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arXiv · 1812.02612

Waring, tangential and cactus decompositions

Alessandra Bernardi·Daniele Taufer
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Abstract

(EN) We revise the famous algorithm for symmetric tensor decomposition due to Brachat, Comon, Mourrain and Tsidgaridas. Afterwards, we generalize it in order to detect possibly different decompositions involving points on the tangential variety of a Veronese variety. Finally, we produce an algorithm for cactus rank and decomposition, which also detects the support of the minimal apolar scheme and its length at each component. (FR) Nous revenons sur le fameux algorithme de Brachat, Comon, Mourrain et Tsidgaridas pour la d\'composition des tenseurs sym\'etriques. Ensuite, nous le g\'en\'eralisons afin de d\'etecter de possibles d\'ecompositions diff\'erentes impliquant des points sur la vari\'et\'e tangentielle d'une vari\'et\'e de Veronese. Enfin, nous proposons un algorithme pour le rang et la d\'ecomposition cactus, qui, lui aussi, d\'etecte le support du sch\'ema apolaire minimal ainsi que sa longueur sur chaque composante.

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Alessandra Bernardi, Daniele Taufer. 2018-12-06. Waring, tangential and cactus decompositions. https://doi.org/10.1016/j.matpur.2020.07.003

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