Positivity of polynomials on the nonnegative part of certain affine hypersurfaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911505664966656 |
|---|---|
| author | Tan, Colin To, Wing-Keung |
| author_facet | Tan, Colin To, Wing-Keung |
| contents | We consider polynomials on the intersection of the closed positive orthant with the height-$1$ level hypersurface of certain polynomials with positive coefficients. We show that any polynomial strictly positive on such a semi-algebraic set can be represented by some polynomial with only positive coefficients. This result generalizes a result of Pólya which corresponds to the case when the semi-algebraic set is the standard simplex. Our proof uses the Archimedean Representation Theorem from real algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10455 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Positivity of polynomials on the nonnegative part of certain affine hypersurfaces Tan, Colin To, Wing-Keung Algebraic Geometry Primary 12D99, 14P10, secondary 13J30, 26C99 We consider polynomials on the intersection of the closed positive orthant with the height-$1$ level hypersurface of certain polynomials with positive coefficients. We show that any polynomial strictly positive on such a semi-algebraic set can be represented by some polynomial with only positive coefficients. This result generalizes a result of Pólya which corresponds to the case when the semi-algebraic set is the standard simplex. Our proof uses the Archimedean Representation Theorem from real algebra. |
| title | Positivity of polynomials on the nonnegative part of certain affine hypersurfaces |
| topic | Algebraic Geometry Primary 12D99, 14P10, secondary 13J30, 26C99 |
| url | https://arxiv.org/abs/2603.10455 |