{VERSION 5 0 "IBM INTEL NT" "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 "" -1 256 "" 1 24 0 0 0 0 1 1 1 0 0 0 0 0 0 1 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple O utput" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }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 1 }1 0 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 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 34 "Nat\374rliche und periodi sche Splines" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "restart; wi th(plots):readlib(spline):with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have bee n redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "x:=[1,4,5,7,9];\ny:=[4,2,1,9,4];\nn:=[seq(i,i=1..nops(x))];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG7'\"\"\"\"\"%\"\"&\"\"(\"\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG7'\"\"%\"\"#\"\"\"\"\"*F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG7'\"\"\"\"\"#\"\"$\"\"%\"\"&" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sn:=spline(x,y,t,cubic);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#snG-%*PIECEWISEG6&7$,*#\"%.;\"$(Q \"\"\"*&#\"#Z\"$s\"F-%\"tGF-!\"\"*&#\"$.#\"%K5F-*$)F2\"\"#F-F-F-*&#F6 \"%'4$F-*$)F2\"\"$F-F-F32F2\"\"%7$,*#\"%dR\"#VF3*&#\"&vq$\"$;&F-F2F-F- *&#\"%Nh\"$W$F-F8F-F3*&#\"%$[\"F7F-F>F-F-2F2\"\"&7$,*#\"'^PK\"%w8F-*&# \"'vS^\"%GTF-F2F-F3*&#\"&0&HFYF-F8F-F-*&#\"%x[FgnF-F>F-F32F2\"\"(7$,*# \"'j()\\FYF3*&#\"'VMaFgnF-F2F-F-*&#\"&`3#FYF-F8F-F3*&#\"%F-F- %*otherwiseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 180 "ks:=plot(t ,t=0..10, 0..10, labels=[``,``],color=white):\npt:=plot([seq([x[i],y[i ]],i=1..nops(x))], style=point, symbol=diamond, color=blue):\nbs:=plot (sn,t=0..10):\ndisplay(ks,bs,pt);" }}{PARA 13 "" 1 "" {GLPLOT2D 600 265 265 {PLOTDATA 2 "6'-%'CURVESG6$7S7$$\"\"!F)F(7$$\"3emmm;arz@!#=F+7 $$\"3[LL$e9ui2%F-F/7$$\"3nmmm\"z_\"4iF-F27$$\"39ommT&phN)F-F57$$\"3KLL e*=)H\\5!#Y2aF:Fbp7$$\"3Znm;zXu9cF:Fep7$$\"34+++]y))GeF:F hp7$$\"3H++]i_QQgF:F[q7$$\"3b++D\"y%3TiF:F^q7$$\"3+++]P![hY'F:Faq7$$\" 3iKLL$Qx$omF:Fdq7$$\"3Y+++v.I%)oF:Fgq7$$\"3?mm\"zpe*zqF:Fjq7$$\"3;,++D \\'QH(F:F]r7$$\"3%HL$e9S8&\\(F:F`r7$$\"3s++D1#=bq(F:Fcr7$$\"3\"HLL$3s? 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