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Reports (Research Report) Year : 1994

Grobner bases of toric ideals


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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inria-00074446 , version 1 (24-05-2006)


  • 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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