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{SCP_R 1 0 47{COM_R 2 0{TEXT 3 61 "USING A GENERALIZED BASIS IN C
ALCULATING THE CURVATURE TENSOR"}}{COM_R 3 0{TEXT 1 184 "\015This
 program was developed in 1986 for the Grad Student Rational Calc
ulator program of F. J. Ernst.  Here we rewrite the program for M
aple.  Reference: J. Math. Phys. 12, 2395 (1971)."}}{COM_R 4 0
{TEXT 1 213 "\015We shall employ a generic procedure to calculate
d the Ricci rotation matrix of differential forms, given the diff
erentials\012of the basic 1-forms e[a], and the metric g[a,b] wit
h respect to that generalized basis.\015"}}{INP_R 5 0 "> "{TEXT 0
 12 "with(share):"}}{COM_R 6 0{TEXT 1 56 "Employ the FJE ENTERPRI
SES revision of difforms package:"}}{INP_R 7 0 "> "{TEXT 0 45 "re
adshare(fjeforms,fjeforms); with(fjeforms):"}}{INP_R 8 0 "> "
{TEXT 0 28 "readshare(RRsolve,fjeforms);"}}{COM_R 9 0{TEXT 1 34 "
Select a block form for the metric"}}{INP_R 10 0 "> "{TEXT 0 32 "
g := array(symmetric,0..3,0..3):"}}{INP_R 11 0 "> "{TEXT 0 13 "g[
0,0] := -1:"}}{INP_R 12 0 "> "{TEXT 0 36 "for a from 1 to 3 do g[
0,a] := 0 od:"}}{COM_R 13 0{TEXT 1 43 "Specify how to display par
tial derivatives:"}}{INP_R 14 0 "> "{TEXT 0 44 "dcomps := [d(x[0]
),`d[0]`],[d(x[1]),`d[1]`],"}}{INP_R 15 0 "> "{TEXT 0 45 "       \+
    [d(x[2]),`d[2]`],[d(x[3]),`d[3]`];"}}{COM_R 16 0{TEXT 1 49 "C
ompute and print out the differential of metric:"}}{INP_R 17 0 ">
 "{TEXT 0 20 "for a from 0 to 3 do"}}{INP_R 18 0 "> "{TEXT 0 25 "
     for b from 0 to 3 do"}}{INP_R 19 0 "> "{TEXT 0 37 "         \+
dg[a,b] := d(g[a,b],dcomps);"}}{INP_R 20 0 "> "{TEXT 0 43 "      \+
   print( evaln(dg[a,b]) = dg[a,b] );"}}{INP_R 21 0 "> "{TEXT 0 8
 "     od;"}}{INP_R 22 0 "> "{TEXT 0 4 " od;"}}{COM_R 23 0{TEXT 1
 37 "Next we specify the choice of tetrad."}}{INP_R 24 0 "> "
{TEXT 0 65 "e[0] := sqrt(F)*(d(x[0])-W[1]*d(x[1])-W[2]*d(x[2])-W[
3]*d(x[3]));"}}{INP_R 25 0 "> "{TEXT 0 48 "for a from 1 to 3 do e
[a] := d(x[a])/sqrt(F) od;"}}{COM_R 26 0{TEXT 1 54 "The different
ials of these basic 1-forms are given by:"}}{INP_R 27 0 "> "{TEXT
 0 48 "for a from 0 to 3 do de[a] := d(e[a],dcomps) od;"}}{COM_R 
28 0{TEXT 1 54 "Now we can express de[a] and dg[a,b] in terms of \+
e[a]:"}}{INP_R 29 0 "> "{TEXT 0 45 "for a from 0 to 3 do e[a] := \+
evaln(e[a]); od:"}}{INP_R 30 0 "> "{TEXT 0 37 "defform(e[0]=1,e[1
]=1,e[2]=1,e[3]=1):"}}{INP_R 31 0 "> "{TEXT 0 49 "for a from 1 to
 3 do d(x[a]) := sqrt(F)*e[a]; od;"}}{INP_R 32 0 "> "{TEXT 0 63 "
d(x[0]) := W[1]*d(x[1])+W[2]*d(x[2])+W[3]*d(x[3])+e[0]/sqrt(F);"}
}{INP_R 33 0 "> "{TEXT 0 57 "for a from 0 to 3 do de[a] := simpfo
rm(expand(de[a])) od;"}}{INP_R 34 0 "> "{TEXT 0 20 "for a from 0 \+
to 3 do"}}{INP_R 35 0 "> "{TEXT 0 25 "     for b from 0 to 3 do"}
}{INP_R 36 0 "> "{TEXT 0 46 "         dg[a,b] := simpform(expand(
dg[a,b]));"}}{INP_R 37 0 "> "{TEXT 0 43 "         print( evaln(dg
[a,b]) = dg[a,b] );"}}{INP_R 38 0 "> "{TEXT 0 7 "     od"}}{INP_R
 39 0 "> "{TEXT 0 4 " od;"}}{COM_R 40 0{TEXT 1 81 "Call RRsolve, \+
which computes the skew-symmetric Ricci rotation matrix Omega[a,b
]."}}{INP_R 41 0 "> "{TEXT 0 17 "RRsolve(de,g,dg);"}}{COM_R 42 0
{TEXT 1 43 "Print out Ricci rotation matrix Omega[a,b]:"}}{INP_R 
43 0 "> "{TEXT 0 20 "for a from 0 to 3 do"}}{INP_R 44 0 "> "{TEXT
 0 24 "    for b from 0 to 3 do"}}{INP_R 45 0 "> "{TEXT 0 47 "   \+
      print( evaln(Omega[a,b]) = Omega[a,b])"}}{INP_R 46 0 "> "
{TEXT 0 6 "    od"}}{INP_R 47 0 "> "{TEXT 0 3 "od;"}}{INP_R 48 0 
"> "{TEXT 0 0 ""}}}{END}
