Amir Hashemi
ABSTRACT
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.
- D. Bayer and M. Stillman. A criterion for detecting m-regularity. Invent. Math., 87(1):1--11, 1987.Google Scholar
Cross Ref
- D. Bayer and M. Stillman. Computation of Hilbert functions. J. Symbolic Comput., 14(1):31--50, 1992. Google ScholarDigital Library
- I. Bermejo and P. Gimenez. Computing the Castelnuovo-Mumford regularity of some subschemes of PnK using quotients of monomial ideals. J. Pure Appl. Algebra, 164(1-2):23--33, 2001. Effective methods in algebraic geometry (Bath, 2000).Google ScholarCross Ref
- I. Bermejo and P. Gimenez. Saturation and Catelnuovo-Mumford regularity. J. Algebra, 303:592--617, 2006.Google ScholarCross Ref
- A. M. Bigatti, P. Conti, L. Robbiano, and C. Traverso. A "divide and conquer" algorithm for Hilbert-Poincaré series, multiplicity and dimension of monomial ideals. In Applied algebra, algebraic algorithms and error-correcting codes (San Juan, PR, 1993), volume 673 of Lecture Notes in Comput. Sci., pages 76--88. Springer, Berlin, 1993. Google ScholarDigital Library
- D. Cox, J. Little, and D. O'Shea. Using algebraic geometry, volume 185 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1998.Google Scholar
- S. Eliahou and M. Kervaire. Minimal resolutions of some monomial ideals. J. Algebra, 129(1):1--25, 1990.Google ScholarCross Ref
- R. Fröberg. An introduction to Gröbner bases. Pure and Applied Mathematics (New York). John Wiley & Sons Ltd., Chichester, 1997.Google Scholar
- G.-M. Greuel, G. Pfister, and H. Schönemann. Singular 3.0. A Computer Algebra System for Polynomial Computations, Centre for Computer Algebra, University of Kaiserslautern, 2005. http://www.singular.uni-kl.de.Google Scholar
- A. Hashemi. Strong Noether Position and Stabilized Regularities. submitted to Applicable Algebra in Engineering, Communication and Computing, 2006.Google Scholar
- J. Herzog, D. Popescu, and M. Vladoiu. On the Ext-modules of ideals of Borel type. In Commutative algebra (Grenoble/Lyon, 2001), volume 331 of Contemp. Math., pages 171--186. Amer. Math. Soc., Providence, RI, 2003.Google Scholar
- A. Imran and A. Sarfraz. Regularity of ideals of Borel type is linearly bounded. Preprint (see math.AC/0610537), 2007.Google Scholar
- E. W. Mayr and A. R. Meyer. The complexity of the word problems for commutative semigroups and polynomial ideals. Adv. in Math., 46(3):305--329, 1982.Google ScholarCross Ref
Index Terms
- Polynomial-time algorithm for Hilbert series of Borel type ideals
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