Hi all,
I was wondering if, using the sympy.tensor module, I can contract two
epsilon tensors to get kronecker deltas?
In particular, if I have something like
from sympy.tensor.tensor import TensorIndexType, tensor_indices
Spin = TensorIndexType('Spin', dummy_fmt='S', dim=3)
i, j, k, l, m = tensor_indices('i, j, k, l, m', Spin)
delta = Spin.delta
eps = Spin.epsilon
q = eps(i,j,k)*eps(-i,l,m)
print(q)
then I get
>>> Eps(S_0, j, k)*Eps(-S_0, l, m)
In 3 dimensions, I would want to contract the $ \epsilon^{ijk}
\epsilon^{ilm} $ to give me
$\delta^{jl}\delta^{km} - \delta^{jm}\delta^{lk}$$. So, I would like to
have something like `q.epsilon_to_delta` to get
q.epsilon_to_delta()
print(q)
>>> KD(j,l)*KD(k,m) - KD(j,m)*KD(l,k)
Is this possible?
Thanks!
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