{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 23 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 1 }{CSTYLE " Blue Emphasis" -1 256 "Times" 0 0 0 0 255 1 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "Green Emphasis" -1 257 "Times" 1 12 0 128 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Maroon Emphasis" -1 258 "Times" 1 12 128 0 128 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Purple Emphasis" -1 263 "Times" 1 12 102 0 230 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Red Emphasis" -1 264 "Tim es" 1 12 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Dark Red Emphasis" -1 265 "Times" 1 12 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Grey Empha sis" -1 266 "Times" 1 12 96 52 84 1 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Norm al" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 3 0 3 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 128 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Maple P lot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 3 3 1 0 1 0 2 2 15 2 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Norma l" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 40 "Graphing functions of a complex v ariable" }}{PARA 0 "" 0 "" {TEXT -1 37 "by Peter Stone, Nanaimo, B.C., Canada" }}{PARA 0 "" 0 "" {TEXT -1 19 "Version: 26.3.2007" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "res tart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 35 "load procedures for complex numbers" }} {PARA 0 "" 0 "" {TEXT -1 17 "The Maple m-file " }{TEXT 266 9 "complex. m" }{TEXT -1 37 " contains the code for the procedure " }{TEXT 0 13 "c onformalplot" }{TEXT -1 25 " used in this worksheet. " }}{PARA 0 "" 0 "" {TEXT -1 123 "It can be read into a Maple session by a command simi lar to the one that follows, where the file path gives its location. \+ " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "read \"K:\\\\Maple/procd rs/complex.m\";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 58 "A procedure for plotting functions of a complex variabl e: " }{TEXT 0 13 "conformalplot" }}{PARA 0 "" 0 "" {TEXT -1 14 "The pr ocedure " }{TEXT 0 13 "conformalplot" }{TEXT -1 58 " is includes the f ollowing modifications of the procedure " }{TEXT 0 9 "conformal" } {TEXT -1 8 " in the " }{TEXT 0 5 "plots" }{TEXT -1 9 " package." }} {PARA 15 "" 0 "" {TEXT -1 104 "There are various colouring options whi ch allow the images of the grid-lines to be coloured differently." }} {PARA 15 "" 0 "" {TEXT -1 36 "Adaptive plotting can be performed ." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 20 "conformalplot: usage" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 259 18 "Calling Sequence:\n" }} {PARA 0 "" 0 "" {TEXT 260 2 " " }{TEXT -1 34 " conformalplot(F,r1,r 2,options) " }{TEXT 261 1 "\n" }{TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 12 "Parameters: " }}{PARA 0 "" 0 "" {TEXT -1 5 " " } {TEXT 23 9 "F - " }{TEXT -1 34 "a complex procedure or expression " }}{PARA 0 "" 0 "" {TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 5 " \+ " }{TEXT 23 9 "r1, r2 - " }{TEXT -1 38 "ranges of the form a..b, o r name=a..b " }}{PARA 0 "" 0 "" {TEXT -1 6 " " }}{PARA 256 "" 0 " " {TEXT -1 12 "Description:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 2 "A " }{TEXT 258 14 "conformal plot" }{TEXT -1 78 " of a complex function F from z = a+bi to w = c+di maps a two-dimensi onal grid" }}{PARA 257 "" 0 "" {TEXT -1 2 " " }{XPPEDIT 18 0 "a<=x" " 6#1%\"aG%\"xG" }{XPPEDIT 18 0 "``<=c" "6#1%!G%\"cG" }{TEXT -1 3 ", " }{XPPEDIT 18 0 "b<=y" "6#1%\"bG%\"yG" }{XPPEDIT 18 0 "``<=d" "6#1%!G% \"dG" }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 369 "from the plane \+ into a second (curved) grid determined by the images of the original g rid lines under F. The size of the original grid (the number of lines \+ in either the x or y direction) is controlled by the user (see below). The result is a set of curves in the plane, which has the property th at they also intersect at right angles at the points where F is analyt ic. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "T he procedure " }{TEXT 0 9 "conformal" }{TEXT -1 428 " function defines a conformal plot of a complex function F, where F can be an expressio n or a procedure. The first range, r1, defines the grid lines in the p lane that are to be conformally mapped via the complex function F. The second range, r2, describes the dimensions of the window in which the conformal plot is to lie. If not present, the defaults are the maximu m and minimum of the resulting conformal lines in the range. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 8 "Options: " }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 10 "grid=[m,n]" }}{PARA 0 "" 0 "" {TEXT -1 219 "If m and n are integers greater than 1, this \+ option specifies the number of grid lines in both x and y directions t hat are to be mapped conformally. The default is 11 lines in either di rection, making an 11 by 11 grid." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 19 "adaptive=true/false" }}{PARA 0 "" 0 "" {TEXT -1 36 "In the default mode \"adaptive=true\" " }{TEXT 0 13 "conf ormalplot" }{TEXT -1 251 " attempts to extract formulas for the real a nd imaginary parts of F(z) by using the Maple procedure \"evalc\", and , if successful, uses the resulting pair of functions to plot the imag es of the grid lines using the adaptive plotting method provided for \+ " }{TEXT 0 4 "plot" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 164 "W hen formulas for the real and imaginary parts of F(z) cannot be extrac ted, adaptive plotting is still performed but by the slower method of \+ using the two functions" }}{PARA 257 "" 0 "" {TEXT -1 2 " " } {XPPEDIT 18 0 "z -> Re(F(z))" "6#f*6#%\"zG7\"6$%)operatorG%&arrowG6\"- %#ReG6#-%\"FG6#F%F*F*F*" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "z -> Im(F (z))" "6#f*6#%\"zG7\"6$%)operatorG%&arrowG6\"-%#ImG6#-%\"FG6#F%F*F*F* " }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 118 "With the option \"ad aptive=false\", non-adaptive plotting is performed using equally space d points along the grid lines." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 11 "numxy=[m,n]" }}{PARA 0 "" 0 "" {TEXT -1 227 "With non-adaptive plotting this option specifies the actual numbe r of points that are to be plotted in each gridline, with m points in \+ the x direction and n points in the y direction. The default is 15 poi nts in each direction." }}{PARA 0 "" 0 "" {TEXT -1 217 "With adaptive \+ plotting this option specifies the minimum number of points to be gene rated in each direction (the default is 40 points in each direction). \+ Often more than the minimum number of points will be generated." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "color=clr or [clr1,clr2]" }}{PARA 0 "" 0 "" {TEXT -1 173 "This option allows th e color for the curves which are images of the horizontal and vertical grid lines in the domain of F to be specified using the standard colo rs used for " }{TEXT 0 4 "plot" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 186 "The lines within a grid-line group can also be coloured \+ differently according to the special standard schemes: cyan_blue, cyan _green, yellow_red, yellow_green, magenta_red, magenta_blue." }}{PARA 0 "" 0 "" {TEXT -1 191 "Finally, the option \"color=arg\" colours the \+ neighbouring section to F(z) along a curve according the argument of t he complex number z in the domain of F, more precisely, the hue is giv en by " }{XPPEDIT 18 0 "1/2+arg(z)/(2*Pi);" "6#,&*&\"\"\"F%\"\"#!\"\" F%*&-%$argG6#%\"zGF%*&F&F%%#PiGF%F'F%" }{TEXT -1 2 ".\n" }}{PARA 0 "" 0 "" {TEXT 263 4 "Note" }{TEXT -1 152 ": The argument colouring option is restricted to non-adaptive plotting to try to prevent the associat ed data structure from becoming inordinately large." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 90 "There are also a number of standard two-dimensional plot options that are applicable with " } {TEXT 0 13 "conformalplot" }{TEXT -1 121 ". These include specificatio ns for style, and the number of horizontal and vertical ticks marks. S ee also ?plot[options]." }}{PARA 0 "" 0 "" {TEXT -1 33 "Of particular \+ note is the option:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 13 "coords=" }}{PARA 0 "" 0 "" {TEXT -1 155 "Indicate s that a plot is in the coordinate system specified by . S ee ?plot[coords] for more information about the choices of coordinate \+ system." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 225 "The result of a call to conformal is a PLOT structure which can b e rendered by the plotting device. The user may assign a PLOT value to a variable, save it in a file, then read it back in for redisplay. Se e ?plot[structure]. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 263 16 "How to activate:" } {TEXT 256 1 "\n" }{TEXT -1 154 "To make the procedure active open the \+ subsection, place the cursor anywhere after the prompt [ > and press \+ [Enter].\nYou can then close up the subsection." }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 29 "conformalplot: implementation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13446 "conformal plot := proc(func,r1)\nlocal proctype,ff,t,x,xmin,xmax,ymin,ymax,curv eseq,gl,glx,gly,i,\nj,varx,numx,numy,p,q,u,v,w,wmax,wmin,xgrid,xinc,y, k,cstart,\nygrid,yinc,z,zmax,zmin,features,s,tt,xcolor,ycolor,addcolor ,\nschm,xscheme,yscheme,xschm,yschm,schms,cx,cy,argt,adapt,\nffr,ffi,p oints,plotpoints,dcoords,zform,Fr,Fi,fxy,makefcn,\ntnumx,tnumy,ft,case ,ii;\n plotpoints := proc(f1,f2,range,numpnts)\n local curve,le xvar,numpts,j;\n curve := `plot/adaptive`(f1,f2,range,numpoints=n umpnts);\n numpts := op(1, [op(2, op(curve))]);\n curve := [ seq([curve[j, 1], curve[j, 2]],j=numpts)];\n if has(curve, 'undef ined') then\n lexvar := true;\n curve := map(subs('_la stundefined=lexvar',\n proc(x)\n global _last undefined;\n if type(x[1],undefined) then\n \+ if _lastundefined then NULL\n else _lastundef ined := true; x\n end if\n else _lastun defined := false; x\n end if\n end proc), curv e)\n end if;\n curve;\n end proc:\n addcolor := proc(cxy ,xyschm,xyscheme,xycolor,glxy,num)\n local curve,clr,k;\n if argt then\n seq(CURVES([[u[k],v[k]],[u[k+1],v[k+1]]],\n \+ COLOR(HUE,evalf(0.5+argument((p[k]+p[k+1])/2\n +(q[k] +q[k+1])/2*I)/(2*Pi)))),k=cstart..num-1);\n else\n if xys cheme then\n if xyschm = cyan_blue then\n clr := COLOR(`RGB`,0,cxy*(glxy-i),1)\n elif xyschm = cyan_gree n then\n clr := COLOR(`RGB`,0,1,cxy*(glxy-i))\n \+ elif xyschm = yellow_red then\n clr := COLOR(`RGB`,1, cxy*(glxy-i),0)\n elif xyschm = yellow_green then\n \+ clr := COLOR(`RGB`,cxy*(glxy-i),1,0)\n elif xyschm = magenta_red then\n clr := COLOR(`RGB`,1,0,cxy*(glxy-i)) \n elif xyschm = magenta_blue then\n clr := C OLOR(`RGB`,cxy*(glxy-i),0,1)\n else\n error \+ \"invalid colour scheme %1\",xyschm;\n end if\n els e\n clr := xycolor;\n end if;\n CURVES(poin ts,clr)\n end if \n end proc;\n makefcn := proc(fxy,a,x,y)\n \+ local fya;\n fya := traperror(subs(x=a,fxy));\n if last error=fya then\n subs(_VAR_=_y,_VAR_ -> undefined)\n else \n fya := eval(fya);\n subs(_VAR_=y,_EXPR_=fya,_VAR_ - > _EXPR_);\n end if;\n end proc;\n ff := func;\n if type(ff ,'procedure') then proctype := 'true'\n elif type(ff,'algebraic') th en\n proctype := 'false';\n varx := indets(ff) intersect ind ets(ff, name);\n if nops(varx) = 1 then varx := op(varx) end if\n else error \"first argument must be type algebraic or type procedur e\"\n end if;\n glx := 11;\n gly := 11;\n tnumx := 0;\n adap t := true;\n argt := false;\n xscheme := false;\n yscheme := fal se;\n schms := \{cyan_blue,cyan_green,yellow_red,\n \+ yellow_green,magenta_red,magenta_blue\};\n xcolor := COLOUR(' RGB',0,1.0,0);\n ycolor := COLOUR('RGB',1.0,0,0);\n features := NU LL;\n curveseq := NULL;\n dcoords := 'cartesian';\n if type(r1,' range') then\n zmin := op(1,r1); zmax := op(2,r1); proctype := 't rue'\n elif type(r1,'equation') and type(op(2,r1),'range') then\n \+ varx := op(1,r1);\n proctype := 'false';\n zmin := op([2, 1],r1);\n zmax := op([2,2],r1)\n else error \"second argument n eeds to be domain information\"\n end if;\n t := 3;\n if 2 'cartesian' then\n if proctype then\n \+ fxy := evalc(ff(zform));\n else\n fxy := evalc(s ubs(varx=zform,ff));\n end if;\n else\n if procty pe then\n fxy := evalc(ff(_x+_y*I));\n else\n \+ fxy := evalc(subs(varx=_x+_y*I,ff));\n end if;\n en d if; \n fxy := subs(I=ii,fxy);\n if member(degree(fxy,i i),\{0,1\}) then\n Fi := traperror(simplify(coeff(fxy,ii,1))); \n if b<>lasterror then\n Fr := simplify(fxy - Fi*i i);\n case := 2;\n end if;\n end if;\n end \+ if;\n\n if tnumx>0 then\n numx := tnumx;\n numy := tnumy; \n elif adapt then\n numx := 50;\n numy := 50;\n else\n \+ numx := 31;\n numy := 31;\n end if;\n if adapt and case= 2 then\n x := xmin;\n for i to glx do\n cstart := 1; \n ffr := makefcn(Fr,x,_x,_y);\n ffi := makefcn(Fi,x,_ x,_y);\n points := plotpoints(ffr,ffi,ymin..ymax,numy);\n \+ curveseq := curveseq,\n addcolor(cy,yschm,yscheme,yc olor,glx,numy);\n x := x + xgrid \n end do;\n y := y min;\n for i to gly do\n cstart := 1;\n ffr := ma kefcn(Fr,y,_y,_x);\n ffi := makefcn(Fi,y,_y,_x); \n \+ points := plotpoints(ffr,ffi,xmin..xmax,numx);\n curveseq := curveseq,\n addcolor(cx,xschm,xscheme,xcolor,gly,numx); \n y := y + ygrid \n end do;\n elif adapt and case=1 th en\n x := xmin;\n for i to glx do\n cstart := 1;\n \+ if dcoords<>'cartesian' then z := subs(\{_x=x\},zform)\n \+ else z := x+_y*I\n end if;\n if proctype then\n \+ ft := eval(ff(z));\n else\n ft := eval(subs( varx=z,ff));\n end if;\n ffr := subs(_EXPR_=ft,_y -> R e(_EXPR_));\n ffi := subs(_EXPR_=ft,_y -> Im(_EXPR_));\n \+ points := plotpoints(ffr,ffi,ymin..ymax,numy);\n curveseq : = curveseq,\n addcolor(cy,yschm,yscheme,ycolor,glx,numy) ;\n x := x + xgrid \n end do;\n y := ymin;\n fo r i to gly do\n cstart := 1;\n if dcoords<>'cartesian' then z := subs(\{_y=y\},zform)\n else z := _x+y*I\n e nd if;\n if proctype then\n ft := eval(ff(z));\n \+ else\n ft := eval(subs(varx=z,ff));\n end if; \n ffr := subs(_EXPR_=ft,_x -> Re(_EXPR_));\n ffi := s ubs(_EXPR_=ft,_x -> Im(_EXPR_)); \n points := plotpoints( ffr,ffi,xmin..xmax,numx);\n curveseq := curveseq,\n \+ addcolor(cx,xschm,xscheme,xcolor,gly,numx);\n y := y + ygrid \+ \n end do;\n else # non-adaptive plotting\n xinc := (xmax \+ - xmin)/(numx - 1);\n yinc := (ymax - ymin)/(numy - 1);\n x \+ := xmin;\n for i to glx do\n y := ymin;\n cstart \+ := 1;\n for j to numy do\n if dcoords<>'cartesian' \+ then \n z := subs(\{_x=x,_y=y\},zform);\n \+ p[j] := evalf(Re(z));\n q[j] := evalf(Im(z));\n \+ else\n z := evalf(x + I*y);\n p[j] := x ;\n q[j] := y;\n end if;\n if proc type then\n w := traperror(evalf(ff(z)));\n \+ if lasterror = w then\n if j = 1 then\n \+ cstart := 2;\n y := y + yinc;\n \+ next\n else\n points:= [seq([u[k],v[k]],k=cstart..j-1)];\n curveseq := cu rveseq,\n addcolor(cy,yschm,yscheme,ycolor,glx, j-1);\n cstart := j + 1;\n y : = y + yinc;\n next\n end if\n \+ end if\n else\n w := traperror(eva lf(subs(varx=z,ff)));\n if lasterror = w then\n \+ if j = 1 then\n cstart := 2;\n \+ y := y + yinc;\n next\n \+ else\n points:=[seq([u[k],v[k]],k=cstart..j-1)]; \n curveseq := curveseq,\n \+ addcolor(cy,yschm,yscheme,ycolor,glx,j-1);\n cstar t := j + 1;\n y := y + yinc;\n \+ next\n end if\n end if\n en d if;\n u[j] := Re(w);\n v[j] := Im(w);\n \+ y := y + yinc\n end do;\n if cstart'cartesi an' then \n z := subs(\{_x=x,_y=y\},zform);\n \+ p[j] := evalf(Re(z));\n q[j] := evalf(Im(z));\n \+ else\n z := evalf(x + I*y);\n p[j] \+ := x;\n q[j] := y;\n end if;\n if \+ proctype then\n w := traperror(evalf(ff(z)));\n \+ if lasterror = w then\n if j = 1 then\n \+ cstart := 2;\n x := x + xinc;\n \+ next\n else\n poin ts:=[seq([u[k],v[k]],k=cstart..j-1)];\n curveseq : = curveseq,\n addcolor(cx,xschm,xscheme,xcolor, gly,j-1);\n cstart := j + 1;\n \+ x := x + xinc;\n next\n end if\n end if\n else\n w := traperror (evalf(subs(varx=z,ff)));\n if lasterror = w then\n \+ if j = 1 then\n cstart := 2;\n \+ x := x + xinc;\n next\n \+ else\n points:=[seq([u[k],v[k]],k=cstart..j-1 )];\n curveseq := curveseq,\n \+ addcolor(cx,xschm,xscheme,xcolor,gly,j-1);\n cs tart := j + 1;\n x := x + xinc;\n \+ next\n end if\n end if\n \+ end if;\n u[j] := Re(w);\n v[j] := Im(w);\n \+ x := x + xinc\n end do;\n if cstart " 0 "" {MPLTEXT 1 0 1 ";" }}}}{PARA 0 "" 0 "" {TEXT -1 39 "Examples are given in the next section." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "examples" {TEXT 0 13 "conformalplot" }{TEXT -1 10 ": examples" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 32 "I llustration of coloring options" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "conformalplot(z,z=-1-I..1+I, adaptive=false,\n color=[blue,brown],thickness=2);" }} {PARA 13 "" 1 "" {GLPLOT2D 240 196 196 {PLOTDATA 2 "69-%'CURVESG6$7A7$ $!\"\"\"\"!F(7$F($!+LLLL$*!#57$F($!+mmmm')F.7$F($!+********zF.7$F($!+K LLLtF.7$F($!+lmmmmF.7$F($!+)*******fF.7$F($!+JLLL`F.7$F($!+kmmmYF.7$F( $!+(*******RF.7$F($!+ILLLLF.7$F($!+jmmmEF.7$F($!+'*******>F.7$F($!+HLL L8F.7$F($!+Bmmmm!#67$F($\"#WFV7$F($\"+6nmmmFV7$F($\"+QLLL8F.7$F($\"+0+ ++?F.7$F($\"+smmmEF.7$F($\"+RLLLLF.7$F($\"+1+++SF.7$F($\"+tmmmYF.7$F($ \"+SLLL`F.7$F($\"+2+++gF.7$F($\"+ummmmF.7$F($\"+TLLLtF.7$F($\"+3+++!)F .7$F($\"+vmmm')F.7$F($\"+ULLL$*F.7$F($\"+,+++5!\"*-%'COLOURG6&%$RGBG$ \")#)eqk!\")$\"))eqk\"FhqFiq-F$6$7A7$$!+++++!)F.F(7$F_rF,7$F_rF07$F_rF 37$F_rF67$F_rF97$F_rF<7$F_rF?7$F_rFB7$F_rFE7$F_rFH7$F_rFK7$F_rFN7$F_rF Q7$F_rFT7$F_rFX7$F_rFen7$F_rFhn7$F_rF[o7$F_rF^o7$F_rFao7$F_rFdo7$F_rFg 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