{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 "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 Output" -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" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 712 "DetByMinors := proc ( A::Matrix, n0::posint )\n local m, n, i;\n if nargs = 1 then \n \+ m := LinearAlgebra:-RowDimension(A);\n n := LinearAlgebra:-Colum nDimension(A);\n if m<>n or m=0 or n=0 then\n error \"Squar e non-empty Matrix expected\"\n end if;\n else\n n := n0;\n \+ end if;\n if n=1 then\n return A[1,1]\n elif n=2 then \n retur n A[1,1]*A[2,2] - A[1,2]*A[2,1]\n else\n return add( (-1)^(i-1)*A[ 1,i]*DetByMinors(A[2..n,\n [seq(j,j=1..i-1), \+ \+ \+ seq(j,j=i+1..n)]], n-1 ), \n i=1..n );\n end if;\nend proc;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%,DetByMinorsGf*6$ '%\"AG%'MatrixG'%#n0G%'posintG6%%\"mG%\"nG%\"iG6\"F1C$@%/9#\"\"\"C%>8$ -_%.LinearAlgebraG%-RowDimensionG6#9$>8%-_F<%0ColumnDimensionGF>@$550F 9FA/F9\"\"!/FAFJYQASquare~non-empty~Matrix~expectedF1>FA9%@'/FAF6O&F?6 $F6F6/FA\"\"#O,&*&FSF6&F?6$FVFVF6F6*&&F?6$F6FVF6&F?6$FVF6F6!\"\"O-%$ad dG6$*()F[o,&8&F6F6F[oF6&F?6$F6FcoF6-F$6$&F?6$;FVFA7$-%$seqG6$%\"jG/F_p ;F6Fbo-F]p6$F_p/F_p;,&FcoF6F6F6FA,&FAF6F6F[oF6/Fco;F6FAF1F1F1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "DetByMinors( Matrix(2,2,[[a, b],[c,d]]) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"aG\"\"\"%\"dGF &F&*&%\"bGF&%\"cGF&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A \+ := RandomMatrix(3,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'RTAB LEG6$\"([qq%-%'MATRIXG6#7%7%\"#(*\"#b\"#87%!##)\"#o!#l7%!#m\"#E\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Determinant(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"'Qg[" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "DetByMinors(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\" 'Qg[" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "time(Determinant(Ra ndomMatrix(5,5)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"$!\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "time(DetByMinors(RandomMatri x(5,5)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#7!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "for n from 5 to 9 do\n n;\n go odtime[n] := time(Determinant(RandomMatrix(n,n)));\n badtime[n] := t ime(DetByMinors(RandomMatrix(n,n)));\nend do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "gp := plots[logplot]([seq([n,goodtime[n]],n=5..9 )], style=POINT, colour=BLUE,symbolsize=30):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "bp := plots[logplot]([seq([n,badtime[n]],n=5..9) ], style=POINT, colour=RED,symbolsize=30):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 24 "plots[display](\{gp,bp\});" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6&7'7$$\"\"&\"\"!$!+T(3 R#=!\"*7$$\"\"'F*$!+u5eq5F-7$$\"\"(F*$!+!\\:#F-7$F/$!+ \"\\dd/#F-7$F4F+7$F:$!+*RY7s\"F-7$F@$!+-?gP:F--FE6&FGFKFKFHFLFP-%*AXES TICKSG6$FS7O/$!\"#F*Q&.1e-16\"/$!+/+(*)p\"F-Q!Fio/$!+X(yG_\"F-F]p/$!+4 +%zR\"F-F]p/$!+'**H5I\"F-F]p/$!+]([=A\"F-F]p/$!+g>!\\:\"F-F]p/$!+8+\"p 4\"F-F]p/$!+\"\\dd/\"F-F]p/$!\"\"F*Q#.1Fio/$!+V+q*)pF>F]p/$!+^uyG_F>F] p/$!+(3+%zRF>F]p/$!+f**H5IF>F]p/$!+(\\([=AF>F]p/$!++'>!\\:F>F]p/$!*H,5 p*F>F]p/$!*2\\dd%F>F]p/FKQ#1.Fio/$\"+d**H5IF>F]p/$\"+\\D@rZF>F]p/$\"+8 **f?gF>F]p/$\"+T+q*)pF>F]p/$\"+.D^\"y(F>F]p/$\"++/)4X)F>F]p/$\"+r)**3. *F>F]p/$\"+$4DCa*F>F]p/$\"\"\"F*Q%.1e2Fio/$\"+'**H5I\"F-F]p/$\"+b77x9F -F]p/$\"+\"**f?g\"F-F]p/$\"+/+(*)p\"F-F]p/$\"+]7:yF-F]p/$\"+4DCa>F-F]p/$\"\"#F*Q%.1e3Fio/$\"+'**H5I#F-F]p/ $\"+b77xCF-F]p/$\"+\"**f?g#F-F]p/$\"+/+(*)p#F-F]p/$\"+]7:yFF-F]p/$\"+S !)4XGF-F]p/$\"+()**3.HF-F]p/$\"+4DCaHF-F]p" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "n := 'n';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "rsolve( \{C( n)=n*C(n-1), C(2)=2\}, C(n) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&G AMMAG6#,&%\"nG\"\"\"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "convert(%,factorial);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%*factori alG6#,&%\"nG\"\"\"F)F)F)F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "simplify(%,factorial);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-% *factorialG6#,&%\"nG\"\"\"F)F)F)F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%*f actorialG6#,&%\"nG\"\"\"F)F)F)F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "6 0 0" 23 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 4707048 }{RTABLE M7R0 I4RTABLE_SAVE/4707048X,%)anythingG6"6"[gl!"%!!!#*"$"$"#(*!##)!#m"#b"#o"#E"#8!#l ""&F& }