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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "Creation of \"Frame-Field
\" for the mixmaster metric with constant basis inner product." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "
" {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" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#%4e:/Grtii(6)/MetricsG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "makeg(mix1);" }}{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 "3;" }}{PARA 6 
"" 1 "" {TEXT -1 50 "Enter coordinates as a LIST (eg. [t,r,theta,phi])
:" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 18 "[Theta,Phi,Psi,T];
" }}{PARA 6 "" 1 "" {TEXT -1 48 "Would you like to enter 1) covariant \+
components," }}{PARA 6 "" 1 "" {TEXT -1 55 "                        2)
 contravariant components, or" }}{PARA 6 "" 1 "" {TEXT -1 32 "        \+
                3) both." }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 
0 2 "1;" }}{PARA 6 "" 1 "" {TEXT -1 111 "Enter the covariant component
s of basis vector '1' as a LIST (eg. [1,0,0,0]) or differential (eg. d
[x] + d[y]):" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 83 "[-exp(a
(T))*(1-Psi^2)^(1/2)/(1-Theta^2)^(1/2),exp(a(T))*Psi*(1-Theta^2)^(1/2)
,0,0];" }}{PARA 6 "" 1 "" {TEXT -1 111 "Enter the covariant components
 of basis vector '2' as a LIST (eg. [1,0,0,0]) or differential (eg. d[
x] + d[y]):" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 84 "[-exp(b(
T))*Psi/(1-Theta^2)^(1/2),-exp(b(T))*(1-Theta^2)^(1/2)*(1-Psi^2)^(1/2)
,0,0];" }}{PARA 6 "" 1 "" {TEXT -1 111 "Enter the covariant components
 of basis vector '3' as a LIST (eg. [1,0,0,0]) or differential (eg. d[
x] + d[y]):" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 48 "[0,Theta
*exp(c(T)),exp(c(T))/(1-Psi^2)^(1/2),0];" }}{PARA 6 "" 1 "" {TEXT -1 
111 "Enter the covariant components of basis vector '4' as a LIST (eg.
 [1,0,0,0]) or differential (eg. d[x] + d[y]):" }}}{EXCHG {PARA 0 "mak
eg>" 0 "" {MPLTEXT 1 0 28 "[0,0,0,exp(a(T)+b(T)+c(T))];" }}{PARA 6 "" 
1 "" {TEXT -1 43 "Is the basis inner product  1) Diagonal, or" }}
{PARA 6 "" 1 "" {TEXT -1 41 "                            2) Symmetric?
" }}}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 2 "1;" }}{PARA 6 "" 1 "
" {TEXT -1 15 "Enter eta[1,1]:" }}}{EXCHG {PARA 0 "makeg>" 0 "" 
{MPLTEXT 1 0 2 "1;" }}{PARA 6 "" 1 "" {TEXT -1 15 "Enter eta[2,2]:" }}
}{EXCHG {PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 2 "1;" }}{PARA 6 "" 1 "" 
{TEXT -1 15 "Enter eta[3,3]:" }}}{EXCHG {PARA 0 "makeg>" 0 "" 
{MPLTEXT 1 0 2 "1;" }}{PARA 6 "" 1 "" {TEXT -1 15 "Enter eta[4,4]:" }}
}{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, 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#/%,Coordinat
esG7&%&ThetaG%$PhiG%$PsiG%\"TG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%/Ba
sis~1-forms:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&omegaG6#\"\"\"-%'
vectorG6#7&,$*&*&-%$expG6#-%\"aG6#%\"TGF'-%%sqrtG6#,&F'F'*$)%$PsiG\"\"
#F'!\"\"F'F'*$-F76#,&F'F'*$)%&ThetaGF=F'F>F'F>F>*(F/F'F<F'-F76#FBF'\"
\"!FI" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&omegaG6#\"\"#-%'vectorG6#
7&,$*&*&-%$expG6#-%\"bG6#%\"TG\"\"\"%$PsiGF6F6*$-%%sqrtG6#,&F6F6*$)%&T
hetaGF'F6!\"\"F6F@F@,$*(F/F6-F:6#F<F6-F:6#,&F6F6*$)F7F'F6F@F6F@\"\"!FJ
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&omegaG6#\"\"$-%'vectorG6#7&\"
\"!*&%&ThetaG\"\"\"-%$expG6#-%\"cG6#%\"TGF/*&F0F/*$-%%sqrtG6#,&F/F/*$)
%$PsiG\"\"#F/!\"\"F/FAF," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%&omegaG
6#\"\"%-%'vectorG6#7&\"\"!F,F,-%$expG6#,(-%\"aG6#%\"TG\"\"\"-%\"bGF3F5
-%\"cGF3F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%@Inner~product~of~basis
~vectors:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%$etaG-%'matrixG6#7&7&
\"\"\"\"\"!F+F+7&F+F*F+F+7&F+F+F*F+7&F+F+F+!\"\"" }}{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 45 "                  2) Re-enter a
 basis vector," }}{PARA 6 "" 1 "" {TEXT -1 48 "                  3) Re
-enter the inner product," }}{PARA 6 "" 1 "" {TEXT -1 44 "            \+
      4) Add/change constraints," }}{PARA 6 "" 1 "" {TEXT -1 48 "     \+
              5) Add a text description, or" }}{PARA 6 "" 1 "" {TEXT 
-1 61 "                  6) Abandon this metric and return to Maple." 
}}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "makeg>" 0 "" 
{MPLTEXT 1 0 2 "5;" }}{PARA 6 "" 1 "" {TEXT -1 23 "Enter text informat
ion:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "Mixmaster metric (e
.g. MTW Box 30.1, Theta = cos(theta), Psi = sin(psi))" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#%AThe~values~you~have~entered~are:G" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#/%,CoordinatesG7&%&ThetaG%$PhiG%$PsiG%\"TG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%/Basis~1-forms:G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/&%&omegaG6#\"\"\"-%'vectorG6#7&,$*&*&-%$expG6#-%\"aG6#
%\"TGF'-%%sqrtG6#,&F'F'*$)%$PsiG\"\"#F'!\"\"F'F'*$-F76#,&F'F'*$)%&Thet
aGF=F'F>F'F>F>*(F/F'F<F'-F76#FBF'\"\"!FI" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/&%&omegaG6#\"\"#-%'vectorG6#7&,$*&*&-%$expG6#-%\"bG6#%\"TG\"\"
\"%$PsiGF6F6*$-%%sqrtG6#,&F6F6*$)%&ThetaGF'F6!\"\"F6F@F@,$*(F/F6-F:6#F
<F6-F:6#,&F6F6*$)F7F'F6F@F6F@\"\"!FJ" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#/&%&omegaG6#\"\"$-%'vectorG6#7&\"\"!*&%&ThetaG\"\"\"-%$expG6#-%\"cG6
#%\"TGF/*&F0F/*$-%%sqrtG6#,&F/F/*$)%$PsiG\"\"#F/!\"\"F/FAF," }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/&%&omegaG6#\"\"%-%'vectorG6#7&\"\"!F,F,-%$e
xpG6#,(-%\"aG6#%\"TG\"\"\"-%\"bGF3F5-%\"cGF3F5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%@Inner~product~of~basis~vectors:G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/%$etaG-%'matrixG6#7&7&\"\"\"\"\"!F+F+7&F+F*F+F+7&F+F+F
*F+7&F+F+F+!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QcoMixmaster~metri
c~(e.g.~MTW~Box~30.1,~Theta~=~cos(theta),~Psi~=~sin(psi))6\"" }}{PARA 
6 "" 1 "" {TEXT -1 54 "You may choose to 0) Use the metric WITHOUT sav
ing it," }}{PARA 6 "" 1 "" {TEXT -1 46 "                  1) Save the \+
metric as it is," }}{PARA 6 "" 1 "" {TEXT -1 45 "                  2) \+
Re-enter a basis vector," }}{PARA 6 "" 1 "" {TEXT -1 48 "             \+
     3) Re-enter the inner product," }}{PARA 6 "" 1 "" {TEXT -1 44 "  \+
                4) Add/change constraints," }}{PARA 6 "" 1 "" {TEXT 
-1 48 "                   5) Add a text description, or" }}{PARA 6 "" 
1 "" {TEXT -1 61 "                  6) Abandon 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 54 "Information wr
itten to: `e:/Grtii(6)/Metrics/mix1.mpl`" }}{PARA 6 "" 1 "" {TEXT -1 
57 "Do you wish to use this spacetime in the current session?" }}
{PARA 6 "" 1 "" {TEXT -1 29 "(1=yes [default], other=no): " }}}{EXCHG 
{PARA 0 "makeg>" 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "19 0 0" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }