{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 0 289 "ImplicitTaylor2:=proc(f,y,x,y0,n)\nglobal app rox;\nlocal i,G;\nif not(type(simplify(log[2](n+1)),integer))\n then \+ return 'procname(args)'\nend if;\nG:=z->subs(y=z,y-f/diff(f,y));\nappr ox:=y0;\nfor i from 1 to simplify(log[2](n+1)) do\n approx:=G(approx) ;\nend do;\nseries(approx,x=0,n+1);\nend proc:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "02." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Im plicitTaylor2(x^2+y^2-1,y,x,1,7);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "03." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "approx;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 297 "ImplicitTaylor3:=proc(f,y,x,y0,n)\nglobal approx;\nl ocal i,G;\nif not(type(simplify(log[2](n+1)),integer))\n then return \+ 'procname(args)'\nend if;\nG:=z->normal(subs(y=z,y-f/diff(f,y)));\napp rox:=y0;\nfor i from 1 to simplify(log[2](n+1)) do\n approx:=G(approx );\nend do;\nseries(approx,x=0,n+1);\nend proc:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Im plicitTaylor3(x^2+y^2-1,y,x,1,7);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "06." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "approx;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "07." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "ImplicitTaylor3(log(y)-x,y,x,1,7);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "08." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "ImplicitTaylor3(y*exp(y)-x,y,x,0,7);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "09." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Implici tTaylor3(x^2*log(y)+1,y,x,0,7);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "10." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 333 "FastImplicitTayl or:=proc(f,y,x,y0,n)\nglobal approx;\nlocal i,G;\nif not(type(simplify (log[2](n+1)),integer))\n then return 'procname(args)'\nend if;\nG:=z ->normal(subs(y=z,y-f/diff(f,y)));\napprox:=y0;\nfor i from 1 to simpl ify(log[2](n+1)) do\n approx:=convert(series(G(approx),x=0,2^i),polyn om);\nend do;\nseries(approx,x=0,n+1);\nend proc:" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 200 3 "11." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 427 "ImplicitTaylor:=proc(F,y,x,y0,n)\nglobal ableitungen;\nlocal i,ystric h,k,f;\nystrich:=-diff(F,x)/diff(F,y);\nableitungen:=[ystrich];\nf:=no rmal(diff(ystrich,x)+diff(ystrich,y)*ystrich);\nfor i from 1 to n-1 do \n ableitungen:=[op(ableitungen),f];\n f:=normal(diff(f,x)+diff(f,y) *ystrich);\nend do;\ny0+add(limit(limit(ableitungen[k],y=y0),x=0)/k!*x ^k,k=1..n);\nend proc:\n\nst:=time():\nimp1:=ImplicitTaylor(x^2+y^2-1, y,x,1,127):\ntime()-st;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "12." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "st:=time():\nimp2:=Implici tTaylor2(x^2+y^2-1,y,x,1,127):\ntime()-st;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "13." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "st:=tim e():\nimp3:=ImplicitTaylor3(x^2+y^2-1,y,x,1,127):\ntime()-st;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "14." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "st:=time():\nimp4:=FastImplicitTaylor(x^2+y^2-1,y,x,1 ,127):\ntime()-st;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "15." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "[convert(imp1,polynom)-conv ert(imp2,polynom),\n convert(imp1,polynom)-convert(imp3,polynom),\n co nvert(imp1,polynom)-convert(imp4,polynom)];" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 200 3 "16." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "st:=t ime():\nFastImplicitTaylor(x^2+y^2-1,y,x,1,511):\ntime()-st;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "17." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "st:=time():\nseries(sqrt(1-x^2),x=0,511):\ntime()-st; " }}}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }