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arXiv · 1803.00800

Waring decompositions and identifiability via Bertini and Macaulay2 software

Elena Angelini
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Abstract

Starting from our previous papers [AGMO] and [ABC], we prove the existence of a non-empty Euclidean open subset whose elements are polynomial vectors with 4 components, in 3 variables, degrees, respectively, 2,3,3,3 and rank 6, which are not identifiable over $ \mathbb{C} $ but are identifiable over $ \mathbb{R} $. This result has been obtained via computer-aided procedures suitably adapted to investigate the number of Waring decompositions for general polynomial vectors over the fields of complex and real numbers. Furthermore, by means of the Hessian criterion ([COV]), we prove identifiability over $ \mathbb{C} $ for polynomial vectors in many cases of sub-generic rank.

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Elena Angelini. 2018-03-02. Waring decompositions and identifiability via Bertini and Macaulay2 software. https://doi.org/10.1016/j.jsc.2018.06.021

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