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% $Id: pstricks.pro 919 2014-05-19 18:42:47Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 1.23, 2014/07/31
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%% 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.
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%
% Define the follwing gs-functions if not known, eg when using distiller
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/Acos {dup dup mul neg 1 add dup 0 lt {		% arc cos, returns 0 when negative root
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  a Div ceiling cvi /x2 ED /y1 ED 
  a Div cvi /x1 ED /y2 y2 y1 sub def 
  clipType   % must be defined in pstricks.tex: clip -- eoclip 
  newpath 
  2 setlinecap 
  systemdict
  /setstrokeadjust known { true setstrokeadjust } if 
  x2 x1 sub 1 add { 
    x1 a mul y1 moveto 0 y2 rlineto stroke 
    /x1 x1 1 add 
      hatchWidthInc 0 gt { CLW add } if 
    def 
    hatchSepInc 0 gt hatchWidthInc 0 gt or { 
      /a a hatchSepInc add def
      CLW hatchWidthInc add SLW 
    } if
  } repeat 
  grestore 
  pop pop } def
%
/DotFill {%	 on stack: dot radius
  /dotRadius ED
  abs CLW add /a ED 
  a 0 dtransform round exch round exch
  2 copy idtransform 
  exch Atan rotate 
  idtransform pop /a ED 
  .25 .25 itransform 
  pathbbox % llx lly urx ury of smallest bounding box
  /y2 ED /x2 ED /y1 ED /x1 ED 
  y2 y1 sub a div 2 add cvi /Ny ED
  x2 x1 sub a div 2 add cvi /Nx ED
  clipType   % must be defined in pstricks.tex: clip -- eoclip 
  newpath 
  /yA y1 dotRadius add CLW add def
  /xA0 x1 dotRadius add CLW add def
  Ny {
     /xA xA0 def
     Nx { 
       newpath 
       xA yA dotRadius 0 360 arc 
       SolidDot { gsave fill grestore } if 
       stroke
       xA a add /xA ED
     } repeat
     yA a add /yA ED
  } repeat
  grestore
} def
%
/PenroseFill {%	 on stack: scaling factor
  /Scale ED
%  1 exch div round /penroseFactor ED 
%  a 0 dtransform round exch round exch
%  2 copy idtransform 
%  exch Atan rotate 
%  idtransform pop /a ED 
%  .25 .25 itransform pathbbox 
%  /y2 ED 
%  a Div ceiling cvi /x2 ED /y1 ED 
%  a Div cvi /x1 ED /y2 y2 y1 sub def 
  clip 
  newpath 
gsave
  220 150 translate
  Scale dup scale
  systemdict /setstrokeadjust known { true setstrokeadjust } if 
  /I/S/L/W/G/+/Z/F/E/D[/def/exch/for{E D}/add{s E get mul}
 { Z -36.2001 1 33 }{25 E S rlineto}{/q Z dup q G E q 1 + G}{Z 2 2}]{cvx def}forall
  [0 72 1008 {dup sin E cos }F ]1 setlinejoin/s W{/a W{/b I 10{/i I 4{/m I moveto
  i m +/j I 10{/l Z b m l + G a l G sub s m get div .2 + floor .3 + 25
  mul j l + S rmoveto}F i L j L stroke }F}F}F}F 
  grestore 
%  pop pop 
} def
%
/PenroseFillA {%  on stack: scaling factor, border color, kite color, dart color
  /Scale ED
  Scale dup scale
  /border_colour ED 
  /kite_colour ED 
  /dart_colour ED
  clip 
  newpath 
  gsave
  100 100 translate
  6 
  Scale 1 lt { 1 Scale dup add div mul cvi } if %%%%   Number of iterations
  10					%%%%   Long side length in millimeters
  /border_width { L 0.06 mul }def		%%%%   Choose the scalefactor for the borders
  /L exch 25.4 div 72 mul def		%%%%   Conversion: mm -> inches -> points
  /f{-1 5 sqrt add 2 div}bind def		%%%%   The reciprocal of the golden ratio
  /l{L f mul}bind def			%%%%   Short side length l = L*f
  /Ll{L l add}bind def			%%%%   Ll =  L + l
  /c{36 cos L mul}bind def		%%%%   c  =  L*cos(36)
  /s{36 sin L mul}bind def		%%%%   s  =  L*sin(36)
  /draw_tile { 0 0 moveto c s lineto 0 lineto gsave closepath gsave fill grestore
	     0 setlinewidth stroke grestore border_colour stroke } bind def
  /half_kite { dup dup 0 gt{ 1 sub gsave f f neg scale -36 rotate half_dart
			   Ll 0 translate 144 rotate kite grestore }
	      		 { kite_colour L draw_tile }ifelse
	     pop } bind def
  /half_dart { dup dup 0 gt{ 1 sub gsave f f scale half_kite
			   -144 rotate Ll neg 0 translate half_dart grestore }
	      		 { dart_colour l draw_tile }ifelse
  	     pop } bind def
  /kite{ gsave half_kite 1 -1 scale half_kite grestore }bind def
  border_width setlinewidth  1 setlinejoin  1 setlinecap
%  450 0 translate  
  dup f exch neg exp dup scale
  5 {kite 72 rotate } repeat stroke 
  grestore
} def
%
%
/TruchetFill { %	 on stack: scaling factor
  10 dict begin
  dup dup scale
  1 exch div round /penroseFactor ED 
  a 0 dtransform round exch round exch
  2 copy idtransform 
  exch Atan rotate 
  idtransform pop /a ED 
  .25 .25 itransform pathbbox 
  /y2 ED 
  a Div ceiling cvi /x2 ED /y1 ED 
  a Div cvi /x1 ED /y2 y2 y1 sub def 
  clip 
  newpath 
  systemdict
  /setstrokeadjust known { true setstrokeadjust } if 
  /ma a neg def
  /ha a 2 div def 
  /mha ha neg def
  /tile { 
    rand dup 2 idiv 2 mul eq { 90 rotate } if
    mha mha moveto ha mha lineto
    ha ha lineto mha ha lineto
%    closepath .1 setlinewidth stroke
    contents
  } def
  /contents{ 
    0 ha moveto ha 0 lineto
    0 mha moveto mha 0 lineto
%    1 setlinewidth stroke
  } def
  /dotiling {
    f ma mul a f a mul { 
      /i exch def
      f ma mul a f a mul { 
        /j exch def
        gsave i j translate
        tile stroke grestore
      } for
    } for
  } def
%
  /f 3 def 
  5 srand dotiling 
  end % local user dict
} def
%
/BeginArrow { 
  ADict begin 			% hold it local, for end see EndArrow
  /@mtrx CM def 
  gsave 
  2 copy T 
  2 index sub neg exch 
  3 index sub exch Atan 
  rotate newpath 
} def
%
/EndArrow { @mtrx setmatrix CP grestore end } def % end the ADict
%
/Arrow { 
  CLW mul add dup 
  2 div /w ED 
  mul dup /h ED 
  mul /a ED 
  { 0 h T 1 -1 scale } if 
  w neg h moveto 
  0 0 L w h L w neg a neg rlineto 
  gsave fill grestore 
} def
%
/ArrowD { % the sides are drawn as curves (hv 20071211)
  CLW mul add dup 
  2 div /w ED 
  mul dup /h ED 
  mul /Inset ED 
  { 0 h T 1 -1 scale } if % changes the direction
% we use y=w/h^2 * x^2 as equation for the control points
% for the coordinates the arrow is seen from top to bottom
% the bottom (tip) is (0;0)
  w neg h moveto % lower left of >
  w 9 div 4 mul neg h 3 div 2 mul
  w 9 div neg       h 3 div  
  0 0 curveto    % tip of >
  w 9 div        h 3 div  
  w 9 div 4 mul  h 3 div 2 mul
  w h curveto % upper left of >
  w neg Inset neg rlineto % move to x=0 and inset
  gsave fill grestore 
} def 
%
/Tbar { 
  CLW mul add /z ED 
  z -2 div CLW 2 div moveto 
  z 0 rlineto stroke 
  0 CLW moveto 
} def
%
/Bracket { 
  CLW mul add dup CLW sub 2 div 
  /x ED mul CLW add /y ED /z CLW 2 div def 
  x neg y moveto 
  x neg CLW 2 div L x CLW 2 div L x y L stroke 
  0 CLW moveto 
} def
%
/RoundBracket { 
  CLW mul add dup 2 div 
  /x ED mul /y ED /mtrx CM def 
  0 CLW 2 div T x y mul 0 ne { x y scale } if 
  1 1 moveto 
  .85 .5 .35 0 0 0 curveto 
  -.35 0 -.85 .5 -1 1 curveto 
  mtrx setmatrix stroke 0 CLW moveto 
} def
%
/SD { 0 360 arc fill } def
%
/EndDot { % DS is the dot size 
  { /z DS def } { /z 0 def } ifelse  	% outer or inner dimen 
  /b ED 				% the color definition
  0 z DS SD 
  b { 0 z DS CLW sub SD } if 
  0 DS z add CLW 4 div sub 
  moveto 
} def
%
/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
  /closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
  load } if ] cvx newpath 3 1 roll T exec } def
%
/NArray { % holds the coordinates and on top of stack the showpoints boolean
  /showpoints ED 
  counttomark 2 div dup cvi /n ED  	% n 2 div on stack 
  n eq not { exch pop } if		% even numbers of points? delete one
  ] aload /Points ED 
  showpoints not { Points aload pop } if
%    { ] aload /Points ED } 
%    { n 2 mul 1 add -1 roll pop } ifelse	% delete the mark symbol 
} def
%
/Line { 
  NArray n 0 eq not 
    { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub def 
      n { Lineto } repeat 
      CP 4 2 roll ArrowB L pop pop 
    } if 
} def
%
/LineToYAxis {
  /Ox ED		% Save the x origin value 
  NArray            % all x-y pairs on stack
  n { 2 copy moveto % go to current point
    Ox exch Lineto   % line to y-axis
    pop             % delete old x-value
  } repeat
} def
%
/LineToXAxis{
  /Oy ED		% Save the y origin value 
  NArray		% all x-y pairs on stack
  n 0 eq not
    { n 1 eq { 0 0 /n 2 def } if
      ArrowA
      /n n 2 sub def
      CP 2 copy moveto pop Oy Lineto
      n { 2 copy moveto pop Oy Lineto } repeat
      CP
      4 2 roll
      ArrowB
      2 copy moveto pop Oy
      L
      pop pop } if
} def
%
/Arcto { 
  /a [ 6 -2 roll ] cvx def 
  a r 
  /arcto load stopped { 5 } { 4 } ifelse { pop } repeat 
  a 
} def
%
/CheckClosed { 
  dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
  and { pop pop /n n 1 sub def } if 
} def
%
/Polygon { 
  NArray n 2 eq { 0 0 /n 3 def } if 
  n 3 lt 
    { n { pop pop } repeat } 
    { n 3 gt { CheckClosed } if 
      n 2 mul -2 roll 
      /y0 ED /x0 ED /y1 ED /x1 ED  
      x1 y1 
      /x1 x0 x1 add 2 div def 
      /y1 y0 y1 add 2 div def 
      x1 y1 moveto 
      /n n 2 sub def 
      n { Lineto } repeat 
      x1 y1 x0 y0 6 4 roll Lineto
      Lineto pop pop closepath } ifelse 
} def
%
/SymbolPolygon {   % on stack [ x y x y ...
  counttomark 					% number of elements
  2 add /m ED
  2 copy m 2 roll				% copy last two
  m 2 div cvi /n ED    				% n pairs
  /YA ED /XA ED					% the start point
  n 1 sub { 
    /YB ED /XB ED
    /XLength XB XA sub def
    /YLength YB YA sub def
    /PAngle YLength XLength Atan def
    /XYLength XLength YLength Pyth def
    /nSym XYLength SymStep Div cvi def
    /Shift Symbol stringwidth pop 2 Div def 
    /deltaX XLength nSym Div def
    /deltaY YLength nSym Div def
    XA Shift sub YA Shift sub moveto 
    nSym { 
      gsave rotateSymbol { PAngle 180 sub CorrAngle sub rotate } if
      Symbol show 
      grestore 
      deltaX deltaY rmoveto
    } repeat
%    XB Shift sub YB Shift sub moveto Symbol show
    /YA YB def /XA XB def
  } repeat 
  pop	% delete the mark symbol
} def
%
/Diamond { 
  /mtrx CM def 
  T rotate 
  /h ED 
  /w ED 
  dup 0 eq { pop } { CLW mul neg 
    /d ED 
    /a w h Atan def 
    /h d a sin Div h add def 
    /w d a cos Div w add def } ifelse 
  mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div 
  /ArrowA { moveto } def 
  /ArrowB { } def 
  false Line 
  closepath mtrx setmatrix } def
%
/Triangle { 
  /mtrx CM def 
  translate 
  rotate /h ED 2 div /w ED 
  dup CLW mul /d ED 
  /h h d w h Atan sin Div sub def 
  /w w d h w Atan 2 div dup cos exch sin Div mul sub def 
  mark 
  0 d w neg d 0 h w d 0 d 
  /ArrowA { moveto } def 
  /ArrowB { } def 
  false 
  Line 
  closepath 
  mtrx
% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)
% setmatrix } def
  setmatrix pop 
} def
% DG/SR modification end
%
/CCA { 
  /y ED /x ED 
  2 copy y sub /dy1 ED 
  x sub /dx1 ED 
  /l1 dx1 dy1 Pyth def 
} def
%
/CC { 
  /l0 l1 def 
  /x1 x dx sub def 
  /y1 y dy sub def 
  /dx0 dx1 def 
  /dy0 dy1 def 
  CCA 
  /dx dx0 l1 c exp mul dx1 l0 c exp mul add def 
  /dy dy0 l1 c exp mul dy1 l0 c exp mul add def 
  /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def 
  /x2 x l0 dx mul m mul sub def
  /y2 y l0 dy mul m mul sub def 
  /dx l1 dx mul m mul neg def 
  /dy l1 dy mul m mul neg def 
} def
%
/IC { 
  /c c 1 add def 
  c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse 
  /a a 2 mul 3 div 45 cos b exp div def 
  CCA 
  /dx 0 def 
  /dy 0 def 
} def
%
/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
/NC { CC x1 y1 x2 y2 x y curveto } def
/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
/NAC { x2 y2 x y curveto CC x1 y1 } def
/EAC { x2 y2 x y ArrowB curveto pop pop } def
%
/OpenCurve { 
  NArray n 3 lt 
    { n { pop pop } repeat } 
    { BOC /n n 3 sub def n { NC } repeat EOC } ifelse 
} def
%
/CurvePath { 
  %% for negative SymStep we calculate the distance 
  SymStep 0 lt { gsave PathLength SymStep div abs /SymStep ED grestore } if
  0.5 setflat
  flattenpath /z 0 def /z0 0 def
  { /y1 ED /x1 ED /y2 y1 def /x2 x1 def 
    x1 Shift sub y1 Shift sub moveto 
    gsave 
    curveticks 
      { x1 y1 translate startAngle rotate 
        0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
        SymbolLinewidth setlinewidth stroke      
      }
      { startAngle rotate Symbol show }
    ifelse 
    grestore /z0 z def }
  { /y ED /x ED PathLength@ z z0 sub SymStep ge {
      x Shift sub y Shift sub moveto 
      gsave 
      curveticks 
        { y yOld sub x xOld sub Atan 180 sub CorrAngle sub /rotAngle ED  
          x y translate rotAngle rotate 
          0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
          SymbolLinewidth setlinewidth stroke
        }
        { 
          rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if        
          Symbol show 
        }
      ifelse 
      grestore /z0 z def } if 
    /yOld y def /xOld x def } 
  {} %% the lineto part
  { /y y2 def /x x2 def PathLength@ 
    x Shift sub y Shift sub moveto 
    gsave
    curveticks 
      { y yOld sub x xOld sub Atan 180 sub /rotAngle ED  
        x y translate rotAngle rotate 
        0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
        SymbolLinewidth setlinewidth stroke
      }
      { 
        x Shift sub y Shift sub moveto 
        rotateSymbol { y yOld sub x xOld sub Atan 180 sub CorrAngle sub rotate } if        
        Symbol show 
      }
    ifelse 
    grestore
  }
  pathforall 
%  curveticks 
%   { gsave 
%     x y translate rotAngle rotate 
%     0 SymbolWidth 2 div moveto 0 SymbolWidth 2 div neg lineto 
%     SymbolLinewidth setlinewidth stroke grestore
%   } if
  z 
} def
%
/OpenSymbolCurve { 
  OpenCurve
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
} def
%
/AltCurve { 
  { false NArray n 2 mul 2 roll 
    [ n 2 mul 3 sub 1 roll ] aload
    /Points ED 
    n 2 mul -2 roll } 
  { false NArray } ifelse 
  n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse 
} def
%
/AltOpenSymbolCurve { 
  AltCurve
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
} def
%
/ClosedCurve { 
  NArray n 3 lt 
    { n { pop pop } repeat } 
    { n 3 gt { CheckClosed } if 
      6 copy n 2 mul 6 add 6 roll 
      IC CC x y moveto n { NC } repeat 
      closepath pop pop 
    } ifelse 
} def
%
/ClosedSymbolCurve { 
  ClosedCurve
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
} def
%
/CalcBezierSpline {%  Christoph Bersch
  10 dict begin
  /getX { Points exch 2 mul get } def
  /getY { Points exch 2 mul 1 add get } def
  /n Points length 1 sub 2 idiv def
  /GetFirstControlPoints {
    /x n array def
    /tmp n array def
    /b 2 def
    x 0 rhs 0 get b div put
    1 1 n 1 sub {
      /i exch def
      tmp i 1 b div dup 4 1 roll put
      i n 1 sub lt { 4 }{ 3.5 } ifelse exch sub /b exch def
      x i rhs i get x i 1 sub get sub b div put
    } for
    1 1 n 1 sub {
      n exch sub
      dup dup x exch 1 sub 2 copy 6 2 roll
      get 3 1 roll tmp exch get
      exch x exch get mul sub
      put	
    } for
    x
  } def
  % 
  n 1 eq {
    0 getX 2 mul 1 getX add 3 div
    0 getY 2 mul 1 getY add 3 div
    exch dup 3 1 roll 2 mul 0 getX sub
    exch dup 3 1 roll 2 mul 0 getY sub
    [ 0 getX 0 getY 7 3 roll 1 getX 1 getY ] /outPoints exch def
  } {
    /outPoints 6 n mul 2 add array def
    0 1 n {
      dup dup 6 mul dup 1 add
      outPoints exch 5 -1 roll getY put
      outPoints exch 3 -1 roll getX put
    } for
    /rhs n array def
    1 1 n 2 sub {
      rhs exch dup dup getX 4 mul exch 1 add getX 2 mul add put
    } for
    rhs 0 0 getX 1 getX 2 mul add put
    rhs n 1 sub dup getX 8 mul n getX add 2 div put
    GetFirstControlPoints
    1 1 n 2 sub {
      rhs exch dup dup getY 4 mul exch 1 add getY 2 mul add put
    } for
    rhs 0 0 getY 1 getY 2 mul add put
    rhs n 1 sub dup getY 8 mul n getY add 2 div put
    GetFirstControlPoints
    0 1 n 1 sub {
      /i exch def
      2 copy
      i get outPoints 6 i mul 3 add 3 -1 roll put
      i get outPoints 6 i mul 2 add 3 -1 roll put
      2 copy
      i n 1 sub lt {
        i 1 add get i 1 add getY 2 mul exch sub outPoints 6 i mul 5 add 3 -1 roll put
        i 1 add get i 1 add getX 2 mul exch sub outPoints 6 i mul 4 add 3 -1 roll put
      }{
        n 1 sub get n getY add 2 div outPoints 6 n 1 sub mul 5 add 3 -1 roll put
        n 1 sub get n getX add 2 div outPoints 6 n 1 sub mul 4 add 3 -1 roll put
      } ifelse
    } for
    pop pop
  } ifelse
  outPoints
  end
} def
/Spline {
  /showpoints ED
  counttomark 2 div dup cvi /n ED
  n eq not { exch pop } if
  ] /Points ED
  n 1 gt {
    CalcBezierSpline
    mark exch aload pop
    ArrowA
    n 2 sub {
      6 2 roll 4 2 roll curveto
    } repeat
    6 2 roll 4 2 roll ArrowB curveto
  } if
} def
/OpenSymbolSpline {
  Spline
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
} def

%
/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def
%
/FontDot { 
  DS 2 mul dup 
  matrix scale matrix concatmatrix exch matrix
  rotate matrix concatmatrix exch 
  findfont exch makefont setfont 
} def
%
/Rect { 
  x1 y1 y2 add 2 div moveto 
  x1 y2 lineto 
  x2 y2 lineto 
  x2 y1 lineto
  x1 y1 lineto 
  closepath 
} def
%
/OvalFrame { 
  x1 x2 eq y1 y2 eq or 
    { pop pop x1 y1 moveto x2 y2 L } 
    { y1 y2 sub abs x1 x2 sub abs 2 copy gt 
      { exch pop } { pop } ifelse 
      2 div exch { dup 3 1 roll mul exch } if 
      2 copy lt { pop } { exch pop } ifelse
      /b ED 
      x1 y1 y2 add 2 div moveto 
      x1 y2 x2 y2 b arcto 
      x2 y2 x2 y1 b arcto
      x2 y1 x1 y1 b arcto 
      x1 y1 x1 y2 b arcto 
      16 { pop } repeat 
      closepath 
    } ifelse 
} def
%
/Frame { 
  CLW mul /a ED 
  3 -1 roll 
  2 copy gt { exch } if 
  a sub /y2 ED 
  a add /y1 ED 
  2 copy gt { exch } if 
  a sub /x2 ED 
  a add /x1 ED 
  1 index 0 eq { pop pop Rect } { OvalFrame } ifelse 
} def
%
/BezierNArray { 
  /f ED 
  counttomark 2 div dup cvi /n ED 
  n eq not { exch pop } if 
  n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat 
  f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse 
} def
%
/OpenBezier { 
  BezierNArray 
  n 1 eq 
    { pop pop } 
    { ArrowA n 4 sub 3 idiv 
      { 6 2 roll 4 2 roll curveto } repeat 
      6 2 roll 4 2 roll ArrowB curveto } ifelse 
} def
%
/OpenSymbolBezier { 
  OpenBezier
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
} def
%
/ClosedBezier { 
  BezierNArray 
  n 1 eq 
    { pop pop } 
    { moveto n 1 sub 3 idiv 
      { 6 2 roll 4 2 roll curveto } repeat 
      closepath } ifelse 
} def
%
/ClosedSymbolBezier { 
  /f ED				 % save showpoints value 
  2 copy /yEnd ED /xEnd ED
  counttomark -2 roll 2 copy /yStart ED /xStart ED
  counttomark 2 roll
  f
  ClosedBezier
  0.1 setflat
  /Shift Symbol stringwidth pop 2 div def 
  CurvePath 
  [ xEnd yEnd xStart yStart SymbolLine 
} def
%
/BezierShowPoints { 
  gsave 
  Points aload length 2 div cvi /n ED 
  moveto 
  n 1 sub { lineto } repeat 
  CLW 2 div SLW [ 4 4 ] 0 setdash stroke 
  grestore 
} def
%
/Parab { 
  /y0 ED /x0 ED /y1 ED /x1 ED 
  /dx x0 x1 sub 3 div def 
  /dy y0 y1 sub 3 div def 
  x0 dx sub y0 dy add x1 y1 ArrowA
  x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB 
  curveto 
  /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def 
} def
%
/Parab1 { % 1 end  |  0 SP
  /ySP ED /xSP ED /y1 ED /x1 ED 
  /dx xSP x1 sub 3 div def 
  /dy ySP y1 sub 3 div def 
  newpath x1 y1 moveto xSP y1 lineto xSP ySP lineto 
                       x1 ySP lineto closepath clip 
  currentpoint
  newpath moveto
  xSP dx sub ySP dy add x1 y1 ArrowA
  xSP dx add ySP dy add xSP 2 mul x1 sub y1 ArrowB 
  curveto 
  /Points [ x1 y1 xSP ySP xSP 2 mul x1 sub y1 ] def 
} def
%
/Grid { 
  newpath 
  /a 4 string def 
  /b ED % 				psk@gridlabels in pt
  /c ED % 				{ \pst@usecolor\psgridlabelcolor }
  /n ED % 				psk@griddots
  cvi dup 1 lt { pop 1 } if 
  /s ED % 				\psk@subgriddiv
  s div dup 0 eq { pop 1 } if 
  /dy ED s div dup 0 eq { pop 1 } if %	\pst@number\psyunit abs
  /dx ED dy div round dy mul %		\pst@number\psxunit abs
  /y0 ED dx div round dx mul 
  /x0 ED dy div round cvi 
  /y2 ED dx div round cvi 
  /x2 ED dy div round cvi 
  /y1 ED dx div round cvi 
  /x1 ED 
  /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def 
  /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def 
  b 0 gt { 
    /z1 b 4 div CLW 2 div add def
%    /Helvetica findfont b scalefont setfont 
    /b b .95 mul CLW 2 div add def } if 
  systemdict /setstrokeadjust known 
    { true setstrokeadjust /t { } def }
    { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
       exch itransform } bind def } ifelse 
  gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse 
  /i x1 def 
  /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def 
  /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def 
  x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if 
  { i dx mul dup y0 moveto 
    b 0 gt 
      { gsave c i a cvs dup stringwidth pop 
        /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse 
	h 0 gt {b neg}{z1} ifelse 
        rmoveto show grestore } if 
    dup t f moveto 
    g t L stroke 
    /i i w add def 
  } repeat 
  grestore 
  gsave 
  n 0 gt
  % DG/SR modification begin - Nov. 7, 1997 - Patch 1
  %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
    { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
  % DG/SR modification end
    { 2 setlinecap } ifelse 
  /i y1 def 
  /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def 
  /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def 
  y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if 
  { newpath i dy mul dup x0 exch moveto 
    b 0 gt { gsave c i a cvs dup stringwidth pop 
      /z2 ED 
      w 0 gt {z1 z2 add neg} {z1} ifelse 
      h 0 gt {z1} {b neg} ifelse 
      rmoveto show grestore } if 
    dup f exch t moveto 
    g exch t L stroke 
    /i i h add def 
  } repeat 
  grestore 
} def
%
/ArcArrow { 
  /d ED /b ED /a ED 
  gsave 
  newpath 0 -1000 moveto clip 
  newpath 
  0 1 0 0 b 
  grestore 
  c mul 
  /e ED 
  pop pop pop r a e d PtoC y add exch x add
  exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
  mul neg d 
} def
%
%
/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 
  /a ED 
  a Rot /RAngle [ RAngle dup a add ] cvx def 
} def
%
/RotEnd { 
  /TMatrix [ TMatrix setmatrix ] cvx def 
  /RAngle [ RAngle pop ] cvx def 
} def
%
/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
%
/Uput {
  /a ED 
  add 2 div /h ED 2 
  div /w ED 
  /s a sin def 
  /c a cos def 
  /b s abs c abs 2 copy gt dup 
    /q ED 
    { pop } { exch pop } ifelse def 
  /w1 c b div w mul def 
  /h1 s b div h mul def 
  q { w1 abs w sub dup c mul abs }{ h1 abs h sub dup s mul abs } ifelse 
} def
%
/UUput { 
  5 dict begin
  /z ED 
  abs /y ED 
  /x ED 
  q { x s div c mul abs y gt }{ x c div s mul abs y gt } ifelse 
    { x x mul y y mul sub z z mul add sqrt z add } 
    { q { x s div } { x c div } ifelse abs 
    } ifelse 
  a PtoC 
  h1 add exch 
  w1 add exch 
  end
} def
%
end
%-----------------------------------------------------------------------------%
%
% END pstricks.pro

% $Id: pst-algparser.pro 919 2014-05-19 18:42:47Z 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
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% 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

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

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

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

%/stringwidth{ 32 rightTrim psStringwidth } bind def

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

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

% $Id: pst-dots.pro 801 2013-07-09 18:10:41Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02,  2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt <tvz@Princeton.EDU>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga  - Dec. 16, 1999
%% Modified by Etienne Riga  - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17 
%
10 dict dup begin			% hold local
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  /FontMatrix [.001 0 0 .001 0 0] def
%  /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
  /FontBBox [-1000 -1000 1000 1000] def  % See end of file in /BuildGlyph
  /Encoding 256 array def
  0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
  Encoding				   % replace with given dot names
    dup (b) 0 get /Bullet put		   % get the numerical position of b in ASCII
%					   % and save /Bullet at this place in Encoding 
    dup (c) 0 get /Circle put
    dup (C) 0 get /BoldCircle put	% 67
    dup (u) 0 get /SolidTriangle put
    dup (t) 0 get /Triangle put
    dup (T) 0 get /BoldTriangle put
    dup (r) 0 get /SolidSquare put
    dup (s) 0 get /Square put
    dup (S) 0 get /BoldSquare put
    dup (q) 0 get /SolidPentagon put
    dup (p) 0 get /Pentagon put
    dup (P) 0 get /BoldPentagon put
%%%		  
    dup (k) 0 get /Asterisk put
    dup (K) 0 get /BoldAsterisk put
    dup (J) 0 get /SolidAsterisk put
    dup (h) 0 get /Hexagon put
    dup (H) 0 get /BoldHexagon put
    dup (G) 0 get /SolidHexagon put
    dup (f) 0 get /Octogon put		% 2008-04-18 hv
    dup (F) 0 get /BoldOctogon put	% 2008-04-18 hv
    dup (g) 0 get /SolidOctogon put	% 2008-04-18 hv
    dup (a) 0 get /Add put
    dup (A) 0 get /BoldAdd put 		% 65
    dup (x) 0 get /Mul put
    dup (X) 0 get /BoldMul put
    dup (m) 0 get /Oplus put
    dup (M) 0 get /BOplus put
    dup (e) 0 get /SolidOplus put
    dup (n) 0 get /Otimes put
    dup (N) 0 get /BOtimes put
    dup (E) 0 get /SolidOtimes put
    dup (i) 0 get /Bar put
    dup (I) 0 get /BoldBar put
    dup (l) 0 get /SolidDiamond put
    dup (d) 0 get /Diamond put
        (D) 0 get /BoldDiamond put
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/CharProcs 47 dict def
CharProcs begin
  /CirclePath {0 0 500 0 360 arc closepath} def
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  /Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
  /BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
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  /Square {SquarePath .89 .89 scale SquarePath eofill} def
  /BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
  /PentagonPath {
    -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
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  /SolidPentagon {PentagonPath fill} def
  /Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
  /BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
%-------------- hv begin 2004/07/25   from: er 2003/03/24
  /HexagonPath {
    0 550 moveto -476 275 lineto -476 -275 lineto
    0 -550 lineto 476 -275 lineto 476 275 lineto closepath
  } def
  /SolidHexagon {HexagonPath fill} def
  /Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
  /BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
%					2008-04-18 hv
  /OctogonPath { 
     550 dup 22.5 tan mul dup neg dup add /xMove exch def 
     exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def 
  /SolidOctogon { OctogonPath fill                             } def
  /Octogon {      OctogonPath .89 .89 scale OctogonPath eofill } def
  /BoldOctogon {  OctogonPath .79 .79 scale OctogonPath eofill } def
%
  /AsteriskPath {
    20 0 moveto 10 250 180 500 0 500 curveto
    -180 500 -10 250 -20 0 curveto closepath
  } def
  /Asterisk {
    AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
    60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
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%
  /Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
  /BoldAsteriskPath {
    50 30 cos 100 mul moveto  Basterp
    60 rotate Basterp 60 rotate Basterp
    60 rotate Basterp 60 rotate Basterp
    60 rotate Basterp closepath
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  /CrossPath {
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    40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
  } def
  /BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
    -550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto 
    80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
  } def
  /Add {CrossPath fill} def
  /Mul {45 rotate CrossPath fill} def
  /BoldAdd {BoldCrossPath fill} def
  /BoldMul {45 rotate BoldCrossPath fill} def
  /Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def 
  /SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def 
  /BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def 
  /Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def 
  /BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def 
  /SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def 
  /BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
  /Bar {BarPath fill} def
  /BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
  /BoldBar {BoldBarPath fill} def
  /DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
  /SolidDiamond {DiamondPath fill} def
  /Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
  /BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
%%%
  /.notdef { } def
end
%
/BuildGlyph {
  exch
  begin 		
%  Metrics 1 index get exec 0
    0 0
%      BBoxes 3 index get exec
    -1000 -1000 1000 1000
%     -571.5 -742.5 571.5 742.5
    setcachedevice
    CharProcs begin load exec end
  end
} def
%
/BuildChar {
  1 index /Encoding get exch get
  1 index /BuildGlyph get exec
} bind def
%
end
/PSTricksDotFont exch definefont pop
%
%% end

%!
% 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
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%     R0 G0 B0 R1 G1 B1 NumLines MidPoint %Angle GradientFill
% D.G. modification end
%
/tx@GradientDict 40 dict def
tx@GradientDict begin
/GradientFill {
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 rotate
 /MidPoint ED
 /NumLines ED
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    /LastYellow ED	% 1.06
    /LastMagenta ED	% 1.06
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    LastMagenta FirstMagenta add 2 div	% 1.06
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    LastRed FirstRed add 2 div
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% D.G. modification begin - Jul. 23, 1997 / Apr.  9, 1998
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% The default center used is the center of the bounding box of the object
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        /Magenta Magenta MagentaIncrement add def
        /Yellow Yellow YellowIncrement add def
        /Black Black BlackIncrement add def
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        /Magenta Magenta MagentaIncrement add def
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        /Black Black BlackIncrement add def
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      } ifelse% D.G. modification end
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%
/GradientFillHSB { %	hv 2006-11-04
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  /Brightness Brightness BrightnessIncrement add def
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%
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%
% END pst-grad.pro

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/BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0
setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC
/CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0
0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1
0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11
0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0
setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0
0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC
/Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0
setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0
0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0
1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC
/PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0
setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{
0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor}
DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70
setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0
setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1
setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end

%Version: 003.002
%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.
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
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dup 50 /two put
dup 52 /four put
dup 56 /eight put
readonly def
currentdict end
currentfile eexec
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