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.

中文翻译：

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张量和多项式的分解算法

我们给出了算法来计算给定多项式的分解，或者更普遍的混合张量，作为一阶张量的总和，并确定这样的分解是否是唯一的。特别是，我们提出了计算一般平面五次幂分解和一般空间三次幂分解的方法；九阶一般平面六合一的两次分解，以及一般平面化粪池的五次分解。此外，我们给出了我们所有算法的 Magma 实现。