FROM ALGEBRAIC-SETS TO MONOMIAL LINEAR BASES BY MEANS OF COMBINATORIAL ALGORITHMS

被引：22

作者：

CERLIENCO, L ^{[1
]}

MUREDDU, M ^{[1
]}

机构：

[1] UNIV CAGLIARI,DIPARTIMENTO MATEMAT,I-09124 CAGLIARI,ITALY

来源：

DISCRETE MATHEMATICS | 1995年 / 139卷 / 1-3期

关键词：

D O I：

10.1016/0012-365X(94)00126-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a field; let P subset of K '' be a finite set and let J(P) subset of K[x(1),...,x(n)] be the ideal of P. A purely combinatorial algorithm to obtain a linear basis of the quotient algebra K[x(1),...,x(n)]/J(P) is given. Such a basis is represented by an n-dimensional Ferrers diagram of monomials which is minimal with respect to the inverse lexicographical order less than or equal to(i.t.). It is also shown how this algorithm can be extended to the case in which P is an algebraic multiset. A few applications are stated (among them, how to determine a reduced Grobner basis of J(P) with respect to less than or equal to(i.t.) without using Buchberger's algorithm).

引用

页码：73 / 87

页数：15