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I know the two tensor case, but how about high order?

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It is a hard problem and to the best of my knowledge nobody is able to provide an algorithm for this today. It is a harder problem than finding the irreducible components of a polynomial.

On finite fields, you can try brute force. For the related problem of factoring polynomials on a finite field, there are some algorithms (or heuristics) that are implemented in Macaulay2, so you could try to take a look there.

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