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Grobner bases of toric ideals

Loïc Pottier 1
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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Submitted on : Wednesday, May 24, 2006 - 3:19:04 PM
Last modification on : Friday, February 4, 2022 - 3:16:20 AM
Long-term archiving on: : Monday, April 5, 2010 - 12:10:23 AM


  • HAL Id : inria-00074446, version 1



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



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