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I've been using Carl Woll's einsum function, but it's missing the ability to handle repeated indices.

For instance np.einsum('i,i->i',w, w) will perform a Hadamard product, so it makes sense for Mathematica's einsum to do the same for einsum[{{1}, {1}} -> {1}, a, a].

Another example, the following einsum in Python produces outer product of diagonal of A with $a\odot b$

np.einsum('ii,j,j->ij', A, b, c)

In Mathematica syntax this could look like this:

einsum[{{1,1}, {2}, {2} -> {1,2}, A, b, c]

Jacob Biamonte visualizes this kind of structure using "COPY-tensor", but it's really just an edge with more than 2 endpoints - a hyper-edge, so it would be useful to have it supported

enter image description here

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  • $\begingroup$ +1 would be nice to have this. I've made a version of EinsteinSummation that can do this EinsteinSummation. It replaces TensorContract with SymbolicTensors`ArrayContract, but it no longer works with the Inactive tensor product, so it doesn't compute optimal contraction order anymore. $\endgroup$
    – swish
    Commented Apr 6, 2023 at 13:10

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