Short Rational Functions for Toric Algebra and Applications

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dc.creatorDe Loera, Jesus
dc.creatorHaws, David
dc.creatorHemmecke, Raymond
dc.creatorHuggins, Peter
dc.creatorSturmfels, Bernd
dc.creatorYoshida, Ruriko
dc.date2003-07-26
dc.date.accessioned2026-07-07T04:59:55Z
dc.date.available2026-07-07T04:59:55Z
dc.descriptionWe encode the binomials belonging to the toric ideal $I_A$ associated with an integral $d \times n$ matrix $A$ using a short sum of rational functions as introduced by Barvinok \cite{bar,newbar}. Under the assumption that $d,n$ are fixed, this representation allows us to compute the Graver basis and the reduced Gröbner basis of the ideal $I_A$, with respect to any term order, in time polynomial in the size of the input. We also derive a polynomial time algorithm for normal form computation which replaces in this new encoding the usual reductions typical of the division algorithm. We describe other applications, such as the computation of Hilbert series of normal semigroup rings, and we indicate further connections to integer programming and statistics.
dc.description13 pages, using elsart.sty and elsart.cls
dc.identifierhttps://arxiv.org/abs/math/0307350
dc.identifierhttp://arxiv.org/abs/math/0307350
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68180
dc.subjectCombinatorics
dc.subject05A15 (primary), 13P10 (secondary)
dc.titleShort Rational Functions for Toric Algebra and Applications
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