{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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 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 "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{CSTYLE "Help Head ing" -1 26 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{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 "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Out put" -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 "Bullet Item" -1 15 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 3 3 1 0 1 0 2 2 15 2 }} {SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 10 "Function: " }{TEXT -1 64 "factrix - take out common scalar factors from a matrix or vector" }} {PARA 0 "" 0 "" {TEXT 26 18 "Calling sequence: " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 12 " factrix(M);" }}{PARA 0 "" 0 "" {TEXT 26 11 "Paramet ers:" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{MPLTEXT 0 21 1 "M" }{TEXT -1 109 " - a Matrix, Vector, matrix, vector, list or listlist, or an e xpression that evaluates to one of these under " }{MPLTEXT 0 21 5 "eva lm" }{TEXT -1 1 "." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 26 13 "Descriptio n: " }}{PARA 15 "" 0 "" {TEXT -1 18 "If the entries of " }{MPLTEXT 0 21 1 "M" }{TEXT -1 22 " have a scalar factor " }{MPLTEXT 0 21 1 "f" } {TEXT -1 48 " in common, the result of this function will be " } {MPLTEXT 0 21 3 "f*N" }{TEXT -1 5 " (or " }{MPLTEXT 0 21 3 "f.N" } {TEXT -1 31 " for a Matrix or Vector) where " }{MPLTEXT 0 21 5 "f*N=M " }{TEXT -1 6 ", and " }{MPLTEXT 0 21 1 "N" }{TEXT -1 22 " has the sam e type as " }{MPLTEXT 0 21 1 "M" }{TEXT -1 1 "." }}{PARA 15 "" 0 "" {TEXT -1 233 "Both numerical and symbolic factors are extracted. Howe ver, in the case of a Matrix or Vector, if the result is evaluated any constant factor will be put back into the Matrix or Vector. You can \+ separate the factors, e.g. by using " }{MPLTEXT 0 21 17 "convert(..., list)" }{TEXT -1 209 ", in the same command. In the case of a list or listlist, a numeric factor can't be extracted if there is no symbolic factor, because Maple immediately puts the numeric factor back into t he list or listlist. " }}{PARA 15 "" 0 "" {TEXT -1 96 "When some entri es are fractions, everything is put over a common denominator which is extracted." }}{PARA 15 "" 0 "" {TEXT -1 166 "There are difficulties w ith factoring when floating-point coefficients are involved. This fun ction treats any two different floats as independent (even 1.0 and 2.0 )." }}{PARA 15 "" 0 "" {TEXT -1 29 "This function is part of the " } {TEXT 256 22 "Maple Advisor Database" }{TEXT -1 9 " library." }}} {SECT 0 {PARA 3 "" 0 "" {TEXT 26 9 "Examples:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "factrix(matrix([[3/4*t^2,6*t^3],[9*q*(t+t^4),3/7 *t]]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%\"tG\"\"\"-%'matrixG6# 7$7$,$F%\"\"(,$*$)F%\"\"#F&\"#c7$,&%\"qG\"#%)*(F6F&)F%\"\"$F&F5F&F&\" \"%F&#F9\"#G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "factrix(Mat rix([[3/4*t^2,6*t^3],[9*q*(t+t^4),3/7*t]]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\".G6$,$%\"tG#\"\"$\"#G-%'RTABLEG6$\"(%)3,)-%'MATRIXG 6#7$7$,$F'\"\"(,$*$)F'\"\"#\"\"\"\"#c7$,&%\"qG\"#%)*(F?F:)F'F)F:F>F:F: \"\"%" }}}{PARA 0 "" 0 "" {TEXT -1 84 "Note that evaluating this resul t puts the constant factor 3/28 back into the Matrix." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "%;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\" .G6$%\"tG-%'RTABLEG6$\")oV1>-%'MATRIXG6#7$7$,$F&#\"\"$\"\"%,$*$)F&\"\" #\"\"\"\"\"'7$,&%\"qG\"\"**(F=F8)F&F2F8F " 0 " " {MPLTEXT 1 0 69 "convert(factrix(Matrix([[3/4*t^2,6*t^3],[9*q*(t+t^4 ),3/7*t]])),list);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$,$%\"tG#\"\"$ \"#G-%'RTABLEG6$\")7i?>-%'MATRIXG6#7$7$,$F%\"\"(,$*$)F%\"\"#\"\"\"\"#c 7$,&%\"qG\"#%)*(F=F8)F%F'F8F " 0 "" {MPLTEXT 1 0 19 "factrix([2/3,4/3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$#\"\"#\"\"$#\"\"%F&" }}}{PARA 0 "" 0 "" {TEXT -1 31 "But it would work for a vector:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "factrix(vector([2/3,4/3]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%'vectorG6#7$\"\"\"\"\"##F)\"\"$" }}}{PARA 0 "" 0 " " {TEXT -1 30 "Some more complicated factors:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "factrix(matrix([[x^2+x, x^3+x^2], \n \+ [x^3+2*x^2+x, x^3+3*x^2+3*x+1], \n [w*x^2+2*w*x+w, 3*x+2+x^2]]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"F&F& F&-%'matrixG6#7%7$F%*$)F%\"\"#F&7$,&F,F&F%F&,(F,F&*&F.F&F%F&F&F&F&7$,& *&%\"wGF&F%F&F&F6F&,&F%F&F.F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "factrix(vector([1+sqrt(2),3+2*sqrt(2)]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&\"\"\"F%*$-%%sqrtG6#\"\"#F%F%F%-%'vectorG6#7$F%F$F% " }}}{PARA 0 "" 0 "" {TEXT -1 33 "Removing a floating-point factor:" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "factrix([15.3*x,15.3*x*y]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%\"xG\"\"\"7$F&%\"yGF&$\"$`\"! \"\"" }}}{PARA 0 "" 0 "" {TEXT -1 51 "However, 4.6 and 2.3 are not rec ognized as related." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "factr ix([4.6*x,2.3*x]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"xG\"\"\"7$$ \"#Y!\"\"$\"#BF)F%" }}}{PARA 0 "" 0 "" {TEXT -1 33 "Try converting to \+ rational first:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "factrix(c onvert([4.6*x,2.3*x],rational));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$ *&%\"xG\"\"\"7$\"\"#F&F&#\"#B\"#5" }}}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 10 "See also: " }{HYPERLNK 17 "array" 2 "array" "" }{TEXT -1 2 ", \+ " }{HYPERLNK 17 "dot" 2 "dot" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "facto r" 2 "factor" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "list" 2 "list" "" } {TEXT -1 2 ", " }{HYPERLNK 17 "matrix" 2 "matrix" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "Matrix" 2 "Matrix" "" }{TEXT -1 3 ", " }{HYPERLNK 17 " vector" 2 "vector" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "Vector" 2 "Vecto r" "" }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 22 "Maple Advisor Database" }{TEXT -1 18 " R. Israel, 1998\n" }}}}{MARK "3 0 3" 2 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 8010884 19064368 19206212 }{RTABLE M6R0 I4RTABLE_SAVE/8010884X,%)anythingG6"6"][[[[[p%"#"#,$%"tG""(,&%"qG"#%)*&F(""$F+" ""F,,$*$F(""#"#c""%F& } {RTABLE M6R0 I5RTABLE_SAVE/19064368X,%)anythingG6"6"][[[[[p%"#"#,$%"tG#""$""%,&%"qG""**&F(F* F-"""F.,$*$F(""#""'#F*""(F& } {RTABLE M6R0 I5RTABLE_SAVE/19206212X,%)anythingG6"6"][[[[[p%"#"#,$%"tG""(,&%"qG"#%)*&F(""$F+ """F,,$*$F(""#"#c""%F& }