# 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
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https://hal.inria.fr/inria-00074446
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 3:19:04 PM
Last modification on : Monday, April 27, 2020 - 10:10:05 PM
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### Identifiers

• HAL Id : inria-00074446, version 1

### Citation

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

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