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arXiv · 2508.15062

A refinement on the local cactus rank algorithm

Alessandra Bernardi·Oriol Reig Fité
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Abstract

We present an algorithm to recover a minimal local apolar scheme to a homogeneous polynomial $F$. The socle degree of the scheme determines whether it is evinced by a Generalized Additive Decomposition (GAD) of $F$ or of an extension. We give constructive procedures for both cases and compute the Hilbert function efficiently via Hankel operators.

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Alessandra Bernardi, Oriol Reig Fité. 2025-08-20. A refinement on the local cactus rank algorithm. https://arxiv.org/abs/2508.15062

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