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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 256 20 "Special Polar Curves" }}
{PARA 19 "" 0 "" {TEXT 257 14 "Brian E. Blank" }}}{SECT 0 {PARA 3 "" 
0 "" {TEXT -1 7 " Load  " }{TEXT 267 13 "(Begin here!)" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "The most frequently \+
used  " }{TEXT 259 5 "Maple" }{TEXT -1 107 " commands are available as
 soon as a session begins. Other commands are collected by topic and s
tored in   " }{HYPERLNK 17 "packages" 2 "index,package" "" }{TEXT -1 
54 ".   Each package that is needed is loaded using the   " }
{HYPERLNK 17 "with" 2 "with" "" }{TEXT -1 22 "   command. For this  " 
}{HYPERLNK 17 "worksheet" 2 "worksheet" "" }{TEXT -1 27 "  we will nee
d to load the " }{HYPERLNK 17 "plots" 2 "plots" "" }{TEXT -1 58 "  pac
kage.  (Ignore any warnings that might pe displayed!)" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "with(plo
ts);  # With cursor on this line, press ENTER key\n              # Ign
ore any warnings that might be displayed!" }}{PARA 7 "" 1 "" {TEXT -1 
50 "Warning, the name changecoords has been redefined\n" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#7Z%(animateG%*animate3dG%-animatecurveG%&arrowG%
-changecoordsG%,complexplotG%.complexplot3dG%*conformalG%,conformal3dG
%,contourplotG%.contourplot3dG%*coordplotG%,coordplot3dG%-cylinderplot
G%,densityplotG%(displayG%*display3dG%*fieldplotG%,fieldplot3dG%)gradp
lotG%+gradplot3dG%,graphplot3dG%-implicitplotG%/implicitplot3dG%(inequ
alG%,interactiveG%-listcontplotG%/listcontplot3dG%0listdensityplotG%)l
istplotG%+listplot3dG%+loglogplotG%(logplotG%+matrixplotG%(odeplotG%'p
aretoG%,plotcompareG%*pointplotG%,pointplot3dG%*polarplotG%,polygonplo
tG%.polygonplot3dG%4polyhedra_supportedG%.polyhedraplotG%'replotG%*roo
tlocusG%,semilogplotG%+setoptionsG%-setoptions3dG%+spacecurveG%1sparse
matrixplotG%+sphereplotG%)surfdataG%)textplotG%+textplot3dG%)tubeplotG
" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 203 "Onc
e loaded, any of the commands in this package may be used. Within a se
ssion, the package will not need to be reloaded. . However, if you rel
oad the worksheet for a new session, or if you execute the  " }
{HYPERLNK 17 "restart" 2 "restart" "" }{TEXT -1 38 "  command, then yo
u must reload the   " }{TEXT 260 5 "plots" }{TEXT -1 52 " package comm
and before using any of its commands.  " }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 3153 "polargridplot := proc()\noption `Copyright (c) by B
rian E. Blank 2000. All rights reserved.`:\nlocal aa, bb, jj, ii, numC
, numR, Circles, Rays, ray, \n      DeltaC, DeltaR, plotList, rho,_rho
, listargs;\nif nargs < 3 then\nERROR(`polargridplot expects three (or
 more) arguments.`);\nelif not type(args[1],\{algebraic,set(algebraic)
,list(algebraic)\}) or not type(args[2],equation) or not type(args[3],
list(posint))\nthen \nprintf(`A typical call is polargridplot(r(theta)
,theta=a..b,[m,n]);`);\nERROR(`Wrong type of argument.`);\nelif not ty
pe(lhs(args[2]),name) or not type(rhs(args[2]),range) \nthen\nERROR(`p
olargridplot expects its second argument to be of the form var = a..b.
`);\nelif not type(op(1,rhs(args[2])),realcons) or\nnot type(op(2,rhs(
args[2])),realcons) then\nERROR(`polargridplot expects real ranges as \+
the right sides of arguments 2 and 3.`);\nelse\naa := op(1,rhs(args[2]
));\nbb := op(2,rhs(args[2]));\nnumR := op(1,args[3]);\nnumC := op(2,a
rgs[3]);\nif numR < 2 or numC < 2 then\nERROR(`The entries of the thir
d argument of polargridplot must be integers greater than 1.`);\nfi:\n
   if evalf(abs(bb-aa)) < evalf(2*Pi) then\n   DeltaC := evalf((bb-aa)
/(numR-1));\n   else DeltaC := evalf(2*Pi/(numR-1));\n   fi:\n\n\nif n
ot type(args[1],\{set,list\}) then\nrho := abs(evalf(subs(lhs(args[2])
=aa,args[1])));\nfor jj from 1 to 50 do\nrho := max(rho,abs(evalf(subs
(lhs(args[2])=aa+jj*(bb-aa)/50,args[1]))));\nod:\nelse\nfor ii from 1 \+
to nops(args[1]) do\n_rho[ii] := abs(evalf(subs(lhs(args[2])=aa,args[1
][ii])));\nfor jj from 1 to 30 do\n_rho[ii] := max(_rho[ii],abs(evalf(
subs(lhs(args[2])=aa+jj*(bb-aa)/30,args[1][ii]))));od:\nod:\nrho := ma
x(seq(_rho[ii],ii=1..nops(args[1])));\nfi:\n\nrho := 1.01*rho;\n\nDelt
aR := rho/(numC-1):\n\n\nif nargs = 3 and not type(args[1],\{set,list
\}) then\nplotList := [plots[polarplot](args[1],args[2],scaling=constr
ained)]:\nelif nargs > 3 and not type(args[1],\{set,list\}) then\nplot
List := [plots[polarplot](args[1],args[2],seq(args[jj],jj=4..nargs),sc
aling=constrained)]:\nelif nargs = 3 and type(args[1],\{set,list\}) th
en\nplotList := [seq(plots[polarplot](args[1][jj],args[2],scaling=cons
trained),jj=1..nops(args[1]))]:\nelse\nfor jj from 4 to nargs do\nif t
ype(rhs(args[jj]),list) then\nfor ii from 1 to nops(args[1]) do\nif ii
 <= nops(rhs(args[jj])) then\nlistargs[jj][ii] := lhs(args[jj])=op(ii,
rhs(args[jj]));\nelse\nlistargs[jj][ii] := lhs(args[jj])=op(nops(rhs(a
rgs[jj])),rhs(args[jj]));\nfi:\nod:\nelse\nfor ii from 1 to nops(args[
1]) do\nlistargs[jj][ii] := args[jj];\nod:\nfi:\nod:\nplotList := [seq
(plots[polarplot](args[1][ii],args[2],seq(listargs[jj][ii],jj=4..nargs
),scaling=constrained),ii=1..nops(args[1]))]:\nfi:\nfor jj from 1 to n
umC-1 do\nCircles[jj] := plots[polarplot](jj*DeltaR,args[2],color = CO
LOR(RGB,.85,.85,.85),scaling=constrained):\nplotList := [op(plotList),
Circles[jj]]:\nod:\n\nfor jj from 0 to numR-1 do\nif cos(aa+jj*DeltaC)
<>0 then\nRays[jj] := plot([t*cos(aa+jj*DeltaC),t*sin(aa+jj*DeltaC),t=
0..rho],color = COLOR(RGB,.85,.85,.85),scaling=constrained):\nelse\nRa
ys[jj] := plot(0,x=0..rho*cos(aa+jj*DeltaC),color = COLOR(RGB,.85,.85,
.85),scaling=constrained):\nfi:\nplotList := [op(plotList),Rays[jj]]:
\nod:\n\nRETURN(plots[display](plotList));\nfi:\nend:" }}}{PARA 3 "" 
0 "" {TEXT -1 1 "\n" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 8 " Circles" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
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a),2*sin(theta),cos(theta-5*Pi/4)],theta=0..2*Pi, color=[NAVY,MAROON,M
AGENTA,PLUM,AQUAMARINE], thickness=2, scaling=constrained);" }}{PARA 
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