some basic tensors with sympy

[Chaffra Affouda]

How do I implement the Levi-Civita and Kroenecker tensors in sympy? I am doing

from sympy.tensor.tensor import TensorIndexType, tensor_indices

from sympy.tensor.tensor import tensorhead, TensorManager

from sympy.tensor.tensor import get_symmetric_group_sgs

from sympy import LeviCivita

Lorentz = TensorIndexType('Lorentz',

                          dim=3,

                          eps_dim=3,

                          metric=False,

                          dummy_fmt='L')

Lorentz.data = [1,1,1]

Lorentz.epsilon.data = [[[LeviCivita(i,j,k) for k in range(3)] 

                         for j in range(3)] 

                        for i in range(3)]

i,j,k,l,m, n = tensor_indices('i,j,k,l,m,n', Lorentz)

eps = Lorentz.epsilon

delta = Lorentz.delta

Is this correct?

[Francesco Bonazzi]

eps is a Levi-Civita symbol.

Be careful, LeviCivita is not part of sympy.tensor.tensor, and is not designed to interoperate with that module.

Also consider that you are defining a Lorentz tensor index type as a 3 dimensional Euclidean index type.

I just noticed that the Kronecker delta is not filled with components data. Opened an issue:
https://github.com/sympy/sympy/issues/8743