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?
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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)