a1+a2 b1+b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   3 -1 roll		% [a2 b2] a2 [a1 b1]
   dup 0 get		% [a2 b2] a2 [a1 b1] a1
   3 -1 roll		% [a2 b2] [a1 b1] a1 a2
   add			% [a2 b2] [a1 b1] a1+a2
   3 1 roll		% a1+a2 [a2 b2] [a1 b1]
   1 get			% a1+a2 [a2 b2] b1
   exch 1 get		% a1+a2 b1 b2
   add 2 array astore
} def
%
/cxneg {		% [a b]
   dup 1 get		% [a b] b
   exch 0 get		% b a
   neg exch neg		% -a -b
   2 array astore
} def
%
/cxsub { cxneg cxadd } def  % same as negative addition
%
% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
/cxmul {		% [a1 b1] [a2 b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   exch 1 get		% [a1 b1] a2 b2
   3 -1 roll		% a2 b2 [a1 b1]
   dup 0 get		% a2 b2 [a1 b1] a1
   exch 1 get		% a2 b2 a1 b1
   dup			% a2 b2 a1 b1 b1
   5 -1 roll dup		% b2 a1 b1 b1 a2 a2
   3 1 roll mul		% b2 a1 b1 a2 b1a2
   5 -2 roll dup		% b1 a2 b1a2 b2 a1 a1
   3 -1 roll dup		% b1 a2 b1a2 a1 a1 b2 b2
   3 1 roll mul		% b1 a2 b1a2 a1 b2 a1b2
   4 -1 roll add		% b1 a2 a1 b2 b3
   4 2 roll mul		% b1 b2 b3 a1a2
   4 2 roll mul sub	% b3 a3
   exch 2 array astore
} def
%
% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
/cxsqr {		% [a b]   square root
   dup 0 get exch 1 get	% a b
   dup dup mul		% a b b^2
   3 -1 roll		% b b^2 a
   dup dup mul 		% b b^2 a a^2
   3 -1 roll sub		% b a a2
   3 1 roll mul 2 mul	% a2 b2
   2 array astore
} def
%
/cxsqrt {		% [a b]
%  dup cxnorm sqrt /r exch def
%  cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
   cxlog 		% log[a b]
   2 cxrdiv 		% log[a b]/2
   aload pop exch	% b a
   2.781 exch exp	% b exp(a)
   exch cxconv exch	% [Re +iIm] exp(a)
   cxrmul		%
} def
%
/cxarg { 		% [a b]
   aload pop 		% a b
   exch atan 		% arctan b/a
   DegtoRad 		% arg(z)=atan(b/a)
} def
%
% log[a b] = [a^2-b^2 2ab] = [a2 b2]
/cxlog {		% [a b]
   dup 			% [a b][a b]
   cxnorm 		% [a b] |z|
   log 			% [a b] log|z|
   exch 			% log|z|[a b]
   cxarg 		% log|z| Theta
   cxmake2 		% [log|z| Theta]
} def
%
% square of magnitude of complex number
/cxnorm2 {		% [a b]
   dup 0 get exch 1 get	% a b
   dup mul			% a b^2
   exch dup mul add	% a^2+b^2
} def
%
/cxnorm {		% [a b]
   cxnorm2 sqrt
} def
%
/cxconj {		% conjugent complex
   dup 0 get exch 1 get	% a b
   neg 2 array astore	% [a -b]
} def
%
/cxre { 0 get } def	% real value
/cxim { 1 get } def	% imag value
%
% 1/[a b] = ([a -b]/(a^2+b^2)
/cxrecip {		% [a b]
   dup cxnorm2 exch	% n2 [a b]
   dup 0 get exch 1 get	% n2 a b
   3 -1 roll		% a b n2
   dup			% a b n2 n2
   4 -1 roll exch div	% b n2 a/n2
   3 1 roll div		% a/n2 b/n2
   neg 2 array astore
} def
%
/cxmake1 { 0 2 array astore } def % make a complex number, real given
/cxmake2 { 2 array astore } def	  % dito, both given
%
/cxdiv { cxrecip cxmul } def
%
% multiplikation by a real number
/cxrmul {		% [a b] r
   exch aload pop	% r a b
   3 -1 roll dup		% a b r r
   3 1 roll mul		% a r b*r
   3 1 roll mul		% b*r a*r
   exch 2 array astore   % [a*r b*r]
} def
%
% division by a real number
/cxrdiv {		% [a b] r
   1 exch div		% [a b] 1/r
   cxrmul
} def
%
% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
/cxconv {		% theta
   RadtoDeg dup sin exch cos cxmake2
} def

%%%%% ### bubblesort ###
%% syntax : array bubblesort --> array2 trie par ordre croissant
%% code de Bill Casselman
%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
/bubblesort { % on stack must be an array [ ... ]
4 dict begin
    /a exch def
    /n a length 1 sub def
    n 0 gt {
       % at this point only the n+1 items in the bottom of a remain to
       % the sorted largest item in that blocks is to be moved up into
       % position n
       n {
          0 1 n 1 sub {
             /i exch def
             a i get a i 1 add get gt {
                % if a[i] > a[i+1] swap a[i] and a[i+1]
                a i 1 add
                a i get
                a i a i 1 add get
                % set new a[i] = old a[i+1]
                put
                % set new a[i+1] = old a[i]
                put
             } if
          } for
          /n n 1 sub def
       } repeat
    } if
    a % return the sorted array
end
} def
%
/concatstringarray{  %  [(a) (b) ... (z)] --> (ab...z)  20100422
   0 1 index { length add } forall
   string
   0 3 2 roll
   { 3 copy putinterval length add }forall
   pop 
} bind def
%
/dot2comma {% on stack a string (...)
   2 dict begin
   /Output exch def
   0 1 Output length 1 sub {
     /Index exch def
     Output Index get 46 eq { Output Index 44 put } if
   } for
   Output
   end
} def
%
/rightTrim { % on stack the string and the character number to be stripped
   /charNo exch def
   dup
   length 1 sub -1 0 {
     /i exch def dup i get charNo ne { exit } if
   } for
   0 i 1 add getinterval
   dup length string copy
} bind def  % leaves the stripped string on the stack

/psStringwidth /stringwidth load def
/psShow /show load def

%/stringwidth{ 32 rightTrim psStringwidth } bind def

%/show { 32 rightTrim psShow } bind def
%-----------------------------------------------------------------------------%

/pgffunctions {
     /pgfsc{}bind def% stroke color is empty by default
     /pgffc{}bind def% fill color is empty by default
     /pgfstr{stroke}bind def%
     /pgffill{fill}bind def%
     /pgfeofill{eofill}bind def%
     /pgfe{a dup 0 rlineto exch 0 exch rlineto neg 0 rlineto closepath}bind def% rectangle
     /pgfw{setlinewidth}bind def% setlinewidth
     /pgfs{save pgfpd 72 Resolution div 72 VResolution div neg scale
       magscale{1 DVImag div dup scale}if
       pgfx neg pgfy neg translate pgffoa .setopacityalpha}bind def% save
     /pgfr{pgfsd restore}bind def %restore
     userdict begin%
     /pgfo{pgfsd /pgfx currentpoint /pgfy exch def def @beginspecial}bind def %open
     /pgfc{newpath @endspecial pgfpd}bind def %close
     /pgfsd{globaldict /pgfdelta /delta where {pop delta} {0} ifelse put}bind def% save delta
     /pgfpd{/delta globaldict /pgfdelta get def}bind def % put delta
     /.setopacityalpha where {pop} {/.setopacityalpha{pop}def} ifelse % install .setopacityalpha
     /.pgfsetfillopacityalpha{/pgffoa exch def
       /pgffill{gsave pgffoa .setopacityalpha fill 1 .setopacityalpha newpath fill grestore newpath}bind def
       /pgfeofill{gsave pgffoa .setopacityalpha eofill 1 .setopacityalpha newpath eofill grestore newpath}bind def}bind def
     /.pgfsetstrokeopacityalpha{/pgfsoa exch def /pgfstr{gsave pgfsoa .setopacityalpha stroke grestore newpath}bind def}bind def
     /pgffoa 1 def
     /pgfsoa 1 def
     end
} def
%-----------------------------------------------------------------------------%
% END pst-tools.pro

%%EndProcSet
%%BeginProcSet: pst-dots.pro 0 0
% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02,  2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt <tvz@Princeton.EDU>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga  - Dec. 16, 1999
%% Modified by Etienne Riga  - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17 
%
10 dict dup begin			% hold local
   /FontType 3 def
   /FontMatrix [.001 0 0 .001 0 0] def
%  /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
   /FontBBox [-1000 -1000 1000 1000] def  % See end of file in /BuildGlyph
   /Encoding 256 array def
   0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
   Encoding				   % replace with given dot names
     dup (b) 0 get /Bullet put		   % get the numerical position of b in ASCII
%					   % and save /Bullet at this place in Encoding
     dup (c) 0 get /Circle put
     dup (C) 0 get /BoldCircle put	% 67
     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
%%%
     dup (k) 0 get /Asterisk put
     dup (K) 0 get /BoldAsterisk put
     dup (J) 0 get /SolidAsterisk put
     dup (h) 0 get /Hexagon put
     dup (H) 0 get /BoldHexagon put
     dup (G) 0 get /SolidHexagon put
     dup (f) 0 get /Octogon put		% 2008-04-18 hv
     dup (F) 0 get /BoldOctogon put	% 2008-04-18 hv
     dup (g) 0 get /SolidOctogon put	% 2008-04-18 hv
     dup (a) 0 get /Add put
     dup (A) 0 get /BoldAdd put 		% 65
     dup (x) 0 get /Mul put
     dup (X) 0 get /BoldMul put
     dup (m) 0 get /Oplus put
     dup (M) 0 get /BOplus put
     dup (e) 0 get /SolidOplus put
     dup (n) 0 get /Otimes put
     dup (N) 0 get /BOtimes put
     dup (E) 0 get /SolidOtimes put
     dup (i) 0 get /Bar put
     dup (I) 0 get /BoldBar put
     dup (l) 0 get /SolidDiamond put
     dup (d) 0 get /Diamond put
         (D) 0 get /BoldDiamond put
%%% 
/CharProcs 47 dict def
CharProcs begin
   /CirclePath {0 0 500 0 360 arc closepath} def
   /Bullet {CirclePath fill} def
   /Circle {CirclePath .9 .9 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
%-------------- hv begin 2004/07/25   from: er 2003/03/24
   /HexagonPath {
     0 550 moveto -476 275 lineto -476 -275 lineto
     0 -550 lineto 476 -275 lineto 476 275 lineto closepath
   } def
   /SolidHexagon {HexagonPath fill} def
   /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
   /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
%					2008-04-18 hv
   /OctogonPath {
      550 dup 22.5 tan mul dup neg dup add /xMove exch def
      exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
   /SolidOctogon { OctogonPath fill                             } def
   /Octogon {      OctogonPath .89 .89 scale OctogonPath eofill } def
   /BoldOctogon {  OctogonPath .79 .79 scale OctogonPath eofill } def
%
   /AsteriskPath {
     20 0 moveto 10 250 180 500 0 500 curveto
     -180 500 -10 250 -20 0 curveto closepath
   } def
   /Asterisk {
     AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
     60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
   } def
%
   /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
   /BoldAsteriskPath {
     50 30 cos 100 mul moveto  Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp closepath
   } def
   /BoldAsterisk {BoldAsteriskPath fill} def
   /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
   /CrossPath {
     40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
     -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
     40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
   } def
   /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
     -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
     80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
   } def
   /Add {CrossPath fill} def
   /Mul {45 rotate CrossPath fill} def
   /BoldAdd {BoldCrossPath fill} def
   /BoldMul {45 rotate BoldCrossPath fill} def
   /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
   /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
   /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
   /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
   /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
   /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
   /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
   /Bar {BarPath fill} def
   /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
   /BoldBar {BoldBarPath fill} def
   /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 .865 .865 scale DiamondPath eofill} def
   /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
%%%
   /.notdef { } def
end
%
/BuildGlyph {
   exch
   begin 
%  Metrics 1 index get exec 0
     0 0
%      BBoxes 3 index get exec
     -1000 -1000 1000 1000
%     -571.5 -742.5 571.5 742.5
     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

%%EndProcSet
%%BeginProcSet: cmmi10.pfb 0 0
%!PS-AdobeFont-1.0: CMMI10 003.002
%%Title: CMMI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMMI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup
/UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI10 def
/FontBBox {-32 -250 1048 750 }readonly def
/UniqueID 5087385 def
/PaintType 0 def
/FontInfo 10 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI10.) readonly def
  /FullName (CMMI10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle -14.04 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
  /ascent 750 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 15 /epsilon1 put
dup 16 /zeta put
dup 17 /eta put
dup 18 /theta put
dup 19 /iota put
dup 20 /kappa put
dup 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 24 /xi put
dup 25 /pi put
dup 26 /rho put
dup 27 /sigma put
dup 28 /tau put
dup 29 /upsilon put
dup 30 /phi put
dup 31 /chi put
dup 32 /psi put
dup 33 /omega put
dup 34 /epsilon put
dup 35 /theta1 put
dup 36 /pi1 put
dup 37 /rho1 put
dup 38 /sigma1 put
dup 39 /phi1 put
dup 40 /arrowlefttophalf put
dup 41 /arrowleftbothalf put
dup 42 /arrowrighttophalf put
dup 43 /arrowrightbothalf put
dup 44 /arrowhookleft put
dup 45 /arrowhookright put
dup 46 /triangleright put
dup 47 /triangleleft put
dup 48 /zerooldstyle put
dup 49 /oneoldstyle put
dup 50 /twooldstyle put
dup 51 /threeoldstyle put
dup 52 /fouroldstyle put
dup 53 /fiveoldstyle put
dup 54 /sixoldstyle put
dup 55 /sevenoldstyle put
dup 56 /eightoldstyle put
dup 57 /nineoldstyle put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 63 /star put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /flat put
dup 92 /natural put
dup 93 /sharp put
dup 94 /slurbelow put
dup 95 /slurabove put
dup 96 /lscript put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /dotlessi put
dup 124 /dotlessj put
dup 125 /weierstrass put
dup 126 /vector put
dup 127 /tie put
dup 128 /psi put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 173 /Omega put
dup 174 /alpha put
dup 175 /beta put
dup 176 /gamma put
dup 177 /delta put
dup 178 /epsilon1 put
dup 179 /zeta put
dup 180 /eta put
dup 181 /theta put
dup 182 /iota put
dup 183 /kappa put
dup 184 /lambda put
dup 185 /mu put
dup 186 /nu put
dup 187 /xi put
dup 188 /pi put
dup 189 /rho put
dup 190 /sigma put
dup 191 /tau put
dup 192 /upsilon put
dup 193 /phi put
dup 194 /chi put
dup 195 /psi put
dup 196 /tie put
readonly def
currentdict end
currentfile eexec

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cleartomark
{restore}if


%%EndProcSet
%%BeginProcSet: cmr10.pfb 0 0
%!PS-AdobeFont-1.0: CMR10 003.002
%%Title: CMR10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMR10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR10 def
/FontBBox {-40 -250 1009 750 }readonly def
/UniqueID 5000793 def
/PaintType 0 def
/FontInfo 9 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
  /FullName (CMR10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle 0 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 15 /ffl put
dup 16 /dotlessi put
dup 17 /dotlessj put
dup 18 /grave put
dup 19 /acute put
dup 20 /caron put
dup 21 /breve put
dup 22 /macron put
dup 23 /ring put
dup 24 /cedilla put
dup 25 /germandbls put
dup 26 /ae put
dup 27 /oe put
dup 28 /oslash put
dup 29 /AE put
dup 30 /OE put
dup 31 /Oslash put
dup 32 /suppress put
dup 33 /exclam put
dup 34 /quotedblright put
dup 35 /numbersign put
dup 36 /dollar put
dup 37 /percent put
dup 38 /ampersand put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 42 /asterisk put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 60 /exclamdown put
dup 61 /equal put
dup 62 /questiondown put
dup 63 /question put
dup 64 /at put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 94 /circumflex put
dup 95 /dotaccent put
dup 96 /quoteleft put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 124 /emdash put
dup 125 /hungarumlaut put
dup 126 /tilde put
dup 127 /dieresis put
dup 128 /suppress put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 171 /sfthyphen put
dup 172 /nbspace put
dup 173 /Omega put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 178 /ffl put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 187 /cedilla put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 196 /dieresis put
readonly def
currentdict end
currentfile eexec

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{pgfA} def /pgfdir { dup 0 exch moveto dup 5 index exch lineto } bind
def} bind def

  /pgfA{ /pgfdiff 8 index round cvi 8 index round cvi sub 2 mul 1 add
def 2 index 6 index sub pgfdiff div 2 index 6 index sub pgfdiff div
2 index 6 index sub pgfdiff div pgfheight 9 index 9 index 9 index 14
index pgfdiff { 3 index 3 index 3 index setrgbcolor pgfdir stroke 4
-1 roll 7 index add 4 -1 roll 6 index add 4 -1 roll 5 index add 4 -1
roll .5 sub } repeat mark 15 1 roll cleartomark exch pop }bind def

  /pgfR1{ newpath dup dup dup 0 360 arc clip newpath dup /pgfendx exch
def /pgfendy exch def 0.875 setlinewidth [] 0 setdash /pgfshade {pgfR}
def /pgfstartx exch def /pgfstarty exch def /pgfdiffx pgfendx pgfstartx
sub def /pgfdiffy pgfendy pgfstarty sub def dup /pgfdomb exch def }bind
def

  /pgfR2{ newpath 0.5 add pgfcircx pgfcircy 3 2 roll 0 360 arc setrgbcolor
fill pop}bind def

  /pgfR{ /pgfdiff 8 index round cvi 8 index round cvi sub 4 mul 1 add
def /pgfcircx pgfstartx 9 index pgfdiffx pgfdomb div mul add def /pgfcircy
pgfstarty 9 index pgfdiffy pgfdomb div mul add def /pgfcircxe pgfstartx
8 index pgfdiffx pgfdomb div mul add def /pgfcircye pgfstarty 8 index
pgfdiffy pgfdomb div mul add def /pgfxstep pgfcircxe pgfcircx sub pgfdiff
div def /pgfystep pgfcircye pgfcircy sub pgfdiff div def 2 index 6
index sub pgfdiff div 2 index 6 index sub pgfdiff div 2 index 6 index
sub pgfdiff div 8 index 8 index 8 index 13 index pgfdiff { 3 index
3 index 3 index setrgbcolor pgfcircx pgfcircy 2 index 0 360 arc closepath
stroke 4 -1 roll 6 index add 4 -1 roll 5 index add 4 -1 roll 4 index
add 4 -1 roll .25 sub /pgfcircx pgfcircx pgfxstep add def /pgfcircy
pgfcircy pgfystep add def } repeat mark 14 1 roll cleartomark exch
pop }bind def

   /pgfsc{}bind def/pgffc{}bind def/pgfstr{stroke}bind def/pgffill{fill}bind
def/pgfeofill{eofill}bind def/pgfe{a dup 0 rlineto exch 0 exch rlineto
neg 0 rlineto closepath}bind def/pgfw{setlinewidth}bind def/pgfs{save
pgfpd 72 Resolution div 72 VResolution div neg scale magscale{1 DVImag
div dup scale}if pgfx neg pgfy neg translate pgffoa .setopacityalpha}bind
def/pgfr{pgfsd restore}bind def userdict begin/pgfo{pgfsd /pgfx currentpoint
/pgfy exch def def @beginspecial}bind def /pgfc{newpath @endspecial
pgfpd}bind def /pgfsd{globaldict /pgfdelta /delta where {pop delta}
{0} ifelse put}bind def/pgfpd{/delta globaldict /pgfdelta get def}bind
def /.setopacityalpha where {pop} {/.setopacityalpha{pop}def} ifelse
/.pgfsetfillopacityalpha{/pgffoa exch def /pgffill{gsave pgffoa .setopacityalpha
fill 1 .setopacityalpha newpath fill grestore newpath}bind def /pgfeofill{gsave
pgffoa .setopacityalpha eofill 1 .setopacityalpha newpath eofill grestore
newpath}bind def}bind def /.pgfsetstrokeopacityalpha{/pgfsoa exch def
/pgfstr{gsave pgfsoa .setopacityalpha stroke grestore newpath}bind
def}bind def /pgffoa 1 def /pgfsoa 1 def end

  /pgf1{gsave exec 1.0 pgfw 2.00002 0.0 moveto -6.00006 4.00005 lineto
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def

  /pgf2{gsave exec 1.0 pgfw 0.8 pgfw [ ] 0.0 setdash 1 setlinecap 1
setlinejoin -3.00003 4.00005 moveto -2.75002 2.50002 0.0 0.24998 0.75
0.0 curveto 0.0 -0.24998 -2.75002 -2.50002 -3.00003 -4.00005 curveto
pgfstr  grestore} bind def

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  grestore} bind def

  /pgf5{gsave exec 1.0 pgfw [ ] 0.0 setdash -2.00002 -5.00005 moveto
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bind def

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  /pgf7{gsave exec 1.0 pgfw -2.50002 0.0 translate [ ] 0.0 setdash 3.00003
0.0 moveto 3.00003 1.65689 1.65689 3.00003 0.0 3.00003 curveto -1.65689
3.00003 -3.00003 1.65689 -3.00003 0.0 curveto -3.00003 -1.65689 -1.65689
-3.00003 0.0 -3.00003 curveto 1.65689 -3.00003 3.00003 -1.65689 3.00003
0.0 curveto closepath gsave pgffc pgffill grestore gsave pgfsc pgfstr
grestore newpath  grestore} bind def

  /pgf8{gsave exec 1.0 pgfw [ ] 0.0 setdash 1.0 0.0 moveto -5.00005
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gsave pgffc pgffill grestore gsave pgfsc pgfstr grestore newpath  grestore}
bind def

@fedspecial end
%%BeginFont: CMR10
%!PS-AdobeFont-1.0: CMR10 003.002
%%Title: CMR10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMR10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR10 def
/FontBBox {-40 -250 1009 750 }readonly def
/PaintType 0 def
/FontInfo 9 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 97 /a put
dup 101 /e put
dup 105 /i put
dup 108 /l put
dup 115 /s put
dup 116 /t put
readonly def
currentdict end
currentfile eexec
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%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.0: CMMI10 003.002
%%Title: CMMI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (<http://www.ams.org>), with Reserved Font Name CMMI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup
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{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI10 def
/FontBBox {-32 -250 1048 750 }readonly def
/PaintType 0 def
/FontInfo 10 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI10.) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/UnderlinePosition -100 def
/UnderlineThickness 50 def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 96 /lscript put
dup 103 /g put
readonly def
currentdict end
currentfile eexec
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/LineFill { % hv ------------ patch 7 -------------
   gsave
   abs /hatchWidthInc ED
   abs /hatchSepInc ED
   abs CLW add /a ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform pathbbox
   /y2 ED
   a Div ceiling cvi /x2 ED /y1 ED
   a Div cvi /x1 ED /y2 y2 y1 sub def
   clipType   % must be defined in pstricks.tex: clip -- eoclip
   newpath
   2 setlinecap
   systemdict
   /setstrokeadjust known { true setstrokeadjust } if
   x2 x1 sub 1 add {
     x1 a mul y1 moveto 0 y2 rlineto stroke
     /x1 x1 1 add
       hatchWidthInc 0 gt { CLW add } if
     def
     hatchSepInc 0 gt hatchWidthInc 0 gt or {
       /a a hatchSepInc add def
       CLW hatchWidthInc add SLW
     } if
   } repeat
   grestore
   pop pop } def
%
/DotFill {%	 on stack: dot radius
   /dotRadius ED
   abs CLW add /a ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform
   pathbbox % llx lly urx ury of smallest bounding box
   /y2 ED /x2 ED /y1 ED /x1 ED
   y2 y1 sub a div 2 add cvi /Ny ED
   x2 x1 sub a div 2 add cvi /Nx ED
   clipType   % must be defined in pstricks.tex: clip -- eoclip
   newpath
   /yA y1 dotRadius add CLW add def
   /xA0 x1 dotRadius add CLW add def
   Ny {
      /xA xA0 def
      Nx {
        newpath
        xA yA dotRadius 0 360 arc
        SolidDot { gsave fill grestore } if
        stroke
        xA a add /xA ED
      } repeat
      yA a add /yA ED
   } repeat
   grestore
} def
%
/PenroseFill {%	 on stack: scaling factor
   /Scale ED
%  1 exch div round /penroseFactor ED 
%  a 0 dtransform round exch round exch
%  2 copy idtransform 
%  exch Atan rotate 
%  idtransform pop /a ED 
%  .25 .25 itransform pathbbox 
%  /y2 ED 
%  a Div ceiling cvi /x2 ED /y1 ED 
%  a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath 
gsave
   220 150 translate
   Scale dup scale
   systemdict /setstrokeadjust known { true setstrokeadjust } if
   /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
  { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
   [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
   i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
   mul j l + S rmoveto}F i L j L stroke }F}F}F}F
   grestore 
%  pop pop 
} def
%
/PenroseFillA {%  on stack: scaling factor, border color, kite color, dart color
   /Scale ED
   Scale dup scale
   /border_colour ED
   /kite_colour ED
   /dart_colour ED
   clip
   newpath
   gsave
   100 100 translate
   6
   Scale 1 lt { 1 Scale dup add div mul cvi } if %%%%   Number of iterations
   10					%%%%   Long side length in millimeters
   /border_width { L 0.06 mul }def		%%%%   Choose the scalefactor for the borders
   /L exch 25.4 div 72 mul def		%%%%   Conversion: mm -> inches -> points
   /f{-1 5 sqrt add 2 div}bind def		%%%%   The reciprocal of the golden ratio
   /l{L f mul}bind def			%%%%   Short side length l = L*f
   /Ll{L l add}bind def			%%%%   Ll =  L + l
   /c{36 cos L mul}bind def		%%%%   c  =  L*cos(36)
   /s{36 sin L mul}bind def		%%%%   s  =  L*sin(36)
   /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
 	     0 setlinewidth stroke grestore border_colour stroke } bind def
   /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
 			   Ll 0 translate 144 rotate kite grestore }
 	      		 { kite_colour L draw_tile }ifelse
 	     pop } bind def
   /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
 			   -144 rotate Ll neg 0 translate half_dart grestore }
 	      		 { dart_colour l draw_tile }ifelse
   	     pop } bind def
   /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
   border_width setlinewidth  1 setlinejoin  1 setlinecap
%  450 0 translate
   dup f exch neg exp dup scale
   5 {kite 72 rotate } repeat stroke
   grestore
} def
%
%
/TruchetFill { %	 on stack: scaling factor
   10 dict begin
   dup dup scale
   1 exch div round /penroseFactor ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform pathbbox
   /y2 ED
   a Div ceiling cvi /x2 ED /y1 ED
   a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath
   systemdict
   /setstrokeadjust known { true setstrokeadjust } if
   /ma a neg def
   /ha a 2 div def
   /mha ha neg def
   /tile {
     rand dup 2 idiv 2 mul eq { 90 rotate } if
     mha mha moveto ha mha lineto
     ha ha lineto mha ha lineto
%    closepath .1 setlinewidth stroke
     contents
   } def
   /contents{
     0 ha moveto ha 0 lineto
     0 mha moveto mha 0 lineto
%    1 setlinewidth stroke
   } def
   /dotiling {
     f ma mul a f a mul {
       /i exch def
       f ma mul a f a mul {
         /j exch def
         gsave i j translate
         tile stroke grestore
       } for
     } for
   } def
%
   /f 3 def
   5 srand dotiling
   end % local user dict
} def
%
/BeginArrow {
   ADict begin 			% hold it local, for end see EndArrow
   /@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 % end the ADict
%
/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
%
/ArrowD { % the sides are drawn as curves (hv 20071211)
   CLW mul add dup
   2 div /w ED
   mul dup /h ED
   mul /Inset ED
   { 0 h T 1 -1 scale } if % changes the direction
% we use y=w/h^2 * x^2 as equation for the control points
% for the coordinates the arrow is seen from top to bottom
% the bottom (tip) is (0;0)
   w neg h moveto % lower left of >
   w 9 div 4 mul neg h 3 div 2 mul
   w 9 div neg       h 3 div
   0 0 curveto    % tip of >
   w 9 div        h 3 div
   w 9 div 4 mul  h 3 div 2 mul
   w h curveto % upper left of >
   w neg Inset neg rlineto % move to x=0 and inset
   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 { % DS is the dot size
   { /z DS def } { /z 0 def } ifelse  	% outer or inner dimen
   /b ED 				% the color definition
   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 { % holds the coordinates and on top of stack the showpoints boolean
   /showpoints ED
   counttomark 2 div dup cvi /n ED  	% n 2 div on stack
   n eq not { exch pop } if		% even numbers of points? delete one
   ] aload /Points ED
   showpoints not { Points aload pop } if
%    { ] aload /Points ED } 
%    { n 2 mul 1 add -1 roll pop } ifelse	% delete the mark symbol 
} 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
%
/LineToYAxis {
   /Ox ED		% Save the x origin value
   NArray            % all x-y pairs on stack
   n { 2 copy moveto % go to current point
     Ox exch Lineto   % line to y-axis
     pop             % delete old x-value
   } repeat
} def
%
/LineToXAxis{
   /Oy ED		% Save the y origin value
   NArray		% all x-y pairs on stack
   n 0 eq not
     { n 1 eq { 0 0 /n 2 def } if
       ArrowA
       /n n 2 sub def
       CP 2 copy moveto pop Oy Lineto
       n { 2 copy moveto pop Oy Lineto } repeat
       CP
       4 2 roll
       ArrowB
       2 copy moveto pop Oy
       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
%
/SymbolPolygon {   % on stack [ x y x y ...
   counttomark 					% number of elements
   2 add /m ED
   2 copy m 2 roll				% copy last two
   m 2 div cvi /n ED    				% n pairs
   /YA ED /XA ED					% the start point
   n 1 sub {
     /YB ED /XB ED
     /XLength XB XA sub def
     /YLength YB YA sub def
     /PAngle YLength XLength Atan def
     /XYLength XLength YLength Pyth def
     /nSym XYLength SymStep Div cvi def
     /Shift Symbol stringwidth pop 2 Div def
     /deltaX XLength nSym Div def
     /deltaY YLength nSym Div def
     XA Shift sub YA Shift sub moveto
     nSym {
       gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
       Symbol show
       grestore
       deltaX deltaY rmoveto
     } repeat
%    XB Shift sub YB Shift sub moveto Symbol show
     /YA YB def /XA XB def
   } repeat
   pop	% delete the mark symbol
} 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
%
/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
%
/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
%
/CurvePath {
   %% for negative SymStep we calculate the distance
   SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
   0.5 setflat
   flattenpath /z 0 def /z0 0 def
   { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
     x1 Shift sub y1 Shift sub moveto
     gsave
     curveticks
       { x1 y1 translate startAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       { startAngle rotate Symbol show }
     ifelse
     grestore /z0 z def }
   { /y ED /x ED PathLength@ z z0 sub SymStep ge {
       x Shift sub y Shift sub moveto
       gsave
       curveticks
         { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
           x y translate rotAngle rotate
           0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
           SymbolLinewidth setlinewidth stroke
         }
         {
           rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
           Symbol show
         }
       ifelse
       grestore /z0 z def } if
     /yOld y def /xOld x def }
   {} %% the lineto part
   { /y y2 def /x x2 def PathLength@
     x Shift sub y Shift sub moveto
     gsave
     curveticks
       { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
         x y translate rotAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       {
         x Shift sub y Shift sub moveto
         rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
         Symbol show
       }
     ifelse
     grestore
   }
   pathforall 
%  curveticks 
%   { gsave 
%     x y translate rotAngle rotate 
%     0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
%     SymbolLinewidth setlinewidth stroke grestore
%   } if
   z 
} def
%
/OpenSymbolCurve {
   OpenCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/AltOpenSymbolCurve {
   AltCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolCurve {
   ClosedCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} def
%
/CalcBezierSpline {%  Christoph Bersch
   10 dict begin
   /getX { Points exch 2 mul get } def
   /getY { Points exch 2 mul 1 add get } def
   /n Points length 1 sub 2 idiv def
   /GetFirstControlPoints {
     /x n array def
     /tmp n array def
     /b 2 def
     x 0 rhs 0 get b div put
     1 1 n 1 sub {
       /i exch def
       tmp i 1 b div dup 4 1 roll put
       i n 1 sub lt { 4 }{ 3.5 } ifelse exch sub /b exch def
       x i rhs i get x i 1 sub get sub b div put
     } for
     1 1 n 1 sub {
       n exch sub
       dup dup x exch 1 sub 2 copy 6 2 roll
       get 3 1 roll tmp exch get
       exch x exch get mul sub
       put
     } for
     x
   } def
   %
   n 1 eq {
     0 getX 2 mul 1 getX add 3 div
     0 getY 2 mul 1 getY add 3 div
     exch dup 3 1 roll 2 mul 0 getX sub
     exch dup 3 1 roll 2 mul 0 getY sub
     [ 0 getX 0 getY 7 3 roll 1 getX 1 getY ] /outPoints exch def
   } {
     /outPoints 6 n mul 2 add array def
     0 1 n {
       dup dup 6 mul dup 1 add
       outPoints exch 5 -1 roll getY put
       outPoints exch 3 -1 roll getX put
     } for
     /rhs n array def
     1 1 n 2 sub {
       rhs exch dup dup getX 4 mul exch 1 add getX 2 mul add put
     } for
     rhs 0 0 getX 1 getX 2 mul add put
     rhs n 1 sub dup getX 8 mul n getX add 2 div put
     GetFirstControlPoints
     1 1 n 2 sub {
       rhs exch dup dup getY 4 mul exch 1 add getY 2 mul add put
     } for
     rhs 0 0 getY 1 getY 2 mul add put
     rhs n 1 sub dup getY 8 mul n getY add 2 div put
     GetFirstControlPoints
     0 1 n 1 sub {
       /i exch def
       2 copy
       i get outPoints 6 i mul 3 add 3 -1 roll put
       i get outPoints 6 i mul 2 add 3 -1 roll put
       2 copy
       i n 1 sub lt {
         i 1 add get i 1 add getY 2 mul exch sub outPoints 6 i mul 5 add 3 -1 roll put
         i 1 add get i 1 add getX 2 mul exch sub outPoints 6 i mul 4 add 3 -1 roll put
       }{
         n 1 sub get n getY add 2 div outPoints 6 n 1 sub mul 5 add 3 -1 roll put
         n 1 sub get n getX add 2 div outPoints 6 n 1 sub mul 4 add 3 -1 roll put
       } ifelse
     } for
     pop pop
   } ifelse
   outPoints
   end
} def
/Spline {
   /showpoints ED
   counttomark 2 div dup cvi /n ED
   n eq not { exch pop } if
   ] /Points ED
   n 1 gt {
     CalcBezierSpline
     mark exch aload pop
     ArrowA
     n 2 sub {
       6 2 roll 4 2 roll curveto
     } repeat
     6 2 roll 4 2 roll ArrowB curveto
   } if
} def
/OpenSymbolSpline {
   Spline
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/OpenSymbolBezier {
   OpenBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolBezier {
   /f ED				 % save showpoints value
   2 copy /yEnd ED /xEnd ED
   counttomark -2 roll 2 copy /yStart ED /xStart ED
   counttomark 2 roll
   f
   ClosedBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath
   [ xEnd yEnd xStart yStart SymbolLine 
} 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 ED /x0 ED /y1 ED /x1 ED
   /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
%
/Parab1 { % 1 end  |  0 SP
   /ySP ED /xSP ED /y1 ED /x1 ED
   /dx xSP x1 sub 3 div def
   /dy ySP y1 sub 3 div def
   newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
                        x1 ySP lineto closepath clip
   currentpoint
   newpath moveto
   xSP dx sub ySP dy add x1 y1 ArrowA
   xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
   curveto
   /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def 
} def
%
/Grid {
   newpath
   /a 4 string def
   /b ED % 				psk@gridlabels in pt
   /c ED % 				{ \pst@usecolor\psgridlabelcolor }
   /n ED % 				psk@griddots
   cvi dup 1 lt { pop 1 } if
   /s ED % 				\psk@subgriddiv
   s div dup 0 eq { pop 1 } if
   /dy ED s div dup 0 eq { pop 1 } if %	\pst@number\psyunit abs
   /dx ED dy div round dy mul %		\pst@number\psxunit abs
   /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 {
   /rotAngle ED
   /mtrx CM def
   T
   rotAngle rotate
   scale 0 0 1 5 3 roll arc
   mtrx setmatrix 
} def
%
/ArcAdjust { %%%% Vincent Guirardel
% given a target length (targetLength) and an initial angle (angle0) [in the stack],
% let  M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
% This computes an angle t such that (x0,y0) is at distance 
% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
% contrary to TvZ's code.
% To achieve, this, one iterates the following process: start with some angle t,
% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
%
% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
% the value of d = add/sub is used to know on which side we have to move.
% It is only used in the initialisation of the angle before the iteration.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input stack:  1: target length 2: initial angle
% variables used : rx, ry, d (=add/sub)
%
   /targetLength ED /angle0 ED
   /x0 rx angle0 cos mul def
   /y0 ry angle0 sin mul def
% we are looking for an angle t such that (x0,y0) is at distance targetLength 
% from the point M(t)=(rx*cos(t),ry*sin(t)))
%initialisation of angle (using 1st order approx = TvZ's code)
   targetLength 57.2958 mul
   angle0 sin rx mul dup mul
   angle0 cos ry mul dup mul
   add sqrt div 
% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
% (if the ellipse is very curved at the point where we draw the arrow, %
% the value can be much more than 360 degrees !)
% this should avoid going on the wrong side (more than 180 degrees) or go near
% a bad attractive point (at 180 degrees)
   dup 90 ge { pop 90 } if
   angle0 exch d % add or sub
% maximum number of times to iterate the iterative procedure:
% iterative procedure: takes an angle t on top of stack, computes a 
% better angle (and put it on top of stack)
   30 { dup
% compute distance D between (x0,y0) and M(t)
     dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
% if D almost equals targetLength, we stop
     dup targetLength sub abs 1e-5 le { pop exit } if
% stack now contains D t
% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
     exch dup cos rx mul x0 sub  exch sin ry mul y0 sub
% stack contains:  y(t)-y0, x(t)-x0, d
     2 index Div targetLength mul y0 add ry Div exch
     2 index Div targetLength mul x0 add rx Div
% stack contains x(t')/rx , y(t')/ry , d
% now compute t', and remove D from stack
     atan exch pop
   } repeat
% we don't look at what happened... in particular, if targetLength is greater 
% than the diameter of the ellipse...
% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
% to give back the result as a an angle relative to angle0 we could add the following line:
% angle0 sub 0 exch d
%
% begin bug fix 2006-01-11
% we want to adjust the new angle t' by a multiple of 360 so that  | t'-angle0 | <= 180
%(we don't want to make the ellipse turn more or less than it should)...
dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
% end bug fix
} def
%
/EllipticArcArrow {
   /d ED      % is add or sub
   /b ED      % arrow procedure
   /a1 ED     % angle
   gsave
   newpath
   0 -1000 moveto
   clip                  % Set clippath far from arrow.
   newpath
   0 1 0 0 b             % Draw arrow to determine length.
   grestore
% Length of arrow is on top of stack. Next 3 numbers are junk.
%
   a1 exch ArcAdjust   % Angular position of base of arrow.
   /a2 ED
   pop pop pop
   a2 cos rx mul xOrig add % hv 2007-08-29   x->xOrig
   a2 sin ry mul yOrig add % hv 2007-08-29   y->yOrig
   a1 cos rx mul xOrig add %
   a1 sin ry mul yOrig add % 
% Now arrow tip coor and base coor are on stack.
   b pop pop pop pop       % Draw arrow, and discard coordinates.
   a2 CLW 8 div
% change value of d (test it by looking if  `` 1 1 d '' gives 2 or not )
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
   ArcAdjust
% resets original value of d
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse  % Adjust angle to give overlap.
} def
%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
%
/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 {
   5 dict begin
   /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
   end
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro

%%EndProcSet
%%BeginProcSet: pst-algparser.pro 0 0
% $Id: pst-algparser.pro 902 2014-03-30 16:23:33Z herbert $
%%
%% PostScript prologue for PSTricks algorithm parser
%% Version 0.05, 2014/03/30
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%%-----------------------------------------------------------------------------%
%
/AlgParser { tx@AlgToPs begin AlgToPs end } def  % Dominique Rodriguez
%
/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
%
% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
%
% 09/2011 DR factorial with ! added
%
% E->T|E+T
% T->FS|T*FS
% FS -> F | +FS | -FS
% F->P|F^SF|P!
% P->(E)|literal
% literal->number|var|var[E]|func(params)
% params->E|E,param
% number->TOBEFINISHED
%
%% E expression, T term, SF signed factor, F factor, P power
%
%% parser
%
%% str
%
%% C->E<condition_operators>E
%% STR index -> STR index+lenExpr
/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp  } def
%
%% analyze Expression List (separator , or | )
%% STR index -> STR index+lenExpr
%% /AnalyzeListOfE {
%%   { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
%%     NextNonBlankChar dup 0 eq { pop exit } if
%%     dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
%%     pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
%%   AnalyzeListOfEPostHook
%% } def
/AnalyzeListOfE {
   /NotFirst false def
   { NextNonBlankChar pop AnalyzeExpr
     NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
     dup Strlen eq { exit } if NextNonBlankChar
     dup 44 ne 1 index 124 ne and
     { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
     if  pop 1 add } loop
   AnalyzeListOfEPostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% E->T|E+T
%% STR index -> STR index+lenExpr
/AnalyzeExpr {
   AnalyzePreHook AnalyzeTerm IsEndingExpr
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% T->FS|T*FS
%% STR index
/AnalyzeTerm {
   AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% FS -> F | +FS | -FS
%% STR index
/AnalyzeSignedFactor {
   AnalyzePreHook 2 copy get dup IsUnaryOp
   { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
   { pop AnalyzeFactor }
   ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% F->P|F^P|P!
%% STR index
/AnalyzeFactor {
   AnalyzePreHook AnalyzePower IsEndingFactor
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { dup 33 eq%% is there a ! DR 09/2011
       { pop 1 add NextNonBlankChar pop EvalFactorial }
       { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
       ifelse
       IsEndingFactor { pop exit } if } loop }
   ifelse  AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% P->(E)|literal
%% STR index
/AnalyzePower {
   %% depending of first char either a number, or a literal
   2 copy get dup 40 eq%%an open par
   { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
   { AnalyzeLiteral }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index STR[index] -> STR index
%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% recognize + or -
%% chr -> T/F
/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadNumber {
   exch dup 3 -1 roll dup 3 1 roll
   %%read mantissa
   { 1 add  2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
   dup 101 eq exch 69 eq or
   %%% there is a "e" or "E" -> read exponant
   { 1 add 2 copy get dup IsUnaryOp
     { pop 1 add 2 copy get } if
     { IsNumber not { exit } if 1 add 2 copy get } loop }
   if
   dup 4 1 roll
   3 -1 roll exch 1 index sub getinterval
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadCondOp {
   NextNonBlankChar 1 index 4 1 roll
   { IsCondOp not { exit } if 1 add  2 copy get } loop
   2 copy 5 -1 roll
   exch 1 index sub getinterval 3 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can contain only : 0123456789.
%% chr -> T/F
/IsLiteral {%
   dup 48 ge exch dup  57 le 3 -1 roll and exch
   dup 65 ge exch dup  90 le 3 -1 roll and 3 -1 roll or exch
   dup 97 ge exch     122 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
%% STR index -> literal STR index' nextchr
/ReadLiteral {
   exch dup 3 -1 roll dup 3 1 roll
   %%read literal core
   { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
   4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a clpar
%% STR index -> STR index STR[index] T/F
/IsEndingExpr {%
   2 copy dup Strlen eq
   %% if end of str is reached -> end !
   { pop pop 0 true }
   %% ending chr -> clpar, comma, |, <, >, =, !,
   {get dup  dup  41 eq
        exch dup 124 eq
        exch dup  93 eq
        exch dup  44 eq
        exch dup  30 eq
        exch dup  60 ge exch 62 le and or or or or or}
   ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a +-
%% STR index -> STR index STR[index] T/F
/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or */
%% STR index -> STR index STR[index] T/F
/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or ^
%% STR index -> STR index STR[index] T/F
/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index STR[index]
/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
%%%%%%%%%%%%%%%%%%%%%%%%
%% DEBUG
/BRK {false} def
/BRKtrue {/BRK true def} def
/BRKStop {BRK {BRKtoto} if } def
/BRKEvalStop {BRK exch if } def
/BRKBRK2true {BRK {BRK2true} if } def
/BRK2 {false} def
/BRK2true {/BRK2 true def} def
/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
end
%
%-------------------------------------------------------------------------------%
%
/tx@AlgToPs 12 dict def tx@AlgToPs begin
%
%% algExpr -> PSVector
/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
/Strlen 0 def
/EvalListOfExpr {} def%
/EvalNumber {%
     ReadNumber  cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
     exch 1 add array astore def NextNonBlankChar pop } def
/EvalAddSub {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
} def
/EvalMulDiv {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
} def
/EvalPower {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   pop /exp cvx exch 1 add array astore def
} def
/EvalFactorial {% DR 09/2011
   /ExpressionVector ExpressionVector aload length
   /fact cvx exch 1 add array astore def
} def
/EvalLiteral {%
   ReadLiteral
   dup 40 eq%%% there is an open par -> function call
   { pop 2 index
     dup (Sum) eq { EvalSum }
     { dup (IfTE) eq { EvalCond }
       { dup (Derive) eq { pop EvalDerive }
 	{ pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
           /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
 	  exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
   { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
     dup 91 eq%%% there is an open bracket -> vector element
     { pop 1 add NextNonBlankChar pop AnalyzeExpr
       /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
     { pop NextNonBlankChar pop }
     ifelse}
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% the derive function : Derive(n,f(x))
%% firstparindex lastparindex ->
/EvalDerive {
   %% manage the function descripiton
   1 add ReadNumber 3 1 roll NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   1 add NextNonBlankChar pop
   3 -1 roll cvi
   dup 0 eq
   { pop AnalyzeExpr 3 -1 roll pop 1 add }
   { 1 sub 3 1 roll (x)  exch tx@Derive begin DeriveIndexed end 4 -1 roll
     { (x) tx@Derive begin Derive end } repeat
     ExpressionVector exch /ExpressionVector [] def
     AlgToPs aload length
     /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll  /l2 exch def /l1 exch def
     l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
     1 index length /Strlen exch def } ifelse
} def
/EvalSum {%
   pop 1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
   5 -1 roll 4 add array astore def
   %% keep ExpressionVector for later and create a new one for internal Sum computation
   ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
   1 add NextNonBlankChar pop AnalyzeExpr
   %% add each term
   /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
   /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
   array astore def 3 -1 roll pop 1 add
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
/EvalCond {%
   pop 1 add AnalyzeCond NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   ExpressionVector 3 1 roll /ExpressionVector [] def
   1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
   NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add AnalyzeExpr
   NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
   ExpressionVector
   /ExpressionVector 6 -1 roll aload length dup
   6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
   1 add 3 -1 roll pop
} def
%% CondOp STR index
/EvalCondOp {%
   3 -1 roll
   dup (=) eq  { /eq } {%
   dup (<) eq  { /lt } {%
   dup (>) eq  { /gt } {%
   dup (>=) eq { /ge } {%
   dup (<=) eq { /ge } {%
   dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
   ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
   cvx exch pop
   /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
/EvalUnaryOp {
   3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook {} bind def
/PreEvalHook {} bind def
/AnalyzeListOfEPostHook {} bind def
/AnalyzePostHook {} def
/RollOp { 3 1 roll } bind def
end   %tx@CoreAnalyzerDict
%
%--------------------------------------------------------------------%
%
/tx@Derive 41 dict def tx@Derive begin
%%increase ^^ for each function added
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable -> PSVector
/Derive {%
   10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
} def
/Strlen 0 def
/InitParser { dup length /Strlen exch def 0 } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable index -> PSVector
/DeriveIndexed {%
   3 1 roll 10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u,v)'=-(u',v')
/EvalListOfExpr {%
   4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
            2 copy 7 -1 roll dup length 4 1 roll putinterval add
   6 -2 roll pop pop
   2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (-u)'=-(u')
/EvalUnaryOp {
   4 -2 roll 4 index (0) eq
   { (0) StrConcat 7 -1 roll pop }
   { 7 -1 roll 45 eq
     { AddSub AddOpPar true } { false } ifelse
     3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (number)'=0
/EvalNumber { ReadNumber (0) 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u+v)'=u'+v'
/EvalAddSub {%
   7 index dup (0) eq
   { pop true }%% du=0 nothing added
   { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
   ifelse
   5 index dup (0) eq
   { pop { (0) } { 4 -2 roll 2 copy pop 0  6 2 roll GetIntervalNewStr } ifelse }%%dv=0
   { exch
     { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
     { 5 -2 roll 7 index 43 eq%%something yet added
       { AddAdd false } { AddSub AddOpPar true } ifelse }
     ifelse 11 1 roll
     3 -1 roll StrConcat 10 -1 roll { AddClPar } if
     2 copy pop 0 6 2 roll GetIntervalNewStr }
   ifelse
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)' or (u/v)'
/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)'=u'*v+u*v'
/EvalMul {%
   4 -2 roll 7 index dup (0) eq
   { pop false }%%du=0
   { (1) eq%%du=1
     { false }
     { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
     3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
     true }%%du!=0
   ifelse
   5 1 roll 5 index (0) eq
   { 5 -1 roll not { (0) StrConcat } if }%%dv=0
   { 5 -1 roll { AddAdd } if
     4 index (1) eq
     { 8 index StrConcat }
     { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
     ifelse
   }%%dv!=0
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u/v)'=(u'*v-u*v')/v^2
/EvalDiv {%
   4 -2 roll
   4 index (0) eq%%dv=0 -> u'/v
   { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
   { 7 index dup (0) eq
     { pop }%%du=0
     { (1) eq%%du=1
       { false }
       { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
       3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
     ifelse
       AddSub
       4 index (1) eq
       { 8 index StrConcat }
       { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
       ifelse
     %}%%dv!=0
     2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
     AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str1 index str2 -> str1 index
/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
/EvalPower {%
   4 -2 roll 7 index (0) eq
   {%%if du=0 then (u^v)'=v'ln(u)u^v
     4 index (0) eq
     { (0) StrConcat }%%if dv=0 then (u^v)'=0
     { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
       8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
       AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
   }
   {%%du!=0
     4 index (0) eq
     {%%if dv=0 then (u^v)'=vu'u^(v-1)
       5 index dup IsStrNumber
       { dup (0) eq
         { StrConcat }
         { dup dup (1) eq exch (1.0) eq or
           { StrConcat  }
 	  { StrConcat
 	    7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
 	    { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
             (*\() StrConcat 8 index StrConcat (\)) StrConcat
             5 index  dup dup (2) eq exch (2.0) eq or
 	    { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
       { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
         5 index StrConcat (-1\)) StrConcat } ifelse
     }
     {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
       7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
       AddOpPar 5 index StrConcat (\)*\() StrConcat
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (-1\)+\() StrConcat
       4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (\)*ln\() StrConcat
       8 index StrConcat AddClPar
     } ifelse
   } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for factorial ! only cst => null derivative
/EvalFactorial {% DR 09/2011
   4 index (0) eq
   { (0) mark 8 -2 roll  cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
   { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str -> true/false
/IsStrNumber {%
   true exch
   { dup 48 lt exch dup 57 gt 3 -1 roll or
     exch dup 46 ne%%.
     exch dup 43 ne%%+
     exch 45 ne%%-
     and and and { pop false } if } forall
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalLiteral {%
   ReadLiteral dup 40 eq%%% there is an open par -> function call
   { pop (EvalFunc_             ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
   { dup 91 eq%%% there is an open bracket -> vector element
     { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
     { pop EvalVariable }
     ifelse }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first last parpos Expr[first:parpos-1] ->
/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (f(u))'=u'f'(u)
/EvalFunc {
   4 2 roll 4 index (1) ne
   { AddOpPar 4 index StrConcat (\)*) StrConcat } if
   (Eval             ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Func derivative -> Eval<func>
/EvalFunc_sin {%
   PreCommonFunc
   { (cos\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_cos {%
   PreCommonFunc
   { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_tan {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_asin {%
   PreCommonFunc
   { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_acos {%
   PreCommonFunc
   { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_atg {%
   PreCommonFunc
   { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_floor {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ln {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_exp {%
   PreCommonFunc
   {  (exp\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_EXP {%
   PreCommonFunc
   {  (EXP\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_sqrt {%
   PreCommonFunc
   { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Fact {%
   PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
   PostCommonFunc } def
/EvalFunc_sh {%
   PreCommonFunc
   { (ch\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ch {%
   PreCommonFunc
   { (sh\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_th {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argsh {%
   PreCommonFunc
   { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argch {%
   PreCommonFunc
   { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argth {%
   PreCommonFunc
   { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/PreCommonFunc {
   1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
   4 2 roll 4 index (0) eq
   { (0) StrConcat false }
   { 4 index (1)  ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
} def
/PostCommonFunc {
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
/EvalFunc_Derive {%
   1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
   4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
   4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
   exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_Sum {%
   1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop 3 -1 roll pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
   1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
   4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_IfTE {%
   3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
   NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   1 add NextNonBlankChar pop dup 5 1 roll
   AnalyzeExpr NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add NextNonBlankChar pop
   AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
   6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% advance in str until a comma is found (no error detection!)
%% str index -> str index'
/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for condition....
/EvalCondOp { 3 -1 roll pop } bind def
/PutIntervalOneAdd {putinterval 1 add} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add close parenthesis in string at the given index
%% str index -> str index+1
/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add 0 in string at the given index
%% str index -> str index+1
/AddZero {2 copy (0) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddMul {2 copy (*) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a plus sign in string at the given index
%% str index -> str index+1
/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a minus sign in string at the given index
%% str index -> str index+1
/AddSub {2 copy (-) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a pipe sign in string at the given index
%% str index -> str index+1
/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook { dup 5 1 roll } bind def
/PreEvalHook {} def
/AnalyzePostHook { 7 -1 roll pop } bind def
/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
/RollOp { 5 1 roll } bind def
end%%%tx@CoreAnalyzerDict
/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NEW FUNC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
%% x -> theta
/asin {%
   dup abs 1 gt { EQDFasinrangeerror  } if
   dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
} def
%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
%% x -> theta
/acos {%
   dup abs 1 gt { EQDFacosrangeerror  } if
   dup dup mul 1 exch sub sqrt exch atan DegtoRad
} def
%% function arctangent in radians
%% x -> theta
/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
%% HYPERBOLIC FUNCTIONS
/sh { dup Ex exch neg Ex sub 2 div } def
/ch { dup Ex exch neg Ex add 2 div } def
/th { dup sh exch ch div } def
/Argsh { dup dup mul 1 add sqrt add ln } def
/Argch { dup dup mul 1 sub sqrt add ln } def
/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
%% modified exponential funtion for 0
%% x n -> x^n
/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
%% modified exponential funtion for 0
%% x -> e^x
/Ex { Euler exch exp } bind def
%%
%% factorial function
%% n -> n!
/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
/fact { Fact } bind def
/! { Fact } bind def
end
%
% END pst-algparser.pro

%%EndProcSet
%%BeginProcSet: pst-tools.pro 0 0
% $Id: pst-tools.pro 842 2013-10-26 10:25:41Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.04, 2013/10/26
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
/Pi2 1.57079632679489661925640 def
/factorial { % n on stack, returns n!
   dup 0 eq { 1 }{
     dup 1 gt { dup 1 sub factorial mul } if }
   ifelse } def 
%
/MoverN { % m n on stack, returns the binomial coefficient m over n
   2 dict begin
   /n exch def /m exch def
   n 0 eq { 1 }{
     m n eq { 1 }{
       m factorial n factorial m n sub factorial mul div } ifelse } ifelse
   end
} def
%
/ps@ReverseOrderOfPoints { % on stack [P1 P2 P3 ...Pn]=>[Pn,Pn-1,...,P2,P1]
   5 dict begin       % all local
   aload length /n ED % number of coors
   n 2 div cvi /m ED  % number of Points
   /n1 n def
   m { n1 2 roll /n1 n1 2 sub def } repeat
   n array astore
   end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% subroutines for complex numbers, given as an array [a b] 
% which is a+bi = Real+i Imag
%
/cxadd {		% [a1 b1] [a2 b2] = [a1+a2 b1+b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   3 -1 roll		% [a2 b2] a2 [a1 b1]
   dup 0 get		% [a2 b2] a2 [a1 b1] a1
   3 -1 roll		% [a2 b2] [a1 b1] a1 a2
   add			% [a2 b2] [a1 b1] a1+a2
   3 1 roll		% a1+a2 [a2 b2] [a1 b1]
   1 get			% a1+a2 [a2 b2] b1
   exch 1 get		% a1+a2 b1 b2
   add 2 array astore
} def
%
/cxneg {		% [a b]
   dup 1 get		% [a b] b
   exch 0 get		% b a
   neg exch neg		% -a -b
   2 array astore
} def
%
/cxsub { cxneg cxadd } def  % same as negative addition
%
% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
/cxmul {		% [a1 b1] [a2 b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   exch 1 get		% [a1 b1] a2 b2
   3 -1 roll		% a2 b2 [a1 b1]
   dup 0 get		% a2 b2 [a1 b1] a1
   exch 1 get		% a2 b2 a1 b1
   dup			% a2 b2 a1 b1 b1
   5 -1 roll dup		% b2 a1 b1 b1 a2 a2
   3 1 roll mul		% b2 a1 b1 a2 b1a2
   5 -2 roll dup		% b1 a2 b1a2 b2 a1 a1
   3 -1 roll dup		% b1 a2 b1a2 a1 a1 b2 b2
   3 1 roll mul		% b1 a2 b1a2 a1 b2 a1b2
   4 -1 roll add		% b1 a2 a1 b2 b3
   4 2 roll mul		% b1 b2 b3 a1a2
   4 2 roll mul sub	% b3 a3
   exch 2 array astore
} def
%
% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
/cxsqr {		% [a b]   square root
   dup 0 get exch 1 get	% a b
   dup dup mul		% a b b^2
   3 -1 roll		% b b^2 a
   dup dup mul 		% b b^2 a a^2
   3 -1 roll sub		% b a a2
   3 1 roll mul 2 mul	% a2 b2
   2 array astore
} def
%
/cxsqrt {		% [a b]
%  dup cxnorm sqrt /r exch def
%  cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
   cxlog 		% log[a b]
   2 cxrdiv 		% log[a b]/2
   aload pop exch	% b a
   2.781 exch exp	% b exp(a)
   exch cxconv exch	% [Re +iIm] exp(a)
   cxrmul		%
} def
%
/cxarg { 		% [a b]
   aload pop 		% a b
   exch atan 		% arctan b/a
   DegtoRad 		% arg(z)=atan(b/a)
} def
%
% log[a b] = [a^2-b^2 2ab] = [a2 b2]
/cxlog {		% [a b]
   dup 			% [a b][a b]
   cxnorm 		% [a b] |z|
   log 			% [a b] log|z|
   exch 			% log|z|[a b]
   cxarg 		% log|z| Theta
   cxmake2 		% [log|z| Theta]
} def
%
% square of magnitude of complex number
/cxnorm2 {		% [a b]
   dup 0 get exch 1 get	% a b
   dup mul			% a b^2
   exch dup mul add	% a^2+b^2
} def
%
/cxnorm {		% [a b]
   cxnorm2 sqrt
} def
%
/cxconj {		% conjugent complex
   dup 0 get exch 1 get	% a b
   neg 2 array astore	% [a -b]
} def
%
/cxre { 0 get } def	% real value
/cxim { 1 get } def	% imag value
%
% 1/[a b] = ([a -b]/(a^2+b^2)
/cxrecip {		% [a b]
   dup cxnorm2 exch	% n2 [a b]
   dup 0 get exch 1 get	% n2 a b
   3 -1 roll		% a b n2
   dup			% a b n2 n2
   4 -1 roll exch div	% b n2 a/n2
   3 1 roll div		% a/n2 b/n2
   neg 2 array astore
} def
%
/cxmake1 { 0 2 array astore } def % make a complex number, real given
/cxmake2 { 2 array astore } def	  % dito, both given
%
/cxdiv { cxrecip cxmul } def
%
% multiplikation by a real number
/cxrmul {		% [a b] r
   exch aload pop	% r a b
   3 -1 roll dup		% a b r r
   3 1 roll mul		% a r b*r
   3 1 roll mul		% b*r a*r
   exch 2 array astore   % [a*r b*r]
} def
%
% division by a real number
/cxrdiv {		% [a b] r
   1 exch div		% [a b] 1/r
   cxrmul
} def
%
% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
/cxconv {		% theta
   RadtoDeg dup sin exch cos cxmake2
} def

%%%%% ### bubblesort ###
%% syntax : array bubblesort --> array2 trie par ordre croissant
%% code de Bill Casselman
%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
/bubblesort { % on stack must be an array [ ... ]
4 dict begin
    /a exch def
    /n a length 1 sub def
    n 0 gt {
       % at this point only the n+1 items in the bottom of a remain to
       % the sorted largest item in that blocks is to be moved up into
       % position n
       n {
          0 1 n 1 sub {
             /i exch def
             a i get a i 1 add get gt {
                % if a[i] > a[i+1] swap a[i] and a[i+1]
                a i 1 add
                a i get
                a i a i 1 add get
                % set new a[i] = old a[i+1]
                put
                % set new a[i+1] = old a[i]
                put
             } if
          } for
          /n n 1 sub def
       } repeat
    } if
    a % return the sorted array
end
} def
%
/concatstringarray{  %  [(a) (b) ... (z)] --> (ab...z)  20100422
   0 1 index { length add } forall
   string
   0 3 2 roll
   { 3 copy putinterval length add }forall
   pop 
} bind def
%
/dot2comma {% on stack a string (...)
   2 dict begin
   /Output exch def
   0 1 Output length 1 sub {
     /Index exch def
     Output Index get 46 eq { Output Index 44 put } if
   } for
   Output
   end
} def
%
/rightTrim { % on stack the string and the character number to be stripped
   /charNo exch def
   dup
   length 1 sub -1 0 {
     /i exch def dup i get charNo ne { exit } if
   } for
   0 i 1 add getinterval
   dup length string copy
} bind def  % leaves the stripped string on the stack

/psStringwidth /stringwidth load def
/psShow /show load def

%/stringwidth{ 32 rightTrim psStringwidth } bind def

%/show { 32 rightTrim psShow } bind def
%-----------------------------------------------------------------------------%

/pgffunctions {
     /pgfsc{}bind def% stroke color is empty by default
     /pgffc{}bind def% fill color is empty by default
     /pgfstr{stroke}bind def%
     /pgffill{fill}bind def%
     /pgfeofill{eofill}bind def%
     /pgfe{a dup 0 rlineto exch 0 exch rlineto neg 0 rlineto closepath}bind def% rectangle
     /pgfw{setlinewidth}bind def% setlinewidth
     /pgfs{save pgfpd 72 Resolution div 72 VResolution div neg scale
       magscale{1 DVImag div dup scale}if
       pgfx neg pgfy neg translate pgffoa .setopacityalpha}bind def% save
     /pgfr{pgfsd restore}bind def %restore
     userdict begin%
     /pgfo{pgfsd /pgfx currentpoint /pgfy exch def def @beginspecial}bind def %open
     /pgfc{newpath @endspecial pgfpd}bind def %close
     /pgfsd{globaldict /pgfdelta /delta where {pop delta} {0} ifelse put}bind def% save delta
     /pgfpd{/delta globaldict /pgfdelta get def}bind def % put delta
     /.setopacityalpha where {pop} {/.setopacityalpha{pop}def} ifelse % install .setopacityalpha
     /.pgfsetfillopacityalpha{/pgffoa exch def
       /pgffill{gsave pgffoa .setopacityalpha fill 1 .setopacityalpha newpath fill grestore newpath}bind def
       /pgfeofill{gsave pgffoa .setopacityalpha eofill 1 .setopacityalpha newpath eofill grestore newpath}bind def}bind def
     /.pgfsetstrokeopacityalpha{/pgfsoa exch def /pgfstr{gsave pgfsoa .setopacityalpha stroke grestore newpath}bind def}bind def
     /pgffoa 1 def
     /pgfsoa 1 def
     end
} def
%-----------------------------------------------------------------------------%
% END pst-tools.pro

%%EndProcSet
%%BeginProcSet: pst-dots.pro 0 0
% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02,  2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt <tvz@Princeton.EDU>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga  - Dec. 16, 1999
%% Modified by Etienne Riga  - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17 
%
10 dict dup begin			% hold local
   /FontType 3 def
   /FontMatrix [.001 0 0 .001 0 0] def
%  /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
   /FontBBox [-1000 -1000 1000 1000] def  % See end of file in /BuildGlyph
   /Encoding 256 array def
   0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
   Encoding				   % replace with given dot names
     dup (b) 0 get /Bullet put		   % get the numerical position of b in ASCII
%					   % and save /Bullet at this place in Encoding
     dup (c) 0 get /Circle put
     dup (C) 0 get /BoldCircle put	% 67
     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
%%%
     dup (k) 0 get /Asterisk put
     dup (K) 0 get /BoldAsterisk put
     dup (J) 0 get /SolidAsterisk put
     dup (h) 0 get /Hexagon put
     dup (H) 0 get /BoldHexagon put
     dup (G) 0 get /SolidHexagon put
     dup (f) 0 get /Octogon put		% 2008-04-18 hv
     dup (F) 0 get /BoldOctogon put	% 2008-04-18 hv
     dup (g) 0 get /SolidOctogon put	% 2008-04-18 hv
     dup (a) 0 get /Add put
     dup (A) 0 get /BoldAdd put 		% 65
     dup (x) 0 get /Mul put
     dup (X) 0 get /BoldMul put
     dup (m) 0 get /Oplus put
     dup (M) 0 get /BOplus put
     dup (e) 0 get /SolidOplus put
     dup (n) 0 get /Otimes put
     dup (N) 0 get /BOtimes put
     dup (E) 0 get /SolidOtimes put
     dup (i) 0 get /Bar put
     dup (I) 0 get /BoldBar put
     dup (l) 0 get /SolidDiamond put
     dup (d) 0 get /Diamond put
         (D) 0 get /BoldDiamond put
%%% 
/CharProcs 47 dict def
CharProcs begin
   /CirclePath {0 0 500 0 360 arc closepath} def
   /Bullet {CirclePath fill} def
   /Circle {CirclePath .9 .9 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
%-------------- hv begin 2004/07/25   from: er 2003/03/24
   /HexagonPath {
     0 550 moveto -476 275 lineto -476 -275 lineto
     0 -550 lineto 476 -275 lineto 476 275 lineto closepath
   } def
   /SolidHexagon {HexagonPath fill} def
   /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
   /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
%					2008-04-18 hv
   /OctogonPath {
      550 dup 22.5 tan mul dup neg dup add /xMove exch def
      exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
   /SolidOctogon { OctogonPath fill                             } def
   /Octogon {      OctogonPath .89 .89 scale OctogonPath eofill } def
   /BoldOctogon {  OctogonPath .79 .79 scale OctogonPath eofill } def
%
   /AsteriskPath {
     20 0 moveto 10 250 180 500 0 500 curveto
     -180 500 -10 250 -20 0 curveto closepath
   } def
   /Asterisk {
     AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
     60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
   } def
%
   /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
   /BoldAsteriskPath {
     50 30 cos 100 mul moveto  Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp closepath
   } def
   /BoldAsterisk {BoldAsteriskPath fill} def
   /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
   /CrossPath {
     40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
     -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
     40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
   } def
   /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
     -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
     80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
   } def
   /Add {CrossPath fill} def
   /Mul {45 rotate CrossPath fill} def
   /BoldAdd {BoldCrossPath fill} def
   /BoldMul {45 rotate BoldCrossPath fill} def
   /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
   /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
   /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
   /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
   /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
   /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
   /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
   /Bar {BarPath fill} def
   /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
   /BoldBar {BoldBarPath fill} def
   /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 .865 .865 scale DiamondPath eofill} def
   /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
%%%
   /.notdef { } def
end
%
/BuildGlyph {
   exch
   begin 
%  Metrics 1 index get exec 0
     0 0
%      BBoxes 3 index get exec
     -1000 -1000 1000 1000
%     -571.5 -742.5 571.5 742.5
     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

%%EndProcSet
%%BeginProcSet: cmmi10.pfb 0 0
%!PS-AdobeFont-1.0: CMMI10 003.002
%%Title: CMMI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMMI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup
/UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI10 def
/FontBBox {-32 -250 1048 750 }readonly def
/UniqueID 5087385 def
/PaintType 0 def
/FontInfo 10 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI10.) readonly def
  /FullName (CMMI10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle -14.04 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
  /ascent 750 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 15 /epsilon1 put
dup 16 /zeta put
dup 17 /eta put
dup 18 /theta put
dup 19 /iota put
dup 20 /kappa put
dup 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 24 /xi put
dup 25 /pi put
dup 26 /rho put
dup 27 /sigma put
dup 28 /tau put
dup 29 /upsilon put
dup 30 /phi put
dup 31 /chi put
dup 32 /psi put
dup 33 /omega put
dup 34 /epsilon put
dup 35 /theta1 put
dup 36 /pi1 put
dup 37 /rho1 put
dup 38 /sigma1 put
dup 39 /phi1 put
dup 40 /arrowlefttophalf put
dup 41 /arrowleftbothalf put
dup 42 /arrowrighttophalf put
dup 43 /arrowrightbothalf put
dup 44 /arrowhookleft put
dup 45 /arrowhookright put
dup 46 /triangleright put
dup 47 /triangleleft put
dup 48 /zerooldstyle put
dup 49 /oneoldstyle put
dup 50 /twooldstyle put
dup 51 /threeoldstyle put
dup 52 /fouroldstyle put
dup 53 /fiveoldstyle put
dup 54 /sixoldstyle put
dup 55 /sevenoldstyle put
dup 56 /eightoldstyle put
dup 57 /nineoldstyle put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 63 /star put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /flat put
dup 92 /natural put
dup 93 /sharp put
dup 94 /slurbelow put
dup 95 /slurabove put
dup 96 /lscript put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /dotlessi put
dup 124 /dotlessj put
dup 125 /weierstrass put
dup 126 /vector put
dup 127 /tie put
dup 128 /psi put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 173 /Omega put
dup 174 /alpha put
dup 175 /beta put
dup 176 /gamma put
dup 177 /delta put
dup 178 /epsilon1 put
dup 179 /zeta put
dup 180 /eta put
dup 181 /theta put
dup 182 /iota put
dup 183 /kappa put
dup 184 /lambda put
dup 185 /mu put
dup 186 /nu put
dup 187 /xi put
dup 188 /pi put
dup 189 /rho put
dup 190 /sigma put
dup 191 /tau put
dup 192 /upsilon put
dup 193 /phi put
dup 194 /chi put
dup 195 /psi put
dup 196 /tie put
readonly def
currentdict end
currentfile eexec

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cleartomark
{restore}if


%%EndProcSet
%%BeginProcSet: cmr10.pfb 0 0
%!PS-AdobeFont-1.0: CMR10 003.002
%%Title: CMR10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMR10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR10 def
/FontBBox {-40 -250 1009 750 }readonly def
/UniqueID 5000793 def
/PaintType 0 def
/FontInfo 9 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
  /FullName (CMR10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle 0 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 15 /ffl put
dup 16 /dotlessi put
dup 17 /dotlessj put
dup 18 /grave put
dup 19 /acute put
dup 20 /caron put
dup 21 /breve put
dup 22 /macron put
dup 23 /ring put
dup 24 /cedilla put
dup 25 /germandbls put
dup 26 /ae put
dup 27 /oe put
dup 28 /oslash put
dup 29 /AE put
dup 30 /OE put
dup 31 /Oslash put
dup 32 /suppress put
dup 33 /exclam put
dup 34 /quotedblright put
dup 35 /numbersign put
dup 36 /dollar put
dup 37 /percent put
dup 38 /ampersand put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 42 /asterisk put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 60 /exclamdown put
dup 61 /equal put
dup 62 /questiondown put
dup 63 /question put
dup 64 /at put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 94 /circumflex put
dup 95 /dotaccent put
dup 96 /quoteleft put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 124 /emdash put
dup 125 /hungarumlaut put
dup 126 /tilde put
dup 127 /dieresis put
dup 128 /suppress put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 171 /sfthyphen put
dup 172 /nbspace put
dup 173 /Omega put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 178 /ffl put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 187 /cedilla put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 196 /dieresis put
readonly def
currentdict end
currentfile eexec

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   /gray_packet exch def
   compression 0 eq
   {
     /number_pixels 1 def
   }
   {
     currentfile byte readhexstring pop 0 get
     /number_pixels exch 1 add def
   } ifelse
   0 1 number_pixels 1 sub
   {
     pixels exch gray_packet put
   } for
   pixels 0 number_pixels getinterval
} bind def

/GrayPseudoClassPacket
{
   %
   % Get a PseudoClass packet;  convert to grayscale.
   %
   % Parameters:
   %   index: index into the colormap.
   %   length: number of pixels minus one of this color (optional).
   %
   currentfile byte readhexstring pop 0 get
   /offset exch 3 mul def
   /color_packet colormap offset 3 getinterval def
   color_packet 0 get 0.299 mul
   color_packet 1 get 0.587 mul add
   color_packet 2 get 0.114 mul add
   cvi
   /gray_packet exch def
   compression 0 eq
   {
     /number_pixels 1 def
   }
   {
     currentfile byte readhexstring pop 0 get
     /number_pixels exch 1 add def
   } ifelse
   0 1 number_pixels 1 sub
   {
     pixels exch gray_packet put
   } for
   pixels 0 number_pixels getinterval
} bind def

/PseudoClassPacket
{
   %
   % Get a PseudoClass packet.
   %
   % Parameters:
   %   index: index into the colormap.
   %   length: number of pixels minus one of this color (optional).
   %
   currentfile byte readhexstring pop 0 get
   /offset exch 3 mul def
   /color_packet colormap offset 3 getinterval def
   compression 0 eq
   {
     /number_pixels 3 def
   }
   {
     currentfile byte readhexstring pop 0 get
     /number_pixels exch 1 add 3 mul def
   } ifelse
   0 3 number_pixels 1 sub
   {
     pixels exch color_packet putinterval
   } for
   pixels 0 number_pixels getinterval
} bind def

/PseudoClassImage
{
   %
   % Display a PseudoClass image.
   %
   % Parameters:
   %   class: 0-PseudoClass or 1-Grayscale.
   %
   currentfile buffer readline pop
   token pop /class exch def pop
   class 0 gt
   {
     currentfile buffer readline pop
     token pop /depth exch def pop
     /grays columns 8 add depth sub depth mul 8 idiv string def
     columns rows depth
     [
       columns 0 0
       rows neg 0 rows
     ]
     { currentfile grays readhexstring pop } image
   }
   {
     %
     % Parameters:
     %   colors: number of colors in the colormap.
     %   colormap: red, green, blue color packets.
     %
     currentfile buffer readline pop
     token pop /colors exch def pop
     /colors colors 3 mul def
     /colormap colors string def
     currentfile colormap readhexstring pop pop
     systemdict /colorimage known
     {
       columns rows 8
       [
         columns 0 0
         rows neg 0 rows
       ]
       { PseudoClassPacket } false 3 colorimage
     }
     {
       %
       % No colorimage operator;  convert to grayscale.
       %
       columns rows 8
       [
         columns 0 0
         rows neg 0 rows
       ]
       { GrayPseudoClassPacket } image
     } ifelse
   } ifelse
} bind def

/DisplayImage
{
   %
   % Display a DirectClass or PseudoClass image.
   %
   % Parameters:
   %   x & y translation.
   %   x & y scale.
   %   label pointsize.
   %   image label.
   %   image columns & rows.
   %   class: 0-DirectClass or 1-PseudoClass.
   %   compression: 0-none or 1-RunlengthEncoded.
   %   hex color packets.
   %
   gsave
   /buffer 512 string def
   /byte 1 string def
   /color_packet 3 string def
   /pixels 768 string def

   currentfile buffer readline pop
   token pop /x exch def
   token pop /y exch def pop
   x y translate
   currentfile buffer readline pop
   token pop /x exch def
   token pop /y exch def pop
   currentfile buffer readline pop
   token pop /pointsize exch def pop
   /Times-Roman findfont pointsize scalefont setfont
   x y scale
   currentfile buffer readline pop
   token pop /columns exch def
   token pop /rows exch def pop
   currentfile buffer readline pop
   token pop /class exch def pop
   currentfile buffer readline pop
   token pop /compression exch def pop
   class 0 gt { PseudoClassImage } { DirectClassImage } ifelse
   grestore
} bind def
%%EndProlog
%%Page:  1 1
%%PageBoundingBox: 0 0 484 511
userdict begin
DisplayImage
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484 511
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   newpath
   /yA y1 dotRadius add CLW add def
   /xA0 x1 dotRadius add CLW add def
   Ny {
      /xA xA0 def
      Nx {
        newpath
        xA yA dotRadius 0 360 arc
        SolidDot { gsave fill grestore } if
        stroke
        xA a add /xA ED
      } repeat
      yA a add /yA ED
   } repeat
   grestore
} def
%
/PenroseFill {%	 on stack: scaling factor
   /Scale ED
%  1 exch div round /penroseFactor ED 
%  a 0 dtransform round exch round exch
%  2 copy idtransform 
%  exch Atan rotate 
%  idtransform pop /a ED 
%  .25 .25 itransform pathbbox 
%  /y2 ED 
%  a Div ceiling cvi /x2 ED /y1 ED 
%  a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath 
gsave
   220 150 translate
   Scale dup scale
   systemdict /setstrokeadjust known { true setstrokeadjust } if
   /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
  { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
   [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
   i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
   mul j l + S rmoveto}F i L j L stroke }F}F}F}F
   grestore 
%  pop pop 
} def
%
/PenroseFillA {%  on stack: scaling factor, border color, kite color, dart color
   /Scale ED
   Scale dup scale
   /border_colour ED
   /kite_colour ED
   /dart_colour ED
   clip
   newpath
   gsave
   100 100 translate
   6
   Scale 1 lt { 1 Scale dup add div mul cvi } if %%%%   Number of iterations
   10					%%%%   Long side length in millimeters
   /border_width { L 0.06 mul }def		%%%%   Choose the scalefactor for the borders
   /L exch 25.4 div 72 mul def		%%%%   Conversion: mm -> inches -> points
   /f{-1 5 sqrt add 2 div}bind def		%%%%   The reciprocal of the golden ratio
   /l{L f mul}bind def			%%%%   Short side length l = L*f
   /Ll{L l add}bind def			%%%%   Ll =  L + l
   /c{36 cos L mul}bind def		%%%%   c  =  L*cos(36)
   /s{36 sin L mul}bind def		%%%%   s  =  L*sin(36)
   /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
 	     0 setlinewidth stroke grestore border_colour stroke } bind def
   /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
 			   Ll 0 translate 144 rotate kite grestore }
 	      		 { kite_colour L draw_tile }ifelse
 	     pop } bind def
   /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
 			   -144 rotate Ll neg 0 translate half_dart grestore }
 	      		 { dart_colour l draw_tile }ifelse
   	     pop } bind def
   /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
   border_width setlinewidth  1 setlinejoin  1 setlinecap
%  450 0 translate
   dup f exch neg exp dup scale
   5 {kite 72 rotate } repeat stroke
   grestore
} def
%
%
/TruchetFill { %	 on stack: scaling factor
   10 dict begin
   dup dup scale
   1 exch div round /penroseFactor ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform pathbbox
   /y2 ED
   a Div ceiling cvi /x2 ED /y1 ED
   a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath
   systemdict
   /setstrokeadjust known { true setstrokeadjust } if
   /ma a neg def
   /ha a 2 div def
   /mha ha neg def
   /tile {
     rand dup 2 idiv 2 mul eq { 90 rotate } if
     mha mha moveto ha mha lineto
     ha ha lineto mha ha lineto
%    closepath .1 setlinewidth stroke
     contents
   } def
   /contents{
     0 ha moveto ha 0 lineto
     0 mha moveto mha 0 lineto
%    1 setlinewidth stroke
   } def
   /dotiling {
     f ma mul a f a mul {
       /i exch def
       f ma mul a f a mul {
         /j exch def
         gsave i j translate
         tile stroke grestore
       } for
     } for
   } def
%
   /f 3 def
   5 srand dotiling
   end % local user dict
} def
%
/BeginArrow {
   ADict begin 			% hold it local, for end see EndArrow
   /@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 % end the ADict
%
/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
%
/ArrowD { % the sides are drawn as curves (hv 20071211)
   CLW mul add dup
   2 div /w ED
   mul dup /h ED
   mul /Inset ED
   { 0 h T 1 -1 scale } if % changes the direction
% we use y=w/h^2 * x^2 as equation for the control points
% for the coordinates the arrow is seen from top to bottom
% the bottom (tip) is (0;0)
   w neg h moveto % lower left of >
   w 9 div 4 mul neg h 3 div 2 mul
   w 9 div neg       h 3 div
   0 0 curveto    % tip of >
   w 9 div        h 3 div
   w 9 div 4 mul  h 3 div 2 mul
   w h curveto % upper left of >
   w neg Inset neg rlineto % move to x=0 and inset
   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 { % DS is the dot size
   { /z DS def } { /z 0 def } ifelse  	% outer or inner dimen
   /b ED 				% the color definition
   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 { % holds the coordinates and on top of stack the showpoints boolean
   /showpoints ED
   counttomark 2 div dup cvi /n ED  	% n 2 div on stack
   n eq not { exch pop } if		% even numbers of points? delete one
   ] aload /Points ED
   showpoints not { Points aload pop } if
%    { ] aload /Points ED } 
%    { n 2 mul 1 add -1 roll pop } ifelse	% delete the mark symbol 
} 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
%
/LineToYAxis {
   /Ox ED		% Save the x origin value
   NArray            % all x-y pairs on stack
   n { 2 copy moveto % go to current point
     Ox exch Lineto   % line to y-axis
     pop             % delete old x-value
   } repeat
} def
%
/LineToXAxis{
   /Oy ED		% Save the y origin value
   NArray		% all x-y pairs on stack
   n 0 eq not
     { n 1 eq { 0 0 /n 2 def } if
       ArrowA
       /n n 2 sub def
       CP 2 copy moveto pop Oy Lineto
       n { 2 copy moveto pop Oy Lineto } repeat
       CP
       4 2 roll
       ArrowB
       2 copy moveto pop Oy
       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
%
/SymbolPolygon {   % on stack [ x y x y ...
   counttomark 					% number of elements
   2 add /m ED
   2 copy m 2 roll				% copy last two
   m 2 div cvi /n ED    				% n pairs
   /YA ED /XA ED					% the start point
   n 1 sub {
     /YB ED /XB ED
     /XLength XB XA sub def
     /YLength YB YA sub def
     /PAngle YLength XLength Atan def
     /XYLength XLength YLength Pyth def
     /nSym XYLength SymStep Div cvi def
     /Shift Symbol stringwidth pop 2 Div def
     /deltaX XLength nSym Div def
     /deltaY YLength nSym Div def
     XA Shift sub YA Shift sub moveto
     nSym {
       gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
       Symbol show
       grestore
       deltaX deltaY rmoveto
     } repeat
%    XB Shift sub YB Shift sub moveto Symbol show
     /YA YB def /XA XB def
   } repeat
   pop	% delete the mark symbol
} 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
%
/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
%
/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
%
/CurvePath {
   %% for negative SymStep we calculate the distance
   SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
   0.5 setflat
   flattenpath /z 0 def /z0 0 def
   { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
     x1 Shift sub y1 Shift sub moveto
     gsave
     curveticks
       { x1 y1 translate startAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       { startAngle rotate Symbol show }
     ifelse
     grestore /z0 z def }
   { /y ED /x ED PathLength@ z z0 sub SymStep ge {
       x Shift sub y Shift sub moveto
       gsave
       curveticks
         { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
           x y translate rotAngle rotate
           0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
           SymbolLinewidth setlinewidth stroke
         }
         {
           rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
           Symbol show
         }
       ifelse
       grestore /z0 z def } if
     /yOld y def /xOld x def }
   {} %% the lineto part
   { /y y2 def /x x2 def PathLength@
     x Shift sub y Shift sub moveto
     gsave
     curveticks
       { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
         x y translate rotAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       {
         x Shift sub y Shift sub moveto
         rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
         Symbol show
       }
     ifelse
     grestore
   }
   pathforall 
%  curveticks 
%   { gsave 
%     x y translate rotAngle rotate 
%     0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
%     SymbolLinewidth setlinewidth stroke grestore
%   } if
   z 
} def
%
/OpenSymbolCurve {
   OpenCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/AltOpenSymbolCurve {
   AltCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolCurve {
   ClosedCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} def
%
/CalcBezierSpline {%  Christoph Bersch
   10 dict begin
   /getX { Points exch 2 mul get } def
   /getY { Points exch 2 mul 1 add get } def
   /n Points length 1 sub 2 idiv def
   /GetFirstControlPoints {
     /x n array def
     /tmp n array def
     /b 2 def
     x 0 rhs 0 get b div put
     1 1 n 1 sub {
       /i exch def
       tmp i 1 b div dup 4 1 roll put
       i n 1 sub lt { 4 }{ 3.5 } ifelse exch sub /b exch def
       x i rhs i get x i 1 sub get sub b div put
     } for
     1 1 n 1 sub {
       n exch sub
       dup dup x exch 1 sub 2 copy 6 2 roll
       get 3 1 roll tmp exch get
       exch x exch get mul sub
       put
     } for
     x
   } def
   %
   n 1 eq {
     0 getX 2 mul 1 getX add 3 div
     0 getY 2 mul 1 getY add 3 div
     exch dup 3 1 roll 2 mul 0 getX sub
     exch dup 3 1 roll 2 mul 0 getY sub
     [ 0 getX 0 getY 7 3 roll 1 getX 1 getY ] /outPoints exch def
   } {
     /outPoints 6 n mul 2 add array def
     0 1 n {
       dup dup 6 mul dup 1 add
       outPoints exch 5 -1 roll getY put
       outPoints exch 3 -1 roll getX put
     } for
     /rhs n array def
     1 1 n 2 sub {
       rhs exch dup dup getX 4 mul exch 1 add getX 2 mul add put
     } for
     rhs 0 0 getX 1 getX 2 mul add put
     rhs n 1 sub dup getX 8 mul n getX add 2 div put
     GetFirstControlPoints
     1 1 n 2 sub {
       rhs exch dup dup getY 4 mul exch 1 add getY 2 mul add put
     } for
     rhs 0 0 getY 1 getY 2 mul add put
     rhs n 1 sub dup getY 8 mul n getY add 2 div put
     GetFirstControlPoints
     0 1 n 1 sub {
       /i exch def
       2 copy
       i get outPoints 6 i mul 3 add 3 -1 roll put
       i get outPoints 6 i mul 2 add 3 -1 roll put
       2 copy
       i n 1 sub lt {
         i 1 add get i 1 add getY 2 mul exch sub outPoints 6 i mul 5 add 3 -1 roll put
         i 1 add get i 1 add getX 2 mul exch sub outPoints 6 i mul 4 add 3 -1 roll put
       }{
         n 1 sub get n getY add 2 div outPoints 6 n 1 sub mul 5 add 3 -1 roll put
         n 1 sub get n getX add 2 div outPoints 6 n 1 sub mul 4 add 3 -1 roll put
       } ifelse
     } for
     pop pop
   } ifelse
   outPoints
   end
} def
/Spline {
   /showpoints ED
   counttomark 2 div dup cvi /n ED
   n eq not { exch pop } if
   ] /Points ED
   n 1 gt {
     CalcBezierSpline
     mark exch aload pop
     ArrowA
     n 2 sub {
       6 2 roll 4 2 roll curveto
     } repeat
     6 2 roll 4 2 roll ArrowB curveto
   } if
} def
/OpenSymbolSpline {
   Spline
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/OpenSymbolBezier {
   OpenBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolBezier {
   /f ED				 % save showpoints value
   2 copy /yEnd ED /xEnd ED
   counttomark -2 roll 2 copy /yStart ED /xStart ED
   counttomark 2 roll
   f
   ClosedBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath
   [ xEnd yEnd xStart yStart SymbolLine 
} 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 ED /x0 ED /y1 ED /x1 ED
   /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
%
/Parab1 { % 1 end  |  0 SP
   /ySP ED /xSP ED /y1 ED /x1 ED
   /dx xSP x1 sub 3 div def
   /dy ySP y1 sub 3 div def
   newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
                        x1 ySP lineto closepath clip
   currentpoint
   newpath moveto
   xSP dx sub ySP dy add x1 y1 ArrowA
   xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
   curveto
   /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def 
} def
%
/Grid {
   newpath
   /a 4 string def
   /b ED % 				psk@gridlabels in pt
   /c ED % 				{ \pst@usecolor\psgridlabelcolor }
   /n ED % 				psk@griddots
   cvi dup 1 lt { pop 1 } if
   /s ED % 				\psk@subgriddiv
   s div dup 0 eq { pop 1 } if
   /dy ED s div dup 0 eq { pop 1 } if %	\pst@number\psyunit abs
   /dx ED dy div round dy mul %		\pst@number\psxunit abs
   /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 {
   /rotAngle ED
   /mtrx CM def
   T
   rotAngle rotate
   scale 0 0 1 5 3 roll arc
   mtrx setmatrix 
} def
%
/ArcAdjust { %%%% Vincent Guirardel
% given a target length (targetLength) and an initial angle (angle0) [in the stack],
% let  M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
% This computes an angle t such that (x0,y0) is at distance 
% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
% contrary to TvZ's code.
% To achieve, this, one iterates the following process: start with some angle t,
% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
%
% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
% the value of d = add/sub is used to know on which side we have to move.
% It is only used in the initialisation of the angle before the iteration.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input stack:  1: target length 2: initial angle
% variables used : rx, ry, d (=add/sub)
%
   /targetLength ED /angle0 ED
   /x0 rx angle0 cos mul def
   /y0 ry angle0 sin mul def
% we are looking for an angle t such that (x0,y0) is at distance targetLength 
% from the point M(t)=(rx*cos(t),ry*sin(t)))
%initialisation of angle (using 1st order approx = TvZ's code)
   targetLength 57.2958 mul
   angle0 sin rx mul dup mul
   angle0 cos ry mul dup mul
   add sqrt div 
% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
% (if the ellipse is very curved at the point where we draw the arrow, %
% the value can be much more than 360 degrees !)
% this should avoid going on the wrong side (more than 180 degrees) or go near
% a bad attractive point (at 180 degrees)
   dup 90 ge { pop 90 } if
   angle0 exch d % add or sub
% maximum number of times to iterate the iterative procedure:
% iterative procedure: takes an angle t on top of stack, computes a 
% better angle (and put it on top of stack)
   30 { dup
% compute distance D between (x0,y0) and M(t)
     dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
% if D almost equals targetLength, we stop
     dup targetLength sub abs 1e-5 le { pop exit } if
% stack now contains D t
% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
     exch dup cos rx mul x0 sub  exch sin ry mul y0 sub
% stack contains:  y(t)-y0, x(t)-x0, d
     2 index Div targetLength mul y0 add ry Div exch
     2 index Div targetLength mul x0 add rx Div
% stack contains x(t')/rx , y(t')/ry , d
% now compute t', and remove D from stack
     atan exch pop
   } repeat
% we don't look at what happened... in particular, if targetLength is greater 
% than the diameter of the ellipse...
% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
% to give back the result as a an angle relative to angle0 we could add the following line:
% angle0 sub 0 exch d
%
% begin bug fix 2006-01-11
% we want to adjust the new angle t' by a multiple of 360 so that  | t'-angle0 | <= 180
%(we don't want to make the ellipse turn more or less than it should)...
dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
% end bug fix
} def
%
/EllipticArcArrow {
   /d ED      % is add or sub
   /b ED      % arrow procedure
   /a1 ED     % angle
   gsave
   newpath
   0 -1000 moveto
   clip                  % Set clippath far from arrow.
   newpath
   0 1 0 0 b             % Draw arrow to determine length.
   grestore
% Length of arrow is on top of stack. Next 3 numbers are junk.
%
   a1 exch ArcAdjust   % Angular position of base of arrow.
   /a2 ED
   pop pop pop
   a2 cos rx mul xOrig add % hv 2007-08-29   x->xOrig
   a2 sin ry mul yOrig add % hv 2007-08-29   y->yOrig
   a1 cos rx mul xOrig add %
   a1 sin ry mul yOrig add % 
% Now arrow tip coor and base coor are on stack.
   b pop pop pop pop       % Draw arrow, and discard coordinates.
   a2 CLW 8 div
% change value of d (test it by looking if  `` 1 1 d '' gives 2 or not )
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
   ArcAdjust
% resets original value of d
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse  % Adjust angle to give overlap.
} def
%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
%
/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 {
   5 dict begin
   /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
   end
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro

%%EndProcSet
%%BeginProcSet: pst-algparser.pro 0 0
% $Id: pst-algparser.pro 902 2014-03-30 16:23:33Z herbert $
%%
%% PostScript prologue for PSTricks algorithm parser
%% Version 0.05, 2014/03/30
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%%-----------------------------------------------------------------------------%
%
/AlgParser { tx@AlgToPs begin AlgToPs end } def  % Dominique Rodriguez
%
/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
%
% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
%
% 09/2011 DR factorial with ! added
%
% E->T|E+T
% T->FS|T*FS
% FS -> F | +FS | -FS
% F->P|F^SF|P!
% P->(E)|literal
% literal->number|var|var[E]|func(params)
% params->E|E,param
% number->TOBEFINISHED
%
%% E expression, T term, SF signed factor, F factor, P power
%
%% parser
%
%% str
%
%% C->E<condition_operators>E
%% STR index -> STR index+lenExpr
/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp  } def
%
%% analyze Expression List (separator , or | )
%% STR index -> STR index+lenExpr
%% /AnalyzeListOfE {
%%   { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
%%     NextNonBlankChar dup 0 eq { pop exit } if
%%     dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
%%     pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
%%   AnalyzeListOfEPostHook
%% } def
/AnalyzeListOfE {
   /NotFirst false def
   { NextNonBlankChar pop AnalyzeExpr
     NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
     dup Strlen eq { exit } if NextNonBlankChar
     dup 44 ne 1 index 124 ne and
     { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
     if  pop 1 add } loop
   AnalyzeListOfEPostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% E->T|E+T
%% STR index -> STR index+lenExpr
/AnalyzeExpr {
   AnalyzePreHook AnalyzeTerm IsEndingExpr
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% T->FS|T*FS
%% STR index
/AnalyzeTerm {
   AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% FS -> F | +FS | -FS
%% STR index
/AnalyzeSignedFactor {
   AnalyzePreHook 2 copy get dup IsUnaryOp
   { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
   { pop AnalyzeFactor }
   ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% F->P|F^P|P!
%% STR index
/AnalyzeFactor {
   AnalyzePreHook AnalyzePower IsEndingFactor
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { dup 33 eq%% is there a ! DR 09/2011
       { pop 1 add NextNonBlankChar pop EvalFactorial }
       { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
       ifelse
       IsEndingFactor { pop exit } if } loop }
   ifelse  AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% P->(E)|literal
%% STR index
/AnalyzePower {
   %% depending of first char either a number, or a literal
   2 copy get dup 40 eq%%an open par
   { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
   { AnalyzeLiteral }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index STR[index] -> STR index
%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% recognize + or -
%% chr -> T/F
/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadNumber {
   exch dup 3 -1 roll dup 3 1 roll
   %%read mantissa
   { 1 add  2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
   dup 101 eq exch 69 eq or
   %%% there is a "e" or "E" -> read exponant
   { 1 add 2 copy get dup IsUnaryOp
     { pop 1 add 2 copy get } if
     { IsNumber not { exit } if 1 add 2 copy get } loop }
   if
   dup 4 1 roll
   3 -1 roll exch 1 index sub getinterval
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadCondOp {
   NextNonBlankChar 1 index 4 1 roll
   { IsCondOp not { exit } if 1 add  2 copy get } loop
   2 copy 5 -1 roll
   exch 1 index sub getinterval 3 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can contain only : 0123456789.
%% chr -> T/F
/IsLiteral {%
   dup 48 ge exch dup  57 le 3 -1 roll and exch
   dup 65 ge exch dup  90 le 3 -1 roll and 3 -1 roll or exch
   dup 97 ge exch     122 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
%% STR index -> literal STR index' nextchr
/ReadLiteral {
   exch dup 3 -1 roll dup 3 1 roll
   %%read literal core
   { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
   4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a clpar
%% STR index -> STR index STR[index] T/F
/IsEndingExpr {%
   2 copy dup Strlen eq
   %% if end of str is reached -> end !
   { pop pop 0 true }
   %% ending chr -> clpar, comma, |, <, >, =, !,
   {get dup  dup  41 eq
        exch dup 124 eq
        exch dup  93 eq
        exch dup  44 eq
        exch dup  30 eq
        exch dup  60 ge exch 62 le and or or or or or}
   ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a +-
%% STR index -> STR index STR[index] T/F
/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or */
%% STR index -> STR index STR[index] T/F
/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or ^
%% STR index -> STR index STR[index] T/F
/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index STR[index]
/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
%%%%%%%%%%%%%%%%%%%%%%%%
%% DEBUG
/BRK {false} def
/BRKtrue {/BRK true def} def
/BRKStop {BRK {BRKtoto} if } def
/BRKEvalStop {BRK exch if } def
/BRKBRK2true {BRK {BRK2true} if } def
/BRK2 {false} def
/BRK2true {/BRK2 true def} def
/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
end
%
%-------------------------------------------------------------------------------%
%
/tx@AlgToPs 12 dict def tx@AlgToPs begin
%
%% algExpr -> PSVector
/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
/Strlen 0 def
/EvalListOfExpr {} def%
/EvalNumber {%
     ReadNumber  cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
     exch 1 add array astore def NextNonBlankChar pop } def
/EvalAddSub {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
} def
/EvalMulDiv {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
} def
/EvalPower {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   pop /exp cvx exch 1 add array astore def
} def
/EvalFactorial {% DR 09/2011
   /ExpressionVector ExpressionVector aload length
   /fact cvx exch 1 add array astore def
} def
/EvalLiteral {%
   ReadLiteral
   dup 40 eq%%% there is an open par -> function call
   { pop 2 index
     dup (Sum) eq { EvalSum }
     { dup (IfTE) eq { EvalCond }
       { dup (Derive) eq { pop EvalDerive }
 	{ pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
           /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
 	  exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
   { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
     dup 91 eq%%% there is an open bracket -> vector element
     { pop 1 add NextNonBlankChar pop AnalyzeExpr
       /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
     { pop NextNonBlankChar pop }
     ifelse}
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% the derive function : Derive(n,f(x))
%% firstparindex lastparindex ->
/EvalDerive {
   %% manage the function descripiton
   1 add ReadNumber 3 1 roll NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   1 add NextNonBlankChar pop
   3 -1 roll cvi
   dup 0 eq
   { pop AnalyzeExpr 3 -1 roll pop 1 add }
   { 1 sub 3 1 roll (x)  exch tx@Derive begin DeriveIndexed end 4 -1 roll
     { (x) tx@Derive begin Derive end } repeat
     ExpressionVector exch /ExpressionVector [] def
     AlgToPs aload length
     /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll  /l2 exch def /l1 exch def
     l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
     1 index length /Strlen exch def } ifelse
} def
/EvalSum {%
   pop 1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
   5 -1 roll 4 add array astore def
   %% keep ExpressionVector for later and create a new one for internal Sum computation
   ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
   1 add NextNonBlankChar pop AnalyzeExpr
   %% add each term
   /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
   /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
   array astore def 3 -1 roll pop 1 add
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
/EvalCond {%
   pop 1 add AnalyzeCond NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   ExpressionVector 3 1 roll /ExpressionVector [] def
   1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
   NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add AnalyzeExpr
   NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
   ExpressionVector
   /ExpressionVector 6 -1 roll aload length dup
   6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
   1 add 3 -1 roll pop
} def
%% CondOp STR index
/EvalCondOp {%
   3 -1 roll
   dup (=) eq  { /eq } {%
   dup (<) eq  { /lt } {%
   dup (>) eq  { /gt } {%
   dup (>=) eq { /ge } {%
   dup (<=) eq { /ge } {%
   dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
   ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
   cvx exch pop
   /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
/EvalUnaryOp {
   3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook {} bind def
/PreEvalHook {} bind def
/AnalyzeListOfEPostHook {} bind def
/AnalyzePostHook {} def
/RollOp { 3 1 roll } bind def
end   %tx@CoreAnalyzerDict
%
%--------------------------------------------------------------------%
%
/tx@Derive 41 dict def tx@Derive begin
%%increase ^^ for each function added
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable -> PSVector
/Derive {%
   10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
} def
/Strlen 0 def
/InitParser { dup length /Strlen exch def 0 } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable index -> PSVector
/DeriveIndexed {%
   3 1 roll 10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u,v)'=-(u',v')
/EvalListOfExpr {%
   4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
            2 copy 7 -1 roll dup length 4 1 roll putinterval add
   6 -2 roll pop pop
   2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (-u)'=-(u')
/EvalUnaryOp {
   4 -2 roll 4 index (0) eq
   { (0) StrConcat 7 -1 roll pop }
   { 7 -1 roll 45 eq
     { AddSub AddOpPar true } { false } ifelse
     3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (number)'=0
/EvalNumber { ReadNumber (0) 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u+v)'=u'+v'
/EvalAddSub {%
   7 index dup (0) eq
   { pop true }%% du=0 nothing added
   { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
   ifelse
   5 index dup (0) eq
   { pop { (0) } { 4 -2 roll 2 copy pop 0  6 2 roll GetIntervalNewStr } ifelse }%%dv=0
   { exch
     { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
     { 5 -2 roll 7 index 43 eq%%something yet added
       { AddAdd false } { AddSub AddOpPar true } ifelse }
     ifelse 11 1 roll
     3 -1 roll StrConcat 10 -1 roll { AddClPar } if
     2 copy pop 0 6 2 roll GetIntervalNewStr }
   ifelse
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)' or (u/v)'
/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)'=u'*v+u*v'
/EvalMul {%
   4 -2 roll 7 index dup (0) eq
   { pop false }%%du=0
   { (1) eq%%du=1
     { false }
     { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
     3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
     true }%%du!=0
   ifelse
   5 1 roll 5 index (0) eq
   { 5 -1 roll not { (0) StrConcat } if }%%dv=0
   { 5 -1 roll { AddAdd } if
     4 index (1) eq
     { 8 index StrConcat }
     { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
     ifelse
   }%%dv!=0
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u/v)'=(u'*v-u*v')/v^2
/EvalDiv {%
   4 -2 roll
   4 index (0) eq%%dv=0 -> u'/v
   { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
   { 7 index dup (0) eq
     { pop }%%du=0
     { (1) eq%%du=1
       { false }
       { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
       3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
     ifelse
       AddSub
       4 index (1) eq
       { 8 index StrConcat }
       { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
       ifelse
     %}%%dv!=0
     2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
     AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str1 index str2 -> str1 index
/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
/EvalPower {%
   4 -2 roll 7 index (0) eq
   {%%if du=0 then (u^v)'=v'ln(u)u^v
     4 index (0) eq
     { (0) StrConcat }%%if dv=0 then (u^v)'=0
     { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
       8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
       AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
   }
   {%%du!=0
     4 index (0) eq
     {%%if dv=0 then (u^v)'=vu'u^(v-1)
       5 index dup IsStrNumber
       { dup (0) eq
         { StrConcat }
         { dup dup (1) eq exch (1.0) eq or
           { StrConcat  }
 	  { StrConcat
 	    7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
 	    { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
             (*\() StrConcat 8 index StrConcat (\)) StrConcat
             5 index  dup dup (2) eq exch (2.0) eq or
 	    { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
       { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
         5 index StrConcat (-1\)) StrConcat } ifelse
     }
     {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
       7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
       AddOpPar 5 index StrConcat (\)*\() StrConcat
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (-1\)+\() StrConcat
       4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (\)*ln\() StrConcat
       8 index StrConcat AddClPar
     } ifelse
   } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for factorial ! only cst => null derivative
/EvalFactorial {% DR 09/2011
   4 index (0) eq
   { (0) mark 8 -2 roll  cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
   { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str -> true/false
/IsStrNumber {%
   true exch
   { dup 48 lt exch dup 57 gt 3 -1 roll or
     exch dup 46 ne%%.
     exch dup 43 ne%%+
     exch 45 ne%%-
     and and and { pop false } if } forall
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalLiteral {%
   ReadLiteral dup 40 eq%%% there is an open par -> function call
   { pop (EvalFunc_             ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
   { dup 91 eq%%% there is an open bracket -> vector element
     { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
     { pop EvalVariable }
     ifelse }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first last parpos Expr[first:parpos-1] ->
/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (f(u))'=u'f'(u)
/EvalFunc {
   4 2 roll 4 index (1) ne
   { AddOpPar 4 index StrConcat (\)*) StrConcat } if
   (Eval             ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Func derivative -> Eval<func>
/EvalFunc_sin {%
   PreCommonFunc
   { (cos\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_cos {%
   PreCommonFunc
   { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_tan {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_asin {%
   PreCommonFunc
   { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_acos {%
   PreCommonFunc
   { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_atg {%
   PreCommonFunc
   { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_floor {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ln {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_exp {%
   PreCommonFunc
   {  (exp\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_EXP {%
   PreCommonFunc
   {  (EXP\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_sqrt {%
   PreCommonFunc
   { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Fact {%
   PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
   PostCommonFunc } def
/EvalFunc_sh {%
   PreCommonFunc
   { (ch\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ch {%
   PreCommonFunc
   { (sh\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_th {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argsh {%
   PreCommonFunc
   { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argch {%
   PreCommonFunc
   { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argth {%
   PreCommonFunc
   { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/PreCommonFunc {
   1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
   4 2 roll 4 index (0) eq
   { (0) StrConcat false }
   { 4 index (1)  ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
} def
/PostCommonFunc {
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
/EvalFunc_Derive {%
   1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
   4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
   4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
   exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_Sum {%
   1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop 3 -1 roll pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
   1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
   4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_IfTE {%
   3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
   NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   1 add NextNonBlankChar pop dup 5 1 roll
   AnalyzeExpr NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add NextNonBlankChar pop
   AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
   6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% advance in str until a comma is found (no error detection!)
%% str index -> str index'
/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for condition....
/EvalCondOp { 3 -1 roll pop } bind def
/PutIntervalOneAdd {putinterval 1 add} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add close parenthesis in string at the given index
%% str index -> str index+1
/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add 0 in string at the given index
%% str index -> str index+1
/AddZero {2 copy (0) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddMul {2 copy (*) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a plus sign in string at the given index
%% str index -> str index+1
/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a minus sign in string at the given index
%% str index -> str index+1
/AddSub {2 copy (-) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a pipe sign in string at the given index
%% str index -> str index+1
/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook { dup 5 1 roll } bind def
/PreEvalHook {} def
/AnalyzePostHook { 7 -1 roll pop } bind def
/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
/RollOp { 5 1 roll } bind def
end%%%tx@CoreAnalyzerDict
/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NEW FUNC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
%% x -> theta
/asin {%
   dup abs 1 gt { EQDFasinrangeerror  } if
   dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
} def
%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
%% x -> theta
/acos {%
   dup abs 1 gt { EQDFacosrangeerror  } if
   dup dup mul 1 exch sub sqrt exch atan DegtoRad
} def
%% function arctangent in radians
%% x -> theta
/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
%% HYPERBOLIC FUNCTIONS
/sh { dup Ex exch neg Ex sub 2 div } def
/ch { dup Ex exch neg Ex add 2 div } def
/th { dup sh exch ch div } def
/Argsh { dup dup mul 1 add sqrt add ln } def
/Argch { dup dup mul 1 sub sqrt add ln } def
/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
%% modified exponential funtion for 0
%% x n -> x^n
/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
%% modified exponential funtion for 0
%% x -> e^x
/Ex { Euler exch exp } bind def
%%
%% factorial function
%% n -> n!
/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
/fact { Fact } bind def
/! { Fact } bind def
end
%
% END pst-algparser.pro

%%EndProcSet
%%BeginProcSet: pst-tools.pro 0 0
% $Id: pst-tools.pro 842 2013-10-26 10:25:41Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.04, 2013/10/26
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
/Pi2 1.57079632679489661925640 def
/factorial { % n on stack, returns n!
   dup 0 eq { 1 }{
     dup 1 gt { dup 1 sub factorial mul } if }
   ifelse } def 
%
/MoverN { % m n on stack, returns the binomial coefficient m over n
   2 dict begin
   /n exch def /m exch def
   n 0 eq { 1 }{
     m n eq { 1 }{
       m factorial n factorial m n sub factorial mul div } ifelse } ifelse
   end
} def
%
/ps@ReverseOrderOfPoints { % on stack [P1 P2 P3 ...Pn]=>[Pn,Pn-1,...,P2,P1]
   5 dict begin       % all local
   aload length /n ED % number of coors
   n 2 div cvi /m ED  % number of Points
   /n1 n def
   m { n1 2 roll /n1 n1 2 sub def } repeat
   n array astore
   end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% subroutines for complex numbers, given as an array [a b] 
% which is a+bi = Real+i Imag
%
/cxadd {		% [a1 b1] [a2 b2] = [a1+a2 b1+b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   3 -1 roll		% [a2 b2] a2 [a1 b1]
   dup 0 get		% [a2 b2] a2 [a1 b1] a1
   3 -1 roll		% [a2 b2] [a1 b1] a1 a2
   add			% [a2 b2] [a1 b1] a1+a2
   3 1 roll		% a1+a2 [a2 b2] [a1 b1]
   1 get			% a1+a2 [a2 b2] b1
   exch 1 get		% a1+a2 b1 b2
   add 2 array astore
} def
%
/cxneg {		% [a b]
   dup 1 get		% [a b] b
   exch 0 get		% b a
   neg exch neg		% -a -b
   2 array astore
} def
%
/cxsub { cxneg cxadd } def  % same as negative addition
%
% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
/cxmul {		% [a1 b1] [a2 b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   exch 1 get		% [a1 b1] a2 b2
   3 -1 roll		% a2 b2 [a1 b1]
   dup 0 get		% a2 b2 [a1 b1] a1
   exch 1 get		% a2 b2 a1 b1
   dup			% a2 b2 a1 b1 b1
   5 -1 roll dup		% b2 a1 b1 b1 a2 a2
   3 1 roll mul		% b2 a1 b1 a2 b1a2
   5 -2 roll dup		% b1 a2 b1a2 b2 a1 a1
   3 -1 roll dup		% b1 a2 b1a2 a1 a1 b2 b2
   3 1 roll mul		% b1 a2 b1a2 a1 b2 a1b2
   4 -1 roll add		% b1 a2 a1 b2 b3
   4 2 roll mul		% b1 b2 b3 a1a2
   4 2 roll mul sub	% b3 a3
   exch 2 array astore
} def
%
% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
/cxsqr {		% [a b]   square root
   dup 0 get exch 1 get	% a b
   dup dup mul		% a b b^2
   3 -1 roll		% b b^2 a
   dup dup mul 		% b b^2 a a^2
   3 -1 roll sub		% b a a2
   3 1 roll mul 2 mul	% a2 b2
   2 array astore
} def
%
/cxsqrt {		% [a b]
%  dup cxnorm sqrt /r exch def
%  cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
   cxlog 		% log[a b]
   2 cxrdiv 		% log[a b]/2
   aload pop exch	% b a
   2.781 exch exp	% b exp(a)
   exch cxconv exch	% [Re +iIm] exp(a)
   cxrmul		%
} def
%
/cxarg { 		% [a b]
   aload pop 		% a b
   exch atan 		% arctan b/a
   DegtoRad 		% arg(z)=atan(b/a)
} def
%
% log[a b] = [a^2-b^2 2ab] = [a2 b2]
/cxlog {		% [a b]
   dup 			% [a b][a b]
   cxnorm 		% [a b] |z|
   log 			% [a b] log|z|
   exch 			% log|z|[a b]
   cxarg 		% log|z| Theta
   cxmake2 		% [log|z| Theta]
} def
%
% square of magnitude of complex number
/cxnorm2 {		% [a b]
   dup 0 get exch 1 get	% a b
   dup mul			% a b^2
   exch dup mul add	% a^2+b^2
} def
%
/cxnorm {		% [a b]
   cxnorm2 sqrt
} def
%
/cxconj {		% conjugent complex
   dup 0 get exch 1 get	% a b
   neg 2 array astore	% [a -b]
} def
%
/cxre { 0 get } def	% real value
/cxim { 1 get } def	% imag value
%
% 1/[a b] = ([a -b]/(a^2+b^2)
/cxrecip {		% [a b]
   dup cxnorm2 exch	% n2 [a b]
   dup 0 get exch 1 get	% n2 a b
   3 -1 roll		% a b n2
   dup			% a b n2 n2
   4 -1 roll exch div	% b n2 a/n2
   3 1 roll div		% a/n2 b/n2
   neg 2 array astore
} def
%
/cxmake1 { 0 2 array astore } def % make a complex number, real given
/cxmake2 { 2 array astore } def	  % dito, both given
%
/cxdiv { cxrecip cxmul } def
%
% multiplikation by a real number
/cxrmul {		% [a b] r
   exch aload pop	% r a b
   3 -1 roll dup		% a b r r
   3 1 roll mul		% a r b*r
   3 1 roll mul		% b*r a*r
   exch 2 array astore   % [a*r b*r]
} def
%
% division by a real number
/cxrdiv {		% [a b] r
   1 exch div		% [a b] 1/r
   cxrmul
} def
%
% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
/cxconv {		% theta
   RadtoDeg dup sin exch cos cxmake2
} def

%%%%% ### bubblesort ###
%% syntax : array bubblesort --> array2 trie par ordre croissant
%% code de Bill Casselman
%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
/bubblesort { % on stack must be an array [ ... ]
4 dict begin
    /a exch def
    /n a length 1 sub def
    n 0 gt {
       % at this point only the n+1 items in the bottom of a remain to
       % the sorted largest item in that blocks is to be moved up into
       % position n
       n {
          0 1 n 1 sub {
             /i exch def
             a i get a i 1 add get gt {
                % if a[i] > a[i+1] swap a[i] and a[i+1]
                a i 1 add
                a i get
                a i a i 1 add get
                % set new a[i] = old a[i+1]
                put
                % set new a[i+1] = old a[i]
                put
             } if
          } for
          /n n 1 sub def
       } repeat
    } if
    a % return the sorted array
end
} def
%
/concatstringarray{  %  [(a) (b) ... (z)] --> (ab...z)  20100422
   0 1 index { length add } forall
   string
   0 3 2 roll
   { 3 copy putinterval length add }forall
   pop 
} bind def
%
/dot2comma {% on stack a string (...)
   2 dict begin
   /Output exch def
   0 1 Output length 1 sub {
     /Index exch def
     Output Index get 46 eq { Output Index 44 put } if
   } for
   Output
   end
} def
%
/rightTrim { % on stack the string and the character number to be stripped
   /charNo exch def
   dup
   length 1 sub -1 0 {
     /i exch def dup i get charNo ne { exit } if
   } for
   0 i 1 add getinterval
   dup length string copy
} bind def  % leaves the stripped string on the stack

/psStringwidth /stringwidth load def
/psShow /show load def

%/stringwidth{ 32 rightTrim psStringwidth } bind def

%/show { 32 rightTrim psShow } bind def
%-----------------------------------------------------------------------------%

/pgffunctions {
     /pgfsc{}bind def% stroke color is empty by default
     /pgffc{}bind def% fill color is empty by default
     /pgfstr{stroke}bind def%
     /pgffill{fill}bind def%
     /pgfeofill{eofill}bind def%
     /pgfe{a dup 0 rlineto exch 0 exch rlineto neg 0 rlineto closepath}bind def% rectangle
     /pgfw{setlinewidth}bind def% setlinewidth
     /pgfs{save pgfpd 72 Resolution div 72 VResolution div neg scale
       magscale{1 DVImag div dup scale}if
       pgfx neg pgfy neg translate pgffoa .setopacityalpha}bind def% save
     /pgfr{pgfsd restore}bind def %restore
     userdict begin%
     /pgfo{pgfsd /pgfx currentpoint /pgfy exch def def @beginspecial}bind def %open
     /pgfc{newpath @endspecial pgfpd}bind def %close
     /pgfsd{globaldict /pgfdelta /delta where {pop delta} {0} ifelse put}bind def% save delta
     /pgfpd{/delta globaldict /pgfdelta get def}bind def % put delta
     /.setopacityalpha where {pop} {/.setopacityalpha{pop}def} ifelse % install .setopacityalpha
     /.pgfsetfillopacityalpha{/pgffoa exch def
       /pgffill{gsave pgffoa .setopacityalpha fill 1 .setopacityalpha newpath fill grestore newpath}bind def
       /pgfeofill{gsave pgffoa .setopacityalpha eofill 1 .setopacityalpha newpath eofill grestore newpath}bind def}bind def
     /.pgfsetstrokeopacityalpha{/pgfsoa exch def /pgfstr{gsave pgfsoa .setopacityalpha stroke grestore newpath}bind def}bind def
     /pgffoa 1 def
     /pgfsoa 1 def
     end
} def
%-----------------------------------------------------------------------------%
% END pst-tools.pro

%%EndProcSet
%%BeginProcSet: pst-dots.pro 0 0
% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02,  2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt <tvz@Princeton.EDU>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga  - Dec. 16, 1999
%% Modified by Etienne Riga  - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17 
%
10 dict dup begin			% hold local
   /FontType 3 def
   /FontMatrix [.001 0 0 .001 0 0] def
%  /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
   /FontBBox [-1000 -1000 1000 1000] def  % See end of file in /BuildGlyph
   /Encoding 256 array def
   0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
   Encoding				   % replace with given dot names
     dup (b) 0 get /Bullet put		   % get the numerical position of b in ASCII
%					   % and save /Bullet at this place in Encoding
     dup (c) 0 get /Circle put
     dup (C) 0 get /BoldCircle put	% 67
     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
%%%
     dup (k) 0 get /Asterisk put
     dup (K) 0 get /BoldAsterisk put
     dup (J) 0 get /SolidAsterisk put
     dup (h) 0 get /Hexagon put
     dup (H) 0 get /BoldHexagon put
     dup (G) 0 get /SolidHexagon put
     dup (f) 0 get /Octogon put		% 2008-04-18 hv
     dup (F) 0 get /BoldOctogon put	% 2008-04-18 hv
     dup (g) 0 get /SolidOctogon put	% 2008-04-18 hv
     dup (a) 0 get /Add put
     dup (A) 0 get /BoldAdd put 		% 65
     dup (x) 0 get /Mul put
     dup (X) 0 get /BoldMul put
     dup (m) 0 get /Oplus put
     dup (M) 0 get /BOplus put
     dup (e) 0 get /SolidOplus put
     dup (n) 0 get /Otimes put
     dup (N) 0 get /BOtimes put
     dup (E) 0 get /SolidOtimes put
     dup (i) 0 get /Bar put
     dup (I) 0 get /BoldBar put
     dup (l) 0 get /SolidDiamond put
     dup (d) 0 get /Diamond put
         (D) 0 get /BoldDiamond put
%%% 
/CharProcs 47 dict def
CharProcs begin
   /CirclePath {0 0 500 0 360 arc closepath} def
   /Bullet {CirclePath fill} def
   /Circle {CirclePath .9 .9 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
%-------------- hv begin 2004/07/25   from: er 2003/03/24
   /HexagonPath {
     0 550 moveto -476 275 lineto -476 -275 lineto
     0 -550 lineto 476 -275 lineto 476 275 lineto closepath
   } def
   /SolidHexagon {HexagonPath fill} def
   /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
   /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
%					2008-04-18 hv
   /OctogonPath {
      550 dup 22.5 tan mul dup neg dup add /xMove exch def
      exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
   /SolidOctogon { OctogonPath fill                             } def
   /Octogon {      OctogonPath .89 .89 scale OctogonPath eofill } def
   /BoldOctogon {  OctogonPath .79 .79 scale OctogonPath eofill } def
%
   /AsteriskPath {
     20 0 moveto 10 250 180 500 0 500 curveto
     -180 500 -10 250 -20 0 curveto closepath
   } def
   /Asterisk {
     AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
     60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
   } def
%
   /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
   /BoldAsteriskPath {
     50 30 cos 100 mul moveto  Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp closepath
   } def
   /BoldAsterisk {BoldAsteriskPath fill} def
   /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
   /CrossPath {
     40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
     -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
     40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
   } def
   /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
     -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
     80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
   } def
   /Add {CrossPath fill} def
   /Mul {45 rotate CrossPath fill} def
   /BoldAdd {BoldCrossPath fill} def
   /BoldMul {45 rotate BoldCrossPath fill} def
   /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
   /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
   /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
   /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
   /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
   /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
   /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
   /Bar {BarPath fill} def
   /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
   /BoldBar {BoldBarPath fill} def
   /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 .865 .865 scale DiamondPath eofill} def
   /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
%%%
   /.notdef { } def
end
%
/BuildGlyph {
   exch
   begin 
%  Metrics 1 index get exec 0
     0 0
%      BBoxes 3 index get exec
     -1000 -1000 1000 1000
%     -571.5 -742.5 571.5 742.5
     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

%%EndProcSet
%%BeginProcSet: cmmi10.pfb 0 0
%!PS-AdobeFont-1.0: CMMI10 003.002
%%Title: CMMI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMMI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup
/UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI10 def
/FontBBox {-32 -250 1048 750 }readonly def
/UniqueID 5087385 def
/PaintType 0 def
/FontInfo 10 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI10.) readonly def
  /FullName (CMMI10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle -14.04 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
  /ascent 750 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 15 /epsilon1 put
dup 16 /zeta put
dup 17 /eta put
dup 18 /theta put
dup 19 /iota put
dup 20 /kappa put
dup 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 24 /xi put
dup 25 /pi put
dup 26 /rho put
dup 27 /sigma put
dup 28 /tau put
dup 29 /upsilon put
dup 30 /phi put
dup 31 /chi put
dup 32 /psi put
dup 33 /omega put
dup 34 /epsilon put
dup 35 /theta1 put
dup 36 /pi1 put
dup 37 /rho1 put
dup 38 /sigma1 put
dup 39 /phi1 put
dup 40 /arrowlefttophalf put
dup 41 /arrowleftbothalf put
dup 42 /arrowrighttophalf put
dup 43 /arrowrightbothalf put
dup 44 /arrowhookleft put
dup 45 /arrowhookright put
dup 46 /triangleright put
dup 47 /triangleleft put
dup 48 /zerooldstyle put
dup 49 /oneoldstyle put
dup 50 /twooldstyle put
dup 51 /threeoldstyle put
dup 52 /fouroldstyle put
dup 53 /fiveoldstyle put
dup 54 /sixoldstyle put
dup 55 /sevenoldstyle put
dup 56 /eightoldstyle put
dup 57 /nineoldstyle put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 63 /star put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /flat put
dup 92 /natural put
dup 93 /sharp put
dup 94 /slurbelow put
dup 95 /slurabove put
dup 96 /lscript put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /dotlessi put
dup 124 /dotlessj put
dup 125 /weierstrass put
dup 126 /vector put
dup 127 /tie put
dup 128 /psi put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 173 /Omega put
dup 174 /alpha put
dup 175 /beta put
dup 176 /gamma put
dup 177 /delta put
dup 178 /epsilon1 put
dup 179 /zeta put
dup 180 /eta put
dup 181 /theta put
dup 182 /iota put
dup 183 /kappa put
dup 184 /lambda put
dup 185 /mu put
dup 186 /nu put
dup 187 /xi put
dup 188 /pi put
dup 189 /rho put
dup 190 /sigma put
dup 191 /tau put
dup 192 /upsilon put
dup 193 /phi put
dup 194 /chi put
dup 195 /psi put
dup 196 /tie put
readonly def
currentdict end
currentfile eexec

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cleartomark
{restore}if


%%EndProcSet
%%BeginProcSet: cmr10.pfb 0 0
%!PS-AdobeFont-1.0: CMR10 003.002
%%Title: CMR10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMR10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR10 def
/FontBBox {-40 -250 1009 750 }readonly def
/UniqueID 5000793 def
/PaintType 0 def
/FontInfo 9 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
  /FullName (CMR10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle 0 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 15 /ffl put
dup 16 /dotlessi put
dup 17 /dotlessj put
dup 18 /grave put
dup 19 /acute put
dup 20 /caron put
dup 21 /breve put
dup 22 /macron put
dup 23 /ring put
dup 24 /cedilla put
dup 25 /germandbls put
dup 26 /ae put
dup 27 /oe put
dup 28 /oslash put
dup 29 /AE put
dup 30 /OE put
dup 31 /Oslash put
dup 32 /suppress put
dup 33 /exclam put
dup 34 /quotedblright put
dup 35 /numbersign put
dup 36 /dollar put
dup 37 /percent put
dup 38 /ampersand put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 42 /asterisk put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 60 /exclamdown put
dup 61 /equal put
dup 62 /questiondown put
dup 63 /question put
dup 64 /at put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 94 /circumflex put
dup 95 /dotaccent put
dup 96 /quoteleft put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 124 /emdash put
dup 125 /hungarumlaut put
dup 126 /tilde put
dup 127 /dieresis put
dup 128 /suppress put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 171 /sfthyphen put
dup 172 /nbspace put
dup 173 /Omega put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 178 /ffl put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 187 /cedilla put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 196 /dieresis put
readonly def
currentdict end
currentfile eexec

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/PSfragDict 6 dict def
/PSfrag { PSfragLib begin load exec end } bind def
end
PSfragLib begin
/RO /readonly      load def
/CP /currentpoint  load def
/CM /currentmatrix load def
/B { bind RO def } bind def
/X { exch def } B
/MD { { X } forall } B
/OE { end exec PSfragLib begin } B
/S false def
/tstr 8 string def
/islev2 { languagelevel } stopped { false } { 2 ge } ifelse def
[ /sM /tM /srcM /dstM /dM /idM /srcFM /dstFM ] { matrix def } forall
sM currentmatrix RO pop
dM defaultmatrix RO idM invertmatrix RO pop
srcFM identmatrix pop
/Hide { gsave { CP } stopped not newpath clip { moveto } if } B
/Unhide { { CP } stopped not grestore { moveto } if } B
/setrepl islev2 {{ /glob currentglobal def true setglobal array astore
                    globaldict exch /PSfrags exch put glob setglobal }}
                 {{ array astore /PSfrags X }} ifelse B
/getrepl islev2 {{ globaldict /PSfrags get aload length }}
                 {{ PSfrags aload length }} ifelse B
/convert {
    /src X src length string
    /c 0 def src length {
       dup c src c get dup 32 lt { pop 32 } if put /c c 1 add def
    } repeat
} B
/Begin {
     /saver save def
     srcFM exch 3 exch put
     0 ne /debugMode X 0 setrepl
     dup /S exch dict def { S 3 1 roll exch convert exch put } repeat
     srcM CM dup invertmatrix pop
     mark { currentdict { end } stopped { pop exit } if } loop
     PSfragDict counttomark { begin } repeat pop
} B
/End {
     mark { currentdict end dup PSfragDict eq { pop exit } if } loop
     counttomark { begin } repeat pop
     getrepl saver restore
     7 idiv dup /S exch dict def {
         6 array astore /mtrx X tstr cvs /K X
         S K [ S K known { S K get aload pop } if mtrx ] put
     } repeat
} B
/Place {
     tstr cvs /K X
     S K known {
         bind /proc X tM CM pop
         CP /cY X /cX X
         0 0 transform idtransform neg /aY X neg /aX X
         S K get dup length /maxiter X
         /iter 1 def {
             iter maxiter ne { /saver save def } if
             tM setmatrix aX aY translate
             [ exch aload pop idtransform ] concat
             cX neg cY neg translate cX cY moveto
             /proc load OE
             iter maxiter ne { saver restore /iter iter 1 add def } if
         } forall
         /noXY { CP /cY X /cX X } stopped def
         tM setmatrix noXY { newpath } { cX cY moveto } ifelse
     } {
         Hide OE Unhide
     } ifelse
} B
/normalize {
     2 index dup mul 2 index dup mul add sqrt div
     dup 4 -1 roll exch mul 3 1 roll mul
} B
/replace {
     aload pop MD
     CP /bY X /lX X gsave sM setmatrix
     str stringwidth abs exch abs add dup 0 eq
         { pop } { 360 exch div dup scale } ifelse
     lX neg bY neg translate newpath lX bY moveto
     str { /ch X ( ) dup 0 ch put false charpath ch Kproc } forall
     flattenpath pathbbox [ /uY /uX /lY /lX ] MD
     CP grestore moveto
     currentfont /FontMatrix get dstFM copy dup
     0 get 0 lt { uX lX /uX X /lX X } if
     3 get 0 lt { uY lY /uY X /lY X } if
     /cX uX lX add 0.5 mul def
     /cY uY lY add 0.5 mul def
     debugMode { gsave 0 setgray 1 setlinewidth
         lX lY moveto lX uY lineto uX uY lineto uX lY lineto closepath
         lX bY moveto uX bY lineto lX cY moveto uX cY lineto
         cX lY moveto cX uY lineto stroke
     grestore } if
     dstFM dup invertmatrix dstM CM srcM
     2 { dstM concatmatrix } repeat pop
     getrepl /temp X
         S str convert get {
             aload pop [ /rot /scl /loc /K ] MD
             /aX cX def /aY cY def
             loc {
                 dup 66  eq { /aY bY def } { % B
                 dup 98  eq { /aY lY def } { % b
                 dup 108 eq { /aX lX def } { % l
                 dup 114 eq { /aX uX def } { % r
                 dup 116 eq { /aY uY def }   % t
                 if } ifelse } ifelse } ifelse } ifelse pop
             } forall
             K srcFM rot tM rotate dstM
             2 { tM concatmatrix } repeat aload pop pop pop
             2 { scl normalize 4 2 roll } repeat
             aX aY transform
             /temp temp 7 add def
         } forall
     temp setrepl
} B
/Rif {
     S 3 index convert known { pop replace } { exch pop OE } ifelse
} B
/XA { bind [ /Kproc /str } B /XC { ] 2 array astore def } B
/xs   { pop } XA XC
/xks  { /kern load OE } XA /kern XC
/xas  { pop ax ay rmoveto } XA /ay /ax XC
/xws  { c eq { cx cy rmoveto } if } XA /c /cy /cx XC
/xaws { ax ay rmoveto c eq { cx cy rmoveto } if }
     XA /ay /ax /c /cy /cx XC
/raws { xaws { awidthshow } Rif } B
/rws  { xws { widthshow } Rif } B
/rks  { xks { kshow } Rif } B
/ras  { xas { ashow } Rif } B
/rs   { xs { show } Rif } B
/rrs { getrepl dup 2 add -1 roll //restore exec setrepl } B
PSfragDict begin
islev2 not { /restore { /rrs PSfrag } B } if
/show       { /rs   PSfrag } B
/kshow      { /rks  PSfrag } B
/ashow      { /ras  PSfrag } B
/widthshow  { /rws  PSfrag } B
/awidthshow { /raws PSfrag } B
end PSfragDict RO pop
end

%%EndProcSet
%%BeginProcSet: pstricks.pro 0 0
% $Id: pstricks.pro 902 2014-03-30 16:23:33Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 1.22, 2014/02/20
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
% Define the follwing gs-functions if not known, eg when using distiller
%
systemdict /.setopacityalpha known not {/.setopacityalpha { pop } def } if
systemdict /.setblendmode known not {/.setblendmode { pop } def } if
systemdict /.setshapealpha known not {/.setshapealpha { pop } def } if
%
/tx@Dict 200 dict def 				% the main PSTricks dictionary
tx@Dict begin
/ADict 25 dict def				% The arrow dictionary
/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
/Sqrt { dup 0 lt { pop 0 } { sqrt } ifelse } def  % return 0 for negative arguments 
/Atan { /atan load stopped { pop pop 0 } if } def % return 0 if atan not known
/ATAN1 {neg -1 atan 180 sub } def		% atan(x) (only one parameter)
/Div { dup 0 eq { pop } { div } ifelse } def  	% control the division
/Log { dup 1e-20 lt { pop -1e30 }{ log } ifelse } def % control the log
/tan { dup cos abs 1.e-10 lt
   { pop 1.e10 } 				% return 1.e10 as infinit
   { dup sin exch cos div } ifelse 		% default sin/cos
} def
/Tan { dup sin exch cos Div } def 		% sin(x)/cos(x) x in degrees
/Acos {dup dup mul neg 1 add dup 0 lt {		% arc cos, returns 0 when negative root
   pop pop 0 }{ sqrt exch atan} ifelse } def
/Acos2 { 2 dict begin
   /x ED /y ED
   y abs 1.0e-20 lt { 1.0e30 } if
   x y div
   dup dup mul neg 1 add dup 0 lt {		% arc cos needs two values x,y
   pop pop 0 }{ sqrt exch atan} ifelse
   y 0 lt { 180 add } if
} def
/NET { neg exch neg exch T } def	      	% change coordinate system to the negative one 
/Pyth { dup mul exch dup mul add sqrt } def   	% Pythagoras, expects 2 parameter
/Pyth2 {					% Pythagoras, xA yA xB yB
   3 -1 roll 		% xA xB yB yA
   sub			% xA xB yB-yA
   3 1 roll 		% yB-yA xA xB
   sub			% yB-yA xA-xB
   Pyth } def
/PtoC { 2 copy cos mul 3 1 roll sin mul } def 	% Polar to Cartesian
%/Rand { rand 4294967295 div } def		% a real random number
/Rand { rand 2147483447 div } def		% a real random number between 0 and 1
%----------------- hv added 20050516 ---------------
/PiDiv2 1.57079632680 def
/Pi 3.14159265359 def 
/TwoPi 6.28318530718 def
/Euler 2.71828182846 def 
%/e Euler bind def
%
/RadtoDeg { 180 mul Pi div } bind def 		% convert from radian to degrees
/DegtoRad { Pi mul 180 div } bind def 		% viceversa
%
/startGlobal { true setglobal globaldict begin } bind def
/endGlobal { end false setglobal } bind def
/pssetRGBcolor /setrgbcolor load def
/pssetCMYKcolor /setcmykcolor load def
/pssetGraycolor /setgray load def
%
%----------------- hv end---------------------------
/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			% BP/PT scaling
/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 % pattern should fit evenly in b
     dup /X ED % pattern array
     0 get /y ED % length of first black segment
     /z 0 X {add} forall def % length of the full pattern
     %% Computation of the scaling factor as described by van Zandt:
     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
     %%%% scaling factor on stack.
     /z ED %% now, z is the scaling factor
     false % for the length test below
     X { z mul } forall X astore %% modification TN 04-08-07
     %%% Checking whether at least one dash in X has positive length:
     {0 gt or} forall
     { 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
%
/SymbolLine {   % on stack [ x y x y ...
   counttomark 					% number of elements
   2 div cvi /n ED     				% n pairs
   /YA ED /XA ED					% the start point
   n 1 sub {
     /YB ED /XB ED
     /XLength XB XA sub def
     /YLength YB YA sub def
     /PAngle YLength XLength Atan def
     /XYLength XLength YLength Pyth def
     %% for negative SymStep we calculate the distance
     SymStep 0 lt
       { %XYLength SymStep div abs cvi
         /nSym SymStep abs cvi def }
       { /nSym XYLength SymStep div cvi def }
     ifelse
     0.5 setflat
     /Shift Symbol stringwidth pop 2 div def
     /deltaX XLength nSym div def
     /deltaY YLength nSym div def
     curveticks
       { XA YA moveto }
       { XA Shift sub YA Shift sub moveto }
     ifelse
     nSym {
       gsave
       curveticks
         { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
           currentpoint translate rotAngle rotate
           0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
           SymbolLinewidth setlinewidth stroke
         }
         {
           rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
           Symbol show
         }
       ifelse
       grestore
       deltaX deltaY rmoveto
     } repeat
     /YA YB def /XA XB def
   } repeat
   curveticks
     { XA YA moveto }
     { XA Shift sub YA Shift sub moveto }
   ifelse
   gsave
   curveticks
     { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED
       XA YA translate rotAngle rotate
       0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
       SymbolLinewidth setlinewidth stroke
     }
     {
       rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
       Symbol show
     }
   ifelse
   grestore
   pop 				% delete the mark symbol
} def
%
/LineFill { % hv ------------ patch 7 -------------
   gsave
   abs /hatchWidthInc ED
   abs /hatchSepInc ED
   abs CLW add /a ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform pathbbox
   /y2 ED
   a Div ceiling cvi /x2 ED /y1 ED
   a Div cvi /x1 ED /y2 y2 y1 sub def
   clipType   % must be defined in pstricks.tex: clip -- eoclip
   newpath
   2 setlinecap
   systemdict
   /setstrokeadjust known { true setstrokeadjust } if
   x2 x1 sub 1 add {
     x1 a mul y1 moveto 0 y2 rlineto stroke
     /x1 x1 1 add
       hatchWidthInc 0 gt { CLW add } if
     def
     hatchSepInc 0 gt hatchWidthInc 0 gt or {
       /a a hatchSepInc add def
       CLW hatchWidthInc add SLW
     } if
   } repeat
   grestore
   pop pop } def
%
/DotFill {%	 on stack: dot radius
   /dotRadius ED
   abs CLW add /a ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform
   pathbbox % llx lly urx ury of smallest bounding box
   /y2 ED /x2 ED /y1 ED /x1 ED
   y2 y1 sub a div 2 add cvi /Ny ED
   x2 x1 sub a div 2 add cvi /Nx ED
   clipType   % must be defined in pstricks.tex: clip -- eoclip
   newpath
   /yA y1 dotRadius add CLW add def
   /xA0 x1 dotRadius add CLW add def
   Ny {
      /xA xA0 def
      Nx {
        newpath
        xA yA dotRadius 0 360 arc
        SolidDot { gsave fill grestore } if
        stroke
        xA a add /xA ED
      } repeat
      yA a add /yA ED
   } repeat
   grestore
} def
%
/PenroseFill {%	 on stack: scaling factor
   /Scale ED
%  1 exch div round /penroseFactor ED 
%  a 0 dtransform round exch round exch
%  2 copy idtransform 
%  exch Atan rotate 
%  idtransform pop /a ED 
%  .25 .25 itransform pathbbox 
%  /y2 ED 
%  a Div ceiling cvi /x2 ED /y1 ED 
%  a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath 
gsave
   220 150 translate
   Scale dup scale
   systemdict /setstrokeadjust known { true setstrokeadjust } if
   /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
  { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
   [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
   i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
   mul j l + S rmoveto}F i L j L stroke }F}F}F}F
   grestore 
%  pop pop 
} def
%
/PenroseFillA {%  on stack: scaling factor, border color, kite color, dart color
   /Scale ED
   Scale dup scale
   /border_colour ED
   /kite_colour ED
   /dart_colour ED
   clip
   newpath
   gsave
   100 100 translate
   6
   Scale 1 lt { 1 Scale dup add div mul cvi } if %%%%   Number of iterations
   10					%%%%   Long side length in millimeters
   /border_width { L 0.06 mul }def		%%%%   Choose the scalefactor for the borders
   /L exch 25.4 div 72 mul def		%%%%   Conversion: mm -> inches -> points
   /f{-1 5 sqrt add 2 div}bind def		%%%%   The reciprocal of the golden ratio
   /l{L f mul}bind def			%%%%   Short side length l = L*f
   /Ll{L l add}bind def			%%%%   Ll =  L + l
   /c{36 cos L mul}bind def		%%%%   c  =  L*cos(36)
   /s{36 sin L mul}bind def		%%%%   s  =  L*sin(36)
   /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
 	     0 setlinewidth stroke grestore border_colour stroke } bind def
   /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
 			   Ll 0 translate 144 rotate kite grestore }
 	      		 { kite_colour L draw_tile }ifelse
 	     pop } bind def
   /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
 			   -144 rotate Ll neg 0 translate half_dart grestore }
 	      		 { dart_colour l draw_tile }ifelse
   	     pop } bind def
   /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
   border_width setlinewidth  1 setlinejoin  1 setlinecap
%  450 0 translate
   dup f exch neg exp dup scale
   5 {kite 72 rotate } repeat stroke
   grestore
} def
%
%
/TruchetFill { %	 on stack: scaling factor
   10 dict begin
   dup dup scale
   1 exch div round /penroseFactor ED
   a 0 dtransform round exch round exch
   2 copy idtransform
   exch Atan rotate
   idtransform pop /a ED
   .25 .25 itransform pathbbox
   /y2 ED
   a Div ceiling cvi /x2 ED /y1 ED
   a Div cvi /x1 ED /y2 y2 y1 sub def
   clip
   newpath
   systemdict
   /setstrokeadjust known { true setstrokeadjust } if
   /ma a neg def
   /ha a 2 div def
   /mha ha neg def
   /tile {
     rand dup 2 idiv 2 mul eq { 90 rotate } if
     mha mha moveto ha mha lineto
     ha ha lineto mha ha lineto
%    closepath .1 setlinewidth stroke
     contents
   } def
   /contents{
     0 ha moveto ha 0 lineto
     0 mha moveto mha 0 lineto
%    1 setlinewidth stroke
   } def
   /dotiling {
     f ma mul a f a mul {
       /i exch def
       f ma mul a f a mul {
         /j exch def
         gsave i j translate
         tile stroke grestore
       } for
     } for
   } def
%
   /f 3 def
   5 srand dotiling
   end % local user dict
} def
%
/BeginArrow {
   ADict begin 			% hold it local, for end see EndArrow
   /@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 % end the ADict
%
/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
%
/ArrowD { % the sides are drawn as curves (hv 20071211)
   CLW mul add dup
   2 div /w ED
   mul dup /h ED
   mul /Inset ED
   { 0 h T 1 -1 scale } if % changes the direction
% we use y=w/h^2 * x^2 as equation for the control points
% for the coordinates the arrow is seen from top to bottom
% the bottom (tip) is (0;0)
   w neg h moveto % lower left of >
   w 9 div 4 mul neg h 3 div 2 mul
   w 9 div neg       h 3 div
   0 0 curveto    % tip of >
   w 9 div        h 3 div
   w 9 div 4 mul  h 3 div 2 mul
   w h curveto % upper left of >
   w neg Inset neg rlineto % move to x=0 and inset
   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 { % DS is the dot size
   { /z DS def } { /z 0 def } ifelse  	% outer or inner dimen
   /b ED 				% the color definition
   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 { % holds the coordinates and on top of stack the showpoints boolean
   /showpoints ED
   counttomark 2 div dup cvi /n ED  	% n 2 div on stack
   n eq not { exch pop } if		% even numbers of points? delete one
   ] aload /Points ED
   showpoints not { Points aload pop } if
%    { ] aload /Points ED } 
%    { n 2 mul 1 add -1 roll pop } ifelse	% delete the mark symbol 
} 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
%
/LineToYAxis {
   /Ox ED		% Save the x origin value
   NArray            % all x-y pairs on stack
   n { 2 copy moveto % go to current point
     Ox exch Lineto   % line to y-axis
     pop             % delete old x-value
   } repeat
} def
%
/LineToXAxis{
   /Oy ED		% Save the y origin value
   NArray		% all x-y pairs on stack
   n 0 eq not
     { n 1 eq { 0 0 /n 2 def } if
       ArrowA
       /n n 2 sub def
       CP 2 copy moveto pop Oy Lineto
       n { 2 copy moveto pop Oy Lineto } repeat
       CP
       4 2 roll
       ArrowB
       2 copy moveto pop Oy
       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
%
/SymbolPolygon {   % on stack [ x y x y ...
   counttomark 					% number of elements
   2 add /m ED
   2 copy m 2 roll				% copy last two
   m 2 div cvi /n ED    				% n pairs
   /YA ED /XA ED					% the start point
   n 1 sub {
     /YB ED /XB ED
     /XLength XB XA sub def
     /YLength YB YA sub def
     /PAngle YLength XLength Atan def
     /XYLength XLength YLength Pyth def
     /nSym XYLength SymStep Div cvi def
     /Shift Symbol stringwidth pop 2 Div def
     /deltaX XLength nSym Div def
     /deltaY YLength nSym Div def
     XA Shift sub YA Shift sub moveto
     nSym {
       gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
       Symbol show
       grestore
       deltaX deltaY rmoveto
     } repeat
%    XB Shift sub YB Shift sub moveto Symbol show
     /YA YB def /XA XB def
   } repeat
   pop	% delete the mark symbol
} 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
%
/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
%
/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
%
/CurvePath {
   %% for negative SymStep we calculate the distance
   SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
   0.5 setflat
   flattenpath /z 0 def /z0 0 def
   { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
     x1 Shift sub y1 Shift sub moveto
     gsave
     curveticks
       { x1 y1 translate startAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       { startAngle rotate Symbol show }
     ifelse
     grestore /z0 z def }
   { /y ED /x ED PathLength@ z z0 sub SymStep ge {
       x Shift sub y Shift sub moveto
       gsave
       curveticks
         { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED
           x y translate rotAngle rotate
           0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
           SymbolLinewidth setlinewidth stroke
         }
         {
           rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
           Symbol show
         }
       ifelse
       grestore /z0 z def } if
     /yOld y def /xOld x def }
   {} %% the lineto part
   { /y y2 def /x x2 def PathLength@
     x Shift sub y Shift sub moveto
     gsave
     curveticks
       { y yOld sub x xOld sub Atan 180 sub /rotAngle ED
         x y translate rotAngle rotate
         0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto
         SymbolLinewidth setlinewidth stroke
       }
       {
         x Shift sub y Shift sub moveto
         rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if
         Symbol show
       }
     ifelse
     grestore
   }
   pathforall 
%  curveticks 
%   { gsave 
%     x y translate rotAngle rotate 
%     0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
%     SymbolLinewidth setlinewidth stroke grestore
%   } if
   z 
} def
%
/OpenSymbolCurve {
   OpenCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/AltOpenSymbolCurve {
   AltCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolCurve {
   ClosedCurve
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} def
%
/CalcBezierSpline {%  Christoph Bersch
   10 dict begin
   /getX { Points exch 2 mul get } def
   /getY { Points exch 2 mul 1 add get } def
   /n Points length 1 sub 2 idiv def
   /GetFirstControlPoints {
     /x n array def
     /tmp n array def
     /b 2 def
     x 0 rhs 0 get b div put
     1 1 n 1 sub {
       /i exch def
       tmp i 1 b div dup 4 1 roll put
       i n 1 sub lt { 4 }{ 3.5 } ifelse exch sub /b exch def
       x i rhs i get x i 1 sub get sub b div put
     } for
     1 1 n 1 sub {
       n exch sub
       dup dup x exch 1 sub 2 copy 6 2 roll
       get 3 1 roll tmp exch get
       exch x exch get mul sub
       put
     } for
     x
   } def
   %
   n 1 eq {
     0 getX 2 mul 1 getX add 3 div
     0 getY 2 mul 1 getY add 3 div
     exch dup 3 1 roll 2 mul 0 getX sub
     exch dup 3 1 roll 2 mul 0 getY sub
     [ 0 getX 0 getY 7 3 roll 1 getX 1 getY ] /outPoints exch def
   } {
     /outPoints 6 n mul 2 add array def
     0 1 n {
       dup dup 6 mul dup 1 add
       outPoints exch 5 -1 roll getY put
       outPoints exch 3 -1 roll getX put
     } for
     /rhs n array def
     1 1 n 2 sub {
       rhs exch dup dup getX 4 mul exch 1 add getX 2 mul add put
     } for
     rhs 0 0 getX 1 getX 2 mul add put
     rhs n 1 sub dup getX 8 mul n getX add 2 div put
     GetFirstControlPoints
     1 1 n 2 sub {
       rhs exch dup dup getY 4 mul exch 1 add getY 2 mul add put
     } for
     rhs 0 0 getY 1 getY 2 mul add put
     rhs n 1 sub dup getY 8 mul n getY add 2 div put
     GetFirstControlPoints
     0 1 n 1 sub {
       /i exch def
       2 copy
       i get outPoints 6 i mul 3 add 3 -1 roll put
       i get outPoints 6 i mul 2 add 3 -1 roll put
       2 copy
       i n 1 sub lt {
         i 1 add get i 1 add getY 2 mul exch sub outPoints 6 i mul 5 add 3 -1 roll put
         i 1 add get i 1 add getX 2 mul exch sub outPoints 6 i mul 4 add 3 -1 roll put
       }{
         n 1 sub get n getY add 2 div outPoints 6 n 1 sub mul 5 add 3 -1 roll put
         n 1 sub get n getX add 2 div outPoints 6 n 1 sub mul 4 add 3 -1 roll put
       } ifelse
     } for
     pop pop
   } ifelse
   outPoints
   end
} def
/Spline {
   /showpoints ED
   counttomark 2 div dup cvi /n ED
   n eq not { exch pop } if
   ] /Points ED
   n 1 gt {
     CalcBezierSpline
     mark exch aload pop
     ArrowA
     n 2 sub {
       6 2 roll 4 2 roll curveto
     } repeat
     6 2 roll 4 2 roll ArrowB curveto
   } if
} def
/OpenSymbolSpline {
   Spline
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/OpenSymbolBezier {
   OpenBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath 
} 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
%
/ClosedSymbolBezier {
   /f ED				 % save showpoints value
   2 copy /yEnd ED /xEnd ED
   counttomark -2 roll 2 copy /yStart ED /xStart ED
   counttomark 2 roll
   f
   ClosedBezier
   0.1 setflat
   /Shift Symbol stringwidth pop 2 div def
   CurvePath
   [ xEnd yEnd xStart yStart SymbolLine 
} 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 ED /x0 ED /y1 ED /x1 ED
   /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
%
/Parab1 { % 1 end  |  0 SP
   /ySP ED /xSP ED /y1 ED /x1 ED
   /dx xSP x1 sub 3 div def
   /dy ySP y1 sub 3 div def
   newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto
                        x1 ySP lineto closepath clip
   currentpoint
   newpath moveto
   xSP dx sub ySP dy add x1 y1 ArrowA
   xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB
   curveto
   /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def 
} def
%
/Grid {
   newpath
   /a 4 string def
   /b ED % 				psk@gridlabels in pt
   /c ED % 				{ \pst@usecolor\psgridlabelcolor }
   /n ED % 				psk@griddots
   cvi dup 1 lt { pop 1 } if
   /s ED % 				\psk@subgriddiv
   s div dup 0 eq { pop 1 } if
   /dy ED s div dup 0 eq { pop 1 } if %	\pst@number\psyunit abs
   /dx ED dy div round dy mul %		\pst@number\psxunit abs
   /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 {
   /rotAngle ED
   /mtrx CM def
   T
   rotAngle rotate
   scale 0 0 1 5 3 roll arc
   mtrx setmatrix 
} def
%
/ArcAdjust { %%%% Vincent Guirardel
% given a target length (targetLength) and an initial angle (angle0) [in the stack],
% let  M(angle0)=(rx*cos(angle0),ry*sin(angle0))=(x0,y0).
% This computes an angle t such that (x0,y0) is at distance 
% targetLength from the point M(t)=(rx*cos(t),ry*sin(t)).
% NOTE: this an absolute angle, it does not have to be added or substracted to angle0
% contrary to TvZ's code.
% To achieve, this, one iterates the following process: start with some angle t,
% compute the point M' at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)].
% Now take t' (= new angle) so that (0,0) M(t') and M' are aligned.
%
% Another difference with TvZ's code is that we need d (=add/sub) to be defined.
% the value of d = add/sub is used to know on which side we have to move.
% It is only used in the initialisation of the angle before the iteration.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Input stack:  1: target length 2: initial angle
% variables used : rx, ry, d (=add/sub)
%
   /targetLength ED /angle0 ED
   /x0 rx angle0 cos mul def
   /y0 ry angle0 sin mul def
% we are looking for an angle t such that (x0,y0) is at distance targetLength 
% from the point M(t)=(rx*cos(t),ry*sin(t)))
%initialisation of angle (using 1st order approx = TvZ's code)
   targetLength 57.2958 mul
   angle0 sin rx mul dup mul
   angle0 cos ry mul dup mul
   add sqrt div 
% if initialisation angle is two large (more than 90 degrees) set it to 90 degrees
% (if the ellipse is very curved at the point where we draw the arrow, %
% the value can be much more than 360 degrees !)
% this should avoid going on the wrong side (more than 180 degrees) or go near
% a bad attractive point (at 180 degrees)
   dup 90 ge { pop 90 } if
   angle0 exch d % add or sub
% maximum number of times to iterate the iterative procedure:
% iterative procedure: takes an angle t on top of stack, computes a 
% better angle (and put it on top of stack)
   30 { dup
% compute distance D between (x0,y0) and M(t)
     dup cos rx mul x0 sub dup mul exch sin ry mul y0 sub dup mul add sqrt
% if D almost equals targetLength, we stop
     dup targetLength sub abs 1e-5 le { pop exit } if
% stack now contains D t
% compute the point M(t') at distance targetLength of (x0,y0) on the semi-line [(x0,y0) M(t)]:
% M(t')= ( (x(t)-x0)*targetLength/d+x0 , (y(t)-y0)*targetLength/d+y0 )
     exch dup cos rx mul x0 sub  exch sin ry mul y0 sub
% stack contains:  y(t)-y0, x(t)-x0, d
     2 index Div targetLength mul y0 add ry Div exch
     2 index Div targetLength mul x0 add rx Div
% stack contains x(t')/rx , y(t')/ry , d
% now compute t', and remove D from stack
     atan exch pop
   } repeat
% we don't look at what happened... in particular, if targetLength is greater 
% than the diameter of the ellipse...
% the final angle will be around /angle0 + 180. maybe we should treat this pathological case...
% after iteration, stack contains an angle t such that M(t) is the tail of the arrow
% to give back the result as a an angle relative to angle0 we could add the following line:
% angle0 sub 0 exch d
%
% begin bug fix 2006-01-11
% we want to adjust the new angle t' by a multiple of 360 so that  | t'-angle0 | <= 180
%(we don't want to make the ellipse turn more or less than it should)...
dup angle0 sub dup abs 180 gt { 180 add 360 div floor 360 mul sub } { pop } ifelse
% end bug fix
} def
%
/EllipticArcArrow {
   /d ED      % is add or sub
   /b ED      % arrow procedure
   /a1 ED     % angle
   gsave
   newpath
   0 -1000 moveto
   clip                  % Set clippath far from arrow.
   newpath
   0 1 0 0 b             % Draw arrow to determine length.
   grestore
% Length of arrow is on top of stack. Next 3 numbers are junk.
%
   a1 exch ArcAdjust   % Angular position of base of arrow.
   /a2 ED
   pop pop pop
   a2 cos rx mul xOrig add % hv 2007-08-29   x->xOrig
   a2 sin ry mul yOrig add % hv 2007-08-29   y->yOrig
   a1 cos rx mul xOrig add %
   a1 sin ry mul yOrig add % 
% Now arrow tip coor and base coor are on stack.
   b pop pop pop pop       % Draw arrow, and discard coordinates.
   a2 CLW 8 div
% change value of d (test it by looking if  `` 1 1 d '' gives 2 or not )
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse
   ArcAdjust
% resets original value of d
   1 1 d 2 eq { /d { sub } def } { /d { add } def } ifelse  % Adjust angle to give overlap.
} def
%%------------------ tvz/DG/hv (2004-05-10) end -------------------%%
%
/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 {
   5 dict begin
   /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
   end
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro

%%EndProcSet
%%BeginProcSet: pst-algparser.pro 0 0
% $Id: pst-algparser.pro 902 2014-03-30 16:23:33Z herbert $
%%
%% PostScript prologue for PSTricks algorithm parser
%% Version 0.05, 2014/03/30
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%%-----------------------------------------------------------------------------%
%
/AlgParser { tx@AlgToPs begin AlgToPs end } def  % Dominique Rodriguez
%
/tx@CoreAnalyzerDict 100 dict def tx@CoreAnalyzerDict begin
%
% PS ANALYZER FOR ALGEBRAIC EXPRESSION V1.13
%
% 09/2011 DR factorial with ! added
%
% E->T|E+T
% T->FS|T*FS
% FS -> F | +FS | -FS
% F->P|F^SF|P!
% P->(E)|literal
% literal->number|var|var[E]|func(params)
% params->E|E,param
% number->TOBEFINISHED
%
%% E expression, T term, SF signed factor, F factor, P power
%
%% parser
%
%% str
%
%% C->E<condition_operators>E
%% STR index -> STR index+lenExpr
/AnalyzeCond { AnalyzeExpr ReadCondOp AnalyzeExpr EvalCondOp  } def
%
%% analyze Expression List (separator , or | )
%% STR index -> STR index+lenExpr
%% /AnalyzeListOfE {
%%   { NextNonBlankChar pop AnalyzeExpr%%dup Strlen eq { exit } if NextNonBlankChar
%%     NextNonBlankChar dup 0 eq { pop exit } if
%%     dup 44 ne 1 index 124 ne and { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse } if
%%     pop NextNonBlankChar dup 0 eq { exit } if 124 ne { PROBLEMCONTACTBILLOU } if 1 add NextNonBlankChar 0 eq {toto} if } loop
%%   AnalyzeListOfEPostHook
%% } def
/AnalyzeListOfE {
   /NotFirst false def
   { NextNonBlankChar pop AnalyzeExpr
     NotFirst { EvalListOfExpr } { /NotFirst true def } ifelse
     dup Strlen eq { exit } if NextNonBlankChar
     dup 44 ne 1 index 124 ne and
     { dup 41 ne { PROBLEMCONTACTBILLOU } { pop exit } ifelse }
     if  pop 1 add } loop
   AnalyzeListOfEPostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% E->T|E+T
%% STR index -> STR index+lenExpr
/AnalyzeExpr {
   AnalyzePreHook AnalyzeTerm IsEndingExpr
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeTerm PreEvalHook EvalAddSub IsEndingExpr { pop exit } if } loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% T->FS|T*FS
%% STR index
/AnalyzeTerm {
   AnalyzePreHook AnalyzeSignedFactor IsEndingTerm
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor PreEvalHook EvalMulDiv IsEndingTerm { pop exit } if} loop }
   ifelse
   AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% FS -> F | +FS | -FS
%% STR index
/AnalyzeSignedFactor {
   AnalyzePreHook 2 copy get dup IsUnaryOp
   { RollOp 1 add NextNonBlankChar pop AnalyzeSignedFactor EvalUnaryOp }
   { pop AnalyzeFactor }
   ifelse AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% F->P|F^P|P!
%% STR index
/AnalyzeFactor {
   AnalyzePreHook AnalyzePower IsEndingFactor
   { dup 0 ne { 32 eq { NextNonBlankChar } if } { pop } ifelse }
   { { dup 33 eq%% is there a ! DR 09/2011
       { pop 1 add NextNonBlankChar pop EvalFactorial }
       { RollOp 1 add NextNonBlankChar pop AnalyzePower PreEvalHook EvalPower }
       ifelse
       IsEndingFactor { pop exit } if } loop }
   ifelse  AnalyzePostHook
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% P->(E)|literal
%% STR index
/AnalyzePower {
   %% depending of first char either a number, or a literal
   2 copy get dup 40 eq%%an open par
   { pop 1 add NextNonBlankChar pop AnalyzeExpr 1 add NextNonBlankChar pop }
   { AnalyzeLiteral }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index STR[index] -> STR index
%/AnalyzeLiteral { IsNumber { EvalNumber } { EvalLiteral } ifelse } def
/AnalyzeLiteral { dup IsUnaryOp exch IsNumber or { EvalNumber } { EvalLiteral } ifelse } def%%dr 09102006
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% recognize + or -
%% chr -> T/F
/IsUnaryOp { dup 43 eq exch 45 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsNumber { dup 48 ge exch dup 57 le 3 -1 roll and exch 46 eq or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadNumber {
   exch dup 3 -1 roll dup 3 1 roll
   %%read mantissa
   { 1 add  2 copy dup Strlen eq { pop pop 0 exit } if get dup IsNumber not { exit } if pop } loop
   dup 101 eq exch 69 eq or
   %%% there is a "e" or "E" -> read exponant
   { 1 add 2 copy get dup IsUnaryOp
     { pop 1 add 2 copy get } if
     { IsNumber not { exit } if 1 add 2 copy get } loop }
   if
   dup 4 1 roll
   3 -1 roll exch 1 index sub getinterval
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a number can contain only : 0123456789.
%% chr -> T/F
/IsCondOp { dup 30 eq exch dup 60 ge exch 62 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index number
%% a number can be of the form [0-9]*.[0-9]*\([eE][+-]?[0-9]+\)?
%% STR index -> STR index' number
/ReadCondOp {
   NextNonBlankChar 1 index 4 1 roll
   { IsCondOp not { exit } if 1 add  2 copy get } loop
   2 copy 5 -1 roll
   exch 1 index sub getinterval 3 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can contain only : 0123456789.
%% chr -> T/F
/IsLiteral {%
   dup 48 ge exch dup  57 le 3 -1 roll and exch
   dup 65 ge exch dup  90 le 3 -1 roll and 3 -1 roll or exch
   dup 97 ge exch     122 le and or } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% a literal can be of the form [a-zA-Z][a-zA-Z0-9]*\(\((Expression)\)|\(\[Expression\]\)\)?
%% STR index -> literal STR index' nextchr
/ReadLiteral {
   exch dup 3 -1 roll dup 3 1 roll
   %%read literal core
   { 2 copy dup Strlen eq { pop pop 0 exit } if get dup IsLiteral not { exit } if pop 1 add } loop
   4 1 roll dup 5 1 roll 3 -1 roll exch 1 index sub getinterval 4 1 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a clpar
%% STR index -> STR index STR[index] T/F
/IsEndingExpr {%
   2 copy dup Strlen eq
   %% if end of str is reached -> end !
   { pop pop 0 true }
   %% ending chr -> clpar, comma, |, <, >, =, !,
   {get dup  dup  41 eq
        exch dup 124 eq
        exch dup  93 eq
        exch dup  44 eq
        exch dup  30 eq
        exch dup  60 ge exch 62 le and or or or or or}
   ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or a +-
%% STR index -> STR index STR[index] T/F
/IsEndingTerm { IsEndingExpr { true } { dup dup 43 eq exch 45 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or */
%% STR index -> STR index STR[index] T/F
/IsEndingFactor { IsEndingTerm { true } { dup dup 42 eq exch 47 eq or } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% expr is ended by end of str or ^
%% STR index -> STR index STR[index] T/F
/IsEndingPower { IsEndingFactor { true } { dup 94 eq } ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% STR index -> STR index STR[index]
/NextNonBlankChar { { dup Strlen eq { 0 exit } if 2 copy get dup neBlkChar { exit } if pop 1 add } loop } bind def
/neBlkChar { dup 32 ne exch dup 10 ne exch 9 ne and and } bind def
%%%%%%%%%%%%%%%%%%%%%%%%
%% DEBUG
/BRK {false} def
/BRKtrue {/BRK true def} def
/BRKStop {BRK {BRKtoto} if } def
/BRKEvalStop {BRK exch if } def
/BRKBRK2true {BRK {BRK2true} if } def
/BRK2 {false} def
/BRK2true {/BRK2 true def} def
/BRK2Stop {BRK2 {BRK2toto} if } def/BRK {false} def
end
%
%-------------------------------------------------------------------------------%
%
/tx@AlgToPs 12 dict def tx@AlgToPs begin
%
%% algExpr -> PSVector
/AlgToPs { tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE pop pop EndingSequence end } def
/EndingSequence { ExpressionVector aload length /end cvx exch 1 add array astore } def
/InitParser { /ExpressionVector [ /tx@AddMathFunc cvx /begin cvx ] def dup length /Strlen exch def 0 } def
/Strlen 0 def
/EvalListOfExpr {} def%
/EvalNumber {%
     ReadNumber  cvr /ExpressionVector ExpressionVector aload length dup 3 add -1 roll cvx
     exch 1 add array astore def NextNonBlankChar pop } def
/EvalAddSub {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   43 eq { /add } { /sub } ifelse cvx exch 1 add array astore def
} def
/EvalMulDiv {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   42 eq { /mul } { /div } ifelse cvx exch 1 add array astore def
} def
/EvalPower {%
   /ExpressionVector ExpressionVector aload length dup 5 add -1 roll
   pop /exp cvx exch 1 add array astore def
} def
/EvalFactorial {% DR 09/2011
   /ExpressionVector ExpressionVector aload length
   /fact cvx exch 1 add array astore def
} def
/EvalLiteral {%
   ReadLiteral
   dup 40 eq%%% there is an open par -> function call
   { pop 2 index
     dup (Sum) eq { EvalSum }
     { dup (IfTE) eq { EvalCond }
       { dup (Derive) eq { pop EvalDerive }
 	{ pop 1 add NextNonBlankChar pop AnalyzeListOfE 2 index TrigoFunc
           /ExpressionVector ExpressionVector aload length dup 5 add -1 roll cvn cvx
 	  exch 1 add array astore def 1 add NextNonBlankChar pop } ifelse } ifelse} ifelse }
   { /ExpressionVector ExpressionVector aload length dup 6 add -1 roll cvn cvx exch 1 add array astore def
     dup 91 eq%%% there is an open bracket -> vector element
     { pop 1 add NextNonBlankChar pop AnalyzeExpr
       /ExpressionVector ExpressionVector aload length /cvi cvx exch /get cvx exch 2 add array astore def 1 add }
     { pop NextNonBlankChar pop }
     ifelse}
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% the derive function : Derive(n,f(x))
%% firstparindex lastparindex ->
/EvalDerive {
   %% manage the function descripiton
   1 add ReadNumber 3 1 roll NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   1 add NextNonBlankChar pop
   3 -1 roll cvi
   dup 0 eq
   { pop AnalyzeExpr 3 -1 roll pop 1 add }
   { 1 sub 3 1 roll (x)  exch tx@Derive begin DeriveIndexed end 4 -1 roll
     { (x) tx@Derive begin Derive end } repeat
     ExpressionVector exch /ExpressionVector [] def
     AlgToPs aload length
     /ExpressionVector 1 index 3 add -1 roll aload length dup 3 add -1 roll  /l2 exch def /l1 exch def
     l1 l2 add 1 add l2 neg roll l1 l2 add array astore def 3 -1 roll pop 1 add
     1 index length /Strlen exch def } ifelse
} def
/EvalSum {%
   pop 1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber cvi 3 1 roll
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   /ExpressionVector ExpressionVector aload length dup 7 add -3 roll 0 4 1 roll
   5 -1 roll 4 add array astore def
   %% keep ExpressionVector for later and create a new one for internal Sum computation
   ExpressionVector 3 1 roll /ExpressionVector [ 6 -1 roll cvn /exch cvx /def cvx ] def
   1 add NextNonBlankChar pop AnalyzeExpr
   %% add each term
   /ExpressionVector ExpressionVector aload length 1 add /add cvx exch array astore def
   /ExpressionVector 4 -1 roll aload length ExpressionVector cvx /for cvx 3 -1 roll 2 add
   array astore def 3 -1 roll pop 1 add
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
/EvalCond {%
   pop 1 add AnalyzeCond NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   ExpressionVector 3 1 roll /ExpressionVector [] def
   1 add AnalyzeExpr ExpressionVector 3 1 roll /ExpressionVector [] def
   NextNonBlankChar 44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add AnalyzeExpr
   NextNonBlankChar 41 ne { ANALYZER_ERROR_missing_ending parenthesis_in_IfTE } if
   ExpressionVector
   /ExpressionVector 6 -1 roll aload length dup
   6 add -1 roll cvx exch dup 4 add -1 roll cvx /ifelse cvx 3 -1 roll 3 add array astore def
   1 add 3 -1 roll pop
} def
%% CondOp STR index
/EvalCondOp {%
   3 -1 roll
   dup (=) eq  { /eq } {%
   dup (<) eq  { /lt } {%
   dup (>) eq  { /gt } {%
   dup (>=) eq { /ge } {%
   dup (<=) eq { /ge } {%
   dup (!=) eq { /ne } { ERROR_non_valid_conditional_operator }
   ifelse } ifelse } ifelse } ifelse } ifelse } ifelse
   cvx exch pop
   /ExpressionVector ExpressionVector aload length dup 3 add -1 roll exch 1 add array astore def } def
/EvalUnaryOp {
   3 -1 roll 45 eq { /ExpressionVector ExpressionVector aload length /neg cvx exch 1 add array astore def } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook {} bind def
/PreEvalHook {} bind def
/AnalyzeListOfEPostHook {} bind def
/AnalyzePostHook {} def
/RollOp { 3 1 roll } bind def
end   %tx@CoreAnalyzerDict
%
%--------------------------------------------------------------------%
%
/tx@Derive 41 dict def tx@Derive begin
%%increase ^^ for each function added
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable -> PSVector
/Derive {%
   10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser AnalyzeListOfE end
} def
/Strlen 0 def
/InitParser { dup length /Strlen exch def 0 } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% algExpr variable index -> PSVector
/DeriveIndexed {%
   3 1 roll 10240 string 3 1 roll 0 3 1 roll
   /Variable exch def
   tx@CoreAnalyzerDict begin InitParser pop 4 -1 roll AnalyzeExpr 4 -2 roll pop pop 4 -2 roll exch pop end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u,v)'=-(u',v')
/EvalListOfExpr {%
   4 2 roll 2 copy 9 -1 roll dup length 4 1 roll putinterval add AddPipe
            2 copy 7 -1 roll dup length 4 1 roll putinterval add
   6 -2 roll pop pop
   2 copy pop 0 6 2 roll GetIntervalNewStr 5 1 roll 2 copy 0 exch getinterval 6 1 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (-u)'=-(u')
/EvalUnaryOp {
   4 -2 roll 4 index (0) eq
   { (0) StrConcat 7 -1 roll pop }
   { 7 -1 roll 45 eq
     { AddSub AddOpPar true } { false } ifelse
     3 1 roll 5 index StrConcat 3 -1 roll { AddClPar } if } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   7 -2 roll pop pop 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (number)'=0
/EvalNumber { ReadNumber (0) 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u+v)'=u'+v'
/EvalAddSub {%
   7 index dup (0) eq
   { pop true }%% du=0 nothing added
   { dup length exch 5 index 5 index 3 -1 roll putinterval 4 -1 roll add 3 1 roll false }
   ifelse
   5 index dup (0) eq
   { pop { (0) } { 4 -2 roll 2 copy pop 0  6 2 roll GetIntervalNewStr } ifelse }%%dv=0
   { exch
     { 5 -2 roll 7 index 45 eq { AddSub } if false } %%nothing yet added
     { 5 -2 roll 7 index 43 eq%%something yet added
       { AddAdd false } { AddSub AddOpPar true } ifelse }
     ifelse 11 1 roll
     3 -1 roll StrConcat 10 -1 roll { AddClPar } if
     2 copy pop 0 6 2 roll GetIntervalNewStr }
   ifelse
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)' or (u/v)'
/EvalMulDiv { 6 index 42 eq {EvalMul} {EvalDiv} ifelse } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u*v)'=u'*v+u*v'
/EvalMul {%
   4 -2 roll 7 index dup (0) eq
   { pop false }%%du=0
   { (1) eq%%du=1
     { false }
     { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
     3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if
     true }%%du!=0
   ifelse
   5 1 roll 5 index (0) eq
   { 5 -1 roll not { (0) StrConcat } if }%%dv=0
   { 5 -1 roll { AddAdd } if
     4 index (1) eq
     { 8 index StrConcat }
     { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
     ifelse
   }%%dv!=0
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u/v)'=(u'*v-u*v')/v^2
/EvalDiv {%
   4 -2 roll
   4 index (0) eq%%dv=0 -> u'/v
   { 7 index (0) eq { (0) StrConcat } { AddOpPar 7 index StrConcat AddClPar AddDiv 5 index StrConcat } ifelse }
   { 7 index dup (0) eq
     { pop }%%du=0
     { (1) eq%%du=1
       { false }
       { AddOpPar 7 index StrConcat AddClPar AddMul AddOpPar true } ifelse
       3 1 roll 6 index StrConcat 3 -1 roll { AddClPar } if}%%du!=0
     ifelse
       AddSub
       4 index (1) eq
       { 8 index StrConcat }
       { AddOpPar 8 index StrConcat AddClPar AddMul AddOpPar 4 index StrConcat AddClPar }
       ifelse
     %}%%dv!=0
     2 copy GetIntervalNewStr 3 1 roll pop 0 AddOpPar 3 -1 roll StrConcat AddClPar
     AddDiv AddOpPar 5 index StrConcat AddClPar 2 copy (^2) putinterval 2 add }
   ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str1 index str2 -> str1 index
/StrConcat { dup length 4 2 roll 2 copy 6 -1 roll putinterval 3 -1 roll add } bind def
/GetIntervalNewStr { 0 exch getinterval dup length string copy } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (u^v)'=(u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
/EvalPower {%
   4 -2 roll 7 index (0) eq
   {%%if du=0 then (u^v)'=v'ln(u)u^v
     4 index (0) eq
     { (0) StrConcat }%%if dv=0 then (u^v)'=0
     { 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if
       8 index (e) ne { (ln\() StrConcat 8 index StrConcat (\)*) StrConcat } if
       AddOpPar 8 index StrConcat (\)^\() StrConcat 5 index StrConcat AddClPar } ifelse
   }
   {%%du!=0
     4 index (0) eq
     {%%if dv=0 then (u^v)'=vu'u^(v-1)
       5 index dup IsStrNumber
       { dup (0) eq
         { StrConcat }
         { dup dup (1) eq exch (1.0) eq or
           { StrConcat  }
 	  { StrConcat
 	    7 index dup (1) ne exch (1.0) ne and%%%dr 09102006 insert du if <> 1
 	    { (*\() StrConcat 7 index StrConcat (\)) StrConcat } if%%%dr 09102006
             (*\() StrConcat 8 index StrConcat (\)) StrConcat
             5 index  dup dup (2) eq exch (2.0) eq or
 	    { pop } { cvr 1 sub 20 string cvs 3 1 roll (^) StrConcat 3 -1 roll StrConcat } ifelse } ifelse } ifelse }
       { pop AddOpPar 5 index StrConcat (\)*\() StrConcat 8 index StrConcat (\)^\() StrConcat
         5 index StrConcat (-1\)) StrConcat } ifelse
     }
     {%%if dv!=0 and du!=0 then (u^v)'=u'vu^(v-1)+v'u^(v)ln(u)
       7 index (1) ne { AddOpPar 7 index StrConcat (\)*) StrConcat } if
       AddOpPar 5 index StrConcat (\)*\() StrConcat
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (-1\)+\() StrConcat
       4 index (1) ne { 4 index StrConcat (\)*\() StrConcat } if
       8 index StrConcat (\)^\() StrConcat
       5 index StrConcat (\)*ln\() StrConcat
       8 index StrConcat AddClPar
     } ifelse
   } ifelse
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for factorial ! only cst => null derivative
/EvalFactorial {% DR 09/2011
   4 index (0) eq
   { (0) mark 8 -2 roll  cleartomark 2 index 7 index dup 4 index exch sub getinterval exch 6 2 roll }
   { DERIVATIVE_ENGINE_ERROR_no_variable_in_factorial } ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% str -> true/false
/IsStrNumber {%
   true exch
   { dup 48 lt exch dup 57 gt 3 -1 roll or
     exch dup 46 ne%%.
     exch dup 43 ne%%+
     exch 45 ne%%-
     and and and { pop false } if } forall
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalLiteral {%
   ReadLiteral dup 40 eq%%% there is an open par -> function call
   { pop (EvalFunc_             ) 9 4 index StrConcat 0 exch getinterval cvn cvx exec }
   { dup 91 eq%%% there is an open bracket -> vector element
     { DERIVATIVE_ENGINE_ERROR_vector_not_yet_implemented }
     { pop EvalVariable }
     ifelse }
   ifelse
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% first last parpos Expr[first:parpos-1] ->
/EvalVariable { 2 index Variable eq { (1) } { (0) } ifelse 4 -1 roll exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (f(u))'=u'f'(u)
/EvalFunc {
   4 2 roll 4 index (1) ne
   { AddOpPar 4 index StrConcat (\)*) StrConcat } if
   (Eval             ) 4 8 index StrConcat 0 exch getinterval cvn cvx exec
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Func derivative -> Eval<func>
/EvalFunc_sin {%
   PreCommonFunc
   { (cos\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_cos {%
   PreCommonFunc
   { (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_tan {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_asin {%
   PreCommonFunc
   { (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_acos {%
   PreCommonFunc
   { (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_atg {%
   PreCommonFunc
   { (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_floor {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ln {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_exp {%
   PreCommonFunc
   {  (exp\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_EXP {%
   PreCommonFunc
   {  (EXP\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_sqrt {%
   PreCommonFunc
   { dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Fact {%
   PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
   PostCommonFunc } def
/EvalFunc_sh {%
   PreCommonFunc
   { (ch\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_ch {%
   PreCommonFunc
   { (sh\() StrConcat 5 index StrConcat AddClPar } if
   PostCommonFunc } def
/EvalFunc_th {%
   PreCommonFunc
   {  dup 0 eq { (1) StrConcat } { 1 sub } ifelse  (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argsh {%
   PreCommonFunc
   { (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argch {%
   PreCommonFunc
   { (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
   PostCommonFunc } def
/EvalFunc_Argth {%
   PreCommonFunc
   { (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
   PostCommonFunc } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/PreCommonFunc {
   1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
   4 2 roll 4 index (0) eq
   { (0) StrConcat false }
   { 4 index (1)  ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
} def
/PostCommonFunc {
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
/EvalFunc_Derive {%
   1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
   4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
   4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
   exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_Sum {%
   1 add NextNonBlankChar pop
   %% read the variable name
   ReadLiteral pop 3 -1 roll pop NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
   %% read the initial value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
   %% read the increment value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
   %% read the limit value
   1 add NextNonBlankChar pop ReadNumber pop
   2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
   1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
   4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_IfTE {%
   3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
   NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
   1 add NextNonBlankChar pop dup 5 1 roll
   AnalyzeExpr NextNonBlankChar
   44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
   1 add NextNonBlankChar pop
   AnalyzeExpr 1 add NextNonBlankChar pop
   4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
   6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
   2 copy pop 0 6 2 roll GetIntervalNewStr
   mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% advance in str until a comma is found (no error detection!)
%% str index -> str index'
/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
   dup (cos) eq 1 index (sin) eq or exch (tan) eq or
   { /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
     array astore def
   } if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for condition....
/EvalCondOp { 3 -1 roll pop } bind def
/PutIntervalOneAdd {putinterval 1 add} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add close parenthesis in string at the given index
%% str index -> str index+1
/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add 0 in string at the given index
%% str index -> str index+1
/AddZero {2 copy (0) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddMul {2 copy (*) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a plus sign in string at the given index
%% str index -> str index+1
/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a minus sign in string at the given index
%% str index -> str index+1
/AddSub {2 copy (-) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a pipe sign in string at the given index
%% str index -> str index+1
/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook { dup 5 1 roll } bind def
/PreEvalHook {} def
/AnalyzePostHook { 7 -1 roll pop } bind def
/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
/RollOp { 5 1 roll } bind def
end%%%tx@CoreAnalyzerDict
/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NEW FUNC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
%% x -> theta
/asin {%
   dup abs 1 gt { EQDFasinrangeerror  } if
   dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
} def
%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
%% x -> theta
/acos {%
   dup abs 1 gt { EQDFacosrangeerror  } if
   dup dup mul 1 exch sub sqrt exch atan DegtoRad
} def
%% function arctangent in radians
%% x -> theta
/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
%% HYPERBOLIC FUNCTIONS
/sh { dup Ex exch neg Ex sub 2 div } def
/ch { dup Ex exch neg Ex add 2 div } def
/th { dup sh exch ch div } def
/Argsh { dup dup mul 1 add sqrt add ln } def
/Argch { dup dup mul 1 sub sqrt add ln } def
/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
%% modified exponential funtion for 0
%% x n -> x^n
/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
%% modified exponential funtion for 0
%% x -> e^x
/Ex { Euler exch exp } bind def
%%
%% factorial function
%% n -> n!
/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
/fact { Fact } bind def
/! { Fact } bind def
end
%
% END pst-algparser.pro

%%EndProcSet
%%BeginProcSet: pst-tools.pro 0 0
% $Id: pst-tools.pro 842 2013-10-26 10:25:41Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.04, 2013/10/26
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%
%
/Pi2 1.57079632679489661925640 def
/factorial { % n on stack, returns n!
   dup 0 eq { 1 }{
     dup 1 gt { dup 1 sub factorial mul } if }
   ifelse } def 
%
/MoverN { % m n on stack, returns the binomial coefficient m over n
   2 dict begin
   /n exch def /m exch def
   n 0 eq { 1 }{
     m n eq { 1 }{
       m factorial n factorial m n sub factorial mul div } ifelse } ifelse
   end
} def
%
/ps@ReverseOrderOfPoints { % on stack [P1 P2 P3 ...Pn]=>[Pn,Pn-1,...,P2,P1]
   5 dict begin       % all local
   aload length /n ED % number of coors
   n 2 div cvi /m ED  % number of Points
   /n1 n def
   m { n1 2 roll /n1 n1 2 sub def } repeat
   n array astore
   end
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% subroutines for complex numbers, given as an array [a b] 
% which is a+bi = Real+i Imag
%
/cxadd {		% [a1 b1] [a2 b2] = [a1+a2 b1+b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   3 -1 roll		% [a2 b2] a2 [a1 b1]
   dup 0 get		% [a2 b2] a2 [a1 b1] a1
   3 -1 roll		% [a2 b2] [a1 b1] a1 a2
   add			% [a2 b2] [a1 b1] a1+a2
   3 1 roll		% a1+a2 [a2 b2] [a1 b1]
   1 get			% a1+a2 [a2 b2] b1
   exch 1 get		% a1+a2 b1 b2
   add 2 array astore
} def
%
/cxneg {		% [a b]
   dup 1 get		% [a b] b
   exch 0 get		% b a
   neg exch neg		% -a -b
   2 array astore
} def
%
/cxsub { cxneg cxadd } def  % same as negative addition
%
% [a1 b1][a2 b2] = [a1a2-b1b2 a1b2+b1a2] = [a3 b3]
/cxmul {		% [a1 b1] [a2 b2]
   dup 0 get		% [a1 b1] [a2 b2] a2
   exch 1 get		% [a1 b1] a2 b2
   3 -1 roll		% a2 b2 [a1 b1]
   dup 0 get		% a2 b2 [a1 b1] a1
   exch 1 get		% a2 b2 a1 b1
   dup			% a2 b2 a1 b1 b1
   5 -1 roll dup		% b2 a1 b1 b1 a2 a2
   3 1 roll mul		% b2 a1 b1 a2 b1a2
   5 -2 roll dup		% b1 a2 b1a2 b2 a1 a1
   3 -1 roll dup		% b1 a2 b1a2 a1 a1 b2 b2
   3 1 roll mul		% b1 a2 b1a2 a1 b2 a1b2
   4 -1 roll add		% b1 a2 a1 b2 b3
   4 2 roll mul		% b1 b2 b3 a1a2
   4 2 roll mul sub	% b3 a3
   exch 2 array astore
} def
%
% [a b]^2 = [a^2-b^2 2ab] = [a2 b2]
/cxsqr {		% [a b]   square root
   dup 0 get exch 1 get	% a b
   dup dup mul		% a b b^2
   3 -1 roll		% b b^2 a
   dup dup mul 		% b b^2 a a^2
   3 -1 roll sub		% b a a2
   3 1 roll mul 2 mul	% a2 b2
   2 array astore
} def
%
/cxsqrt {		% [a b]
%  dup cxnorm sqrt /r exch def
%  cxarg 2 div RadtoDeg dup cos r mul exch sin r mul cxmake2
   cxlog 		% log[a b]
   2 cxrdiv 		% log[a b]/2
   aload pop exch	% b a
   2.781 exch exp	% b exp(a)
   exch cxconv exch	% [Re +iIm] exp(a)
   cxrmul		%
} def
%
/cxarg { 		% [a b]
   aload pop 		% a b
   exch atan 		% arctan b/a
   DegtoRad 		% arg(z)=atan(b/a)
} def
%
% log[a b] = [a^2-b^2 2ab] = [a2 b2]
/cxlog {		% [a b]
   dup 			% [a b][a b]
   cxnorm 		% [a b] |z|
   log 			% [a b] log|z|
   exch 			% log|z|[a b]
   cxarg 		% log|z| Theta
   cxmake2 		% [log|z| Theta]
} def
%
% square of magnitude of complex number
/cxnorm2 {		% [a b]
   dup 0 get exch 1 get	% a b
   dup mul			% a b^2
   exch dup mul add	% a^2+b^2
} def
%
/cxnorm {		% [a b]
   cxnorm2 sqrt
} def
%
/cxconj {		% conjugent complex
   dup 0 get exch 1 get	% a b
   neg 2 array astore	% [a -b]
} def
%
/cxre { 0 get } def	% real value
/cxim { 1 get } def	% imag value
%
% 1/[a b] = ([a -b]/(a^2+b^2)
/cxrecip {		% [a b]
   dup cxnorm2 exch	% n2 [a b]
   dup 0 get exch 1 get	% n2 a b
   3 -1 roll		% a b n2
   dup			% a b n2 n2
   4 -1 roll exch div	% b n2 a/n2
   3 1 roll div		% a/n2 b/n2
   neg 2 array astore
} def
%
/cxmake1 { 0 2 array astore } def % make a complex number, real given
/cxmake2 { 2 array astore } def	  % dito, both given
%
/cxdiv { cxrecip cxmul } def
%
% multiplikation by a real number
/cxrmul {		% [a b] r
   exch aload pop	% r a b
   3 -1 roll dup		% a b r r
   3 1 roll mul		% a r b*r
   3 1 roll mul		% b*r a*r
   exch 2 array astore   % [a*r b*r]
} def
%
% division by a real number
/cxrdiv {		% [a b] r
   1 exch div		% [a b] 1/r
   cxrmul
} def
%
% exp(i theta) = cos(theta)+i sin(theta) polar<->cartesian
/cxconv {		% theta
   RadtoDeg dup sin exch cos cxmake2
} def

%%%%% ### bubblesort ###
%% syntax : array bubblesort --> array2 trie par ordre croissant
%% code de Bill Casselman
%% http://www.math.ubc.ca/people/faculty/cass/graphics/text/www/
/bubblesort { % on stack must be an array [ ... ]
4 dict begin
    /a exch def
    /n a length 1 sub def
    n 0 gt {
       % at this point only the n+1 items in the bottom of a remain to
       % the sorted largest item in that blocks is to be moved up into
       % position n
       n {
          0 1 n 1 sub {
             /i exch def
             a i get a i 1 add get gt {
                % if a[i] > a[i+1] swap a[i] and a[i+1]
                a i 1 add
                a i get
                a i a i 1 add get
                % set new a[i] = old a[i+1]
                put
                % set new a[i+1] = old a[i]
                put
             } if
          } for
          /n n 1 sub def
       } repeat
    } if
    a % return the sorted array
end
} def
%
/concatstringarray{  %  [(a) (b) ... (z)] --> (ab...z)  20100422
   0 1 index { length add } forall
   string
   0 3 2 roll
   { 3 copy putinterval length add }forall
   pop 
} bind def
%
/dot2comma {% on stack a string (...)
   2 dict begin
   /Output exch def
   0 1 Output length 1 sub {
     /Index exch def
     Output Index get 46 eq { Output Index 44 put } if
   } for
   Output
   end
} def
%
/rightTrim { % on stack the string and the character number to be stripped
   /charNo exch def
   dup
   length 1 sub -1 0 {
     /i exch def dup i get charNo ne { exit } if
   } for
   0 i 1 add getinterval
   dup length string copy
} bind def  % leaves the stripped string on the stack

/psStringwidth /stringwidth load def
/psShow /show load def

%/stringwidth{ 32 rightTrim psStringwidth } bind def

%/show { 32 rightTrim psShow } bind def
%-----------------------------------------------------------------------------%

/pgffunctions {
     /pgfsc{}bind def% stroke color is empty by default
     /pgffc{}bind def% fill color is empty by default
     /pgfstr{stroke}bind def%
     /pgffill{fill}bind def%
     /pgfeofill{eofill}bind def%
     /pgfe{a dup 0 rlineto exch 0 exch rlineto neg 0 rlineto closepath}bind def% rectangle
     /pgfw{setlinewidth}bind def% setlinewidth
     /pgfs{save pgfpd 72 Resolution div 72 VResolution div neg scale
       magscale{1 DVImag div dup scale}if
       pgfx neg pgfy neg translate pgffoa .setopacityalpha}bind def% save
     /pgfr{pgfsd restore}bind def %restore
     userdict begin%
     /pgfo{pgfsd /pgfx currentpoint /pgfy exch def def @beginspecial}bind def %open
     /pgfc{newpath @endspecial pgfpd}bind def %close
     /pgfsd{globaldict /pgfdelta /delta where {pop delta} {0} ifelse put}bind def% save delta
     /pgfpd{/delta globaldict /pgfdelta get def}bind def % put delta
     /.setopacityalpha where {pop} {/.setopacityalpha{pop}def} ifelse % install .setopacityalpha
     /.pgfsetfillopacityalpha{/pgffoa exch def
       /pgffill{gsave pgffoa .setopacityalpha fill 1 .setopacityalpha newpath fill grestore newpath}bind def
       /pgfeofill{gsave pgffoa .setopacityalpha eofill 1 .setopacityalpha newpath eofill grestore newpath}bind def}bind def
     /.pgfsetstrokeopacityalpha{/pgfsoa exch def /pgfstr{gsave pgfsoa .setopacityalpha stroke grestore newpath}bind def}bind def
     /pgffoa 1 def
     /pgfsoa 1 def
     end
} def
%-----------------------------------------------------------------------------%
% END pst-tools.pro

%%EndProcSet
%%BeginProcSet: pst-dots.pro 0 0
% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02,  2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt <tvz@Princeton.EDU>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga  - Dec. 16, 1999
%% Modified by Etienne Riga  - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17 
%
10 dict dup begin			% hold local
   /FontType 3 def
   /FontMatrix [.001 0 0 .001 0 0] def
%  /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
   /FontBBox [-1000 -1000 1000 1000] def  % See end of file in /BuildGlyph
   /Encoding 256 array def
   0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
   Encoding				   % replace with given dot names
     dup (b) 0 get /Bullet put		   % get the numerical position of b in ASCII
%					   % and save /Bullet at this place in Encoding
     dup (c) 0 get /Circle put
     dup (C) 0 get /BoldCircle put	% 67
     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
%%%
     dup (k) 0 get /Asterisk put
     dup (K) 0 get /BoldAsterisk put
     dup (J) 0 get /SolidAsterisk put
     dup (h) 0 get /Hexagon put
     dup (H) 0 get /BoldHexagon put
     dup (G) 0 get /SolidHexagon put
     dup (f) 0 get /Octogon put		% 2008-04-18 hv
     dup (F) 0 get /BoldOctogon put	% 2008-04-18 hv
     dup (g) 0 get /SolidOctogon put	% 2008-04-18 hv
     dup (a) 0 get /Add put
     dup (A) 0 get /BoldAdd put 		% 65
     dup (x) 0 get /Mul put
     dup (X) 0 get /BoldMul put
     dup (m) 0 get /Oplus put
     dup (M) 0 get /BOplus put
     dup (e) 0 get /SolidOplus put
     dup (n) 0 get /Otimes put
     dup (N) 0 get /BOtimes put
     dup (E) 0 get /SolidOtimes put
     dup (i) 0 get /Bar put
     dup (I) 0 get /BoldBar put
     dup (l) 0 get /SolidDiamond put
     dup (d) 0 get /Diamond put
         (D) 0 get /BoldDiamond put
%%% 
/CharProcs 47 dict def
CharProcs begin
   /CirclePath {0 0 500 0 360 arc closepath} def
   /Bullet {CirclePath fill} def
   /Circle {CirclePath .9 .9 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
%-------------- hv begin 2004/07/25   from: er 2003/03/24
   /HexagonPath {
     0 550 moveto -476 275 lineto -476 -275 lineto
     0 -550 lineto 476 -275 lineto 476 275 lineto closepath
   } def
   /SolidHexagon {HexagonPath fill} def
   /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
   /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
%					2008-04-18 hv
   /OctogonPath {
      550 dup 22.5 tan mul dup neg dup add /xMove exch def
      exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
   /SolidOctogon { OctogonPath fill                             } def
   /Octogon {      OctogonPath .89 .89 scale OctogonPath eofill } def
   /BoldOctogon {  OctogonPath .79 .79 scale OctogonPath eofill } def
%
   /AsteriskPath {
     20 0 moveto 10 250 180 500 0 500 curveto
     -180 500 -10 250 -20 0 curveto closepath
   } def
   /Asterisk {
     AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
     60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
   } def
%
   /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
   /BoldAsteriskPath {
     50 30 cos 100 mul moveto  Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp 60 rotate Basterp
     60 rotate Basterp closepath
   } def
   /BoldAsterisk {BoldAsteriskPath fill} def
   /SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
   /CrossPath {
     40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
     -550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
     40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
   } def
   /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
     -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
     80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
   } def
   /Add {CrossPath fill} def
   /Mul {45 rotate CrossPath fill} def
   /BoldAdd {BoldCrossPath fill} def
   /BoldMul {45 rotate BoldCrossPath fill} def
   /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
   /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
   /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
   /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
   /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
   /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
   /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
   /Bar {BarPath fill} def
   /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
   /BoldBar {BoldBarPath fill} def
   /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 .865 .865 scale DiamondPath eofill} def
   /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
%%%
   /.notdef { } def
end
%
/BuildGlyph {
   exch
   begin 
%  Metrics 1 index get exec 0
     0 0
%      BBoxes 3 index get exec
     -1000 -1000 1000 1000
%     -571.5 -742.5 571.5 742.5
     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

%%EndProcSet
%%BeginProcSet: cmmi10.pfb 0 0
%!PS-AdobeFont-1.0: CMMI10 003.002
%%Title: CMMI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMMI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup
/UniqueID get 5087385 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMMI10 def
/FontBBox {-32 -250 1048 750 }readonly def
/UniqueID 5087385 def
/PaintType 0 def
/FontInfo 10 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMMI10.) readonly def
  /FullName (CMMI10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle -14.04 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
  /ascent 750 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /alpha put
dup 12 /beta put
dup 13 /gamma put
dup 14 /delta put
dup 15 /epsilon1 put
dup 16 /zeta put
dup 17 /eta put
dup 18 /theta put
dup 19 /iota put
dup 20 /kappa put
dup 21 /lambda put
dup 22 /mu put
dup 23 /nu put
dup 24 /xi put
dup 25 /pi put
dup 26 /rho put
dup 27 /sigma put
dup 28 /tau put
dup 29 /upsilon put
dup 30 /phi put
dup 31 /chi put
dup 32 /psi put
dup 33 /omega put
dup 34 /epsilon put
dup 35 /theta1 put
dup 36 /pi1 put
dup 37 /rho1 put
dup 38 /sigma1 put
dup 39 /phi1 put
dup 40 /arrowlefttophalf put
dup 41 /arrowleftbothalf put
dup 42 /arrowrighttophalf put
dup 43 /arrowrightbothalf put
dup 44 /arrowhookleft put
dup 45 /arrowhookright put
dup 46 /triangleright put
dup 47 /triangleleft put
dup 48 /zerooldstyle put
dup 49 /oneoldstyle put
dup 50 /twooldstyle put
dup 51 /threeoldstyle put
dup 52 /fouroldstyle put
dup 53 /fiveoldstyle put
dup 54 /sixoldstyle put
dup 55 /sevenoldstyle put
dup 56 /eightoldstyle put
dup 57 /nineoldstyle put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 63 /star put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /flat put
dup 92 /natural put
dup 93 /sharp put
dup 94 /slurbelow put
dup 95 /slurabove put
dup 96 /lscript put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /dotlessi put
dup 124 /dotlessj put
dup 125 /weierstrass put
dup 126 /vector put
dup 127 /tie put
dup 128 /psi put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 173 /Omega put
dup 174 /alpha put
dup 175 /beta put
dup 176 /gamma put
dup 177 /delta put
dup 178 /epsilon1 put
dup 179 /zeta put
dup 180 /eta put
dup 181 /theta put
dup 182 /iota put
dup 183 /kappa put
dup 184 /lambda put
dup 185 /mu put
dup 186 /nu put
dup 187 /xi put
dup 188 /pi put
dup 189 /rho put
dup 190 /sigma put
dup 191 /tau put
dup 192 /upsilon put
dup 193 /phi put
dup 194 /chi put
dup 195 /psi put
dup 196 /tie put
readonly def
currentdict end
currentfile eexec

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cleartomark
{restore}if


%%EndProcSet
%%BeginProcSet: cmr10.pfb 0 0
%!PS-AdobeFont-1.0: CMR10 003.002
%%Title: CMR10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright:  (<http://www.ams.org>), with Reserved Font Name CMR10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments

FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup
/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse
{save true}{false}ifelse}{false}ifelse
11 dict begin
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0 ]readonly def
/FontName /CMR10 def
/FontBBox {-40 -250 1009 750 }readonly def
/UniqueID 5000793 def
/PaintType 0 def
/FontInfo 9 dict dup begin
  /version (003.002) readonly def
  /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050<http://www.ams.org>\051, with Reserved Font Name CMR10.) readonly def
  /FullName (CMR10) readonly def
  /FamilyName (Computer Modern) readonly def
  /Weight (Medium) readonly def
  /ItalicAngle 0 def
  /isFixedPitch false def
  /UnderlinePosition -100 def
  /UnderlineThickness 50 def
end readonly def
/Encoding 256 array
  0 1 255 { 1 index exch /.notdef put} for
dup 0 /Gamma put
dup 1 /Delta put
dup 2 /Theta put
dup 3 /Lambda put
dup 4 /Xi put
dup 5 /Pi put
dup 6 /Sigma put
dup 7 /Upsilon put
dup 8 /Phi put
dup 9 /Psi put
dup 10 /Omega put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 15 /ffl put
dup 16 /dotlessi put
dup 17 /dotlessj put
dup 18 /grave put
dup 19 /acute put
dup 20 /caron put
dup 21 /breve put
dup 22 /macron put
dup 23 /ring put
dup 24 /cedilla put
dup 25 /germandbls put
dup 26 /ae put
dup 27 /oe put
dup 28 /oslash put
dup 29 /AE put
dup 30 /OE put
dup 31 /Oslash put
dup 32 /suppress put
dup 33 /exclam put
dup 34 /quotedblright put
dup 35 /numbersign put
dup 36 /dollar put
dup 37 /percent put
dup 38 /ampersand put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 42 /asterisk put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 60 /exclamdown put
dup 61 /equal put
dup 62 /questiondown put
dup 63 /question put
dup 64 /at put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 94 /circumflex put
dup 95 /dotaccent put
dup 96 /quoteleft put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 124 /emdash put
dup 125 /hungarumlaut put
dup 126 /tilde put
dup 127 /dieresis put
dup 128 /suppress put
dup 160 /space put
dup 161 /Gamma put
dup 162 /Delta put
dup 163 /Theta put
dup 164 /Lambda put
dup 165 /Xi put
dup 166 /Pi put
dup 167 /Sigma put
dup 168 /Upsilon put
dup 169 /Phi put
dup 170 /Psi put
dup 171 /sfthyphen put
dup 172 /nbspace put
dup 173 /Omega put
dup 174 /ff put
dup 175 /fi put
dup 176 /fl put
dup 177 /ffi put
dup 178 /ffl put
dup 179 /dotlessi put
dup 180 /dotlessj put
dup 181 /grave put
dup 182 /acute put
dup 183 /caron put
dup 184 /breve put
dup 185 /macron put
dup 186 /ring put
dup 187 /cedilla put
dup 188 /germandbls put
dup 189 /ae put
dup 190 /oe put
dup 191 /oslash put
dup 192 /AE put
dup 193 /OE put
dup 194 /Oslash put
dup 195 /suppress put
dup 196 /dieresis put
readonly def
currentdict end
currentfile eexec

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