{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 18 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 "Text \+ Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -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 "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Ti mes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 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 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "read \"grii.m\";" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "grtensor();" }}{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" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 259 24 "Rotierendes Bezugssystem" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 38 "omega:=Vector([omega1,omega2,omega3]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&omegaG-%'RTABLEG6$\")'>-?\"-%'MATRI XG6#7%7#%'omega1G7#%'omega2G7#%'omega3G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "xx:=Vector([x1,x2,x3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#xxG-%'RTABLEG6$\");&[8\"-%'MATRIXG6#7%7#%#x1G7#%#x2G7#%#x3G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#7hq%$AddG%(AdjointG%3BackwardSubstitut eG%+BandMatrixG%&BasisG%-BezoutMatrixG%/BidiagonalFormG%-BilinearFormG %5CharacteristicMatrixG%9CharacteristicPolynomialG%'ColumnG%0ColumnDim ensionG%0ColumnOperationG%,ColumnSpaceG%0CompanionMatrixG%0ConditionNu mberG%/ConstantMatrixG%/ConstantVectorG%2CreatePermutationG%-CrossProd uctG%-DeleteColumnG%*DeleteRowG%,DeterminantG%/DiagonalMatrixG%*Dimens ionG%+DimensionsG%+DotProductG%,EigenvaluesG%-EigenvectorsG%&EqualG%2F orwardSubstituteG%.FrobeniusFormG%4GaussianEliminationG%2GenerateEquat ionsG%/GenerateMatrixG%2GetResultDataTypeG%/GetResultShapeG%5GivensRot ationMatrixG%,GramSchmidtG%-HankelMatrixG%,HermiteFormG%3HermitianTran sposeG%/HessenbergFormG%.HilbertMatrixG%2HouseholderMatrixG%/IdentityM atrixG%2IntersectionBasisG%+IsDefiniteG%-IsOrthogonalG%*IsSimilarG%*Is UnitaryG%2JordanBlockMatrixG%+JordanFormG%(LA_MainG%0LUDecompositionG% -LeastSquaresG%,LinearSolveG%$MapG%%Map2G%*MatrixAddG%.MatrixInverseG% 5MatrixMatrixMultiplyG%+MatrixNormG%5MatrixScalarMultiplyG%5MatrixVect orMultiplyG%2MinimalPolynomialG%&MinorG%)MultiplyG%,NoUserValueG%%Norm G%*NormalizeG%*NullSpaceG%3OuterProductMatrixG%*PermanentG%&PivotG%0QR DecompositionG%-RandomMatrixG%-RandomVectorG%%RankG%6ReducedRowEchelon FormG%$RowG%-RowDimensionG%-RowOperationG%)RowSpaceG%-ScalarMatrixG%/S calarMultiplyG%-ScalarVectorG%*SchurFormG%/SingularValuesG%*SmithFormG %*SubMatrixG%*SubVectorG%)SumBasisG%0SylvesterMatrixG%/ToeplitzMatrixG %&TraceG%*TransposeG%0TridiagonalFormG%+UnitVectorG%2VandermondeMatrix G%*VectorAddG%,VectorAngleG%5VectorMatrixMultiplyG%+VectorNormG%5Vecto rScalarMultiplyG%+ZeroMatrixG%+ZeroVectorG%$ZipG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "g00=1-CrossProduct((omega),xx) . CrossProduct ((omega),xx);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%$g00G,*\"\"\"F&*&-% *conjugateG6#,&*&%'omega2GF&%#x3GF&F&*&%'omega3GF&%#x2GF&!\"\"F&F+F&F2 *&-F)6#,&*&F0F&%#x1GF&F&*&%'omega1GF&F.F&F2F&F6F&F2*&-F)6#,&*&F:F&F1F& F&*&F-F&F8F&F2F&F>F&F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "g 0alpha=CrossProduct((omega),xx);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/% (g0alphaG-%'RTABLEG6$\")Ojf5-%'MATRIXG6#7%7#,&*&%'omega2G\"\"\"%#x3GF1 F1*&%'omega3GF1%#x2GF1!\"\"7#,&*&F4F1%#x1GF1F1*&%'omega1GF1F2F1F67#,&* &F " 0 "" {MPLTEXT 1 0 11 " makeg(rot);" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 46 "Makeg 2.0: GRTensor metric/bas is entry utility" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 41 "To quit makeg, type 'exit' at any prompt." }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 44 "Do you wish to ente r 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 basis [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 a s a LIST (eg. [t,r,theta,phi]):" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 10 "[t,x,y,z];" }}{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 0 207 "(1-((omega2*z-omega3*y)^2+(omega3*x-omega1*z)^2+(ome ga1*y-omega2*x)^2))*d[t]^2 - 2*(omega2*z-omega3*y)*d[t]*d[x] - 2*(omeg a3*x-omega1*z)*d[t]*d[y]- 2*(omega1*y-omega2*x)*d[t]*d[z] - d[x]^2 - d [y]^2 - d[z]^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 "for 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&%\"tG%\"xG%\"yG%\"zG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(Metric:G" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/*&&%\"gG6#%\"tG\"\"\"&%!GF'F),6F)F)*&)%'omega2G\"\"#F))%\"zGF0F)!\" \"*,F0F)F/F)F2F)%'omega3GF)%\"yGF)F)*&)F5F0F))F6F0F)F3*&F8F))%\"xGF0F) F3*,F0F)F5F)FF0F)F1F)F3*&F@F)F9F)F3*,F0F)F>F) F6F)F/F)F" 0 "" {MPLTEXT 1 0 2 "1;" }} {PARA 6 "" 1 "" {TEXT -1 17 "Initializing: rot" }}{PARA 6 "" 1 "" {TEXT -1 36 "Calculated ds for rot (.015000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2Default~spacetimeG%$rotG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%7For~the~rot~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%,CoordinatesG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"xG6#%#upG " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/)%#x~G%\"aG-%'vectorG6#7&%\"tG%\" xG%\"yG%\"zG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%-Line~elementG" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#/*$)%$~dsG\"\"#\"\"\",0*(,6F(F(*&)%'om ega2GF'F()%\"zGF'F(!\"\"*,F'F(F.F(F0F(%'omega3GF(%\"yGF(F(*&)F3F'F()F4 F'F(F1*&F6F()%\"xGF'F(F1*,F'F(F3F(F:F(%'omega1GF(F0F(F(*&)FF(F7F(F1*,F'F(F " 0 "" {MPLTEXT 1 0 22 "grcalc(Chr(dn,dn,dn));" }} {PARA 6 "" 1 "" {TEXT -1 46 "Calculated g(dn,dn,pdn) for rot (.015000 \+ sec.)" }}{PARA 6 "" 1 "" {TEXT -1 48 "Calculated Chr(dn,dn,dn) for rot (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#Z !\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "grdisplay(Chr(dn,dn ,dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%7For~the~rot~spacetime:G" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#%`oChristoffel~symbol~of~the~first~ki nd~(symmetric~in~first~two~indices)G" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/&%&GammaG6#*(%\"tG\"\"\"%\"tGF)%\"xGF),**&)%'omega3G\"\"#F)%\"xGF)F )*(F/F)%'omega1GF)%\"zGF)!\"\"*(F3F)%\"yGF)%'omega2GF)F5*&)F8F0F)F1F)F )" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%\"tG\"\"\"%\"tGF)% \"yGF),**(%'omega2GF)%\"zGF)%'omega3GF)!\"\"*&)F0\"\"#F)%\"yGF)F)*&)%' omega1GF4F)F5F)F)*(F8F)F.F)%\"xGF)F1" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/&%&GammaG6#*(%\"tG\"\"\"%\"tGF)%\"zGF),**&)%'omega2G\"\"#F)%\"zGF)F )*(F/F)%'omega3GF)%\"yGF)!\"\"*(F3F)%\"xGF)%'omega1GF)F5*&)F8F0F)F1F)F )" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%\"tG\"\"\"%\"xGF)% \"tGF),**&)%'omega3G\"\"#F)%\"xGF)!\"\"*(F/F)%'omega1GF)%\"zGF)F)*(F4F )%\"yGF)%'omega2GF)F)*&)F8F0F)F1F)F2" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/&%&GammaG6#*(%\"tG\"\"\"%\"xGF)%\"yGF),$%'omega3G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%\"tG\"\"\"%\"xGF)%\"zGF)%'omega2 G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%\"tG\"\"\"%\"yGF)% \"tGF),**(%'omega2GF)%\"zGF)%'omega3GF)F)*&)F0\"\"#F)%\"yGF)!\"\"*&)%' omega1GF3F)F4F)F5*(F8F)F.F)%\"xGF)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/&%&GammaG6#*(%\"tG\"\"\"%\"yGF)%\"xGF)%'omega3G" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#/&%&GammaG6#*(%\"tG\"\"\"%\"yGF)%\"zGF),$%'omega1G!\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%\"tG\"\"\"%\"zGF) %\"tGF),**&)%'omega2G\"\"#F)%\"zGF)!\"\"*(F/F)%'omega3GF)%\"yGF)F)*(F4 F)%\"xGF)%'omega1GF)F)*&)F8F0F)F1F)F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%\"tG\"\"\"%\"zGF)%\"xGF),$%'omega2G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%\"tG\"\"\"%\"zGF)%\"yGF)%'ome ga1G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "grcalc(Chr(dn,dn,up ));" }}{PARA 6 "" 1 "" {TEXT -1 39 "Calculated detg for rot (0.000000 \+ sec.)" }}{PARA 6 "" 1 "" {TEXT -1 43 "Calculated g(up,up) for rot (0.0 00000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 48 "Calculated Chr(dn,dn,up) f or rot (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~ G$\"\"!F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "grdisplay(Chr( dn,dn,up));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%7For~the~rot~spacetime :G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%aoChristoffel~symbol~of~the~sec ond~kind~(symmetric~in~first~two~indices)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"tG\"\"\"%\"tGF*F*)%!G%\"xGF*,**&)%'o mega3G\"\"#F*%\"xGF*!\"\"*(F2F*%'omega1GF*%\"zGF*F**(F7F*%\"yGF*%'omeg a2GF*F**&)F;F3F*F4F*F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG 6#*&%\"tG\"\"\"%\"tGF*F*)%!G%\"yGF*,**(%'omega2GF*%\"zGF*%'omega3GF*F* *&)F3\"\"#F*%\"yGF*!\"\"*&)%'omega1GF6F*F7F*F8*(F;F*F1F*%\"xGF*F*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"tG\"\"\"%\"tGF*F*)% !G%\"zGF*,**&)%'omega2G\"\"#F*%\"zGF*!\"\"*(F2F*%'omega3GF*%\"yGF*F**( F7F*%\"xGF*%'omega1GF*F**&)F;F3F*F4F*F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"tG\"\"\"%\"xGF*F*)%!G%\"yGF*%'omega3G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"tG\"\"\"%\"xGF*F*)% !G%\"zGF*,$%'omega2G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&Gam maG6#*&%\"tG\"\"\"%\"yGF*F*)%!G%\"xGF*,$%'omega3G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"tG\"\"\"%\"yGF*F*)%!G%\"zGF*%'o mega1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"tG\"\"\"% \"zGF*F*)%!G%\"xGF*%'omega2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%& GammaG6#*&%\"tG\"\"\"%\"zGF*F*)%!G%\"yGF*,$%'omega1G!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 27 "Frei-fallendes Bezugssystem" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "makeg(freifall);" }}{PARA 6 "" 1 " " {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 46 "Makeg 2.0: GRTensor metric/basis entry utility" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 41 "To quit makeg, type 'exit' 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-hol onomic basis [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 "1;" }}{PARA 6 "" 1 "" {TEXT -1 50 "Enter coordinates as a LIST (eg. [t,r,theta,phi]) :" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 10 "[t,x,y,z];" }} {PARA 6 "" 1 "" {TEXT -1 30 "Is the metric 1) Diagonal, or" }}{PARA 6 "" 1 "" {TEXT -1 28 " 2) Symmetric?" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 2 "1;" }}{PARA 6 "" 1 "" {TEXT -1 13 "Ent er g[t,t]:" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 10 "(1+g*x)^2 ;" }}{PARA 6 "" 1 "" {TEXT -1 13 "Enter g[x,x]:" }}}{EXCHG {PARA 0 "ma keg>" 0 "" {MPLTEXT 1 0 3 "-1;" }}{PARA 6 "" 1 "" {TEXT -1 13 "Enter g [y,y]:" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 3 "-1;" }}{PARA 6 "" 1 "" {TEXT -1 13 "Enter g[z,z]:" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 3 "-1;" }}{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 "for this spacetime, pleas e 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&%\"tG%\"xG%\"yG%\"zG " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(Metric:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%\"gG6#%\"aG\"\"\"&%!G6#%\"bGF)-%'matrixG6#7&7&*$), &F)F)*&F&F)%\"xGF)F)\"\"#F)\"\"!F9F97&F9!\"\"F9F97&F9F9F;F97&F9F9F9F; " }}{PARA 6 "" 1 "" {TEXT -1 54 "You may choose to 0) Use the metric W ITHOUT saving it," }}{PARA 6 "" 1 "" {TEXT -1 46 " 1) Save the metric as it is," }}{PARA 6 "" 1 "" {TEXT -1 54 " \+ 2) Correct an element of the metric," }}{PARA 6 "" 1 "" {TEXT -1 41 " 3) Re-enter the metric," }}{PARA 6 "" 1 "" {TEXT -1 54 " 4) Add/change constraint equations, " } }{PARA 6 "" 1 "" {TEXT -1 47 " 5) Add a text descript ion, or" }}{PARA 6 "" 1 "" {TEXT -1 61 " 6) Abandon t his metric and return to Maple." }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 2 "1;" }}{PARA 6 "" 1 "" {TEXT -1 22 "Initializing: freifall" }}{PARA 6 "" 1 "" {TEXT -1 42 "Ca lculated ds for freifall (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2Default~spacetimeG%)freifallG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 22 "grcalc(Chr(dn,dn,dn));" }} {PARA 6 "" 1 "" {TEXT -1 52 "Calculated g(dn,dn,pdn) for freifall (0.0 00000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 53 "Calculated Chr(dn,dn,dn) f or freifall (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~ Time~G$\"\"!F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "grdisplay (Chr(dn,dn,dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 22 "grcalc(Chr(dn,dn,up));" }} {PARA 6 "" 1 "" {TEXT -1 44 "Calculated detg for freifall (0.000000 se c.)" }}{PARA 6 "" 1 "" {TEXT -1 48 "Calculated g(up,up) for freifall ( 0.000000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 53 "Calculated Chr(dn,dn,up ) for freifall (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*C PU~Time~G$\"\"!F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "grdisp lay(Chr(dn,dn,up));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% " 0 "" {MPLTEXT 1 0 12 "make g(eukl);" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 46 "Makeg 2.0: GRTensor metric/basis \+ entry utility" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 41 "To quit makeg, type 'exit' at any prompt." }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 44 "Do you wish to ente r a 1) metric [g(dn,dn)]," }}{PARA 6 "" 1 "" {TEXT -1 44 " \+ 2) line element [ds]," }}{PARA 6 "" 1 "" {TEXT -1 63 " \+ 3) non-holonomic basis [e(1)...e(n)], or" }}{PARA 6 "" 1 "" {TEXT -1 49 " 4) NP tetrad [l,n,m,mbar]? " }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 2 "2;" }}{PARA 6 "" 1 "" {TEXT -1 50 "Enter coordinates a s a LIST (eg. [t,r,theta,phi]):" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 14 "[r,theta,phi];" }}{PARA 6 "" 1 "" {TEXT -1 64 "Enter \+ the line element using d[coord] to indicate differentials." }}{PARA 6 "" 1 "" {TEXT -1 55 "(for example, r^2*(d[theta]^2 + sin(theta)^2*d[p hi]^2)" }}{PARA 6 "" 1 "" {TEXT -1 27 "[Type 'exit' to quit makeg]" }} {PARA 6 "" 1 "" {TEXT -1 8 " ds^2 = " }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 48 "d[r]^2+r^2*d[theta]^2+r^2*sin(theta)^2*d[phi]^2;" }} {PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 67 "If there \+ are any complex valued coordinates, constants or functions" }}{PARA 6 "" 1 "" {TEXT -1 66 "for this spacetime, please enter them as a SET ( \+ eg. \{ z, psi \} )." }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 " " {TEXT -1 33 "Complex quantities [default=\{\}]: " }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 3 "\{\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #%AThe~values~you~have~entered~are:G" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/%,CoordinatesG7%%\"rG%&thetaG%$phiG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(Metric:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%\"gG6#%\"aG\" \"\"&%!G6#%\"bGF)K%'matrixG6#7%7%F)\"\"!F37%F3*$)%\"rG\"\"#F)F37%F3F3* &F6F))-%$sinG6#%&thetaGF8F)Q(pprint06\"" }}{PARA 6 "" 1 "" {TEXT -1 54 "You may choose to 0) Use the metric WITHOUT saving it," }}{PARA 6 "" 1 "" {TEXT -1 46 " 1) Save 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 description, or" }}{PARA 6 "" 1 "" {TEXT -1 61 " 6) Abandon this metric and return to Ma ple." }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 2 "1;" }}{PARA 6 "" 1 "" {TEXT -1 18 "Initializing: eukl " }}{PARA 6 "" 1 "" {TEXT -1 38 "Calculated ds for eukl (0.010000 sec. )" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2Default~spacetimeG%%euklG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%8For~the~eukl~spacetime: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%%\"rG%&thetaG%$phiGQ(pprint16\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%-Line~elementG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*$) %$~dsG\"\"#\"\"\",(*&%#~dGF()%\"rG%#2~GF(F(*()F-F'F(F+F()%&thetaGF.F(F (**F0F()-%$sinG6#F2F'F(F+F()%$phiGF.F(F(" }}{PARA 6 "" 1 "" {TEXT -1 18 "makeg() completed." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "g rcalc(Chr(dn,dn,dn));" }}{PARA 6 "" 1 "" {TEXT -1 48 "Calculated g(dn, dn,pdn) for eukl (0.010000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 49 "Calcu lated Chr(dn,dn,dn) for eukl (0.010000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#I!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "grdisplay(Chr(dn,dn,dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%8For~the~eukl~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%`oChristoffel~symbol~of~the~first~kind~(symmetric~in~f irst~two~indices)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(% \"rG\"\"\"%&thetaGF)%&thetaGF)%\"rG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #/&%&GammaG6#*(%\"rG\"\"\"%$phiGF)%$phiGF)*&%\"rGF))-%$sinG6#%&thetaG \"\"#F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%&thetaG\"\" \"%&thetaGF)%\"rGF),$%\"rG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&% &GammaG6#*(%&thetaG\"\"\"%$phiGF)%$phiGF)*()%\"rG\"\"#F)-%$sinG6#%&the taGF)-%$cosGF2F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%$ph iG\"\"\"%$phiGF)%\"rGF),$*&%\"rGF))-%$sinG6#%&thetaG\"\"#F)!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%$phiG\"\"\"%$phiGF)%&th etaGF),$*()%\"rG\"\"#F)-%$sinG6#%&thetaGF)-%$cosGF3F)!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "grcalc(Chr(dn,dn,up));" }}{PARA 6 " " 1 "" {TEXT -1 40 "Calculated detg for eukl (0.000000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 44 "Calculated g(up,up) for eukl (0.010000 sec.)" } }{PARA 6 "" 1 "" {TEXT -1 49 "Calculated Chr(dn,dn,up) for eukl (0.010 000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#?!\"$" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "grdisplay(Chr(dn,dn,up)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%8For~the~eukl~spacetime:G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%aoChristoffel~symbol~of~the~second~ki nd~(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\"\"\"%$phi GF*F*)%!G%$phiGF**&F*F*%\"rG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/ *&&%&GammaG6#*&%&thetaG\"\"\"%&thetaGF*F*)%!G%\"rGF*,$%\"rG!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%&thetaG\"\"\"%$phiGF* F*)%!G%$phiGF**&-%$sinG6#%&thetaG!\"\"-%$cosGF2F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%$phiG\"\"\"%$phiGF*F*)%!G%\"rGF*,$*&% \"rGF*)-%$sinG6#%&thetaG\"\"#F*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/*&&%&GammaG6#*&%$phiG\"\"\"%$phiGF*F*)%!G%&thetaGF*,$*&-%$sinG6#%&t hetaGF*-%$cosGF3F*!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 20 "Schwa rzschild-Metrik" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "makeg(SS );" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 1 " " } }{PARA 6 "" 1 "" {TEXT -1 46 "Makeg 2.0: GRTensor metric/basis entry u tility" }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 41 "To quit makeg, type 'exit' 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 basis [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 a s 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 "Ente r 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 83 "(1-2*M/r)*d[t]^2 - 1/(1-2*M/r)*d[r]^2 - r^2*d[theta ]^2 - r^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 coordinat es, constants or functions" }}{PARA 6 "" 1 "" {TEXT -1 66 "for this sp acetime, 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~a re:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%,CoordinatesG7&%\"tG%\"rG%&t hetaG%$phiG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(Metric:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%\"gG6#%\"aG\"\"\"&%!G6#%\"bGF)K%'matrixG6# 7&7&,&F)F)*(\"\"#F)%\"MGF)%\"rG!\"\"F8\"\"!F9F97&F9,$*&F)F)F3F8F8F9F97 &F9F9,$*$)F7F5F)F8F97&F9F9F9,$*&F@F))-%$sinG6#%&thetaGF5F)F8Q(pprint26 \"" }}{PARA 6 "" 1 "" {TEXT -1 54 "You may choose to 0) Use the metric WITHOUT saving it," }}{PARA 6 "" 1 "" {TEXT -1 46 " \+ 1) Save 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 des cription, or" }}{PARA 6 "" 1 "" {TEXT -1 61 " 6) Aban don this metric and return to Maple." }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 2 "1;" }}{PARA 6 "" 1 "" {TEXT -1 16 "Initializing: SS" }}{PARA 6 "" 1 "" {TEXT -1 36 "Calculat ed ds for SS (0.000000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2Def ault~spacetimeG%#SSG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%6For~the~SS~s pacetime: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%$phiGQ(pprint36\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%-Line~elementG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*$)%$~dsG\"\"#\"\"\",**(,&F(F(*(F'F(%\"MGF(%\"rG!\"\"F /F(%#~dGF()%\"tG%#2~GF(F(*(F+F/F0F()F.F3F(F/*()F.F'F(F0F()%&thetaGF3F( F/**F7F()-%$sinG6#F9F'F(F0F()%$phiGF3F(F/" }}{PARA 6 "" 1 "" {TEXT -1 18 "makeg() completed." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "g rcalc(Chr(dn,dn,dn));" }}{PARA 6 "" 1 "" {TEXT -1 46 "Calculated g(dn, dn,pdn) for SS (0.010000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 47 "Calcula ted Chr(dn,dn,dn) for SS (0.010000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#I!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "grdisplay(Chr(dn,dn,dn));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%6F or~the~SS~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%`oChristoffe l~symbol~of~the~first~kind~(symmetric~in~first~two~indices)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%\"tG\"\"\"%\"tGF)%\"rGF),$*&% \"MGF)%\"rG!\"#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*( %\"tG\"\"\"%\"rGF)%\"tGF)*&%\"MGF)%\"rG!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%\"rG\"\"\"%\"rGF)%\"rGF)*&%\"MGF),&%\"rG F)*&\"\"#F)F-F)!\"\"!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG 6#*(%\"rG\"\"\"%&thetaGF)%&thetaGF),$%\"rG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%\"rG\"\"\"%$phiGF)%$phiGF),$*&%\"rGF))-% $sinG6#%&thetaG\"\"#F)!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&Gam maG6#*(%&thetaG\"\"\"%&thetaGF)%\"rGF)%\"rG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%&thetaG\"\"\"%$phiGF)%$phiGF),$*()%\"rG \"\"#F)-%$sinG6#%&thetaGF)-%$cosGF3F)!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*(%$phiG\"\"\"%$phiGF)%\"rGF)*&%\"rGF))-%$s inG6#%&thetaG\"\"#F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&GammaG6#*( %$phiG\"\"\"%$phiGF)%&thetaGF)*()%\"rG\"\"#F)-%$sinG6#%&thetaGF)-%$cos GF2F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "grcalc(Chr(dn,dn,u p));" }}{PARA 6 "" 1 "" {TEXT -1 38 "Calculated detg for SS (0.000000 \+ sec.)" }}{PARA 6 "" 1 "" {TEXT -1 42 "Calculated g(up,up) for SS (0.01 0000 sec.)" }}{PARA 6 "" 1 "" {TEXT -1 47 "Calculated Chr(dn,dn,up) fo r SS (0.010000 sec.)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$ \"#I!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "grdisplay(Chr(d n,dn,up));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%6For~the~SS~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%aoChristoffel~symbol~of~the~second~kind~(symmetric~in~first~two ~indices)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"tG\" \"\"%\"tGF*F*)%!G%\"rGF**(,&%\"rGF**&\"\"#F*%\"MGF*!\"\"F*F1!\"$F4F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"tG\"\"\"%\"rGF*F* )%!G%\"tGF**(%\"rG!\"\",&F0F**&\"\"#F*%\"MGF*F1F1F5F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"rG\"\"\"%\"rGF*F*)%!G%\"rGF*,$* (%\"rG!\"\",&F1F**&\"\"#F*%\"MGF*F2F2F6F*F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"rG\"\"\"%&thetaGF*F*)%!G%&thetaGF**& F*F*%\"rG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%\"r G\"\"\"%$phiGF*F*)%!G%$phiGF**&F*F*%\"rG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%&thetaG\"\"\"%&thetaGF*F*)%!G%\"rGF*,& %\"rG!\"\"*&\"\"#F*%\"MGF*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%& GammaG6#*&%&thetaG\"\"\"%$phiGF*F*)%!G%$phiGF**&-%$sinG6#%&thetaG!\"\" -%$cosGF2F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&%$phiG \"\"\"%$phiGF*F*)%!G%\"rGF*,$*&,&%\"rGF**&\"\"#F*%\"MGF*!\"\"F*)-%$sin G6#%&thetaGF4F*F6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%&GammaG6#*&% $phiG\"\"\"%$phiGF*F*)%!G%&thetaGF*,$*&-%$sinG6#%&thetaGF*-%$cosGF3F*! \"\"" }}}}{MARK "55" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 12002196 11348516 10596336 }{RTABLE M7R0 I5RTABLE_SAVE/12002196X*%)anythingG6"6"[gl!#%!!!"$"$%'omega1G%'omega2G%'omega3G F& } {RTABLE M7R0 I5RTABLE_SAVE/11348516X*%)anythingG6"6"[gl!#%!!!"$"$%#x1G%#x2G%#x3GF& } {RTABLE M7R0 I5RTABLE_SAVE/10596336X*%)anythingG6"6"[gl!#%!!!"$"$,&*&%'omega2G"""%#x3GF*F**& %'omega3GF*%#x2GF*!"",&*&F-F*%#x1GF*F**&%'omega1GF*F+F*F/,&*&F4F*F.F*F**&F)F*F2 F*F/F& }