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%% This program can be redistributed and/or modified under the terms
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% the bottom (tip) is (0;0)
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%
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%
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/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
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 {
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
{ 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
%%EndProcSet
%%BeginProcSet: pst-algparser.pro 0 0
% $Id: pst-algparser.pro 446 2017-04-19 11:40:55Z 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->EE
%% 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
/EvalFunc_sin {%
PreCommonFunc
{ (cos\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_cos {%
PreCommonFunc
{ (\(-sin\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_tan {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/cos\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
PostCommonFunc } def
/EvalFunc_asin {%
PreCommonFunc
{ (1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_acos {%
PreCommonFunc
{ (-1/sqrt\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_atg {%
PreCommonFunc
{ (1/\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_floor {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_ln {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_exp {%
PreCommonFunc
{ (exp\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_EXP {%
PreCommonFunc
{ (EXP\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_sqrt {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/\(2*sqrt\() StrConcat 5 index StrConcat (\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_Fact {%
PreCommonFunc { DERIVATIVE_ENGINE_ERROR_no_variable_expression_in_Fact } if
PostCommonFunc } def
/EvalFunc_sh {%
PreCommonFunc
{ (ch\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_ch {%
PreCommonFunc
{ (sh\() StrConcat 5 index StrConcat AddClPar } if
PostCommonFunc } def
/EvalFunc_th {%
PreCommonFunc
{ dup 0 eq { (1) StrConcat } { 1 sub } ifelse (/ch\() StrConcat 5 index StrConcat (\)^2) StrConcat } if
PostCommonFunc } def
/EvalFunc_Argsh {%
PreCommonFunc
{ (1/sqrt\(1+\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_Argch {%
PreCommonFunc
{ (1/sqrt\(\() StrConcat 5 index StrConcat (\)^2-1\)\)) StrConcat } if
PostCommonFunc } def
/EvalFunc_Argth {%
PreCommonFunc
{ (1/\(1-\() StrConcat 5 index StrConcat (\)^2\)\)) StrConcat } if
PostCommonFunc } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
/PreCommonFunc {
1 add NextNonBlankChar pop 3 -1 roll 5 1 roll AnalyzeExpr 1 add NextNonBlankChar pop
4 2 roll 4 index (0) eq
{ (0) StrConcat false }
{ 4 index (1) ne { AddOpPar 4 index StrConcat (\)*) StrConcat } if true } ifelse
} def
/PostCommonFunc {
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
/EvalFunc_Derive {%
1 add ReadNumber cvi 1 add dup cvr log 1 add cvi string cvs
4 -1 roll pop 5 1 roll 1 add NextNonBlankChar pop AnalyzeExpr 1 add
4 -2 roll (Derive\() StrConcat 7 -1 roll StrConcat (,) StrConcat 6 -1 roll StrConcat AddClPar
2 copy pop 0 6 2 roll GetIntervalNewStr 6 -1 roll pop 2 index 6 index dup 4 index exch sub getinterval
exch 6 2 roll } def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_Sum {%
1 add NextNonBlankChar pop
%% read the variable name
ReadLiteral pop 3 -1 roll pop NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_first_comma_in_Sum } if
%% read the initial value
1 add NextNonBlankChar pop ReadNumber pop
2 copy get 44 ne { ANALYZER_ERROR_missing_second_comma_in_Sum } if
%% read the increment value
1 add NextNonBlankChar pop ReadNumber pop
2 copy get 44 ne { ANALYZER_ERROR_missing_third_comma_in_Sum } if
%% read the limit value
1 add NextNonBlankChar pop ReadNumber pop
2 copy get 44 ne { ANALYZER_ERROR_missing_fourth_comma_in_Sum } if
1 add NextNonBlankChar pop dup 6 1 roll 3 -1 roll pop AnalyzeExpr 1 add NextNonBlankChar pop
4 -2 roll 3 index 8 index dup 9 index exch sub getinterval StrConcat
4 index StrConcat AddClPar
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 9 -3 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% literal switch -> func call, vector, variables
/EvalFunc_IfTE {%
3 -1 roll pop 1 add NextNonBlankChar pop SkipCond
NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_first_comma_in_IfTE } if
1 add NextNonBlankChar pop dup 5 1 roll
AnalyzeExpr NextNonBlankChar
44 ne { ANALYZER_ERROR_missing_second_comma_in_IfTE } if
1 add NextNonBlankChar pop
AnalyzeExpr 1 add NextNonBlankChar pop
4 -2 roll 3 index 10 index dup 11 index exch sub getinterval StrConcat
6 index StrConcat (,) StrConcat 4 index StrConcat AddClPar
2 copy pop 0 6 2 roll GetIntervalNewStr
mark 11 -5 roll cleartomark 2 index 6 index dup 4 index exch sub getinterval exch 6 2 roll
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% advance in str until a comma is found (no error detection!)
%% str index -> str index'
/SkipCond { { 1 add 2 copy get 44 eq {exit } if } loop } bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Convert to radians if trigo function call
%% (name) ->
/TrigoFunc {
dup (cos) eq 1 index (sin) eq or exch (tan) eq or
{ /ExpressionVector ExpressionVector aload length Pi /div cvx 180 /mul cvx 5 -1 roll 4 add
array astore def
} if
} def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% No derivative for condition....
/EvalCondOp { 3 -1 roll pop } bind def
/PutIntervalOneAdd {putinterval 1 add} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddOpPar {2 copy (\() PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add close parenthesis in string at the given index
%% str index -> str index+1
/AddClPar {2 copy (\)) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add 0 in string at the given index
%% str index -> str index+1
/AddZero {2 copy (0) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddMul {2 copy (*) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add open parenthesis in string at the given index
%% str index -> str index+1
/AddDiv {2 copy (/) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a plus sign in string at the given index
%% str index -> str index+1
/AddAdd {2 copy (+) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a minus sign in string at the given index
%% str index -> str index+1
/AddSub {2 copy (-) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Add a pipe sign in string at the given index
%% str index -> str index+1
/AddPipe {2 copy (|) PutIntervalOneAdd} bind def
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% H O O K S
/AnalyzePreHook { dup 5 1 roll } bind def
/PreEvalHook {} def
/AnalyzePostHook { 7 -1 roll pop } bind def
/AnalyzeListOfEPostHook { 6 -1 roll mark 6 1 roll cleartomark } bind def
/RollOp { 5 1 roll } bind def
end%%%tx@CoreAnalyzerDict
/tx@AddMathFunc 12 dict def tx@AddMathFunc begin
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% NEW FUNC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% function arcsine in radians asin(x)=atan(x/sqrt(1-x^2))
%% x -> theta
/asin {%
dup abs 1 gt { EQDFasinrangeerror } if
dup dup dup mul 1 exch sub sqrt atan exch 0 lt { 360 sub } if DegtoRad
} def
%% function arccosine in radians acos(x)=atan(sqrt(1-x^2)/x)
%% x -> theta
/acos {%
dup abs 1 gt { EQDFacosrangeerror } if
dup dup mul 1 exch sub sqrt exch atan DegtoRad
} def
%% function arctangent in radians
%% x -> theta
/atg { 1 atan dup 90 gt { 360 sub } if DegtoRad } bind def
%% HYPERBOLIC FUNCTIONS
/sh { dup Ex exch neg Ex sub 2 div } def
/ch { dup Ex exch neg Ex add 2 div } def
/th { dup sh exch ch div } def
/Argsh { dup dup mul 1 add sqrt add ln } def
/Argch { dup dup mul 1 sub sqrt add ln } def
/Argth { dup 1 add exch 1 exch sub div ln 2 div } def
%% modified exponential funtion for 0
%% x n -> x^n
/Exp { dup 0 eq { pop pop 1 } { exp } ifelse } bind def
%% modified exponential funtion for 0
%% x -> e^x
/Ex { Euler exch exp } bind def
%%
%% factorial function
%% n -> n!
/Fact { 1 exch 2 exch 1 exch { mul } for } bind def
/fact { Fact } bind def
/! { Fact } bind def
end
%
% END pst-algparser.pro
%%EndProcSet
%%BeginProcSet: pst-tools.pro 0 0
% $Id: pst-tools.pro 842 2013-10-26 10:25:41Z herbert $
%
%% PostScript tools prologue for pstricks.tex.
%% Version 0.06, 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)
1 dict begin
exch dup length
2 index length add string
dup dup 4 2 roll copy length
4 -1 roll putinterval
end
} 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
/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
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%%BeginProcSet: pst-dots.pro 0 0
% $Id: pst-dots.pro 446 2017-04-19 11:40:55Z herbert $
%
%% PostScript prologue for pstricks.tex.
%% Version 2.02, 2009/06/16
%%
%% For distribution, see pstricks.tex.
%%
%% Timothy Van Zandt
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% Modified by Etienne Riga - Dec. 16, 1999
%% Modified by Etienne Riga - 2005/01/01 (er)
%% to add /Diamond, /SolidDiamond and /BoldDiamond
%% Modified by Herbert Voss (hv) - 2008/04/17
%
10 dict dup begin % hold local
/FontType 3 def
/FontMatrix [.001 0 0 .001 0 0] def
% /FontBBox [-571.5 -742.5 571.5 742.5] def % changed to next line 20060616 hv
/FontBBox [-1000 -1000 1000 1000] def % See end of file in /BuildGlyph
/Encoding 256 array def
0 1 255 {Encoding exch /.notdef put} for % fill the array with /.notdef
Encoding % replace with given dot names
dup (b) 0 get /Bullet put % get the numerical position of b in ASCII
% % and save /Bullet at this place in Encoding
dup (c) 0 get /Circle put
dup (C) 0 get /BoldCircle put % 67
dup (u) 0 get /SolidTriangle put
dup (t) 0 get /Triangle put
dup (T) 0 get /BoldTriangle put
dup (r) 0 get /SolidSquare put
dup (s) 0 get /Square put
dup (S) 0 get /BoldSquare put
dup (q) 0 get /SolidPentagon put
dup (p) 0 get /Pentagon put
dup (P) 0 get /BoldPentagon put
%%%
dup (k) 0 get /Asterisk put
dup (K) 0 get /BoldAsterisk put
dup (J) 0 get /SolidAsterisk put
dup (h) 0 get /Hexagon put
dup (H) 0 get /BoldHexagon put
dup (G) 0 get /SolidHexagon put
dup (f) 0 get /Octogon put % 2008-04-18 hv
dup (F) 0 get /BoldOctogon put % 2008-04-18 hv
dup (g) 0 get /SolidOctogon put % 2008-04-18 hv
dup (a) 0 get /Add put
dup (A) 0 get /BoldAdd put % 65
dup (x) 0 get /Mul put
dup (X) 0 get /BoldMul put
dup (m) 0 get /Oplus put
dup (M) 0 get /BOplus put
dup (e) 0 get /SolidOplus put
dup (n) 0 get /Otimes put
dup (N) 0 get /BOtimes put
dup (E) 0 get /SolidOtimes put
dup (i) 0 get /Bar put
dup (I) 0 get /BoldBar put
dup (l) 0 get /SolidDiamond put
dup (d) 0 get /Diamond put
(D) 0 get /BoldDiamond put
%%%
/CharProcs 47 dict def
CharProcs begin
/CirclePath {0 0 500 0 360 arc closepath} def
/Bullet {CirclePath fill} def
/Circle {CirclePath .9 .9 scale CirclePath eofill} def
/BoldCircle {CirclePath .8 .8 scale CirclePath eofill} def
/TrianglePath {0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath} def
/SolidTriangle {TrianglePath fill} def
/Triangle {TrianglePath .85 .85 scale TrianglePath eofill} def
/BoldTriangle {TrianglePath .7 .7 scale TrianglePath eofill} def
/SquarePath {-450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath} def
/SolidSquare {SquarePath fill} def
/Square {SquarePath .89 .89 scale SquarePath eofill} def
/BoldSquare {SquarePath .78 .78 scale SquarePath eofill} def
/PentagonPath {
-337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto
0 574.7 lineto -546.6 177.6 lineto closepath
} def
/SolidPentagon {PentagonPath fill} def
/Pentagon {PentagonPath .89 .89 scale PentagonPath eofill} def
/BoldPentagon {PentagonPath .78 .78 scale PentagonPath eofill} def
%-------------- hv begin 2004/07/25 from: er 2003/03/24
/HexagonPath {
0 550 moveto -476 275 lineto -476 -275 lineto
0 -550 lineto 476 -275 lineto 476 275 lineto closepath
} def
/SolidHexagon {HexagonPath fill} def
/Hexagon {HexagonPath .89 .89 scale HexagonPath eofill} def
/BoldHexagon {HexagonPath .79 .79 scale HexagonPath eofill} def
% 2008-04-18 hv
/OctogonPath {
550 dup 22.5 tan mul dup neg dup add /xMove exch def
exch moveto 7 { xMove 0 rlineto 45 rotate } repeat closepath } def
/SolidOctogon { OctogonPath fill } def
/Octogon { OctogonPath .89 .89 scale OctogonPath eofill } def
/BoldOctogon { OctogonPath .79 .79 scale OctogonPath eofill } def
%
/AsteriskPath {
20 0 moveto 10 250 180 500 0 500 curveto
-180 500 -10 250 -20 0 curveto closepath
} def
/Asterisk {
AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath
60 rotate AsteriskPath 60 rotate AsteriskPath 60 rotate AsteriskPath fill
} def
%
/Basterp {50 250 220 500 0 500 curveto -220 500 -50 250 -50 30 cos 100 mul curveto} def
/BoldAsteriskPath {
50 30 cos 100 mul moveto Basterp
60 rotate Basterp 60 rotate Basterp
60 rotate Basterp 60 rotate Basterp
60 rotate Basterp closepath
} def
/BoldAsterisk {BoldAsteriskPath fill} def
/SolidAsterisk {CirclePath .9 .9 scale BoldAsteriskPath eofill} def
/CrossPath {
40 550 moveto -40 550 lineto -40 40 lineto -550 40 lineto
-550 -40 lineto -40 -40 lineto -40 -550 lineto 40 -550 lineto
40 -40 lineto 550 -40 lineto 550 40 lineto 40 40 lineto closepath
} def
/BoldCrossPath {80 550 moveto -80 550 lineto -80 80 lineto -550 80 lineto
-550 -80 lineto -80 -80 lineto -80 -550 lineto 80 -550 lineto
80 -80 lineto 550 -80 lineto 550 80 lineto 80 80 lineto closepath
} def
/Add {CrossPath fill} def
/Mul {45 rotate CrossPath fill} def
/BoldAdd {BoldCrossPath fill} def
/BoldMul {45 rotate BoldCrossPath fill} def
/Oplus {CirclePath .9 .9 scale CirclePath eofill .775 .775 scale CrossPath fill } def
/SolidOplus {CirclePath .775 .775 scale BoldCrossPath eofill} def
/BOplus {CirclePath .8 .8 scale CirclePath eofill .775 .775 scale BoldCrossPath fill} def
/Otimes {CirclePath .9 .9 scale CirclePath eofill 45 rotate .775 .775 scale CrossPath fill} def
/BOtimes {CirclePath .8 .8 scale CirclePath eofill 45 rotate .775 .775 scale BoldCrossPath fill } def
/SolidOtimes {CirclePath 45 rotate .775 .775 scale BoldCrossPath eofill} def
/BarPath {40 660 moveto -40 660 lineto -40 -660 lineto 40 -660 lineto closepath} def
/Bar {BarPath fill} def
/BoldBarPath {80 660 moveto -80 660 lineto -80 -660 lineto 80 -660 lineto closepath} def
/BoldBar {BoldBarPath fill} def
/DiamondPath {0 742.5 moveto -428.5 0 lineto 0 -742.5 lineto 428.5 0 lineto closepath} def
/SolidDiamond {DiamondPath fill} def
/Diamond {DiamondPath .865 .865 scale DiamondPath eofill} def
/BoldDiamond {DiamondPath .73 .73 scale DiamondPath eofill} def
%%%
/.notdef { } def
end
%
/BuildGlyph {
exch
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% Metrics 1 index get exec 0
0 0
% BBoxes 3 index get exec
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% -571.5 -742.5 571.5 742.5
setcachedevice
CharProcs begin load exec end
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%
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%
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%%EndFont
%%BeginFont: CMMI10
%!PS-AdobeFont-1.0: CMMI10 003.002
%%Title: CMMI10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMMI10.
% This Font Software is licensed under the SIL Open Font License, Version 1.1.
% This license is in the accompanying file OFL.txt, and is also
% available with a FAQ at: http://scripts.sil.org/OFL.
%%EndComments
FontDirectory/CMMI10 known{/CMMI10 findfont dup/UniqueID known{dup
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/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\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
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0 1 255 {1 index exch /.notdef put} for
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dup 65 /A put
dup 66 /B put
dup 112 /p put
readonly def
currentdict end
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSY10
%!PS-AdobeFont-1.0: CMSY10 003.002
%%Title: CMSY10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSY10.
% 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/CMSY10 known{/CMSY10 findfont dup/UniqueID known{dup
/UniqueID get 5096651 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 /CMSY10 def
/FontBBox {-29 -960 1116 775 }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\051, with Reserved Font Name CMSY10.) readonly def
/FullName (CMSY10) 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 91 /union put
dup 92 /intersection put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMBX6
%!PS-AdobeFont-1.0: CMBX6 003.002
%%Title: CMBX6
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMBX6.
% 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/CMBX6 known{/CMBX6 findfont dup/UniqueID known{dup
/UniqueID get 5000764 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 /CMBX6 def
/FontBBox {-49 -250 1367 753 }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\051, with Reserved Font Name CMBX6.) readonly def
/FullName (CMBX6) 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 19 /acute put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMMIB6
%!PS-AdobeFont-1.0: CMMIB6 003.002
%%Title: CMMIB6
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMMIB6.
% 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/CMMIB6 known{/CMMIB6 findfont dup/UniqueID known{dup
/UniqueID get 5087388 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 /CMMIB6 def
/FontBBox {2 -250 1423 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\051, with Reserved Font Name CMMIB6.) readonly def
/FullName (CMMIB6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle -14.035 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 83 /S put
dup 97 /a put
dup 101 /e put
dup 104 /h put
dup 109 /m put
dup 115 /s put
dup 116 /t put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSS8
%!PS-AdobeFont-1.0: CMSS8 003.002
%%Title: CMSS8
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSS8.
% 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/CMSS8 known{/CMSS8 findfont dup/UniqueID known{dup
/UniqueID get 5000801 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 /CMSS8 def
/FontBBox {-65 -250 1062 761 }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\051, with Reserved Font Name CMSS8.) readonly def
/FullName (CMSS8) 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 19 /acute put
dup 49 /one put
dup 50 /two put
dup 55 /seven put
dup 58 /colon put
dup 80 /P put
dup 83 /S put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 105 /i put
dup 108 /l put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 120 /x 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: (), 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\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 19 /acute put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMMIB10
%!PS-AdobeFont-1.0: CMMIB10 003.002
%%Title: CMMIB10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMMIB10.
% 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/CMMIB10 known{/CMMIB10 findfont dup/UniqueID known{dup
/UniqueID get 5087392 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 /CMMIB10 def
/FontBBox {-15 -250 1216 750 }readonly def
/PaintType 0 def
/FontInfo 8 dict dup begin
/version (003.002) readonly def
/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMIB10.) readonly def
/FullName (CMMIB10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
/ascent 750 def
end readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 83 /S put
dup 97 /a put
dup 101 /e put
dup 104 /h put
dup 109 /m put
dup 115 /s put
dup 116 /t put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSS10
%!PS-AdobeFont-1.0: CMSS10 003.002
%%Title: CMSS10
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSS10.
% 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/CMSS10 known{/CMSS10 findfont dup/UniqueID known{dup
/UniqueID get 5000803 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 /CMSS10 def
/FontBBox {-61 -250 999 759 }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\051, with Reserved Font Name CMSS10.) readonly def
/FullName (CMSS10) 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 19 /acute put
dup 46 /period put
dup 58 /colon put
dup 67 /C put
dup 83 /S put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 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 120 /x put
readonly def
currentdict end
currentfile eexec
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cleartomark
{restore}if
%%EndFont
%%BeginFont: CMSS12
%!PS-AdobeFont-1.0: CMSS12 003.002
%%Title: CMSS12
%Version: 003.002
%%CreationDate: Mon Jul 13 16:17:00 2009
%%Creator: David M. Jones
%Copyright: Copyright (c) 1997, 2009 American Mathematical Society
%Copyright: (), with Reserved Font Name CMSS12.
% 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/CMSS12 known{/CMSS12 findfont dup/UniqueID known{dup
/UniqueID get 5000804 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 /CMSS12 def
/FontBBox {-62 -251 978 758 }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\051, with Reserved Font Name CMSS12.) readonly def
/FullName (CMSS12) 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 19 /acute put
dup 55 /seven put
dup 58 /colon put
dup 80 /P put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 105 /i put
dup 108 /l put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 120 /x put
readonly def
currentdict end
currentfile eexec
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