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

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