{VERSION 4 0 "IBM INTEL NT" "4.0" } {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 "" 0 1 0 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 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "m:=5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "S[1]:=[[1],[2]];\nfor j from 2 to m do\n S[j]:=[[op(S[j-1][ 1]),1],seq([op(S[j-1][i]),2], i=1..nops(S[j-1]))];\n print(seq(binom ial(j,i), i=0..j)); \n od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"S G6#\"\"\"7$7#F'7#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"SG6#\" \"#7%7$\"\"\"F*7$F*F'7$F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\" \"\"#F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"SG6#\"\"$7&7%\"\"\"F*F *7%F*F*\"\"#7%F*F,F,7%F,F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6&\"\"\" \"\"$F$F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"SG6#\"\"%7'7&\"\"\"F *F*F*7&F*F*F*\"\"#7&F*F*F,F,7&F*F,F,F,7&F,F,F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6'\"\"\"\"\"%\"\"'F$F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>&%\"SG6#\"\"&7(7'\"\"\"F*F*F*F*7'F*F*F*F*\"\"#7'F*F*F*F,F,7'F*F*F,F, F,7'F*F,F,F,F,7'F,F,F,F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6(\"\"\"\" \"&\"#5F%F$F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)-> exp(x*y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6$%\"xG%\"yG6\"6$% )operatorG%&arrowGF)-%$expG6#*&9$\"\"\"9%F2F)F)F)" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 19 "D[op(S[5][1])] (f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF'*&)9%\"\"&\"\"\" -%$expG6#*&9$F/F-F/F/F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "for j from 0 to m do\n binomial(m,j)*D[op(S[m][j+1])](f)(x,y);\n od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%\"yG\"\"&\"\"\"-%$expG6# *&%\"xGF'F%F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&)%\"yG\"\"$\"\" \"-%$expG6#*&%\"xGF(F&F(F(\"#?**\"\"&F(F-F()F&\"\"%F(F)F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&%\"yG\"\"\"-%$expG6#*&%\"xGF&F%F&F&\"#g* *F,F&F+F&)F%\"\"#F&F'F&F&**\"#5F&)F+F/F&)F%\"\"$F&F'F&F&" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,(*&%\"xG\"\"\"-%$expG6#*&F%F&%\"yGF&F&\"#g**F,F &)F%\"\"#F&F+F&F'F&F&**\"#5F&)F%\"\"$F&)F+F/F&F'F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&)%\"xG\"\"$\"\"\"-%$expG6#*&F&F(%\"yGF(F(\"#?** \"\"&F()F&\"\"%F(F-F(F)F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%\"x G\"\"&\"\"\"-%$expG6#*&F%F'%\"yGF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "5 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }