A new estimate for the number of solutions of a system of polynomial equations
| hal.structure.identifier | Institut de Mathématiques de Jussieu [IMJ] | |
| dc.contributor.author | PHILIPPON, Patrice | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | SOMBRA, Martin | |
| dc.date.accessioned | 2024-04-04T02:42:12Z | |
| dc.date.available | 2024-04-04T02:42:12Z | |
| dc.date.issued | 2007 | |
| dc.identifier.issn | 0764-4442 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191223 | |
| dc.description.abstractEn | A theorem of Kuˇsnirenko and Bernˇstein shows that the number of isolated roots in the torus of a system of polynomials is bounded above by the mixed volume of the Newton polytopes of the given polynomials, and that this upper bound is generically exact. We improve on this result by introducing refined combinatorial invariants of polynomials and a generalization of the mixed volume of convex bodies: the mixed integral of concave functions. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | A new estimate for the number of solutions of a system of polynomial equations | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| bordeaux.journal | Comptes rendus de l'Académie des sciences. Série I, Mathématique | |
| bordeaux.page | 335-340 | |
| bordeaux.volume | 345 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00358711 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00358711v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Comptes%20rendus%20de%20l'Acad%C3%A9mie%20des%20sciences.%20S%C3%A9rie%20I,%20Math%C3%A9matique&rft.date=2007&rft.volume=345&rft.spage=335-340&rft.epage=335-340&rft.eissn=0764-4442&rft.issn=0764-4442&rft.au=PHILIPPON,%20Patrice&SOMBRA,%20Martin&rft.genre=article |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||