Trouble with epsilon_to_delta

Question

Hi,

With the following definitions

{i,j,k,m,n,p}::Indices(space, position=free);
{i,j,k,m,n,p}::Integer(1..4);
{a,b,c,d,e}::Indices(gauge, parent=space, position=free);
{a,b,c,d,e}::Integer(1..3);
\delta{#}::KroneckerDelta;
\epsilon{#}::EpsilonTensor(delta=\delta);

I would like to calculate the below product of two Epsilon tensors e transform them to a delta function

ex:=\epsilon_{a b c}\epsilon_{a i j 4};
epsilon_to_delta(_);

How can I tell to Cadabra that in this situation uses the a,b,c,... indices instead to i,j,... indices because of the one fixed index to 4?

Answer 1

I would make sure not to mix epsilons with different dimensions, so I would first

substitute(_, $\epsilon_{a i j 4} = \epsilon_{a i j}$);

and then the epsilon_to_delta does the right thing.