Details:
Title  Short rational functions for toric algebra and applications  Author(s)  Jesus A. de Loera, D. Haws, Raymond Hemmecke, P. Huggins, Bernd Sturmfels, R. Yoshida  Type  Article in Journal  Abstract  We encode the binomials belonging to the toric ideal IA associated with an integral d×n matrix A using a short sum of rational functions as introduced by Barvinok (Math. Operations Research 19 (1994) 769) and Barvinok and Woods (J. Amer. Math. Soc. 16 (2003) 957). Under the assumption that d and n are fixed, this representation allows us to compute a universal Gröbner basis and the reduced Gröbner basis of the ideal IA, 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 computations 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 applications to enumerative combinatorics, integer programming, and statistics.  Keywords  Gröbner basis, Toric ideals, Hilbert series, Short rational function, Barvinok’s algorithm, Ehrhart polynomial, Lattice points, Magic cubes and squares  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717104000252 
Language  English  Journal  Journal of Symbolic Computation  Volume  38  Number  2  Pages  959  973  Year  2004  Edition  0  Translation 
No  Refereed 
No 
