{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 } {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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{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 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 "" {MPLTEXT 1 0 40 "x:=[-3,-1,0,2,5,9]: \+ y:=[6,2,-1,4,12,18]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "for i to 5 do\nfor j to 6-i do y[j]:=(y[j+1]-y[j])/(x[j+i]-x[j]) end do; \+ print(y[1]) end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!\"\"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#8\"#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!#6\"$?\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#V\"%?V" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "pol:=6-2*(z-x[1])-1/3*mul(z-x[j],j=1..2)+13/30*mul(z -x[j],j=1..3)\n-11/120*mul(z-x[j],j=1..4)+43/4320*mul(z-x[j],j=1..5); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polG,,*&\"\"#\"\"\"%\"zGF(!\"\" *(\"\"$F*,&F)F(F,F(F(,&F)F(F(F(F(F**,\"#8F(\"#IF*F-F(F.F(F)F(F(*.\"#6F (\"$?\"F*F-F(F.F(F)F(,&F)F(F'F*F(F**0\"#VF(\"%?VF*F-F(F.F(F)F(F5F(,&F) F(\"\"&F*F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "seq(eval(p ol,z=x[j]),j=1..6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6(\"\"'\"\"#!\"\" \"\"%\"#7\"#=" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q2" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "x:=[-3,-1,0,2,5,9]: y:=[6,2, -1,4,12,18]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "f[1]:=x->1. : f[2]:=x->x: f[3]:=x->sin(x*1.): f[4]:=x->cos(x*1.):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "C:=matrix(4,4):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "for i to 4 do for j to 4 do C[i,j]:=add(f[i ](x[k])*f[j](x[k]),k=1..6) od od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "B:=[seq(add(y[k]*f[i](x[k]),k=1..6),i=1..4)]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have bee n redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "A:=augment(C,B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'mat rixG6#7&7'$\"\"'\"\"!$\"#7F,$!+eN*4?'!#5$!+O50L\\F1$\"#TF,7'F-\"$?\"$ \"+c3(y*>!\"*$!+=*zW=&F:\"$5#7'F/F8$\"+'\\(=WEF:$!+\"RY3M\"F:$!+w3V\") HF:7'F2F;FA$\"+.D\"eN$F:$!+?O._?!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "A:=stackmatrix(A,[a,b,c,d,_]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7'7'$\"\"'\"\"!$\"#7F,$!+eN*4?'!#5$!+ O50L\\F1$\"#TF,7'F-\"$?\"$\"+c3(y*>!\"*$!+=*zW=&F:\"$5#7'F/F8$\"+'\\(= WEF:$!+\"RY3M\"F:$!+w3V\")HF:7'F2F;FA$\"+.D\"eN$F:$!+?O._?!\")7'%\"aG% \"bG%\"cG%\"dG%\"_G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A:=s waprow(A,1,2): A:=swapcol(A,1,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"AG-%'matrixG6#7'7'\"$?\"$\"#7\"\"!$\"+c3(y*>!\"*$!+=*zW=&F0\"$5#7'F +$\"\"'F-$!+eN*4?'!#5$!+O50L\\F9$\"#TF-7'F.F7$\"+'\\(=WEF0$!+\"RY3M\"F 0$!+w3V\")HF07'F1F:FA$\"+.D\"eN$F0$!+?O._?!\")7'%\"bG%\"aG%\"cG%\"dG% \"_G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "for j from 2 to 4 d o A:=addrow(A,1,j,-A[j,1]/A[1,1]) end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7'7'\"$?\"$\"#7\"\"!$\"+c3(y*>!\"*$!+ =*zW=&F0\"$5#7'$F-F-$\"+++++[F0$!+9W'))>)!#5$\"*#))G9DF:$\"+++++?!\")7 'F.$!+eN*4?'F:$\"+'\\(=WEF0$!+\"RY3M\"F0$!+w3V\")HF07'F1$!+O50L\\F:FE$ \"+.D\"eN$F0$!+?O._?F?7'%\"bG%\"aG%\"cG%\"dG%\"_G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7'7'\"$?\"$\"#7\"\"!$\"+c3(y*>!\"*$!+ =*zW=&F0\"$5#7'$F-F-$\"+++++[F0$!+9W'))>)!#5$\"*#))G9DF:$\"+++++?!\")7 'F5F8$\"+'4D4h#F0$!+!QIXD\"F0$!+u[qxkF07'F1$!+O50L\\F:$!+\"RY3M\"F0$\" +.D\"eN$F0$!+?O._?F?7'%\"bG%\"aG%\"cG%\"dG%\"_G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7'7'\"$?\"$\"#7\"\"!$\"+c3(y*>!\"*$!+ =*zW=&F0\"$5#7'$F-F-$\"+++++[F0$!+9W'))>)!#5$\"*#))G9DF:$\"+++++?!\")7 'F5F8$\"+'4D4h#F0$!+!QIXD\"F0$!+u[qxkF07'F5F;FC$\"+OA#=8$F0$!+M'\\Z9\" F?7'%\"bG%\"aG%\"cG%\"dG%\"_G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "for j from 3 to 4 do A:=addrow(A,2,j,-A[j,2]/A[2,2]) end do;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7'7'\"$?\"$\"#7\"\"! $\"+c3(y*>!\"*$!+=*zW=&F0\"$5#7'$F-F-$\"+++++[F0$!+9W'))>)!#5$\"*#))G9 DF:$\"+++++?!\")7'F5F5$\"+f0)3Z#F0$!+JdB]7F0$!+o8^hIF07'F5F;$!+!QIXD\" F0$\"+OA#=8$F0$!+M'\\Z9\"F?7'%\"bG%\"aG%\"cG%\"dG%\"_G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7'7'\"$?\"$\"#7\"\"!$\"+c3(y*>! \"*$!+=*zW=&F0\"$5#7'$F-F-$\"+++++[F0$!+9W'))>)!#5$\"*#))G9DF:$\"+++++ ?!\")7'F5F5$\"+f0)3Z#F0$!+JdB]7F0$!+o8^hIF07'F5F5FC$\"+N0pJJF0$!+PeAb6 F?7'%\"bG%\"aG%\"cG%\"dG%\"_G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "A:=swaprow(A,3,4): A:=swapcol(A,3,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7'7'\"$?\"$\"#7\"\"!$!+=*zW=&!\"*$\"+ c3(y*>F0\"$5#7'$F-F-$\"+++++[F0$\"*#))G9D!#5$!+9W'))>)F:$\"+++++?!\")7 'F5F5$\"+N0pJJF0$!+JdB]7F0$!+PeAb6F?7'F5F5FC$\"+f0)3Z#F0$!+o8^hIF07'% \"bG%\"aG%\"dG%\"cG%\"_G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "A:=addrow(A,3,4,-A[4,3]/A[3,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"AG-%'matrixG6#7'7'\"$?\"$\"#7\"\"!$!+=*zW=&!\"*$\"+c3(y*>F0\"$5#7'$ F-F-$\"+++++[F0$\"*#))G9D!#5$!+9W'))>)F:$\"+++++?!\")7'F5F5$\"+N0pJJF0 $!+JdB]7F0$!+PeAb6F?7'F5F5F5$\"+e0wr>F0$!+-ATtwF07'%\"bG%\"aG%\"dG%\"c G%\"_G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "c:=A[4,5]/A[4,4]; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG$!+'=b;*Q!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "d:=(A[3,5]-A[3,4]*c)/A[3,3];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG$!+tVXU_!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "a:=(A[2,5]-A[2,4]*c-A[2,3]*d)/A[2,2];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG$\"+<[RHN!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "b:=(A[1,5]-A[1,4]*c-A[1,3]*d-A[1,2]*a)/A[ 1,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG$\"+%Rd`B\"!\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "seq(y[k]-(a*f[1](x[k])+b*f[2 ](x[k])+c*f[3](x[k])+d*f[4](x[k])),k=1..6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6($\"*hk\\P%!\"*$!*f@CO(F%$\"*c&fIrF%$!*h$oIkF%$\")^;5\\F %$\"*WGlz\"F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q3" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "L[0]:=1: alpha[0]:=2:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "for i to 4 do L[i]:=X^i-add (int(X^i*L[k],X=-1..1)*L[k]/alpha[k],k=0..i-1);\nalpha[i]:=int(L[i]^2, X=-1..1) end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f:=eval (1/(1.+x^2),x=1+2*X):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "a: =[seq(int(f*L[k],X=-1..1)/alpha[k],k=0..4)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG7'$\"+S)4h3&!#5$!+u'o9h%F($!+?AFkAF($\"+@7r3')F($ !+2!fvm&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "sqrt((int(f^2 ,X=-1..1)-evalm(a&*[seq(int(f*L[k],X=-1..1),k=0..4)]))/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+I0<1P!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "pol:=expand(eval(evalm(a&*[seq(L[k],k=0..4)]),X=(x-1) /2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polG,,$\"+><_h%*!#5\"\"\"* &$\"+%**3+a\"F(F)%\"xGF)!\"\"*&$\"+hC>0ZF(F))F-\"\"#F)F.*&$\"+b'yH\\#F (F))F-\"\"$F)F)*&$\"+zVAUN!#6F))F-\"\"%F)F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(pol-1/(1+x^2),x=-1..3);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6%-%'CURVESG6$7ep7$$!\"\"\"\"!$!3E+ +!4%G'3b\"!#=7$$!3%pmm\"HU,\"*)*F-$!334O(>_>YU\"F-7$$!3!RLL$e%G?y*F-$! 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