English

Decomposition algorithms for tensors and polynomials

Algebraic Geometry 2021-07-12 v1 Mathematical Software Symbolic Computation

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.

Keywords

Cite

@article{arxiv.2107.04097,
  title  = {Decomposition algorithms for tensors and polynomials},
  author = {Antonio Laface and Alex Massarenti and Rick Rischter},
  journal= {arXiv preprint arXiv:2107.04097},
  year   = {2021}
}

Comments

19 pages

R2 v1 2026-06-24T04:01:15.258Z