Decomposition algorithms for tensors and polynomials

Antonio Laface; Alex Massarenti; Rick Rischter

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arXiv · 2107.04097

Decomposition algorithms for tensors and polynomials

Antonio Laface·Alex Massarenti·Rick Rischter

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Abstract

We give algorithms to compute decompositions of a given polynomial, or more generally mixed tensor, as sum of rank one tensors, and to establish whether such a decomposition is unique. In particular, we present methods to compute the decomposition of a general plane quintic in seven powers, and of a general space cubic in five powers; the two decompositions of a general plane sextic of rank nine, and the five decompositions of a general plane septic. Furthermore, we give Magma implementations of all our algorithms.

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Antonio Laface, Alex Massarenti, Rick Rischter. 2021-07-08. Decomposition algorithms for tensors and polynomials. https://arxiv.org/abs/2107.04097

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