{VERSION 2 3 "DEC ALPHA UNIX" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{PSTYLE " Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }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 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "d:=3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "N:=array(1..d,1..d,sparse):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "for i to d-1 do N[i,i+1]:=1 \+ od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(N);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7%\"\"!\"\"\"F(7%F(F(F)7%F(F(F (" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "M:=evalm(1+2*N+3*N^2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'MATRIXG6#7%7%\"\"\"\"\"# \"\"$7%\"\"!F*F+7%F.F.F*" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "N; " "I\"NG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "sum((n+1)*x^ n,n=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$,&%\"xG\"\"\"! \"\"F&!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalm((N-1)^( -2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7%\"\"\"\"\"#\" \"$7%\"\"!F(F)7%F,F,F(" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "M^k = (N-1)^(-2*k);" "/)%\"MG%\"kG),&%\"NG\"\"\"\"\"\"!\"\",$*&\"\"#F)F%F)F +" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalm((N-1)^(-2*3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7%\"\"\"\"\"'\"#@7%\" \"!F(F)7%F,F,F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "R[0]:=ev alm((N-1)^(-1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"RG6#\"\"!-%'M ATRIXG6#7%7%!\"\"F-F-7%F'F-F-7%F'F'F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalm(R[0]^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%' MATRIXG6#7%7%\"\"\"\"\"#\"\"$7%\"\"!F(F)7%F,F,F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "l:=convert(series(ln(1+x),x,d),polynom);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"lG,&%\"xG\"\"\"*$F&\"\"##!\"\"F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "L:=evalm(subs(x=M-1,l)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG-%'MATRIXG6#7%7%\"\"!\"\"#\" \"\"7%F*F*F+7%F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "lin alg[exponential](L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7% 7%\"\"\"\"\"#\"\"$7%\"\"!F(F)7%F,F,F(" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "M = exp(L);" "/%\"MG-%$expG6#%\"LG" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 12 "racine carre" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "R^2 = M;" "/*$%\"RG\"\"#%\"MG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "R = R[0]*S;" "/%\"RG*&&F#6#\"\"!\"\"\"%\"SGF(" }}} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "S = R[0]^(-1)*R;" "/%\"SG*&)&%\" RG6#\"\"!,$\"\"\"!\"\"\"\"\"F'F-" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "R[0]*S*R[0]*S = R[0]^2;" "/**&%\"RG6#\"\"!\"\"\"%\"SGF(&F%6#F'F( F)F(*$&F%6#F'\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "S*R[0]*S \+ = R[0];" "/*(%\"SG\"\"\"&%\"RG6#\"\"!F%F$F%&F'6#F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "S:=matrix(d,d,s):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(S);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7%7%-%\"sG6$\"\"\"F+-F)6$F+\"\"#-F)6$F+ \"\"$7%-F)6$F.F+-F)6$F.F.-F)6$F.F17%-F)6$F1F+-F)6$F1F.-F)6$F1F1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "A:=evalm(S&*R[0]&*S);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'MATRIXG6#7%7%,(*$-%\"sG6$\"\" \"F/\"\"#!\"\"*&,&F,F1-F-6$F/F0F1F/-F-6$F0F/F/F/*&,(F,F1F4F1-F-6$F/\" \"$F1F/-F-6$F " 0 "" {MPLTEXT 1 0 48 "sys:=\{seq(seq(A[i,j]=R[0][i,j],j=1..d),i =1..d)\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "inc:=\{seq(seq (s(i,j),j=1..d),i=1..d)\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "sol:=[solve(sys,inc)];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$solG7 $<+/-%\"sG6$\"\"\"\"\"#\"\"!/-F)6$F+F+F+/-F)6$F+\"\"$F-/-F)6$F,F+F-/-F )6$F,F,F+/-F)6$F,F4F-/-F)6$F4F+F-/-F)6$F4F,F-/-F)6$F4F4F+<+F'/F/!\"\"F 1F5/F9FIF;F>FA/FEFI" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "SOL[ 1]:=subs(sol[1],eval(S));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$SOLG6 #\"\"\"-%'MATRIXG6#7%7%F'\"\"!F-7%F-F'F-7%F-F-F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "SOL[2]:=subs(sol[2],eval(S));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$SOLG6#\"\"#-%'MATRIXG6#7%7%!\"\"\"\"!F.7%F.F-F .7%F.F.F-" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "R;" "I\"RG6\"" }}} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "R = R[0];" "/%\"RG&F#6#\"\"!" }} }{EXCHG {PARA 0 "" 0 "" {XPPEDIT 18 0 "R = -R[0];" "/%\"RG,$&F#6#\"\"! !\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "35 0 0 " 0 }{VIEWOPTS 1 1 0 1 1 1803 }