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arXiv · 1307.3314

Apolarity and direct sum decomposability of polynomials

Weronika Buczyńska·Jarosław Buczyński·Johannes Kleppe·Zach Teitler
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Abstract

A polynomial is a direct sum if it can be written as a sum of two non-zero polynomials in some distinct sets of variables, up to a linear change of variables. We analyze criteria for a homogeneous polynomial to be decomposable as a direct sum, in terms of the apolar ideal of the polynomial. We prove that the apolar ideal of a polynomial of degree $d$ strictly depending on all variables has a minimal generator of degree $d$ if and only if it is a limit of direct sums.

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Weronika Buczyńska, Jarosław Buczyński, Johannes Kleppe, Zach Teitler. 2015-02-24. Apolarity and direct sum decomposability of polynomials. https://arxiv.org/abs/1307.3314

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