{VERSION 4 0 "IBM INTEL LINUX" "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 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 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 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 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 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 "" {TEXT 256 21 "Examples of programs." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "1) The Eu clidean Algorithm." }}{PARA 0 "" 0 "" {TEXT -1 50 " Let a,b be pol ynomials in x. Compute the GCD:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 300 "MyGCD:=proc(a,b,x)\n local aa;\n # options trace;\n if b=0 then\n a\n elif degree(b,x)>degree(a,x) then\n procname(b, a,x)\n else \n # now degree(a,x) >= degree(b,x),\n # so if \+ we take the remainder the\n # degree goes down:\n aa := rem( a,b,x);\n procname(aa,b,x)\n fi\nend;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&MyGCDGR6%%\"aG%\"bG%\"xG6#%#aaG6\"F,@'/9%\"\"!9$2-%' degreeG6$F19&-F46$F/F6-9!6%F/F1F6C$>8$-%$remG6%F1F/F6-F:6%F>F/F6F,F,F, " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "MyGCD(x^3-1,x^4-1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&!\"\"\"\"\"%\"xGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "MyGCD:=proc(a,b,x)\n if b=0 then a \n else procname( b, rem(a,b,x) ,x)\n fi;\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&MyGCDGR6%%\"aG%\"bG%\"xG6\"F*F*@%/9%\"\"!9$-9!6%F--% $remG6%F/F-9&F6F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "i: =0; j:=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"!" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"jG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 188 "do\n i:=i+1;\n if i>7 then break # go to the en d\n elif i>3 then next # go back to the top\n fi;\n j:=j+1; \+ # this ; is not necessary because of the od\nod; now_we_are_at_the_en d;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"jG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"i G\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"jG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"jG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"%" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"iG\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"iG\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# %6now_we_are_at_the_endG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "S:=0 ;for k from -3 to 9 by 2 do\n S:=S+k^2;\nod;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"SG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG \"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG\"#5" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"SG\"#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG \"#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG\"#X" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"SG\"#%*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG \"$v\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "i:=0; while i < 5 do i:=i+1 od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\" \"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"%" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"iG\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "myREM:=proc(a,b,x)\n local r,q,k;\n options trace;\n r:=a;\n while degree(r,x) >= degree(b,x) do\n ...\n od;\n r\nend;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Complete the above implementation \+ of myREM." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "f:=randpoly(x, degree=10); g:=randpoly(x,degree=5,coeffs=rand(-3..3));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"fG,.*$)%\"xG\"\"(\"\"\"!#%)*&\"#>F*)F(\"\"'F *F**&\"#]F*)F(\"\"&F*!\"\"*&\"#))F*)F(\"\"%F*F**&\"#`F*)F(\"\"$F*F4*& \"#&)F*F(F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,.*$)%\"xG\"\"& \"\"\"!\"$*$)F(\"\"%F*F**&\"\"$F*)F(F0F*!\"\"*&\"\"#F*)F(F4F*F**&F0F*F (F*F*F0F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "rem(f,g,x);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"xG\"\"%\"\"\"#\"$a\"\"\"$*&\" $u\"F()F&F+F(!\"\"*&\"$2\"F(F&F(F(*&#\"$<#F+F(*$)F&\"\"#F(F(F/\"#JF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "myREM(f,g,x); # check if \+ it's the same." }}}}{MARK "9 0 0" 43 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }