{VERSION 3 0 "DEC ALPHA UNIX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 1 18 0 0 0 0 1 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 -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 3 }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 }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 }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 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 263 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 264 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 265 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 194 "Program for the hamilto nian treatment of general relativity (ADM) based on the 3+1 split of s pace-time. Here the program is adapted to Bianchi I space-time, but ca n be adapted to other metrics." }}{PARA 259 "" 0 "" {TEXT -1 6 "Autho r" }{TEXT 256 60 " : D.N. Vulcanov - The West University of Timisoara, Romania" }}{PARA 265 "" 0 "" {TEXT 261 4 "See " }{TEXT -1 2 ": " } {TEXT 262 31 "gr-qc/0010085 , physics/0010053" }}}{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 .77~(R5)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%+3~May~2000G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%ZDeveloped~by~Peter~Musgrave,~Denis~Pollney ~and~Kayll~LakeG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%DCopyright~1994-2 000~by~the~authors.G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%inLatest~vers ion~available~from:~http://grtensor.phy.queensu.ca/G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%P/afs/aei-potsdam.mpg.de/u/vulcan/grii/mymetricsG%N /afs/aei-potsdam.mpg.de/u/vulcan/grii/metricsG" }}}{EXCHG {PARA 260 " " 0 "" {TEXT -1 57 "Some general definitions, before downloading the m etric !" }}{PARA 0 "" 0 "" {TEXT 260 25 "The main notations are : " }} {PARA 0 "" 0 "" {TEXT -1 43 "ha0 the hamiltonian constrai nt" }}{PARA 0 "" 0 "" {TEXT -1 40 "ha(i) the momentum const raint" }}{PARA 0 "" 0 "" {TEXT -1 32 "Ni(i) the shift vector " }}{PARA 0 "" 0 "" {TEXT -1 35 "N the lapse function" }}{PARA 0 "" 0 "" {TEXT -1 45 "g(i,j) the three-dimensional \+ metric" }}{PARA 0 "" 0 "" {TEXT -1 73 "pi(i,j) the momenta ca nonical conjugate to the metric components" }}{PARA 0 "" 0 "" {TEXT -1 66 "derge(i,j) the dynamic equation for the three-dimensional metr ic " }}{PARA 0 "" 0 "" {TEXT -1 61 "derpi(i,j) the dynamic equation \+ for the momentum conponents" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "grdef(`tr := pi\{^i i\}`);" }}{PARA 6 "" 1 "" {TEXT -1 59 "`Warnin g ` = (`No definition found for object` = pi(up,dn))" }}{PARA 6 "" 1 " " {TEXT -1 25 "Created definition for tr" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "grdef(`ha0:=-sqrt(detg)*(Ricciscalar\{\}+(1/detg)*((1 /2)*(tr\{\})^2-pi\{i j\}*pi\{ ^i ^j \}))`);" }}{PARA 6 "" 1 "" {TEXT -1 59 "`Warning ` = (`No definition found for object` = pi(dn,dn))" }} {PARA 6 "" 1 "" {TEXT -1 59 "`Warning ` = (`No definition found for ob ject` = pi(up,up))" }}{PARA 6 "" 1 "" {TEXT -1 26 "Created definition \+ for ha0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "grdef(`ha\{ ^i \+ \}:=-2*(pi\{ ^i ^j ;j\}-pi\{ ^i ^j \}*Chr\{ p j ^p \})`);" }}{PARA 6 " " 1 "" {TEXT -1 63 "`Warning ` = (`No definition found for object` = p i(up,up,cdn))" }}{PARA 6 "" 1 "" {TEXT -1 59 "`Warning ` = (`No defini tion found for object` = pi(up,up))" }}{PARA 6 "" 1 "" {TEXT -1 29 "Cr eated definition for ha(up)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "grdef(`derge\{ i j \}:=2*N(x,t)*(detg)^(-1/2)*(pi\{ i j \} - (1/2 )*g\{ i j\}*tr)+Ni\{ i ;j \} + Ni\{ j ;i \}`);" }}{PARA 6 "" 1 "" {TEXT -1 59 "`Warning ` = (`No definition found for object` = pi(dn,dn ))" }}{PARA 6 "" 1 "" {TEXT -1 60 "`Warning ` = (`No definition found \+ for object` = Ni(dn,cdn))" }}{PARA 6 "" 1 "" {TEXT -1 35 "Created defi nition for derge(dn,dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " grdef(`Ndd\{ " }{TEXT -1 0 "" }{MPLTEXT 1 0 24 "^m j \}:= Nd\{ ^m ;j \+ \}`); " }}{PARA 6 "" 1 "" {TEXT -1 60 "`Warning ` = (`No definition fo und for object` = Nd(up,cdn))" }}{PARA 6 "" 1 "" {TEXT -1 33 "Created \+ definition for Ndd(up,dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "grdef(`bum\{ ^i ^j ^m\}:=pi\{ ^i ^j \}*Ni\{ ^m \}`);" }}{PARA 6 " " 1 "" {TEXT -1 56 "`Warning ` = (`No definition found for object` = N i(up))" }}{PARA 6 "" 1 "" {TEXT -1 59 "`Warning ` = (`No definition fo und for object` = pi(up,up))" }}{PARA 6 "" 1 "" {TEXT -1 36 "Created d efinition for bum(up,up,up)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "grdef(`bla\{ ^i ^j \}:=bum\{ ^i ^j ^m ;m \}`);" }}{PARA 6 "" 1 "" {TEXT -1 45 "Created a definition for bum(up,up,up,cdn)" }}{PARA 6 "" 1 "" {TEXT -1 33 "Created definition for bla(up,up)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 354 "grdef(`derpi\{ ^i ^j \}:=-N(x,t)*( detg)^(1/2)*(R\{ ^i ^j \}-(1/2)*g\{ ^i ^j \}*Ricciscalar)+ (1/2)*N(x,t )*(detg)^(-1/2)*g\{ ^i ^j \}*(pi\{ ^k ^l \}*pi\{ k l \}-(1/2)*(tr)^2 )-2*N(x,t)*(detg)^(-1/2)*(pi\{ ^i ^m \}*pi\{ ^j m \}-(1/2)*pi\{ ^i ^j \+ \}*tr)+ (detg)^(1/2)*(Ndd\{ ^i ^j \}-g\{ ^i ^j \}*Ndd\{ ^m m \}) + bla \{ ^i ^j \} - Ni\{ ^i ;m \}*pi\{ ^m ^j \}-Ni\{ ^j ;m \}*pi\{ ^m ^i \+ \}`);" }}{PARA 6 "" 1 "" {TEXT -1 34 "Created definition for Ndd(up,up ) " }}{PARA 6 "" 1 "" {TEXT -1 59 "`Warning ` = (`No definition found \+ for object` = pi(up,dn))" }}{PARA 6 "" 1 "" {TEXT -1 60 "`Warning ` = \+ (`No definition found for object` = Ni(up,cdn))" }}{PARA 6 "" 1 "" {TEXT -1 32 "Created definition for R(up,up) " }}{PARA 6 "" 1 "" {TEXT -1 59 "`Warning ` = (`No definition found for object` = pi(dn,dn ))" }}{PARA 6 "" 1 "" {TEXT -1 59 "`Warning ` = (`No definition found \+ for object` = pi(up,up))" }}{PARA 6 "" 1 "" {TEXT -1 35 "Created defin ition for derpi(up,up)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 25 "Now do wnload the metric (" }{TEXT 258 12 "biaI_din.mpl" }{TEXT 259 7 " file) " }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "qload( `biaI_din`);" }}{PARA 6 "" 1 "" {TEXT -1 42 "Calculated ds for biaI_di n (.003000 sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2Default~spacet imeG%)biaI_dinG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 43 "grdef(`Nd\{ ^ m \} := [diff(N(x,t),x),0,0]`); " }}{PARA 6 "" 1 "" {TEXT -1 40 "Components assigned for metric: biaI_ din" }}{PARA 6 "" 1 "" {TEXT -1 29 "Created definition for Nd(up)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "grdef(`Ni\{ ^i \} := [N1(x,t ), N2(x,t), N3(x,t)]`);" }}{PARA 6 "" 1 "" {TEXT -1 40 "Components ass igned for metric: biaI_din" }}{PARA 6 "" 1 "" {TEXT -1 29 "Created def inition for Ni(up)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "grdef (`vi1\{^i\}:=[pix(x,t)*(2*XX(x,t))^(-1),0,0]`);" }}{PARA 6 "" 1 "" {TEXT -1 40 "Components assigned for metric: biaI_din" }}{PARA 6 "" 1 "" {TEXT -1 30 "Created definition for vi1(up)" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 40 "grdef(`vi3\{^i\}:=[0,0,piy*(4*YY)^(-1)]`);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 6 "" 1 "" {TEXT -1 40 "Com ponents assigned for metric: biaI_din" }}{PARA 6 "" 1 "" {TEXT -1 30 " Created definition for vi3(up)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "grdef(`vi2\{^i\}:=[0,piy*(4*YY)^(-1),0]`);" }}{PARA 6 "" 1 "" {TEXT -1 40 "Components assigned for metric: biaI_din" }}{PARA 6 "" 1 "" {TEXT -1 30 "Created definition for vi2(up)" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 97 "grdef(`pi\{ ^i ^j \} := vi1\{ ^i \}*kdelta\{^j $x\}+vi2\{ ^i \}*kdelta\{ ^j$y \}+vi3\{ ^i \}*kdelta\{^j $z\}`);" }} {PARA 6 "" 1 "" {TEXT -1 32 "Created definition for pi(up,up)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "grcalc(pi(up,up));" }}{PARA 6 "" 1 "" {TEXT -1 53 "Calculated kdelta(up,dn) for biaI_din (.007000 \+ sec.) " }}{PARA 6 "" 1 "" {TEXT -1 49 "Calculated pi(up,up) for biaI_d in (.017000 sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\" #R!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "grdisplay(pi(up,u p));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%7%F>,$*&%$piyGF8%#YYGF;#F(\"\"%F>7%F>F>F @" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "grdef(`de1\{ i \}:=[di ff(grcomponent(g(dn,dn),[x,x]),t),0,0]`);" }}{PARA 6 "" 1 "" {TEXT -1 40 "Components assigned for metric: biaI_din" }}{PARA 6 "" 1 "" {TEXT -1 30 "Created definition for de1(dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "grdef(`de2\{ i \}:=[0,diff(grcomponent(g(dn,dn),[y,y] ),t),0]`);" }}{PARA 6 "" 1 "" {TEXT -1 40 "Components assigned for met ric: biaI_din" }}{PARA 6 "" 1 "" {TEXT -1 30 "Created definition for d e2(dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "grdef(`de3\{ i \} :=[0,0,diff(grcomponent(g(dn,dn),[z,z]),t)]`);" }}{PARA 6 "" 1 "" {TEXT -1 40 "Components assigned for metric: biaI_din" }}{PARA 6 "" 1 "" {TEXT -1 30 "Created definition for de3(dn)" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 91 "grdef(`ddgt(\{ i j \}:=de1\{ i \}*kdelta\{j $x \}+de2\{ i \}*kdelta\{ j$y \}+de3\{ i \}*kdelta\{ j $z\}`);" }}{PARA 6 "" 1 "" {TEXT -1 34 "Created definition for ddgt(dn,dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "grcalc(ddgt(dn,dn));" }}{PARA 6 "" 1 "" {TEXT -1 53 "Calculated kdelta(dn,dn) for biaI_din (.006000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 51 "Calculated ddgt(dn,dn) for biaI_din \+ (.053000 sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#v! \"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "grdisplay(ddgt(dn,dn ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%7%F>F>F>F?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "grdef(`act:=pi\{ ^i ^j \}*ddgt\{ i j \}`);" }} {PARA 6 "" 1 "" {TEXT -1 26 "Created definition for act" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "grcalc(act);" }}{PARA 6 "" 1 "" {TEXT -1 43 "Calculated act for biaI_din (.004000 sec.) " }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#:!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grdisplay(act);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 12 "grcalc(ha0); " }}{PARA 6 "" 1 "" {TEXT -1 33 "Created definition for pi(up,dn) " }} {PARA 6 "" 1 "" {TEXT -1 33 "Created definition for pi(dn,dn) " }} {PARA 6 "" 1 "" {TEXT -1 49 "Calculated pi(up,dn) for biaI_din (.01300 0 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 42 "Calculated tr for biaI_din (. 004000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 44 "Calculated detg for biaI _din (.004000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 48 "Calculated g(up,u p) for biaI_din (.011000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 52 "Calcul ated g(dn,dn,pdn) for biaI_din (.018000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 53 "Calculated Chr(dn,dn,dn) for biaI_din (.016000 sec.) " }} {PARA 6 "" 1 "" {TEXT -1 53 "Calculated Chr(dn,dn,up) for biaI_din (.0 22000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 48 "Calculated R(dn,dn) for b iaI_din (.018000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 51 "Calculated Ric ciscalar for biaI_din (.003000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 49 " Calculated pi(dn,dn) for biaI_din (.038000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 43 "Calculated ha0 for biaI_din (.034000 sec.) " }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$'H!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "gralter(ha0,simplify);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component simplification of a GRTensorII object:" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 39 "Applying routine si mplify to object ha0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$ \"$)=!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grdisplay(ha0) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 15 "grcalc(ha(up));" }}{PARA 6 "" 1 "" {TEXT -1 41 "Created a definition for pi(up,up,cd n)" }}{PARA 6 "" 1 "" {TEXT -1 53 "Calculated pi(up,up,cdn) for biaI_d in (.040000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 46 "Calculated ha(up) f or biaI_din (.010000 sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~ Time~G$\"$b%!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "grdispl ay(ha(up));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 21 "grca lc(derge(dn,dn));" }}{PARA 6 "" 1 "" {TEXT -1 30 "Created definition f or Ni(dn) " }}{PARA 6 "" 1 "" {TEXT -1 38 "Created a definition for \+ Ni(dn,cdn)" }}{PARA 6 "" 1 "" {TEXT -1 46 "Calculated Ni(dn) for biaI _din (.007000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 50 "Calculated Ni(dn, cdn) for biaI_din (.017000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 52 "Calc ulated derge(dn,dn) for biaI_din (.022000 sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$#[!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "gralter(derge(dn,dn),simplify);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component simplification of a GRTensorII object:" }} {PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 48 "Applying routine simplify to object derge(dn,dn)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$,$!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "grdisplay(derge(dn,dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 54 "dertx:=(2*XX(x))^(- 1)*grcomponent(derge(dn,dn),[x,x]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #>%&dertxG,$*&*&-%#XXG6$%\"xG%\"tG\"\"\",**(-%\"NGF*\"\"\")F(\"\"#F--% $pixGF*F2F2**F0F-F(F2%#YYGF2%$piyGF2!\"\"*(-%#N1GF*F2-%%diffG6$F(F+F2- %%sqrtG6#*&F3F-)F8\"\"%F-F-FF*(F(F--F?6$F " 0 "" {MPLTEXT 1 0 16 "si mplify(dertx);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,$*&*&-%#XXG6$%\"xG% \"tG\"\"\",**(-%\"NGF(\"\"\")F&\"\"#F+-%$pixGF(F0F0**F.F+F&F0%#YYGF0%$ piyGF0!\"\"*(-%#N1GF(F0-%%diffG6$F&F)F0-%%sqrtG6#*&F1F+)F6\"\"%F+F+FD* (F&F+-F=6$F:F)F0F?F+FDF0F+*&-F'6#F)\"\"\"-F@6#FBF+!\"\"#F0FD" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "derty:=(2*YY)^(-1)*grcompone nt(derge(dn,dn),[y,y]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&dertyG,$ *&**%#YYG\"\"\"-%\"NG6$%\"xG%\"tGF)-%#XXGF,F)-%$pixGF,F)\"\"\"*$-%%sqr tG6#*&)F/\"\"#F3)F(\"\"%F3F3!\"\"#!\"\"F<" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 16 "simplify(derty);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #,$*&**%#YYG\"\"\"-%\"NG6$%\"xG%\"tGF'-%#XXGF*F'-%$pixGF*F'\"\"\"*$-%% sqrtG6#*&)F-\"\"#F1)F&\"\"%F1F1!\"\"#!\"\"F:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "grcalc(derpi(up,up));" }}{PARA 6 "" 1 "" {TEXT -1 38 "Created a definition for Nd(up,cdn)" }}{PARA 6 "" 1 "" {TEXT -1 38 "Created a definition for Ni(up,cdn)" }}{PARA 6 "" 1 " " {TEXT -1 50 "Calculated Nd(up,cdn) for biaI_din (.017000 sec.) " }} {PARA 6 "" 1 "" {TEXT -1 50 "Calculated Ndd(up,dn) for biaI_din (.0080 00 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 50 "Calculated Ndd(up,up) for bi aI_din (.013000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 50 "Calculated Ni(u p,cdn) for biaI_din (.014000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 48 "Ca lculated R(up,up) for biaI_din (.016000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 53 "Calculated bum(up,up,up) for biaI_din (.023000 sec.) " }} {PARA 6 "" 1 "" {TEXT -1 57 "Calculated bum(up,up,up,cdn) for biaI_din (.140000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 50 "Calculated bla(up,up) for biaI_din (.010000 sec.) " }}{PARA 6 "" 1 "" {TEXT -1 52 "Calculat ed derpi(up,up) for biaI_din (.064000 sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"%47!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "gralter(derpi(up,up),simplify,sqrt,expand);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component simplification of a GRTensorII object :" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 48 "App lying routine simplify to object derpi(up,up)" }}{PARA 6 "" 1 "" {TEXT -1 56 "Applying routine `simplify[sqrt]` to object derpi(up,up) " }}{PARA 6 "" 1 "" {TEXT -1 46 "Applying routine expand to object der pi(up,up)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$q&!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "grdisplay(derpi(up,up)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#F(\"\")*&*&-%%diffG6$F3F'F(-%#N1GF0F(F6F8F>#F( F5*&*&F3F6-FN6$FPF'F(F6F8F>#!\"\"F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #/*&)%&derpiG%\"yG\"\"\")%!G%\"xGF(,$*&*&-%$pixG6$F+%\"tGF(-%%diffG6$- %#N2GF1F+F(\"\"\"-%#XXGF1!\"\"#!\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&)%&derpiG%\"zG\"\"\")%!G%\"xGF(,$*&*&-%$pixG6$F+%\"t GF(-%%diffG6$-%#N3GF1F+F(\"\"\"-%#XXGF1!\"\"#!\"\"\"\"#" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/*&)%&derpiG%\"xG\"\"\")%!G%\"yGF(,$*&*&-%$pixG6 $F'%\"tGF(-%%diffG6$-%#N2GF1F'F(\"\"\"-%#XXGF1!\"\"#!\"\"\"\"#" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#/*&)%&derpiG%\"yG\"\"\")%!GF'F(,,*&*(- %#XXG6$%\"xG%\"tGF(-%\"NGF0F()-%$pixGF0\"\"#\"\"\"F9*$)%#YYG\"\"%F9!\" \"#F(\"#;*&*&%$piyGF(-%%diffG6$-%#N1GF0F1F(F9F#F(\"\"%*&*(FCF9FGF(- FE6$F.F1F(F9*&F.\"\"\"F<\"\"\"F>FI*&-FE6$F3-%\"$G6$F1F8F(F.F9!\"\"*&-F E6$F3F1F(FMF9FX" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&)%&derpiG%\"xG\" \"\")%!G%\"zGF(,$*&*&-%$pixG6$F'%\"tGF(-%%diffG6$-%#N3GF1F'F(\"\"\"-%# XXGF1!\"\"#!\"\"\"\"#" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&)%&derpiG% \"zG\"\"\")%!GF'F(,,*&*(-%#XXG6$%\"xG%\"tGF(-%\"NGF0F()-%$pixGF0\"\"# \"\"\"F9*$)%#YYG\"\"%F9!\"\"#F(\"#;*&*&%$piyGF(-%%diffG6$-%#N1GF0F1F(F 9F#F(\"\"%*&*(FCF9FGF(-FE6$F.F1F(F9*&F.\"\"\"F<\"\"\"F>FI*&-FE6$F3- %\"$G6$F1F8F(F.F9!\"\"*&-FE6$F3F1F(FMF9FX" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 91 "dertpix:=2*XX(x)*(grcomponent(derpi(up,up),[x,x]) + (1/2)*(1/(XX(x)*XX(x)))*pix(x)*dertx);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(dertpixG,$*&-%#XXG6#%\"xG\"\"\",,*&*&-%\"NG6$F*%\"tG F+)-%$pixGF1\"\"#\"\"\"F7*&-F(F1\"\"\")%#YYG\"\"#F7!\"\"#!\"$\"#;*&*(F /F7F4F+%$piyGF+F7*&)F9\"\"#F7F<\"\"\"F>#F+\"\")*&*&-%%diffG6$F4F*F+-%# N1GF1F+F7F9F>#F+F6*&*&F4F7-FN6$FPF*F+F7F9F>#!\"\"F6*&*(-F5F)F+F9F7,**( F/F7)F9F6F7F4F7F+**F/F7F9F+FFIF+F6 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "simplify(dertpix);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#,$*&,2*,-%\"NG6$%\"xG%\"tG\"\"\")-%$pi xGF)\"\"#\"\"\"-%#XXGF)F,)-F36#F*\"\"$F1-%%sqrtG6#*&)F2F0F1)%#YYG\"\"% F1F1!\"$*.F'F1F.F,%$piyGF,F>F,F4F1F8F1F0*.-%%diffG6$F.F*F,-%#N1GF)F,F2 F1)F>F0F1F4F1F8F1\"\")*.F.F1-FE6$FGF*F,F2F1FIF1F4F1F8F1!\")*,-F/F6F,)F 2\"\"&F1FIF1F'F1F.F1F0*,FPF1)F2F?F1)F>F7F1F'F1FBF1!\"#*.FPF1)F2F7F1FIF 1FGF1-FE6$F2F*F,F8F1FJ*,FPF1FTF1FIF1FLF1F8F1FJF1**)F5\"\"#F1)F2\"\"#F1 )F>\"\"#F1-F96#F;F1!\"\"#F,FJ" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "dertpiy:=4*YY*(grcomponent(derpi(up,up),[y,y]) + (1/4)*(1/(YY*YY ))*piy*derty);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(dertpiyG,$*&%#YYG \"\"\",.*&*(-%#XXG6$%\"xG%\"tGF(-%\"NGF.F()-%$pixGF.\"\"#\"\"\"F7*$)F' \"\"%F7!\"\"#F(\"#;*&*&%$piyGF(-%%diffG6$-%#N1GF.F/F(F7F'F;#F(\"\"%*&* (F@F7FDF(-FB6$F,F/F(F7*&F,\"\"\"F'\"\"\"F;FF*&-FB6$F1-%\"$G6$F/F6F(F,F 7!\"\"*&-FB6$F1F/F(FJF7FU*&**F@F7F1F7F,F7F4F(F7*&F'\"\"\"-%%sqrtG6#*&) F,F6F7)F'FGF7F7F;#FUF=F(FG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "simplify(dertpiy);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,$*&,.**)-%# XXG6$%\"xG%\"tG\"\"#\"\"\"-%\"NGF*\"\"\")-%$pixGF*F-F.-%%sqrtG6#*&F'F. )%#YYG\"\"%F.F.F1*,%$piyGF1-%%diffG6$-%#N1GF*F+F1)F:\"\"$F.F(F1F5F.F;* ,F=F.FAF1-F?6$F(F+F1FCF.F5F.F;**-F?6$F/-%\"$G6$F+F-F1F'F.F9F.F5F.!#;*, -F?6$F/F+F1FFF.F9F.F(F.F5F.FN*,F=F.F/F.F'F.F3F1FCF.!\"\"F.*()F:\"\"$F. F(\"\"\"-F66#F8F.!\"\"#F1F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "grdef(`haf0 := ha0 + pif(x,t)*sqrt(1-( diff(phi(x,t),x)^2*(1/(XX(x ,t)^2)) ))`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 6 "" 1 " " {TEXT -1 27 "Created definition for haf0" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 85 "grdef(`haf\{ ^i \} := ha\{ ^i \} +pif(x,t)*diff(ph i(x,t),x)/(XX(x,t)^2)*kdelta\{^i $x\}`);" }}{PARA 6 "" 1 "" {TEXT -1 30 "Created definition for haf(up)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "grcalc(haf0);" }}{PARA 6 "" 1 "" {TEXT -1 44 "Calcula ted haf0 for biaI_din (.067000 sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#x!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "grcalc(haf(up));" }}{PARA 6 "" 1 "" {TEXT -1 47 "Calculated haf(up ) for biaI_din (.008000 sec.) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*C PU~Time~G$\"#;!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "gralt er(haf0,simplify,sqrt);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component simp lification of a GRTensorII object:" }}{PARA 6 "" 1 "" {TEXT -1 1 " " } }{PARA 6 "" 1 "" {TEXT -1 40 "Applying routine simplify to object haf0 " }}{PARA 6 "" 1 "" {TEXT -1 48 "Applying routine `simplify[sqrt]` to \+ object haf0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$%Q!\"$ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "grdisplay(haf0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 26 "gralter(haf(up),simp lify);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component simplification of a G RTensorII object:" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 43 "Applying routine simplify to object haf(up)" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#F!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "grdisplay(haf(up));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 12 "phi(x,t):=t;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%$phiG6$%\"xG%\"tGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "grcalc(haf0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*C PU~Time~G$\"\"&!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "grca lc(haf(up));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"\"$!\" $" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "grdisplay(haf0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 19 "grdisplay(haf(up));" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#% " 0 "" {MPLTEXT 1 0 30 "aaa:=grcomponent(haf(up),[x]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$aaaG,$*&-%%diffG6$-%$pixG6$%\"xG%\"tGF-\"\"\" -%#XXGF,!\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "pdsol ve(aaa,pix(x,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'&whereG6$/-%$p ixG6$%\"xG%\"tG-%$_F1G6#F+7#-%!G6$F,%:~are~arbitrary~functions.G" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "pix(x,t):=C;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%$pixG6$%\"xG%\"tG%\"CG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "bbb:=grcomponent(haf0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$bbbG,$*&,(*&)-%#XXG6$%\"xG%\"tG\"\"#\"\"\")%\"CGF/F0 \"\"\"**F*F3F2F3%#YYGF3%$piyGF3!\"#*(-%$pifGF,F3-%%sqrtG6#*$F)F0F0)F5F /F0\"\")F0*&F*\"\"\")F5\"\"#F0!\"\"#F3F@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "pif(x,t):=solve(bbb,pif(x,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%$pifG6$%\"xG%\"tG,$*&*&%\"CG\"\"\",&*&-%#XXGF&\"\"\" F,F2F2*&%#YYGF2%$piyGF2!\"#F2F-*$)F4\"\"#F-!\"\"#!\"\"\"\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "pif(x,t);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,$*&*&%\"CG\"\"\",&*&-%#XXG6$%\"xG%\"tG\"\"\"F&F/F/*& %#YYGF/%$piyGF/!\"#F/F'*$)F1\"\"#F'!\"\"#!\"\"\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 1 }{VIEWOPTS 1 1 0 1 1 1803 }