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 new 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.
Decomposition Algorithms for Tensors and Polynomials
Massarenti A.
;
2023
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 new 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.File in questo prodotto:
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