Today I have been looking at the sympy tensor package. I have attached a
script in which I am trying to end of defining the Einstein tensor: R_{a b}
- 1/2 *g_{a b} * R. But the script does not succeed on the last step of
evaluating the above expression and hence fails to agree to create the
Einstein tensor. I am wondering what I am doing incorrectly?
Thanks for advice.
Comer
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from sympy import Matrix, eye
from sympy.combinatorics import Permutation
from sympy.core import S, Rational, Symbol, Basic
from sympy.core.containers import Tuple
from sympy.core.symbol import symbols
from sympy.external import import_module
#from sympy.functions.elementary.miscellaneous import sqrt
from sympy.printing.pretty.pretty import pretty
from sympy.tensor.tensor import TensorIndexType, tensor_indices, TensorSymmetry, \
get_symmetric_group_sgs, TensorType, TensorIndex, tensor_mul, TensAdd, \
riemann_cyclic_replace, riemann_cyclic, TensMul, \
tensorsymmetry, tensorhead, TensorManager, TensExpr, TIDS
Lorentz = TensorIndexType('Lorentz', dummy_fmt='L')
d0, d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, d11 =tensor_indices('d0:12', Lorentz)
a,b,c,d = tensor_indices('a,b,c,d',Lorentz)
Riem = tensorhead('Riem', [Lorentz]*4, [[2, 2]])
sym2 = tensorsymmetry([1]*2)
S2 = TensorType([Lorentz]*2,sym2)
Ric = S2('Ric')
Ric = Riem(d0, -d1, -d0, -d3)
print Ric(-a,-b)
R = Ric(d0,-d0)
g = Lorentz.metric
Ric(-a,-b) -tensor_mul(Rational(1,2)*g(-a,-b) * R)
