{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 } {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 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }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 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Outpu t" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "Using Maple for Interpolat ion Polynomials - Lagrange and Newton differences" }}{PARA 0 "" 0 "" {TEXT -1 52 "Data from lynx pelts of Hudson Bay Company 1900-1910" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "with(plots):with(CurveFitting):" }}{PARA 7 "" 1 "" {TEXT -1 50 " Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "lynx:=[[0,4],[1,6.1],[2,9.8],[3,35.2],[4, 59.4],[5,41.7],[6,19],[7,13],[8,8.3],[9,9.1],[10,7.4]];" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#>%%lynxG7-7$\"\"!\"\"%7$\"\"\"$\"#h!\"\"7$\"\"#$ \"#)*F-7$\"\"$$\"$_$F-7$F($\"$%fF-7$\"\"&$\"$<%F-7$\"\"'\"#>7$\"\"(\"# 87$\"\")$\"#$)F-7$\"\"*$\"#\"*F-7$\"#5$\"#uF-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "lynxx:=[0,1,2,3,4,5];lynxy:=[4,6.1,9.8,35.2,59.4 ,41.7];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&lynxxG7(\"\"!\"\"\"\"\"# \"\"$\"\"%\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&lynxyG7(\"\"%$\" #h!\"\"$\"#)*F)$\"$_$F)$\"$%fF)$\"$<%F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "p1:=PolynomialInterpolation(lynx, x);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#p1G,8*&$\"+J7(*HB!#8\"\"\")%\"xG\"#5F*F**&$\"+z _Pg7!#6F*)F,\"\"*F*!\"\"*&$\"+K6&\\f#!\"(F*F,F*F4*&$\"+$z?#=H!#5F*)F, \"\")F*F**&$\"+y&p!orF8F*)F,\"\"#F*F**&$\"+ftPpP!\"*F*)F,\"\"(F*F4*&$ \"+z;BexF8F*)F,\"\"$F*F4*&$\"+)flg'H!\")F*)F,\"\"'F*F**&$\"+JIS,WF8F*) F,\"\"%F*F**&$\"+(4(*pX\"F8F*)F,\"\"&F*F4FYF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "p2:=PolynomialInterpolation(lynxx,lynxy, x, form =Lagrange);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#p2G,.*.\"#I!\"\",&% \"xG\"\"\"F+F(F+,&F*F+\"\"#F(F+,&F*F+\"\"$F(F+,&F*F+\"\"%F(F+,&F*F+\" \"&F(F+F(*.$\"+nmmTD!#5F+F*F+F,F+F.F+F0F+F2F+F+*.$\"+nmmm\")F7F+F*F+F) F+F.F+F0F+F2F+F(*.$\"+LLLLH!\"*F+F*F+F)F+F,F+F0F+F2F+F+*.$\"++++vCF>F+ F*F+F)F+F,F+F.F+F2F+F(*.$\"++++vMF7F+F*F+F)F+F,F+F.F+F0F+F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "expand(p2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,.\"\"%\"\"\"*&$\"+(*****yB!\")F%%\"xGF%F%*&$\"+PL $e%RF)F%)F*\"\"#F%!\"\"*&$\"++++X@F)F%)F*\"\"$F%F%*&$\"*mm;*QF)F%)F*F$ F%F0*&$\"+++++@!#5F%)F*\"\"&F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "PolynomialInterpolation(lynxx,lynxy, x);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,.*&$\"+.+++@!#5\"\"\")%\"xG\"\"&F(F(*&$\"+qmm \"*Q!\"*F()F*\"\"%F(!\"\"*&$\"++++zB!\")F(F*F(F(*&$\"+,++X@F6F()F*\"\" $F(F(*&$\"+ML$e%RF6F()F*\"\"#F(F2F1F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "p3:=PolynomialInterpolation(lynxx,lynxy, x, form=Newt on);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#p3G,&*&,&*&,&*&,&*&,&*&$\"+ .+++@!#5\"\"\"%\"xGF2F2$\"+ommJE!\"*!\"\"F2,&F3F2\"\"$F7F2F2$\"++++]LF 6F2F2,&F3F2\"\"#F7F2F2$\"+++++!)F1F2F2,&F3F2F2F7F2F2$\"#@F7F2F2F3F2F2 \"\"%F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "expand(p3);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#,.*&$\"+.+++@!#5\"\"\")%\"xG\"\"&F(F(* &$\"+qmm\"*Q!\"*F()F*\"\"%F(!\"\"*&$\"++++zB!\")F(F*F(F(*&$\"+,++X@F6F ()F*\"\"$F(F(*&$\"+ML$e%RF6F()F*\"\"#F(F2F1F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "F1:=plot(lynx, style=point, symbol=circle, colou r=blue):\nF2:=plot(p1,x=0..10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "display(\{F1,F2\});" }}{PARA 13 "" 1 "" {GLPLOT2D 253 253 253 {PLOTDATA 2 "6&-%'CURVESG6$7ep7$$\"\"!F)$\"\"%F)7$$\"3ALL$3FWYs#!#>$!3 5-u)*Qej`D!#<7$$\"3WmmmT&)G\\aF/$!32]qbJc#Q8)F27$$\"3m****\\7G$R<)F/$! 33K=Ep8j#G\"!#;7$$\"3GLLL3x&)*3\"!#=$!3YV&)zBH:r;F=7$$\"3$*****\\ilyM; 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