{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {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 } {CSTYLE "" -1 257 "" 0 1 0 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 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 0 }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 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 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 } {PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 18 "" 0 "" {TEXT -1 23 "Catalogue of Spacetimes" }} {PARA 19 "" 0 "" {TEXT -1 27 "Thomas Mueller, Frank Grave" }}{PARA 0 " " 0 "" {TEXT 257 67 "Barriola-Vilenkin metric in spherical caoordinate s (t,r,theta,phi)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "Date: 20.04.2009" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "restart:grtw();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%=GRTensorII~Version~1.79~(R4)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%06~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#%B /home/muelleta/local/Grii/metricsG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "makeg(BarriolaVilenkin);" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 46 "M akeg 2.0: GRTensor metric/basis entry utility" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 41 "To quit makeg, type 'exi t' at any prompt." }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 44 "Do you wish to enter a 1) metric [g(dn,dn)]," }}{PARA 6 " " 1 "" {TEXT -1 44 " 2) line element [ds]," }} {PARA 6 "" 1 "" {TEXT -1 63 " 3) non-holonomic b asis [e(1)...e(n)], or" }}{PARA 6 "" 1 "" {TEXT -1 49 " \+ 4) NP tetrad [l,n,m,mbar]?" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }} }{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 2 "2:" }}{PARA 6 "" 1 "" {TEXT -1 50 "Enter coordinates as a LIST (eg. [t,r,theta,phi]):" }}} {EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 16 "[t,r,theta,phi]:" }} {PARA 6 "" 1 "" {TEXT -1 64 "Enter the line element using d[coord] to \+ indicate differentials." }}{PARA 6 "" 1 "" {TEXT -1 55 "(for example, \+ r^2*(d[theta]^2 + sin(theta)^2*d[phi]^2)" }}{PARA 6 "" 1 "" {TEXT -1 27 "[Type 'exit' to quit makeg]" }}{PARA 6 "" 1 "" {TEXT -1 8 " ds^2 = " }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 62 "-c^2*d[t]^2+d[r]^2 +k^2*r^2*(d[theta]^2+sin(theta)^2*d[phi]^2);" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 67 "If there are any complex valued coordinates, constants or functions" }}{PARA 6 "" 1 "" {TEXT -1 66 "f or this spacetime, please enter them as a SET ( eg. \{ z, psi \} )." } }{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 33 "Complex \+ quantities [default=\{\}]: " }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 3 "\{\}:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%AThe~values~you~have~ entered~are:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%,CoordinatesG7&%\"t G%\"rG%&thetaG%$phiG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(Metric:G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%\"gG6#%\"aG\"\"\"&%!G6#%\"bGF)K%' matrixG6#7&7&,$*$)%\"cG\"\"#F)!\"\"\"\"!F9F97&F9F)F9F97&F9F9*&)%\"kGF7 F))%\"rGF7F)F97&F9F9F9*(F=F)F?F))-%$sinG6#%&thetaGF7F)Q(pprint06\"" }} {PARA 6 "" 1 "" {TEXT -1 54 "You may choose to 0) Use the metric WITHO UT saving it," }}{PARA 6 "" 1 "" {TEXT -1 46 " 1) Sav e the metric as it is," }}{PARA 6 "" 1 "" {TEXT -1 54 " \+ 2) Correct an element of the metric," }}{PARA 6 "" 1 "" {TEXT -1 41 " 3) Re-enter the metric," }}{PARA 6 "" 1 "" {TEXT -1 54 " 4) Add/change constraint equations, " } }{PARA 6 "" 1 "" {TEXT -1 47 " 5) Add a text descript ion, or" }}{PARA 6 "" 1 "" {TEXT -1 61 " 6) Abandon t his metric and return to Maple." }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 2 "0:" }}{PARA 6 "" 1 "" {TEXT -1 50 "Calculated ds for BarriolaVilenkin (0.000000 sec.)" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/%2Default~spacetimeG%1BarriolaVilenki nG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%DFor~the~BarriolaVilenkin~space time:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%,CoordinatesG" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%\"xG6#%#upG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #/)%#x~G%\"aGK%'vectorG6#7&%\"tG%\"rG%&thetaG%$phiGQ(pprint16\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%-Line~elementG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*$)%$~dsG\"\"#\"\"\",**()%\"cGF'F(%#~dGF()%\"tG%#2~GF( !\"\"*&F-F()%\"rGF0F(F(**)%\"kGF'F()F4F'F(F-F()%&thetaGF0F(F(*,F6F(F8F ()-%$sinG6#F:F'F(F-F()%$phiGF0F(F(" }}{PARA 6 "" 1 "" {TEXT -1 18 "mak eg() completed." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "grcalcd( Chr2);" }}{PARA 6 "" 1 "" {TEXT -1 52 "Calculated detg for BarriolaVil enkin (0.000000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 56 "Calculated g(up, up) for BarriolaVilenkin (0.000000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 60 "Calculated g(dn,dn,pdn) for BarriolaVilenkin (0.000000 sec.)" }} {PARA 6 "" 1 "" {TEXT -1 61 "Calculated Chr(dn,dn,dn) for BarriolaVile nkin (0.004000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 61 "Calculated Chr(dn ,dn,up) for BarriolaVilenkin (0.004000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"\")!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%DFor~the~BarriolaVilenkin~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%aoChristoffel~symbol~of~the~second~kind~(symmetric~in~ first~two~indices)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#* &%\"rG\"\"\"%&thetaGF*F*)%!G%&thetaGF**&F*F*%\"rG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"rG\"\"\"%$phiGF*F*)%!G%$phiGF** &F*F*%\"rG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%&t hetaG\"\"\"%&thetaGF*F*)%!G%\"rGF*,$*&)%\"kG\"\"#F*%\"rGF*!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%&thetaG\"\"\"%$phiGF* F*)%!G%$phiGF**&-%$sinG6#%&thetaG!\"\"-%$cosGF2F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%$phiG\"\"\"%$phiGF*F*)%!G%\"rGF*,$*()% \"kG\"\"#F*%\"rGF*)-%$sinG6#%&thetaGF3F*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%$phiG\"\"\"%$phiGF*F*)%!G%&thetaGF*,$* &-%$sinG6#%&thetaGF*-%$cosGF3F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "grcalcd(Riemann);" }}{PARA 6 "" 1 "" {TEXT -1 62 "Cal culated R(dn,dn,dn,dn) for BarriolaVilenkin (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"\"%!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%DFor~the~BarriolaVilenkin~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%2Covariant~RiemannG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%#R~G6#**%&thetaG\"\"\"%$phiGF)%&thetaGF)%$phiGF),&*()%\"kG\" \"#F))%\"rGF1F))-%$sinG6#%&thetaGF1F)F)*()F0\"\"%F)F2F)F4F)!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grcalcd(Ricci);" }}{PARA 6 " " 1 "" {TEXT -1 56 "Calculated R(dn,dn) for BarriolaVilenkin (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"\"!F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%DFor~the~BarriolaVilenkin~spacetime:G " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0Covariant~RicciG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"RG6$%#dnGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #/*&&%#R~G6#%\"aG\"\"\"&%!G6#%\"bGF)K%'matrixG6#7&7&\"\"!F3F3F3F27&F3F 3,&F)F)*$)%\"kG\"\"#F)!\"\"F37&F3F3F3,&*$)-%$sinG6#%&thetaGF9F)F)*&F7F )F>F)F:Q(pprint26\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "grca lcd(Ricciscalar);" }}{PARA 6 "" 1 "" {TEXT -1 59 "Calculated Ricciscal ar for BarriolaVilenkin (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"\"!F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%DFor~t he~BarriolaVilenkin~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%-R icci~scalarG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%#R~G,$**\"\"#\"\"\", &F(!\"\"*$)%\"kGF'F(F(F(F-!\"#%\"rGF.F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "grcalcd(RiemSq);" }}{PARA 6 "" 1 "" {TEXT -1 38 "Crea ted definition for R(dn,dn,up,up) " }}{PARA 6 "" 1 "" {TEXT -1 62 "Cal culated R(dn,dn,up,up) for BarriolaVilenkin (0.004000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 54 "Calculated RiemSq for BarriolaVilenkin (0.00000 0 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#7!\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%DFor~the~BarriolaVilenkin~spacetime:G " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 28 "g_compts:=grarray(g(dn,dn)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "codegen[C](g_compts,optimized);" }}{PARA 6 "" 1 "" {TEXT -1 15 " t1 = c*c;" }}{PARA 6 "" 1 "" {TEXT -1 15 " t2 \+ = k*k;" }}{PARA 6 "" 1 "" {TEXT -1 15 " t3 = r*r;" }}{PARA 6 "" 1 "" {TEXT -1 17 " t4 = t2*t3;" }}{PARA 6 "" 1 "" {TEXT -1 22 " \+ t5 = sin(theta);" }}{PARA 6 "" 1 "" {TEXT -1 17 " t6 = t5*t5; " }}{PARA 6 "" 1 "" {TEXT -1 27 " g_compts[0][0] = -t1;" }}{PARA 6 "" 1 "" {TEXT -1 27 " g_compts[0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 27 " g_compts[0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 27 " g_compts[0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 27 " \+ g_compts[1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 27 " g_compts[1 ][1] = 1.0;" }}{PARA 6 "" 1 "" {TEXT -1 27 " g_compts[1][2] = 0.0 ;" }}{PARA 6 "" 1 "" {TEXT -1 27 " g_compts[1][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 27 " g_compts[2][0] = 0.0;" }}{PARA 6 " " 1 "" {TEXT -1 27 " g_compts[2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 26 " g_compts[2][2] = t4;" }}{PARA 6 "" 1 "" {TEXT -1 27 " g_compts[2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 27 " \+ g_compts[3][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 27 " g_compts[3 ][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 27 " g_compts[3][2] = 0.0 ;" }}{PARA 6 "" 1 "" {TEXT -1 29 " g_compts[3][3] = t4*t6;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "christoffel:=grarray(Chr2): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "codegen[C](christoffel, optimized);" }}{PARA 6 "" 1 "" {TEXT -1 15 " t1 = 1/r;" }}{PARA 6 "" 1 "" {TEXT -1 15 " t2 = k*k;" }}{PARA 6 "" 1 "" {TEXT -1 16 " t3 = t2*r;" }}{PARA 6 "" 1 "" {TEXT -1 22 " t4 = sin(theta );" }}{PARA 6 "" 1 "" {TEXT -1 22 " t6 = cos(theta);" }}{PARA 6 " " 1 "" {TEXT -1 19 " t7 = 1/t4*t6;" }}{PARA 6 "" 1 "" {TEXT -1 17 " t8 = t4*t4;" }}{PARA 6 "" 1 "" {TEXT -1 33 " christoffe l[0][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0] [0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][0][ 2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][1][0] = 0.0 ;" }}{PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][1][1] = 0.0;" } }{PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][1][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][1][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][2][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][2][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][2][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][2][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][3][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][3][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][3][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[0][3][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][0][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][0][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][0][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][0][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][1][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][1][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][1][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][1][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][2][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][2][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 32 " christoffel[1][2][2] = t1;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][2][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][3][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][3][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[1][3][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 32 " christoffel[1][3][3] = t1;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][0][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][0][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][0][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][0][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][1][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][1][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 32 " christoffel[2][1][2] = t1;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][1][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][2][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][2][1] = -t3;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][2][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][2][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][3][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][3][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[2][3][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 32 " christoffel[2][3][3] = t7;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][0][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][0][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][0][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][0][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][1][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][1][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][1][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 32 " christoffel[3][1][3] = t1;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][2][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][2][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][2][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 32 " christoffel[3][2][3] = t7;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][3][0] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 36 " christoffel[3][3][1] = -t3*t8;" }} {PARA 6 "" 1 "" {TEXT -1 36 " christoffel[3][3][2] = -t4*t6;" }} {PARA 6 "" 1 "" {TEXT -1 33 " christoffel[3][3][3] = 0.0;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "grcalcd(Chr(dn,dn,up,pdn)): " }}{PARA 6 "" 1 "" {TEXT -1 42 "Created a definition for Chr(dn,dn,up ,pdn)" }}{PARA 6 "" 1 "" {TEXT -1 64 "Calculated Chr(dn,dn,up,pdn) for BarriolaVilenkin (.009000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/% *CPU~Time~G$\"#>!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%DFor~the~Barr iolaVilenkin~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%2Chr(dn,d n,up,pdn)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*(&%&GammaG6#*&%\"rG\" \"\"%&thetaGF*F*)%!GF+F*&F-6#*&%\",GF*F)F*F*,$*&F*F**$)F)\"\"#F*!\"\"F 7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*(&%&GammaG6#*&%\"rG\"\"\"%$phiG F*F*)%!GF+F*&F-6#*&%\",GF*F)F*F*,$*&F*F**$)F)\"\"#F*!\"\"F7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*(&%&GammaG6#*&%&thetaG\"\"\"F)F*F*)%!G%\"r GF*&F,6#*&%\",GF*F-F*F*,$*$)%\"kG\"\"#F*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*(&%&GammaG6#*&%&thetaG\"\"\"%$phiGF*F*)%!GF+F*&F-6#*& %\",GF*F)F*F*,$*&,&*$)-%$cosG6#F)\"\"#F*F**$)-%$sinGF9F:F*F*F**$F " 0 "" {MPLTEXT 1 0 35 "chrisD:=grarray(Chr(dn,dn,up,pdn)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "codegen[C](chrisD,optimized);" }}{PARA 6 "" 1 "" {TEXT -1 15 " t1 = r*r;" }}{PARA 6 "" 1 "" {TEXT -1 16 " \+ t2 = 1/t1;" }}{PARA 6 "" 1 "" {TEXT -1 15 " t3 = k*k;" }} {PARA 6 "" 1 "" {TEXT -1 22 " t4 = cos(theta);" }}{PARA 6 "" 1 " " {TEXT -1 17 " t5 = t4*t4;" }}{PARA 6 "" 1 "" {TEXT -1 22 " \+ t6 = sin(theta);" }}{PARA 6 "" 1 "" {TEXT -1 17 " t7 = t6*t6;" } }{PARA 6 "" 1 "" {TEXT -1 23 " t10 = (t5+t7)/t7;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[0][0][1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[0][0][1][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0 ][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][1][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][2][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][2][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][3][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][3][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][0][3][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[0][1][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[0][1][0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1 ][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1][0][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1][1][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1][1][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1][2][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1][2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[0][1][3][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[0][1][3][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1 ][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][1][3][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][0][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][0][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][1][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[0][2][2][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[0][2][2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2 ][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][2][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][3][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][3][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][2][3][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[0][3][1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[0][3][1][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3 ][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][1][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][2][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][2][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][3][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][3][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[0][3][3][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[1][0][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[1][0][0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0 ][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0][0][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0][1][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0][1][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0][2][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0][2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[1][0][3][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[1][0][3][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0 ][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][0][3][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][0][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][0][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][1][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[1][1][2][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[1][1][2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1 ][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][2][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][3][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][3][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][1][3][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[1][2][1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[1][2][1][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2 ][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][1][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][2][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][2][1] = -t2;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][3][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][3][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][2][3][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[1][3][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[1][3][0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3 ][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3][0][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3][1][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3][1][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3][2][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3][2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[1][3][3][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[1][3][3][1] = -t2;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3 ][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[1][3][3][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][0][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][0][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][1][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[2][0][2][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[2][0][2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0 ][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][2][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][3][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][3][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][0][3][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[2][1][1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[2][1][1][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1 ][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][1][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][2][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][2][1] = -t2;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][3][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][3][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][1][3][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[2][2][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[2][2][0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2 ][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2][0][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2][1][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2][1][1] = -t3;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2][2][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2][2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[2][2][3][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[2][2][3][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2 ][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][2][3][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][0][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][0][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][1][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[2][3][2][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[2][3][2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3 ][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][2][3 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][3][0] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][3][1] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 32 " chrisD[2][3][3][2] = -t10;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[2][3][3][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[3][0][1][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[3][0][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0 ][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][2][0 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][2][1] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][2][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][3][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][3][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][0][3][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[3][1][0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[3][1][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1 ][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1][1][0 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1][1][1] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1][1][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1][2][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1][2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1][3][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[3][1][3][1] = -t2;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[3][1][3][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][1 ][3][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][0][0 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][0][1] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][0][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][1][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][1][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][2][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[3][2][2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chris D[3][2][2][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2 ][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][3][0 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][3][1] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 32 " chrisD[3][2][3][2] = -t10;" } }{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][2][3][3] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][3][0][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][3][0][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][3][0][2] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][3][0][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][3][1][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 34 " chrisD[3][3][1][1] = -t3*t7;" }}{PARA 6 "" 1 "" {TEXT -1 43 " \+ chrisD[3][3][1][2] = -2.0*t3*r*t6*t4;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][3][1][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " \+ chrisD[3][3][2][0] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " ch risD[3][3][2][1] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 34 " chrisD[3 ][3][2][2] = -t5+t7;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][3 ][2][3] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][3][3][0 ] = 0.0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][3][3][1] = 0. 0;" }}{PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][3][3][2] = 0.0;" }} {PARA 6 "" 1 "" {TEXT -1 31 " chrisD[3][3][3][3] = 0.0;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }