{VERSION 4 0 "SUN SPARC SOLARIS" "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 "" 1 12 0 128 128 1 0 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 "" -1 256 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 261 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 12 0 0 0 0 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "Courier" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 1 14 0 0 0 0 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 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 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 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 2 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 2 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 2 }} {SECT 0 {SECT 0 {PARA 3 "" 0 "" {TEXT 257 10 "Function: " }{TEXT 262 54 "RefPkg[Ref] - compute the row echelon form of a matrix" }}{PARA 0 "" 0 "" {TEXT 256 17 "Calling Sequence:" }}{PARA 0 "" 0 "" {TEXT 263 14 "RefPkg[Ref](A)" }}{PARA 0 "" 0 "" {TEXT 264 17 "RefPkg[Ref](A, m) " }}{PARA 0 "" 0 "" {TEXT 258 11 "Parameters:" }}{PARA 0 "" 0 "" {TEXT 265 4 "A -" }{TEXT -1 9 " a Matrix" }}{PARA 0 "" 0 "" {TEXT 266 4 "m -" }{TEXT -1 23 " a non-negative integer" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 259 12 "Description:" }}{PARA 256 "" 0 "" {TEXT -1 134 "The call Ref(A) returns the row echelon form of the matrix A, whe re elimination stops after the last row/column, whichever comes first " }}{PARA 257 "" 0 "" {TEXT -1 139 "The call Ref(A,m) returns the row \+ echelon form of the matrix A, where elimination stops in column m, unl ess it reaches the bottom row first" }}{PARA 258 "" 0 "" {TEXT -1 79 " if infolevel[RefPkg] > 2 a trace of the Gaussian elimination process i s printed" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 260 9 "Examples:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "with(RefPkg, Ref);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#%$RefG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "infolevel['RefPkg']:=3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "B := Matrix([[1, 1, 1, 1, 1, 1],[-1, -1, 0, 0, 1, -1 ],[-2, -2, 0, 0, 3, 1],[0,0,1,1,3,-1],[1, 1, 2, 2,4,1]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'RTABLEG6$\"(+-\"e-%'MATRIXG6#7'7(\"\" \"F.F.F.F.F.7(!\"\"F0\"\"!F1F.F07(!\"#F3F1F1\"\"$F.7(F1F1F.F.F4F07(F.F .\"\"#F7\"\"%F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Ref(B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%3Searching~column~1G" }}{PARA 11 " " 1 "" {XPPMATH 20 "6%%3Added~row~1~times~G\"\"\"%*~to~row~2G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"(c'=e-%'MATRIXG6#7'7(\" \"\"F,F,F,F,F,7(\"\"!F.F,F,\"\"#F.7(!\"#F1F.F.\"\"$F,7(F.F.F,F,F2!\"\" 7(F,F,F/F/\"\"%F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%3Added~row~1~tim es~G\"\"#%*~to~row~3G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$ \"(c'=e-%'MATRIXG6#7'7(\"\"\"F,F,F,F,F,7(\"\"!F.F,F,\"\"#F.7(F.F.F/F/ \"\"&\"\"$7(F.F.F,F,F2!\"\"7(F,F,F/F/\"\"%F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%3Added~row~1~times~G\"\"!%*~to~row~4G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"(c'=e-%'MATRIXG6#7'7(\"\"\"F,F,F,F,F ,7(\"\"!F.F,F,\"\"#F.7(F.F.F/F/\"\"&\"\"$7(F.F.F,F,F2!\"\"7(F,F,F/F/\" \"%F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%3Added~row~1~times~G!\"\"%*~ to~row~5G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"(c'=e-%'MAT RIXG6#7'7(\"\"\"F,F,F,F,F,7(\"\"!F.F,F,\"\"#F.7(F.F.F/F/\"\"&\"\"$7(F. F.F,F,F2!\"\"7(F.F.F,F,F2F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%3Searc hing~column~2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%3Searching~column~3 G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%3Added~row~2~times~G!\"#%*~to~ro w~3G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"(c'=e-%'MATRIXG6 #7'7(\"\"\"F,F,F,F,F,7(\"\"!F.F,F,\"\"#F.7(F.F.F.F.F,\"\"$7(F.F.F,F,F1 !\"\"7(F.F.F,F,F1F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%3Added~row~2~t imes~G!\"\"%*~to~row~4G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6 $\"(c'=e-%'MATRIXG6#7'7(\"\"\"F,F,F,F,F,7(\"\"!F.F,F,\"\"#F.7(F.F.F.F. F,\"\"$7(F.F.F.F.F,!\"\"7(F.F.F,F,F1F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%3Added~row~2~times~G!\"\"%*~to~row~5G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"(c'=e-%'MATRIXG6#7'7(\"\"\"F,F,F,F,F,7(\" \"!F.F,F,\"\"#F.7(F.F.F.F.F,\"\"$7(F.F.F.F.F,!\"\"7(F.F.F.F.F,F." }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%3Searching~column~4G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%3Searching~column~5G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%3Added~row~3~times~G!\"\"%*~to~row~4G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"(c'=e-%'MATRIXG6#7'7(\"\"\"F,F,F,F,F ,7(\"\"!F.F,F,\"\"#F.7(F.F.F.F.F,\"\"$7(F.F.F.F.F.!\"%7(F.F.F.F.F,F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%3Added~row~3~times~G!\"\"%*~to~row~ 5G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"(c'=e-%'MATRIXG6#7 '7(\"\"\"F,F,F,F,F,7(\"\"!F.F,F,\"\"#F.7(F.F.F.F.F,\"\"$7(F.F.F.F.F.! \"%7(F.F.F.F.F.!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%3Searching~col umn~6G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%3Added~row~4~times~G#!\"$\" \"%%*~to~row~5G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"(c'=e -%'MATRIXG6#7'7(\"\"\"F,F,F,F,F,7(\"\"!F.F,F,\"\"#F.7(F.F.F.F.F,\"\"$7 (F.F.F.F.F.!\"%7(F.F.F.F.F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RT ABLEG6$\"(c'=e-%'MATRIXG6#7'7(\"\"\"F,F,F,F,F,7(\"\"!F.F,F,\"\"#F.7(F. F.F.F.F,\"\"$7(F.F.F.F.F.!\"%7(F.F.F.F.F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "infolevel['RefPkg']:=1: Ref(B,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"(S'Hg-%'MATRIXG6#7'7(\"\"\"F,F,F,F,F ,7(\"\"!F.F,F,\"\"#F.7(F.F.F/F/\"\"&\"\"$7(F.F.F,F,F2!\"\"7(F.F.F,F,F2 F." }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 261 10 "See Also: " }{HYPERLNK 17 "RefPkg[XRef]" 2 "RefPkg[XRef]" "" }{TEXT 267 2 ", " }{HYPERLNK 17 "RefPkg[MySolve]" 2 "RefPkg[MySolve]" "" }}}}{MARK "0 0 1" 8 } {VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 } {RTABLE_HANDLES 5810200 5818656 6029640 }{RTABLE M6R0 I4RTABLE_SAVE/5810200X,%)anythingG6"6"][[[[[p?"&"'"""!""!"#""!F'F'F(F)F*F'F'F*F *F'""#F'F*F*F'F+F'F'""$F,""%F'F(F'F(F'F& } {RTABLE M6R0 I4RTABLE_SAVE/5818656X,%)anythingG6"6"][[[[[p?"&"'"""""!F(F(F(F'F(F(F(F(F'F'F(F (F(F'F'F(F(F(F'""#F'F(F(F'F(""$!"%F(F& } {RTABLE M6R0 I4RTABLE_SAVE/6029640X,%)anythingG6"6"][[[[[p?"&"'"""""!F(F(F(F'F(F(F(F(F'F'""# F'F'F'F'F)F'F'F'F)""&""$F+F'F(F+!""F(F& }