{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 "Times" 1 11 0 0 0 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 1 } 1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 1 }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 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 255 0 0 1 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "grtw();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%=GRTensorII~Version~1.79~(R6)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%02~February~2001G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% ZDeveloped~by~Peter~Musgrave,~Denis~Pollney~and~Kayll~LakeG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%DCopyright~1994-2001~by~the~authors.G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%inLatest~version~available~from:~http ://grtensor.phy.queensu.ca/G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%4e:/G rtii(6)/MetricsG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "with(co degen,cost):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "First note how cost counts:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "C:=x+y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"CG,&%\"xG\"\"\"%\"yGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "codegen[cost](C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*additionsG" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "C1:=x+y+z;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#C1G,(%\"xG\"\"\"%\"yGF'%\"zGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "codegen[cost](C1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%*additionsG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "interface(labelling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "qload(threed);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/%2Default~spacetimeG%'threedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%: For~the~threed~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%,Coordi natesG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"xG6#%#upG" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/)%#x~G%\"aG-%'vectorG6#7%%#x1G%#x2G%#x3G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%-Line~elementG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*$)%$~dsG\"\"#\"\"\",.*(-%\"aG6%%#x1G%#x2G%#x3GF(%#~dG F()F.%#2~GF(F(*.F'F(-%\"bGF-F(F1F()F.%\"~GF(%#d~GF()F/F8F(F(*.F'F(-%\" cGF-F(F1F(F7F(F9F()F0F8F(F(*(-%\"dGF-F(F1F()F/F3F(F(*.F'F(-%\"eGF-F(F1 F(F:F(F9F(F>F(F(*(-%\"fGF-F(F1F()F0F3F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 23 "grOptionDefaultSimp:=0:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 39 "grdef(`RR11:=g\{^c ^d\}*R\{c $x1 $x1 d\}`):" }} {PARA 6 "" 1 "" {TEXT -1 27 "Created definition for RR11" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "grdef(`RR12:=g\{^c ^d\}*R\{c $x1 $x 2 d\}`):" }}{PARA 6 "" 1 "" {TEXT -1 27 "Created definition for RR12" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "grcalc(RR11):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#I!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "codegen[cost](numer(grcomponent(RR11,[])));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%*additionsG\"$:%*&\"%?C\"\"\"%0mu ltiplicationsGF(F(*&\"%)y#F(%*functionsGF(F(" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 23 "415 additions=416 terms" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "grcalc(RR12):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G $\"\"!F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "codegen[cost](n umer(grcomponent(RR12,[])));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%*ad ditionsG\"$=&*&\"%_H\"\"\"%0multiplicationsGF(F(*&\"%=NF(%*functionsGF (F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "518 additions=519 terms" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }}{MARK "16 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }