{VERSION 5 0 "SGI MIPS UNIX" "5.0" } {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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 294 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 296 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 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 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple P lot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 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 }} {SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT -1 48 "Maple Summer Workshop 2004 : Programming Tutorial" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Michael Monagan, June 2004." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 147 "A progra m for animating the complex roots of a polynomial on a parameter.\nFir st we compute and plot the complex roots for the following polynomial. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f := x^5-x-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,(*$)%\"xG\"\"&\"\"\"F*F(!\"\"F*F+" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "R := [fsolve(f=0,x,complex) ];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"RG7'^$$!+OV%)[w!#5$!+garCNF) ^$F'$\"+garCNF)^$$\"+XWK7=F)$!+,T&R3\"!\"*^$F0$\"+,T&R3\"F4$\"+yRIn6F4 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "P := map( z-> [Re(z),Im (z)], R );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"PG7'7$$!+OV%)[w!#5$! +garCNF)7$F'$\"+garCNF)7$$\"+XWK7=F)$!+,T&R3\"!\"*7$F0$\"+,T&R3\"F47$$ \"+yRIn6F4$\"\"!F<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "P := \+ POINTS( op(P), COLOR(RGB,1,0,0), SYMBOL(CROSS) );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"PG-%'POINTSG6)7$$!+OV%)[w!#5$!+garCNF+7$F)$\"+garCN F+7$$\"+XWK7=F+$!+,T&R3\"!\"*7$F2$\"+,T&R3\"F67$$\"+yRIn6F6$\"\"!F>-%& COLORG6&%$RGBG\"\"\"F>F>-%'SYMBOLG6#%&CROSSG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "PLOT(P,AXESSTYLE(BOX));" }}{PARA 13 "" 1 "" {INLPLOT "6$-%'POINTSG6)7$$!+OV%)[w!#5$!+garCNF)7$F'$\"+garCNF)7$$\"+X WK7=F)$!+,T&R3\"!\"*7$F0$\"+,T&R3\"F47$$\"+yRIn6F4$\"\"!F<-%&COLORG6&% $RGBG\"\"\"F " 0 "" {MPLTEXT 1 0 15 "f := x^5-a*x+1;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"fG,(*$)%\"xG\"\"&\"\"\"F**&%\"aGF*F(F*!\"\"F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Now suppose we want to animate \+ the above polynomial f(" }{TEXT 296 1 "x" }{TEXT -1 5 ") for" }{TEXT 294 3 " a " }{TEXT -1 12 "= -2..8 for " }{TEXT 295 1 "n" }{TEXT -1 9 " frames. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 602 "RootsAnimatio n := proc(f,x,a::name=range,n::posint)\nlocal t,L,R,h,i,F,style,frames ;\n t := lhs(a); L,R := lhs(rhs(a)),rhs(rhs(a)); \n h := evalf(R-L )/n;\n style := COLOR(RGB,1,0,0), SYMBOL(CROSS);\n for i from 0 to n do\n F[i] := [fsolve(eval(f,t=L+i*h),x,complex)]; \n if type(F[i],list(complex(float))) then\n F[i] := map( z->[Re(z ),Im(z)], F[i] );\n F[i] := PLOT( POINTS(op(F[i]), style ) ); \n else F[i] := PLOT(POINTS()); # empty frame\n fi;\n o d;\n frames := [seq(F[i],i=0..n)];\n plots[display]( frames, inseq uence=true, args[5..nargs] );\nend: \n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "RootsAnimation(x^5-a*x+1,x,a=-2..6,50,axes=boxed );" }}{PARA 13 "" 1 "" {INLPLOT "6$-%(ANIMATEG6U7#-%'POINTSG6)7$$!+*oN (=q!#5$!+z>(pz)F-7$F+$\"+z>(pz)F-7$$!+f.*Q'[F-$\"\"!F77$$\"+o3o]%*F-$! +W^DZ$*F-$!+%GF46'F-$!+d\"ygg)F-7$Fcp$\"+d\"ygg)F-7$$!+d0, ZgF-F67$$\"+$zCW8*F-$!+laBi!)F-7$F^q$\"+laBi!)F-F@FE7#-F(6)7$$!+w4()* \\'F-F67$$!+xHKvdF-$!+C`l)e)F-7$F\\r$\"+C`l)e)F-7$$\"+l%e_-*F-$!+Q)>Z) yF-7$Fdr$\"+Q)>Z)yF-F@FE7#-F(6)7$$!+S(>i'pF-F67$$!+QOTJaF-$!+,L>,')F-7 $Fbs$\"+,L>,')F-7$$\"+3N_9*)F-$!+P)ovp(F-7$Fjs$\"+P)ovp(F-F@FE7#-F(6)7 $$!+CJHLuF-F67$$!+Et)e3&F-$!+j?nW')F-7$Fht$\"+j?nW')F-7$$\"+()Q`-))F-$ !+j!G)*\\(F-7$F`u$\"+j!G)*\\(F-F@FE7#-F(6)7$$!+,_q*)yF-F67$$!+S;([u%F- $!+_9p<()F-7$F^v$\"+_9p<()F-7$$\"+TUs*o)F-$!+cAX!H(F-7$Ffv$\"+cAX!H(F- F@FE7#-F(6)7$$!+q/LF$)F-F67$$!+2E,8WF-$!+\")zK<))F-7$Fdw$\"+\")zK<))F- 7$$\"+Uynw&)F-$!+[9JoqF-7$F\\x$\"+[9JoqF-F@FE7#-F(6)7$$!+aPlT()F-F67$$ !+@zK$4%F-$!+(pg,%*)F-7$Fjx$\"+(pg,%*)F-7$$\"+)zaTY)F-$!+([0A$oF-7$Fby $\"+([0A$oF-F@FE7#-F(6)7$$!+ms1J\"*F-F67$$!+c=e(y$F-$!+')R(H3*F-7$F`z$ \"+')R(H3*F-7$$\"+*[:JN)F-$!+j%))3e'F-7$Fhz$\"+j%))3e'F-F@FE7#-F(6)7$$ !+Dp'e\\*F-F67$$!+&p(z'\\$F-$!+hP.V#*F-7$Ff[l$\"+hP.V#*F-7$$\"+e6tW#)F -$!+F?58jF-7$F^\\l$\"+F?58jF-F@FE7#-F(6)7$$!+(3*RP)*F-F67$$!++6n@KF-$! 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