{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "Text" -1 200 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{PSTYLE "Normal" -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 2 0 2 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "01." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 27 "series(arctan(x)^2,x=0,11);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 4 "02. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 475 "read \"FPS.mpl\";\nwith(gfun):\n\nTPS:=proc(f,x,ord)\nlocal DE,F, RE,A,n,rules,i;\nDE:=HolonomicDE(f,F(x));\nRE:=diffeqtorec(DE,F(x),A(k ));\nif type(RE,set)\n then RE:=op(select(has,RE,k))\nend if;\nn:=max (op(map(z->op(1,z)-k,select(has,indets(RE),A))));\nRE:=solve(RE,A(k+n) );\nrules:=\{seq(A(i)=limit(diff(f,[x$i]),x=0)/i!,i=0..n-1)\}; \nfor i from n to ord do\n rules:=\{op(rules),A(i)=subs(rules,subs(k=i-n,RE) )\}\nend do;\nsubs(rules,add(A(i)*x^i,i=0..ord))\nend proc:\n\nTPS(arc tan(x)^2,x,10);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "03." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "start:=time():\nseries(arcta n(x)^2,x=0,500):\ntime()-start;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "start:=time():\nT PS(arctan(x)^2,x,500):\ntime()-start;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "series( exp(x)*cos(x),x=0,20);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "06." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "TPS(exp(x)*cos(x),x,20);" } }}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "07." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 59 "start:=time():\nseries(exp(x)*cos(x),x=0,250):\ntim e()-start;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "08." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "start:=time():\nTPS(exp(x)*cos(x),x ,250):\ntime()-start;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "09." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "start:=time():\nps:=FPS(exp( x)*cos(x),x,k);\ntime()-start;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "10." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "start:=time():\nsum (op(1,ps),k=0..250):\ntime()-start;" }}}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }