论文信息 - Polynomial complexity for Hilbert series of Borel type ideals

Polynomial complexity for Hilbert series of Borel type ideals

In this paper, it is shown that the Hilbert series of a Borel type ideal may be computed within a complexity which is polynomial in Dn where n + 1 is the number of unknowns and D is the highest degree of a minimal generator of input (monomial) ideal.

AMIR HASHEMI | A. Hashemi

[1] Amir Hashemi,et al. Polynomial-time algorithm for Hilbert series of Borel type ideals , 2007, SNC '07.

[2] D. Bayer,et al. A criterion for detecting m-regularity , 2008 .

[3] Ralf Fröberg,et al. An introduction to Gröbner bases , 1997, Pure and applied mathematics.

[4] Sarfraz Ahmad,et al. Regularity of ideals of Borel type is linearly bounded , 2006, math/0610537.

[5] Hans Schönemann,et al. SINGULAR: a computer algebra system for polynomial computations , 2001, ACCA.

[6] Michael Eugene Stillman,et al. Computation of Hilbert Functions , 1992, J. Symb. Comput..

[7] Philippe Gimenez,et al. Computing the Castelnuovo–Mumford regularity of some subschemes of PKn using quotients of monomial ideals , 2001 .

[8] Carlo Traverso,et al. A "Divide and Conquer" Algorithm for Hilbert-Poincaré Series, Multiplicity and Dimension of Monomial Ideals , 1993, AAECC.

[9] Michel Kervaire,et al. Minimal resolutions of some monomial ideals , 1990 .

[10] A. Meyer,et al. The complexity of the word problems for commutative semigroups and polynomial ideals , 1982 .