{"ID":2885506,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.04027","arxiv_id":"2508.04027","title":"Non-negative polynomials without hyperbolic certificates of non-negativity","abstract":"In this paper we study the relationship between the set of all non-negative multivariate homogeneous polynomials and those, which we call hyperwrons, whose non-negativity can be deduced from an identity involving the Wronskians of hyperbolic polynomials. We give a sufficient condition on positive integers $m$ and $2y$ such that there are non-negative polynomials of degree $2y$ in $m$ variables that are not hyperwrons. Furthermore, we give an explicit example of a non-negative quartic form that is not a sum of hyperwrons. We partially extend our results to hyperzouts, which are polynomials whose non-negativity can be deduced from an identity involving the Bézoutians of hyperbolic polynomials.","short_abstract":"In this paper we study the relationship between the set of all non-negative multivariate homogeneous polynomials and those, which we call hyperwrons, whose non-negativity can be deduced from an identity involving the Wronskians of hyperbolic polynomials. We give a sufficient condition on positive integers $m$ and $2y$...","url_abs":"https://arxiv.org/abs/2508.04027","url_pdf":"https://arxiv.org/pdf/2508.04027v3","authors":"[\"H. L. Brian Ng\",\"James Saunderson\"]","published":"2025-08-06T02:42:54Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.AG\"]","methods":"[]","has_code":false}