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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 138 "Demonstration 1 (rnds): C
alculation of the invariants $R$,$R_\{ab\}^\{~~ab\}$,$R_\{abcd\}^\{~~~
~abcd\}$,$R_\{,a\}^\{~~,a\}$, and $R_\{ab;c\}^\{~~~~ab;c\}$" }}{PARA 
0 "" 0 "" {TEXT -1 43 "in the Reissner-Nordstrom-de Sitter metric." }}
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" {MPLTEXT 1 0 7 "grtw():" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%=GRTenso
rII~Version~1.79~(R6)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%02~February
~2001G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%ZDeveloped~by~Peter~Musgrav
e,~Denis~Pollney~and~Kayll~LakeG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%D
Copyright~1994-2001~by~the~authors.G" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#%inLatest~version~available~from:~http://grtensor.phy.queensu.ca/G" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "grlib(dinvar):" }}{PARA 
6 "" 1 "" {TEXT -1 25 "`Differential Invariants`" }}{PARA 6 "" 1 "" 
{TEXT -1 29 "`Last modified Jan. 20, 1995`" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "qload(rnds);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2
Default~spacetimeG%%rndsG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%8For~the
~rnds~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&%\"rG%&thetaG%$phiG%\"tG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%-Line~elementG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/*$)%$~dsG\"\"#\"\"\",**&*&%#~dGF()%\"rG%#2~GF(F(,*F(F(
*&*&F'F(%\"mGF(F(F.!\"\"F4*&#F(\"\"$F(*&%'LambdaGF()F.F'F(F(F4*&*$)%\"
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strom-de~Sitter~metricG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "
grcalc(Ricciscalar,RicciSq,RiemSq,Dsq[Ricciscalar],diRicci);" }}{PARA 
6 "" 1 "" {TEXT -1 32 "Created definition for R(up,dn) " }}{PARA 6 "" 
1 "" {TEXT -1 38 "Created definition for R(dn,dn,up,up) " }}{PARA 6 "
" 1 "" {TEXT -1 32 "Created definition for R(dn,up) " }}{PARA 6 "" 1 "
" {TEXT -1 37 "Created a definition for R(dn,up,cdn)" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#/%*CPU~Time~G$\"$]%!\"$" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "gralter(_,2,7);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Com
ponent simplification of a GRTensorII object:" }}{PARA 6 "" 1 "" 
{TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 55 "Applying routine `simplif
y[trig]` to object Ricciscalar" }}{PARA 6 "" 1 "" {TEXT -1 51 "Applyin
g routine `simplify[trig]` to object RicciSq" }}{PARA 6 "" 1 "" {TEXT 
-1 50 "Applying routine `simplify[trig]` to object RiemSq" }}{PARA 6 "
" 1 "" {TEXT -1 60 "Applying routine `simplify[trig]` to object Dsq[Ri
cciscalar]" }}{PARA 6 "" 1 "" {TEXT -1 51 "Applying routine `simplify[
trig]` to object diRicci" }}{PARA 6 "" 1 "" {TEXT -1 45 "Applying rout
ine factor to object Ricciscalar" }}{PARA 6 "" 1 "" {TEXT -1 41 "Apply
ing routine factor to object RicciSq" }}{PARA 6 "" 1 "" {TEXT -1 40 "A
pplying routine factor to object RiemSq" }}{PARA 6 "" 1 "" {TEXT -1 
50 "Applying routine factor to object Dsq[Ricciscalar]" }}{PARA 6 "" 
1 "" {TEXT -1 41 "Applying routine factor to object diRicci" }}{PARA 
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Ricci~scalarG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%#R~G,$%'LambdaG\"\"
%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%:Full~Contraction~of~RicciG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/%)RicciSq~G,$*&,&*&)%'LambdaG\"\"#\"
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" {XPPMATH 20 "6#%<Full~Contraction~of~RiemannG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/%#K~G,$*&,**&)%\"mG\"\"#\"\"\")%\"rGF+F,\"#=**\"#OF,F*
F,F.F,)%\"eGF+F,!\"\"*&)%'LambdaGF+F,)F.\"\")F,F,*&\"#@F,)F3\"\"%F,F,F
,*$F8F,F4#F9\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%6~g|fr^a~^b|hr~X
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}}{PARA 11 "" 1 "" {XPPMATH 20 "6#%9~R_|fra~b~;~e|hr~R^|fra~b~;~e|hrG
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