epsilon_to_delta function failed to evaluate

Question

I use the following code provided in the tutorial to convert a product of epsilon tensors to generalised delta functions, and the code works for \epsilon{a b c}\epsilon{a b c} but it fails when I tried to use \epsilon{a b c} \epsilon{a d e}. It just outputs the same input without evaluating. Here are the inputs

{a,b,c,d}::Indices. 
{a,b,c,d}::Integer(1..3). 
\delta{#}::KroneckerDelta; 
\epsilon_{a b c}::EpsilonTensor(delta=\delta);
ex:=\epsilon_{a b c} \epsilon_{a d e}; 
epsilon_to_delta(_); 
expand_delta(_);`

The output for the last command above is:

\epsilon_{abc}\epsilon_{ade}

without converting to the expect product of two \delta's.

This problem persists for all \epsilon products, for example:

{m,n,p,q,r,s,a,b,c,d}::Indices;
{m,n,p,q,r,s,a,b,c,d}::Integer(1..6).
\delta{#}::KroneckerDelta;
\epsilon_{m n p q r s}::EpsilonTensor(delta=\delta);
\xi_{a b}::AntiSymmetric;
ex:=\epsilon_{l q r s a b} \xi_{a b} \epsilon_{p u v l c d}\xi_{c d};
epsilon_to_delta(_);

The output for the last line above is the same as the Latex expression for "ex", namely

\epsilon_{l q r s a b} \xi_{a b} \epsilon_{p u v l c d}\xi_{c d}

I am not sure whether this is a bug ? I am using a terminal windows on MacOS Mojave 10.14.6. I tried to attach a screenshot showing the problem here but there is no option for me to attach a screenshot. I hope my description is not too confusing. Thanks in advance for any help possible.

Answer 1

The problem is that you are using indices on the epsilon symbols which are not part of the index set. In your first example, if you add the e index to the set by writing, instead of the first two lines,

{a,b,c,d,e}::Indices. 
{a,b,c,d,e}::Integer(1..3). 

then it works. In the second example, you need to add l, u, v in order to make it work.

Comments

Thank you. That does the trick. Stupid of me not to think of that.

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XD We all have happened through that!