box% python
Python 3.8.6 (default, Sep 30 2020, 04:00:38)
[GCC 10.2.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> V1_indices = (1,2,3)
>>> V2_indices = (1,2,3,4,5)
>>> V1_tensor_V2_indices = tuple((i,j) for i in V1_indices for j in V2_indices)
>>> V1_tensor_V2_indices
((1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5))
>>> len(V1_tensor_V2_indices)
15
>>>
>>> def describe(name, indices): return f"{name} has basis vectors {', '.join(f'e_{i}' for i in indices)}"
...
>>> describe('V1', V1_indices)
'V1 has basis vectors e_1, e_2, e_3'
>>> describe('V2', V2_indices)
'V2 has basis vectors e_1, e_2, e_3, e_4, e_5'
>>> describe('V1_tensor_V2', V1_tensor_V2_indices)
'V1_tensor_V2 has basis vectors e_(1, 1), e_(1, 2), e_(1, 3), e_(1, 4), e_(1, 5), e_(2, 1), e_(2, 2), e_(2, 3), e_(2, 4), e_(2, 5), e_(3, 1), e_(3, 2), e_(3, 3), e_(3, 4), e_(3, 5)'
>>>