{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 0 1 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE " " -1 -1 "Courier" 1 8 0 0 0 1 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 136 "Function Reflector Movie s (Bruce & Tami's functional form)\nCreated with Maple 5 Release 5.1, \+ by John Pais, pais@kinetigram.com, 07-20-03" }{TEXT -1 7 " " }} {PARA 0 "" 0 "" {TEXT -1 61 "Define Reflector procedure to create para meterized functions." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Reflector:= proc(k1,n1,c1)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "local k,n,c,f,g: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "k:=k1:n:=n1:c:=c1:" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 23 "f:=unapply(k*x^n -c,x):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 30 "g:=unapply(((x+c)/k)^(1/n),x):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 5 "[f,g]" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Initialize Reflector and print functions." }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "k:='k':n:='n':c:='c':" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "f:=op(1,Reflector(k,n,c)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "g:=op(2,Reflector(k,n,c)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "'f(x)'=f(x);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "'g (x)'=g(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"fG6#%\"xG,&*&%\"kG \"\"\")F'%\"nGF+F+%\"cG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"g G6#%\"xG)*&,&F'\"\"\"%\"cGF+\"\"\"%\"kG!\"\"*&F-F-%\"nGF/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Initialize Reflector with specific values, print and plot funct ions." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 252 "k:=1:n:=3:c:=1:\np1:=plot (f(x),x=-4..4,y=-4..4,color=blue):\np2:=plot(g(x),x=-c..4,y=-4..4,colo r=red):\n# Note that the branch below (p3) must be done separately,\n# in order to trick Maple into ploting it.\np3:=plot(-g(-x-2*c),x=-4..- c,y=-4..4,color=navy):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "'f(x)'=f( x);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "'g(x)'=g(x);\nplots[display] ([p1,p2,p3],scaling=constrained);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/ -%\"fG6#%\"xG,&*$)F'\"\"$\"\"\"\"\"\"!\"\"F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"gG6#%\"xG*$),&F'\"\"\"F+F+#F+\"\"$\"\"\"" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6$7S7$$!\"% \"\"!$!#lF*7$$!1nmmmFiDQ!#:$!1xtBZz%*)p&!#97$$!1LLLo!)*Qn$F0$!1!)3KVQ& )e]F37$$!1nmmwxE.NF0$!16?-&H?&*R%F37$$!1mmmOk]JLF0$!1U)*3&QF37$$!1+++:v2*\\#F0$!1I/yy4x g;F37$$!1LLL8>1DBF0$!1tCD>#3pN\"F37$$!1nmmw))yr@F0$!1e]Aw/OC6F37$$!1++ +S(R#**>F0$!1!=KvM!)3**)F07$$!1++++@)f#=F0$!1,S8F*3#)3(F07$$!1+++gi,f; F0$!1TIeO%ohc&F07$$!1nmm\"G&R2:F0$!1\\&e:mk^U%F07$$!1LLLtK5F8F0$!1lF[' R)HPLF07$$!1MLL$HsV<\"F0$!1uy5\")ej>EF07$$!1-++]&)4n**!#;$!1mja/?;!*>F 07$$!1PLLL\\[%R)Faq$!1bC+Pt`\"f\"F07$$!1)*****\\&y!pmFaq$!1&R)4(*zh'H \"F07$$!1******\\O3E]Faq$!1[\"[o\\mp7\"F07$$!1KLLL3z6LFaq$!1Q$*\\%eBj. \"F07$$!1MLL$)[`PqM8F0$\"1\\LoApn x8F07$$\"1++++.W2:F0$\"13!p\"[:ZDCF07$$\"1LLLep'Rm\"F0$\"1')Rj#[org$F0 7$$\"1+++S>4N=F0$\"1TQ`pmyz^F07$$\"1mmm6s5'*>F0$\"1*\\:QSxL&pF07$$\"1+ ++lXTk@F0$\"1`R:a@hR\"*F07$$\"1mmmmd'*GBF0$\"1ZPwA+Dj6F37$$\"1+++DcB,D F0$\"1109Uz\"[Y\"F37$$\"1MLLt>:nEF0$\"1kYh0=L(z\"F37$$\"1LLL.a#o$GF0$ \"1X([_ZdH=#F37$$\"1nmm^Q40IF0$\"1/&4`wwPh#F37$$\"1+++!3:(fJF0$\"1j,\" y9'faIF37$$\"1nmmc%GpL$F0$\"1&f1xP+dh$F37$$\"1LLL8-V&\\$F0$\"1CYb^zsqT F37$$\"1+++XhUkOF0$\"1`Prz$)f?[F37$$\"1+++:o%f'**Faq$\"1\\$4'Q*\\X]\"Faq7$$!1m\"HK*Q)=$**Faq$\"1Z>FQTh&*=Fa q7$$!1]P%)Re#y*)*Faq$\"1b`Y-l$*p@Faq7$$!1L$ekynP')*Faq$\"1drGbTK)Q#Faq 7$$!1+voz;l&z*Faq$\"1f8Rw'[Rt#Faq7$$!1nm\"HdNvs*Faq$\"1x'=s()*44IFaq7$ $!1,]PfLI\"f*Faq$\"1+xr'[fXW$Faq7$$!1ML$e9r]X*Faq$\"1*)Qaw#G7z$Faq7$$! 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R7g(=F0$!1lJ*zJV$o&*Faq7$$!1++]A0%=\"=F0$!1;A*fe_(G$*Faq7$$!1+]i&zf9v \"F0$!1'pV`'Q\\\"4*Faq7$$!1+]7QXM)o\"F0$!1@Re:L[H))Faq7$$!1++]PyjE;F0$ !1yM.`;Md&)Faq7$$!1+]iSm.i:F0$!1(>&4k3b_#)Faq7$$!1+++5!=)*\\\"F0$!1')= fs@/OzFaq7$$!1++vt/>O9F0$!1OSm(e!*Qe(Faq7$$!1+]i0)*3t8F0$!1C\"=*fE)*)> (Faq7$$!1+++Xo5:8F0$!1#f0MKh[!oFaq7$$!1++vG=l[7F0$!1x%)*Q!4E)G'Faq7$$! 1+++qO@*=\"F0$!1[\"G#e`&4u&Faq7$$!1+]i&>Se7\"F0$!1Ag&>gx6,&Faq7$$!1+++ X>^&4\"F0$!1]gC!H%3rXFaq7$$!1+]P%p$=l5F0$!1!QO+\")4X-%Faq7$$!1]7yqx))[ 5F0$!1Og$f#)4ll$Faq7$$!1+v=Z=fK5F0$!1VS0`bD%>$Faq7$$!1D1R&)QWC5F0$!1h9 6sP<-HFaq7$$!1]PfBfH;5F0$!1?me7BGNDFaq7$$!17`pU>A75F0$!17@U\\oX.BFaq7$ $!1vozhz935F0$!1'==]!\\D7?Faq7$$!1cwMr4615F0$!12!oH\"\\DG=Faq7$$!1Q%)* 3)R2/5F0$!1Lq_wx7(f\"Faq7$$!1>#\\/*p.-5F0$!1ALHc6kn7FaqFf[l-F][l6&F_[l $\")!\\DP\"Fb[lF``n$\")viobFb[l-%+AXESLABELSG6$Q\"x6\"Q\"yFh`n-%(SCALI NGG6#%,CONSTRAINEDG-%%VIEWG6$;F(FhzFaan" 1 2 0 1 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Define Function Reflector Movie \+ procedure." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "FunctionReflectorMovi e:=proc(k,n,frame)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "local f,g,m,n _str,i,c,c_str,txtcolor,rp," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "movi e_frame,j,reflector_movie,FunctionReflector:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Digits:=4:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "m:=40 :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "n_str:=convert(n,string):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for i from 0 to m do" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 209 "if i <= 20 then\nc:=i*.1:\nelse\nc:=-(i-20)*. 1:\nfi:\nc_str:=convert(evalf(abs(c),2),string):\nif c = 0 then\nc_st r:=\"0.\".c_str:\nfi:\nif 0 < abs(c) and abs(c) < 1 then\nc_str:=\"0\" .c_str:\nfi:\nf:=op(1,Reflector(k,n,c)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 168 "g:=op(2,Reflector(k,n,c)):\n#Setup axes: don't use d efault axes, in order \n#to obtain a less clutered view.\nrp[1]:=plot( [[-2.,-0.075],[-2.,0.075]], " }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 51 " linestyle=1,color=black): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "rp[2]:=plots[textplot]([-2.,-0. 3,`-2`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " \+ font=[HELVETICA,DEFAULT,10]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " \+ color=black):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "rp[3]:=plot([[2.,-0.075],[2.,0.075]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " linestyle=1,color=black):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "rp[4]:=plots[textplot]([2.,-0.3,` 2`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " fo nt=[HELVETICA,DEFAULT,10]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " \+ color=black):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "rp[5]:=plot([[-0.1,-2.],[0.1,-2.]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " linestyle=1,color=black):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "rp[6]:=plots[textplot]([-0.28,-2.,`-2`], " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " font=[ HELVETICA,DEFAULT,10]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " \+ color=black):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "rp [7]:=plot([[-0.1,2.],[0.1,2.]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " linestyle=1,color=black):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "rp[8]:=plots[textplot]([-0.25,2.,`2`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " font=[HELVETICA,DE FAULT,10]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " \+ color=black):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "rp[9]:=plot([[ -4.,-0.075],[-4.,0.075]], " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " linestyle=1,color=black):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "rp[10]:=plots[textplot]([-4.,-0.3 ,`-4`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 92 " \+ font=[HELVETICA,DEFAULT,10],\n color=black): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "rp[11]:=plot([[4.,-0.075],[4.,0 .075]]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " \+ linestyle=1,color=black):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "rp[1 2]:=plots[textplot]([4.,-0.3,`4`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " font=[HELVETICA,DEFAULT,10]," }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 38 " color=black):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "rp[13]:=plot([[-0.1,-4.],[0.1,-4.]] ," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " line style=1,color=black):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "rp[14]:=pl ots[textplot]([-0.25,-3.8,`-4`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " font=[HELVETICA,DEFAULT,10]," }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 38 " color=black):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "rp[15]:=plot([[-0.1,4.],[0.1,4.]], " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " lines tyle=1,color=black):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "rp[16]:=plo ts[textplot]([-0.25,4.0,`4`]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " \+ font=[HELVETICA,DEFAULT,10]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 167 " color=black):\n#Plot fun ctions, lines, points (Note that plotting these\n#first resulted in an intended blue color of the numbers\n#on the axes.)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "rp[17]:=plot(f(x),x=-4..4,-4..4,color=blue):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "rp[18]:=plot(g(x),x=-c..4,-4..4,co lor=red):\nrp[19]:=plot(-g(-x-2*c),x=-4..-c,y=-4..4,color=red):\nrp[20 ]:=plot([[-4,-4],[4,4]],linestyle=2,color=magenta):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "rp[21]:=plots[textplot]([-1.8,2.99,n_str]," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 " font=[HELVE TICA,DEFAULT,11]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 121 " \+ color=blue,align=RIGHT):\nif c >= 0 then\nrp[22]:=plots[tex tplot]([-3.3,2.8,`f(x) = x - `.c_str]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " font=[HELVETICA,DEFAULT,12], " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 111 " color =blue,align=RIGHT):\nelse\nrp[22]:=plots[textplot]([-3.3,2.8,`f(x) = x +`.c_str]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " \+ font=[HELVETICA,DEFAULT,12]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " color=blue,align=RIGHT):\nfi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "rp[23]:=plots[textplot]([-3.4,1.8,`g(x) = ? `]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " fon t=[HELVETICA,DEFAULT,12]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 " \+ color=red,align=RIGHT):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "rp[24]:=plot([[0,f(0)],[f(0),0]],\n li nestyle=2,color=magenta):\nrp[25]:=plot([[0,f(0)]],style=POINT,symbol= CIRCLE,color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "rp[26]:=plot ([[f(0),0]],style=POINT,symbol=CIRCLE,color=red):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 298 "rp[27]:=plot([[2,g(2)],[g(2),2]],\n \+ linestyle=2,color=magenta):\nrp[28]:=plot([[2,g(2)]],style=POINT,symbo l=CIRCLE,color=red):\nrp[29]:=plot([[g(2),2]],style=POINT,symbol=CIRCL E,color=blue):\nrp[30]:=plot([[-2,-g(-(-2)-2*c)],[-g(-(-2)-2*c),-2]], \n linestyle=2,color=magenta):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 200 "rp[31]:=plot([[-2,-g(-(-2)-2*c)]],style=POINT,symbol =CIRCLE,color=red):\nrp[32]:=plot([[-g(-(-2)-2*c),-2]],style=POINT,sym bol=CIRCLE,color=blue):\nmovie_frame[i+1]:=plots[display]([seq(rp[j],j =1..32)]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "od:\nif frame = 0 the n\n##### Create Maple movie.\nreflector_movie[frame]:=plots[display]( " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 175 " [movie_frame[ 1],movie_frame[1],movie_frame[1], \+ seq(movie_frame[j],j=2. .21)," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 " movie_fr ame[21],movie_frame[21],movie_frame[21]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 212 " movie_frame[1],movie_frame[1],movi e_frame[1], \+ seq(movie _frame[j],j=22..41)," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 " \+ movie_frame[41],movie_frame[41],movie_frame[41]], " }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 36 " insequence = true," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " scaling=constrain ed," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " labels=[`` ,``]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " xtickmar ks=0,ytickmarks=0," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " \+ titlefont=[HELVETICA,DEFAULT,14]," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 202 " title=`Inverse functions are reflections in y = x `):\nelse\n##### Create individual frames to export to *.gif s for animated gif or Java movie.\nreflector_movie[frame]:=plots[displ ay](" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 " [movie_fra me[frame]]," }}{PARA 0 "> " 0 "" 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