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%%BeginProcSet: pstricks.pro 0 0
% $Id: pstricks.pro 317 2021-11-16 20:47:25Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 1.41, 2021/11/16
%%
%% 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
%
revision 952 gt 
{
    systemdict /.setopacityalpha known not 
      { 
         (\n\n%%%% WARNING: Transparency operations ignored - need to use -dALLOWPSTRANSPARENCY\n\n) print flush
         /.setopacityalpha { pop } bind def 
         /.setshapealpha { pop } bind def 
         /.setfillconstantalpha { pop } bind def 
         /.setstrokeconstantalpha { pop } bind def 
      }
      {
        /.setopacityalpha /.setfillconstantalpha load def 
%        /.setblendmode { pop } def   %% works again    hv 20210825
        /.setshapealpha {dup .setfillconstantalpha .setstrokeconstantalpha true .setalphaisshape } def  
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}
{
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} ifelse
%
%%<bool> .setalphaisshape -
%%    If true, the values set by setstrokeconstantalpha and setfillconstantalpha are interpreted as shape values. The initial value of the AIS flag is false. 
%
%
/tx@Dict 200 dict def 				% the main PSTricks dictionary
tx@Dict begin
/ADict 25 dict def				% The arrow dictionary
/fill@Dict 30 dict def				% the fill 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
/Power { %  a^b   latest ghostscript don't allow -4^-3.1
  2 dict begin	% hold all local
  /b ED
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  a 0 lt % prevent something like (-4)^(-3.1)=> 1/(-4)^3
    { b 0 lt 
      { a b cvi exp }
      { a b exp } ifelse 
    }
    { a 0 eq { 0 }{ a b exp } ifelse
    } ifelse
  end
} 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
/addCoors { 
  3 -1 roll 		% xA xB yB yA
  add			% xA xB yB+yA
  3 1 roll 		% yB+yA xA xB
  add			% yB+yA xA+xB
  exch                  % xA+xB yA+yB
} def
/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 (original)
/PtoCrel { pst@angleunit PtoC } def % Polar to Cartesian with \degrees[??]
/PtoCab { dup cos 4 -1 roll mul 3 1 roll sin mul } def % Polar to Cartesian (Ellipse) a b phi-> x y 
/AnytoDeg { pst@angleunit } def 
/DegtoAny { 1 pst@angleunit div} def
/AnytoRad { AnytoDeg DegtoRad } def 
/RadtoAny { RadtoDeg DegtoAny } def
%
%/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 { 
  10 dict begin
  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 
  end
} 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 { 
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  } 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
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        /nSym SymStep abs cvi def } 
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    ifelse
    0.5 setflat
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    nSym { 
      gsave 
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        { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED  
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          0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
          SymbolLinewidth setlinewidth stroke
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        { 
          rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
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      ifelse 
      grestore 
      deltaX deltaY rmoveto
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    /YA YB def /XA XB def
  } repeat 
  curveticks 
    { XA YA moveto }
    { XA Shift sub YA Shift sub moveto }
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  gsave 
  curveticks 
    { PAngle 180 sub CorrAngle sub tickAngle add /rotAngle ED  
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      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 
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  .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
  40 dict begin
  /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 
  end % userdict
} def
%
/PenroseFillA {%  on stack: scaling factor, border color, kite color, dart color
  50 dict begin
  /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
  end % userdict
} 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 
%
/ArrowT { % like tikz
  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
  w 2 mul /w exch def
  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
%  CLW SLW
%  1 0 0 setrgbcolor
  2 setlinejoin
  stroke
  0 0 moveto
} 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 { 
%  5 dict begin
  NArray n 3 lt 
    { n { pop pop } repeat } 
    { BOC /n n 3 sub def n { NC } repeat EOC } ifelse 
%  end
} 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 
  x1 y1 lineto  % counter clockwise path
  x2 y1 lineto 
  x2 y2 lineto
  x1 y2 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 {
  40 dict begin 
  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 
%    is set in pstricks.tex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%    
%     /NimbusSanL-Regu 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 
  dup % run loop two times: lines and labels
  { i dx mul dup xGridOffset add y0 moveto % draw the lines
    dup t f moveto 
    g t L stroke 
    /i i w add def 
  } repeat 
  /i x1 def 
  GridDX div ceiling cvi 
  { i dx mul GridDX mul dup xGridOffset add y0 moveto % plot the labels
    b 0 gt 
      { gsave c i GridDX mul a cvs dup stringwidth pop /z2 ED  
        w 0 gt {z1} {z1 z2 add neg} ifelse 
	h 0 gt {b neg}{z1} ifelse exch GridDX div z2 2 div sub exch 
        rmoveto show grestore } if 
    /i i w add def 
  } repeat 
  grestore 
  gsave 
  n 0 gt
    { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
    { 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 
  dup % run loop two times: lines and labels
  { newpath i dy mul dup yGridOffset add x0 exch moveto 
    dup f exch t moveto 
    g exch t L stroke 
    /i i h add def 
  } repeat 
  /i y1 def 
  GridDY div ceiling cvi
  { newpath i dy mul GridDY mul dup yGridOffset add x0 exch moveto 
    b 0 gt { gsave c i GridDY mul a cvs dup stringwidth pop 
      /z2 ED 
      w 0 gt {z1 z2 add neg} {z1} ifelse 
      h 0 gt {z1} {b neg} ifelse GridDY div b 2 div sub
      rmoveto show grestore } if 
    /i i h add def 
  } repeat 
  grestore 
  end
} 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
%
%
/isbool { type (booleantype) cvn eq } def
%
/Ellipse { 
  dup isbool { /MoveToStart ED }{ /MoveToStart false def }ifelse  % false or true
  /rotAngle ED
  /mtrx CM def 
  T 
  rotAngle rotate
  scale 
  MoveToStart { 0 0 moveto 1 0 rmoveto } if  % move to the start position
  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 
  /RotAngle ED 
  RotAngle Rot /RAngle [ RAngle dup RotAngle 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 4 2020-06-09 08:32:19Z herbert $
%%
%% PostScript prologue for PSTricks algorithm parser
%% Version 0.07, 2014/08/01
%%
%% 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.
%%
%%-----------------------------------------------------------------------------%
%
%currentdict /Pi known not { /Pi 3.14159265359 def } if
%
/AlgParser { tx@AlgToPs begin AlgToPs end } def  % Dominique Rodriguez
/I2P { AlgParser cvx exec } def  % Infix to Postfix
%
/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 3.1415926 /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 249 2021-09-14 10:22:55Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.06, 2017/12/03
%%
%% 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
%
/concatstrings{ % (a) (b) -> (ab)  
  exch dup length    
  2 index length add string    
  dup dup 4 2 roll copy length
  4 -1 roll putinterval
} def
%
/reversestring { % (aBC) -> (CBa)
  5 dict begin
  /str exch def
  /L str length def
  /strTemp L string def
  /i 0 def
  L { 
    /I L 1 sub i sub def
    strTemp i str I 1 getinterval putinterval
    /i i 1 add def
  } repeat
  strTemp
  end
} def
%
/concatarray{ % [a c] [b d] -> [a c b d]  
  2 dict begin
  /a2 exch def
  /a1 exch def
  [ a1 aload pop a2 aload pop ]
  end
} 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  
  1 dict begin
  /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
  end
} 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 291 2021-10-01 09:22:45Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 0.02,  2021/10/01
%%
%% 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 
%
12 dict dup begin
/FontType 1 def
/FontName /PSTricksDotFont def
/FontInfo 9 dict dup begin
/version (001.000) def
/Notice (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 
Converted to OpenType by Marcel Krueger 2021
) def
/FullName (PSTricks Dots) def
/FamilyName (PSTricksDotFont) def
/Weight (Regular) def
/FSType 0 def
end def
/PaintType 0 def
/FontMatrix [0.001 0 0 0.001 0 0] def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put } for
dup 65 /BoldAdd put
dup 67 /BoldCircle put	% 67
dup 68 /BoldDiamond put
dup 69 /SolidOtimes put
dup 70 /BoldOctogon put
dup 71 /SolidHexagon put
dup 72 /BoldHexagon put
dup 73 /BoldBar put
dup 74 /SolidAsterisk put
dup 75 /BoldAsterisk put
dup 77 /BOplus put
dup 78 /BOtimes put
dup 80 /BoldPentagon put
dup 83 /BoldSquare put
dup 84 /BoldTriangle put
dup 88 /BoldMul put
dup 97 /Add put
dup 98 /Bullet put
dup 99 /Circle put
dup 100 /Diamond put
dup 101 /SolidOplus put
dup 102 /Octogon put
dup 103 /SolidOctogon put
dup 104 /Hexagon put
dup 105 /Bar put
dup 107 /Asterisk put
dup 108 /SolidDiamond put
dup 109 /Oplus put
dup 110 /Otimes put
dup 112 /Pentagon put
dup 113 /SolidPentagon put
dup 114 /SolidSquare put
dup 115 /Square put
dup 116 /Triangle put
dup 117 /SolidTriangle put
dup 120 /Mul put
readonly def
/FontBBox {-572 -743 572 743} def
end
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%%EndProcSet
%%BeginProcSet: pst-grad.pro 0 0
%!
% PostScript prologue for pst-grad.tex.
% Version 1.05, 2006/11/04 
% prepared by Herbert Voss
% For copying restrictions, see pstricks.tex.
%
% For the PSTricks gradient fillstyle.%
% Based on some EPS files by leeweyr!bill@nuchat.sccsi.com (W. R. Lee).%
% Syntax:% D.G. modification begin - Apr.  9, %1998
%%%%%% R0 G0 B0 R1 G1 B1 NumLines MidPoint Angle GradientFill
%   ifGradientCircle GradientScale %GradientPosX GradientPosY
%     R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill
% D.G. modification end
%
/tx@GradientDict 40 dict def
tx@GradientDict begin
/GradientFill {
 /ifCMYK exch def   % do we have rgb or cmyk? hv 1.06
 rotate
 /MidPoint ED
 /NumLines ED
 ifCMYK {
    /LastBlack ED	% 1.06
    /LastYellow ED	% 1.06
    /LastMagenta ED	% 1.06
    /LastCyan ED	% 1.06
    /FirstBlack ED	% 1.06
    /FirstYellow ED	% 1.06
    /FirstMagenta ED	% 1.06
    /FirstCyan ED	% 1.06
 }{ /LastBlue ED
    /LastGreen ED
    /LastRed ED
    /FirstBlue ED
    /FirstGreen ED
    /FirstRed ED
 } ifelse
 /GradientPosY ED
 /GradientPosX ED
 /GradientScale ED
 /ifGradientCircle ED
 % This avoids gaps due to rounding errors:
 clip
 pathbbox           %leave llx,lly,urx,ury on stack
 4 copy /ury ED /urx ED /lly ED /llx ED
 /y ED /x ED
 ifGradientCircle
   { 0 GradientPosX eq { 0 GradientPosX eq {2 copy translate} if } if }
   {2 copy translate} ifelse
 y sub neg /y ED
 x sub neg /x ED  % This avoids gaps due to rounding errors:
 ifCMYK {				% 1.06
    LastCyan FirstCyan add 2 div	% 1.06
    LastMagenta FirstMagenta add 2 div	% 1.06
    LastYellow FirstYellow add 2 div	% 1.06
    LastBlack FirstBlack add 2 div	% 1.06
    setcmykcolor			% 1.06
  }{
    LastRed FirstRed add 2 div
    LastGreen FirstGreen add 2 div
    LastBlue FirstBlue add 2 div
    setrgbcolor
  } ifelse
 ifGradientCircle
   { /YSizePerLine y NumLines div def
     /CurrentY y 2 div def
     /MidLine NumLines 2 div 1 MidPoint sub mul abs cvi def
   }{
     fill
     /YSizePerLine y NumLines div def
     /CurrentY 0 def
     /MidLine NumLines 1 MidPoint sub mul abs cvi def
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 MidLine NumLines 2 sub gt 
   { /MidLine NumLines def }
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 MidLine 0 gt {
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    /Magenta FirstMagenta def
    /Yellow FirstYellow def
    /Black FirstBlack def
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    /MagentaIncrement LastMagenta FirstMagenta sub MidLine 1 sub div def
    /YellowIncrement LastYellow FirstYellow sub MidLine 1 sub div def
    /BlackIncrement LastBlack FirstBlack sub MidLine 1 sub div def
  }{
    /Red FirstRed def
    /Green FirstGreen def
    /Blue FirstBlue def
    /RedIncrement LastRed FirstRed sub MidLine 1 sub div def
    /GreenIncrement LastGreen FirstGreen sub MidLine 1 sub div def
    /BlueIncrement LastBlue FirstBlue sub MidLine 1 sub div def
  } ifelse
  MidLine { GradientLoop } repeat
 } if
 MidLine NumLines lt {
  ifCMYK {
    /Cyan LastCyan def
    /Magenta LastMagenta def
    /Yellow LastYellow def
    /Black LastBlack def
    /CyanIncrement FirstCyan LastCyan sub NumLines MidLine sub 1 sub div def
    /MagentaIncrement FirstMagenta LastMagenta sub NumLines MidLine sub 1 sub div def
    /YellowIncrement FirstYellow LastYellow sub NumLines MidLine sub 1 sub div def
    /BlackIncrement FirstBlack LastBlack sub NumLines MidLine sub 1 sub div def
  }{
    /Red LastRed def
    /Green LastGreen def
    /Blue LastBlue def
    /RedIncrement FirstRed LastRed sub NumLines MidLine sub 1 sub div def
    /GreenIncrement FirstGreen LastGreen sub NumLines MidLine sub 1 sub div def
    /BlueIncrement FirstBlue LastBlue sub NumLines MidLine sub 1 sub div def
  } ifelse
  NumLines MidLine sub { GradientLoop } repeat  
 } if
} def/GradientLoop {
% D.G. modification begin - Jul. 23, 1997 / Apr.  9, 1998
  ifGradientCircle
   {CurrentY 0 gt {
% The default center used is the center of the bounding box of the object
      0 GradientPosX eq        {0 GradientPosX eq
           {/GradientPosX urx llx sub 2 div def
            /GradientPosY ury lly sub 2 div def} if} if
      GradientPosX GradientPosY CurrentY GradientScale mul 0 360 arc
      ifCMYK { Cyan Magenta Yellow Black setcmykcolor }
           { Red Green Blue setrgbcolor } ifelse 
      fill
      /CurrentY CurrentY YSizePerLine sub def
      ifCMYK {
        /Cyan Cyan CyanIncrement add def
        /Magenta Magenta MagentaIncrement add def
        /Yellow Yellow YellowIncrement add def
        /Black Black BlackIncrement add def
      }{	
        /Blue Blue BlueIncrement add def
        /Green Green GreenIncrement add def
        /Red Red RedIncrement add def
      } ifelse
  } if }   { 0 CurrentY moveto    x 0 rlineto
    0 YSizePerLine rlineto    x neg 0 rlineto    closepath
      ifCMYK { Cyan Magenta Yellow Black setcmykcolor }
           { Red Green Blue setrgbcolor } ifelse 
      fill    
      /CurrentY CurrentY YSizePerLine add def
      ifCMYK {
        /Cyan Cyan CyanIncrement add def
        /Magenta Magenta MagentaIncrement add def
        /Yellow Yellow YellowIncrement add def
        /Black Black BlackIncrement add def
      }{	
        /Blue Blue BlueIncrement add def
        /Green Green GreenIncrement add def
        /Red Red RedIncrement add def
      } ifelse
      } ifelse% D.G. modification end
    }def
%
/GradientFillHSB { %	hv 2006-11-04
  rotate
  /MidPoint ED
  /NumLines ED
  /LastBrightness ED
  /LastSaturation ED
  /LastHue ED
  /FirstBrightness ED
  /FirstSaturation ED
  /FirstHue ED
  % This avoids gaps due to rounding errors:
  clip
  pathbbox           %leave llx,lly,urx,ury on stack
  /y ED /x ED
  2 copy translate
  y sub neg /y ED
  x sub neg /x ED
  % This avoids gaps due to rounding errors:
  LastHue FirstHue add 2 div
  LastSaturation FirstSaturation add 2 div
  LastBrightness FirstBrightness add 2 div
  sethsbcolor
  fill
  /YSizePerLine y NumLines div def
  /CurrentY 0 def
  /MidLine NumLines 1 MidPoint sub mul abs cvi def
  MidLine NumLines 2 sub gt
  { /MidLine NumLines def }
  { MidLine 2 lt { /MidLine 0 def } if }
  ifelse
  MidLine 0 gt
  {
    /Hue FirstHue def
    /Saturation FirstSaturation def
    /Brightness FirstBrightness def
    /HueIncrement LastHue FirstHue sub MidLine 1 sub div def
    /SaturationIncrement LastSaturation FirstSaturation sub MidLine 1 sub
                         div def
    /BrightnessIncrement LastBrightness FirstBrightness sub MidLine 1 sub
                         div def
    MidLine { GradientLoopHSB } repeat
  } if
  MidLine NumLines lt
  {
    /Hue LastHue def
    /Saturation LastSaturation def
    /Brightness LastBrightness def
    /HueIncrement FirstHue LastHue sub NumLines MidLine sub 1 sub div def
    /SaturationIncrement FirstSaturation LastSaturation sub
                         NumLines MidLine sub 1 sub div def
    /BrightnessIncrement FirstBrightness LastBrightness sub
                         NumLines MidLine sub 1 sub div def
    NumLines MidLine sub { GradientLoopHSB } repeat
  } if
} def
/GradientLoopHSB {
  0 CurrentY moveto
  x 0 rlineto
  0 YSizePerLine rlineto
  x neg 0 rlineto
  closepath
  Hue Saturation Brightness sethsbcolor fill
  /CurrentY CurrentY YSizePerLine add def
  /Brightness Brightness BrightnessIncrement add def
  /Saturation Saturation SaturationIncrement add def
  /Hue Hue HueIncrement add def
} def
%
end
%
% END pst-grad.pro

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%%BeginProcSet: cm-super-ts1.enc 0 0
% This file is generated from `TS1uni.map' and `glyphlist.txt', `gl-other.txt'
/TS1Encoding [
% 0x00
/Grave
/Acute
/Circumflex % ?
/Tilde % ?
/Dieresis
/Hungarumlaut
/Ring % ?
/Caron
/Breve % ?
/Macron
/Dotaccent % ?
/cedilla
/ogonek
/quotesinglbase.ts1
/.notdef
/.notdef
% 0x10
/.notdef
/.notdef
/quotedblbase.ts1
/.notdef
/.notdef
/twelveudash % ?
/threequartersemdash
/afii61664.cap % ?
/arrowleft
/arrowright
/tieaccentlowercase % ?
/tieaccentcapital % ?
/tieaccentlowercase.new % ?
/tieaccentcapital.new % ?
/.notdef
/afii61664.asc % ?
% 0x20
/uni2422
/.notdef
/.notdef
/.notdef
/dollar
/.notdef
/.notdef
/quotesingle
/.notdef
/.notdef
/asteriskmath
/.notdef
/comma
/hyphendbl % ?
/period
/fraction
% 0x30
/zerooldstyle
/oneoldstyle
/twooldstyle
/threeoldstyle
/fouroldstyle
/fiveoldstyle
/sixoldstyle
/sevenoldstyle
/eightoldstyle
/nineoldstyle
/.notdef
/.notdef
/angleleft
/minus
/angleright
/.notdef
% 0x40
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
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/uni2127
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/circle
% 0x50
/.notdef
/.notdef
/.notdef
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/Omega
/.notdef
/.notdef
/.notdef
/uni301A
/.notdef
/uni301B
/arrowup
/arrowdown
% 0x60
/grave.ts1
/.notdef
/born % ?
/divorced % ?
/died % ?
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/leaf % ?
/married % ?
/musicalnote
/.notdef
% 0x70
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/tildelow % ?
/hyphendbl.alt % ?
% 0x80
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/caron.ts1
/hungarumlaut.ts1
/dblgrave.ts1
/dagger
/daggerdbl
/uni2016
/perthousand
/bullet
/uni2103
/dollaroldstyle
/centoldstyle
/florin
/colonmonetary
/uni20A9
/uni20A6
% 0x90
/guarani % ?
/peso % ?
/lira
/recipe % ?
/uni203D
/gnaborretni % ?
/dong
/trademark
/uni2031
/paragraph.alt % ?
/uni0E3F
/afii61352
/discount % ?
/estimated
/openbullet
/uni2120
% 0xA0
/uni2045
/uni2046
/cent
/sterling
/currency
/yen
/brokenbar
/section
/dieresis.ts1
/copyright
/ordfeminine
/copyleft % ?
/logicalnot
/uni2117
/registered
/macron.ts1
% 0xB0
/degree
/plusminus
/twosuperior
/threesuperior
/acute.ts1
/mu
/paragraph
/periodcentered
/uni203B
/onesuperior
/ordmasculine
/radical
/onequarter
/onehalf
/threequarters
/Euro % or /Euro.alt
% 0xC0
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
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% 0xD0
/.notdef
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/multiply
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% 0xE0
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% 0xF0
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/divide
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
/.notdef
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%!
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMSSBX10
%!PS-AdobeFont-1.0: CMSSBX10 003.002
%%Title: CMSSBX10
%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 CMSSBX10.
% 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/CMSSBX10 known{/CMSSBX10 findfont dup/UniqueID known{dup
/UniqueID get 5000806 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 /CMSSBX10 def
/FontBBox {-71 -250 1099 780 }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 CMSSBX10.) readonly def
/FullName (CMSSBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) 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 46 /period put
dup 49 /one put
dup 50 /two put
dup 65 /A put
dup 67 /C put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 76 /L put
dup 80 /P put
dup 83 /S put
dup 84 /T 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 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o 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 121 /y put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMTI10
%!PS-AdobeFont-1.0: CMTI10 003.002
%%Title: CMTI10
%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 CMTI10.
% 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/CMTI10 known{/CMTI10 findfont dup/UniqueID known{dup
/UniqueID get 5000828 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 /CMTI10 def
/FontBBox {-35 -250 1124 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 CMTI10.) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 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 14 /ffi put
dup 97 /a put
dup 99 /c put
dup 101 /e put
dup 108 /l put
dup 114 /r put
dup 116 /t put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.0: CMR12 003.002
%%Title: CMR12
%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 CMR12.
% 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/CMR12 known{/CMR12 findfont dup/UniqueID known{dup
/UniqueID get 5000794 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 /CMR12 def
/FontBBox {-34 -251 988 750 }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 CMR12.) readonly def
/FullName (CMR12) 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 11 /ff put
dup 14 /ffi put
dup 40 /parenleft put
dup 41 /parenright put
dup 45 /hyphen put
dup 46 /period put
dup 47 /slash 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 76 /L put
dup 77 /M 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 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 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p 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
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.0: CMCSC10 003.002
%%Title: CMCSC10
%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 CMCSC10.
% 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/CMCSC10 known{/CMCSC10 findfont dup/UniqueID known{dup
/UniqueID get 5087402 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 /CMCSC10 def
/FontBBox {14 -250 1077 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 CMCSC10.) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 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 44 /comma put
dup 46 /period put
dup 65 /A put
dup 66 /B put
dup 71 /G put
dup 72 /H put
dup 76 /L put
dup 77 /M put
dup 97 /a put
dup 98 /b put
dup 101 /e put
dup 105 /i put
dup 107 /k put
dup 110 /n put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 121 /y put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%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
/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
/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 58 /period put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMBX10
%!PS-AdobeFont-1.0: CMBX10 003.002
%%Title: CMBX10
%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 CMBX10.
% 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/CMBX10 known{/CMBX10 findfont dup/UniqueID known{dup
/UniqueID get 5000768 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 /CMBX10 def
/FontBBox {-56 -250 1164 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 CMBX10.) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) 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 49 /one put
dup 50 /two put
dup 53 /five put
dup 57 /nine put
dup 63 /question put
dup 65 /A put
dup 67 /C put
dup 79 /O put
dup 84 /T put
dup 97 /a put
dup 100 /d put
dup 101 /e put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 119 /w put
dup 120 /x put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%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 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period 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 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 73 /I put
dup 74 /J put
dup 76 /L put
dup 77 /M put
dup 78 /N 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 91 /bracketleft put
dup 93 /bracketright 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
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMTI12
%!PS-AdobeFont-1.0: CMTI12 003.002
%%Title: CMTI12
%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 CMTI12.
% 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/CMTI12 known{/CMTI12 findfont dup/UniqueID known{dup
/UniqueID get 5000829 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 /CMTI12 def
/FontBBox {-36 -251 1103 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 CMTI12.) readonly def
/FullName (CMTI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 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 84 /T put
dup 97 /a put
dup 101 /e put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 121 /y put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: CMBX8
%!PS-AdobeFont-1.0: CMBX8 003.002
%%Title: CMBX8
%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 CMBX8.
% 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/CMBX8 known{/CMBX8 findfont dup/UniqueID known{dup
/UniqueID get 5000766 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 /CMBX8 def
/FontBBox {-59 -250 1235 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 CMBX8.) readonly def
/FullName (CMBX8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) 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 45 /hyphen put
dup 58 /colon put
dup 67 /C put
dup 68 /D put
dup 76 /L put
dup 80 /P put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 105 /i put
dup 108 /l put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 121 /y put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont 
%%BeginFont: SFRM0800
%!FontType1-1.0: SFRM0800 0.3
%%CreationDate: Wed Sep 12 2001
% Copyright (c) 2001 Vladimir Volovich <vvv@vsu.ru>.
% See the file COPYING (GNU General Public License) for license conditions.
% Converted from METAFONT EC/TC and LH fonts:
% ecrm0800, tcrm0800, larm0800, lbrm0800, lcrm0800, rxrm0800.
11 dict begin
/FontInfo 6 dict dup begin
/version (0.3) def
/FullName (Computer Modern Roman) def
/FamilyName (Computer Modern) def
/ItalicAngle 0 def
/isFixedPitch false def
/Weight (Medium) def
end readonly def
/FontName /SFRM0800 def
/Encoding StandardEncoding def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] def
/FontBBox{-203 -320 1554 938}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.0: CMR8 003.002
%%Title: CMR8
%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 CMR8.
% 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/CMR8 known{/CMR8 findfont dup/UniqueID known{dup
/UniqueID get 5000791 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 /CMR8 def
/FontBBox {-36 -250 1070 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 CMR8.) readonly def
/FullName (CMR8) 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 11 /ff put
dup 12 /fi put
dup 38 /ampersand put
dup 40 /parenleft put
dup 41 /parenright 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 65 /A put
dup 67 /C put
dup 68 /D put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 87 /W put
dup 89 /Y put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i 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
readonly def
currentdict end
currentfile eexec
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%%EndFont 
%%BeginFont: CMBX12
%!PS-AdobeFont-1.0: CMBX12 003.002
%%Title: CMBX12
%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 CMBX12.
% 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/CMBX12 known{/CMBX12 findfont dup/UniqueID known{dup
/UniqueID get 5000769 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 /CMBX12 def
/FontBBox {-53 -251 1139 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 CMBX12.) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) 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 46 /period put
dup 49 /one put
dup 50 /two put
dup 65 /A put
dup 67 /C put
dup 71 /G put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 88 /X put
dup 89 /Y put
dup 97 /a put
dup 100 /d put
dup 101 /e put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 119 /w put
dup 120 /x put
dup 121 /y put
readonly def
currentdict end
currentfile eexec
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