Maxima Function
riemann (dis)
A function in the ctensor
(component tensor)
package. riemann
computes the Riemann curvature tensor
from the given metric and the corresponding Christoffel symbols. The following
index conventions are used:
l _l _l _l _m _l _m R[i,j,k,l] = R = | - | + | | - | | ijk ij,k ik,j mk ij mj ik
This notation is consistent with the notation used by the itensor
package and its icurvature
function.
If the optional argument dis is true
,
the non-zero components riem[i,j,k,l]
will be displayed.
As with the Einstein tensor, various switches set by the user
control the simplification of the components of the Riemann tensor.
If ratriemann
is true
, then
rational simplification will be done. If ratfac
is true
then
each of the components will also be factored.
If the variable cframe_flag
is false
, the Riemann tensor is
computed directly from the Christoffel-symbols. If cframe_flag
is
true
, the covariant Riemann-tensor is computed first from the
frame field coefficients.