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• W2950486559 abstract "We 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 Grobner 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." @default.
• W2950486559 created "2019-06-27" @default.
• W2950486559 creator A5027670183 @default.
• W2950486559 creator A5049318367 @default.
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• W2950486559 creator A5074935193 @default.
• W2950486559 creator A5079338715 @default.
• W2950486559 date "2003-07-26" @default.
• W2950486559 modified "2023-10-03" @default.
• W2950486559 title "Short Rational Functions for Toric Algebra and Applications" @default.
• W2950486559 cites W1817594923 @default.
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• W2950486559 hasPublicationYear "2003" @default.
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