Non-negative polynomials without hyperbolic certificates of non-negativity
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910028442632192 |
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| author | Ng, H. L. Brian Saunderson, James |
| author_facet | Ng, H. L. Brian Saunderson, James |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04027 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-negative polynomials without hyperbolic certificates of non-negativity Ng, H. L. Brian Saunderson, James Optimization and Control Algebraic Geometry 14P10, 52A20, 13J30 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. |
| title | Non-negative polynomials without hyperbolic certificates of non-negativity |
| topic | Optimization and Control Algebraic Geometry 14P10, 52A20, 13J30 |
| url | https://arxiv.org/abs/2508.04027 |