Dear community,
I'm using SAGE with SageManifolds to calculate Lie derivatives. First, I
would like to congratulate all the team of developers, because day to day
sagemanifolds get more useful. Next, the "problem".
I'm trying to find the most general rank two tensor compatible with O(3)
symmetry. Here some code:
# The manifold
M = Manifold(4, 'M')
# The patch
X.<t,r,th,ph> = M.chart(r't r:(0,+oo) th:(0,pi):\theta ph:(0,2*pi):\phi')
# Killing vectors
Lx = M.vector_field('Lx')
Lx[:] = ( 0, 0, -cos(ph), cot(th)*sin(ph) )
Ly = M.vector_field('Ly')
Ly[:] = ( 0, 0, sin(ph), cot(th)*cos(ph) )
Lz = M.vector_field('Lz')
Lz[:] = ( 0, 0, 0, 1)
# The general tensor
T = M.tensor_field( 0, 2, 'T' )
for i in xrange(4):
for j in xrange(4):
T[i,j] = function("T%s%s" % (i,j))(t, r, th, ph)
# One of the Lie derivatives
LxT = T.lie_der(Lx)
LxT.display_comp()
Then, the "problem" is that the PDE displayed show partial derivatives with
respect to `th` or `ph` instead of using the LaTeX symbols as defined on
the patch.
Is there a way to correct this behaviour?
Cheers.
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