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.

翻译：我们给出了算法来计算某一多面性分解,或者更一般地说混合色分解,作为一等数的一等数之和,并确定这种分解是否独特。 特别是,我们给出了方法来计算普通平面五等分解为七等数的分解和五等数的普通空间立方体的分解;九等分层一般平面性分解的两种分解,以及普通平面化化的五等分解。 此外,我们给出了马格玛对我们所有算法的运用。