# Grobner bases of toric ideals

1 SAFIR - Algebraic Formal Systems for Industry and Research
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We study here \grobner\ bases of ideals which define toric varieties. We connect these ideals with the sub-lattices of $Z^d$, then deduce properties on their \grobner\ bases, and give applications of these results. The main contributions of the report are a bound on the degree of the \grobner\ bases, the fact that they contain Minkowski successive minima of a lattice (in particular shortest vector), and the algorithm (derived from Buchberger algorithm), which starts with ideal of polynomials with less variables than usual
Keywords :
Type de document :
Rapport
[Research Report] RR-2224, INRIA. 1994
Domaine :

https://hal.inria.fr/inria-00074446
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 15:19:04
Dernière modification le : samedi 27 janvier 2018 - 01:31:36
Document(s) archivé(s) le : lundi 5 avril 2010 - 00:10:23

### Identifiants

• HAL Id : inria-00074446, version 1

### Citation

Loïc Pottier. Grobner bases of toric ideals. [Research Report] RR-2224, INRIA. 1994. 〈inria-00074446〉

### Métriques

Consultations de la notice

## 178

Téléchargements de fichiers