. Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with l.... Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with lattice point counting. More precisely, by using combinatorial tools, we prove that there exists a polytope such that the image of Hilbert function in some degree is equal to the number of lattice points of this polytope.展开更多
We give an algorithm for computing the factor ring of a given ideal in a Dedekind domain with finite rank, which runs in deterministic and polynomial time. We provide two applications of the algorithm:judging whether ...We give an algorithm for computing the factor ring of a given ideal in a Dedekind domain with finite rank, which runs in deterministic and polynomial time. We provide two applications of the algorithm:judging whether a given ideal is prime or prime power. The main algorithm is based on basis representation of finite rings which is computed via Hermite and Smith normal forms.展开更多
文摘. Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with lattice point counting. More precisely, by using combinatorial tools, we prove that there exists a polytope such that the image of Hilbert function in some degree is equal to the number of lattice points of this polytope.
基金supported by National Natural Science Foundation of China (Grant Nos. 11601202, 11471314 and 11401312)the Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No. 14KJB110012)+1 种基金the High-Level Talent Scientific Research Foundation of Jinling Institute of Technology (Grant No. jit-b-201527)the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences
文摘We give an algorithm for computing the factor ring of a given ideal in a Dedekind domain with finite rank, which runs in deterministic and polynomial time. We provide two applications of the algorithm:judging whether a given ideal is prime or prime power. The main algorithm is based on basis representation of finite rings which is computed via Hermite and Smith normal forms.
