Maxima Function
igeodesic_coords (expr, name)
Causes undifferentiated Christoffel symbols and
first derivatives of the metric tensor vanish in expr. The name
in the igeodesic_coords
function refers to the metric name
(if it appears in expr) while the connection coefficients must be
called with the names ichr1
and/or ichr2
. The following example
demonstrates the verification of the cyclic identity satisfied by the Riemann
curvature tensor using the igeodesic_coords
function.
(%i1) load(itensor); (%o1) /share/tensor/itensor.lisp (%i2) ishow(icurvature([r,s,t],[u]))$ u u %1 u (%t2) - ichr2 - ichr2 ichr2 + ichr2 r t,s %1 s r t r s,t u %1 + ichr2 ichr2 %1 t r s (%i3) ishow(igeodesic_coords(%,ichr2))$ u u (%t3) ichr2 - ichr2 r s,t r t,s (%i4) ishow(igeodesic_coords(icurvature([r,s,t],[u]),ichr2)+ igeodesic_coords(icurvature([s,t,r],[u]),ichr2)+ igeodesic_coords(icurvature([t,r,s],[u]),ichr2))$ u u u u (%t4) - ichr2 + ichr2 + ichr2 - ichr2 t s,r t r,s s t,r s r,t u u - ichr2 + ichr2 r t,s r s,t (%i5) canform(%); (%o5) 0