grobner meaning in English
格勒布纳
格罗布纳
Examples
- An algorithm for grobner basis for an ideal of a polynomial ring over a group algebra of a finite group over a field is given
?给出了准确计算域上有限群的群代数上的多项式环的理想的gr ( ? ) bner基的算法。 - So finding the minimal polynomial of a block circulant matrix is transformed into computing the reduced grobner basis of a kernel of a ring homomorphism
因此，将求域上块循环矩阵的极小多项式转化为求一个环同态的核的简化gr ( - The aim of this paper is to study the applications of grobner bases in finding the minimal polynomial of a given matrix and its inverse if it is nonsingular and to discuss selfdualities over a polynomial ring
) bner基理论在求矩阵极小多项式，判定矩阵可逆性和求逆矩阵等方面的应用，并讨论了多项式环的分次自对偶问题。 - B . buchberger introduced the concepts of term orders in the set of all power products and presented an algorithm for finding a special generators , a reduced grobner basis which is unique for a given term order , of a given ideal of a polynomial ring over a field from any generators of the ideal by means of s - polynomials
Buchberger在域上的多项式环的单项式的集合中引入项序，并利用s -多项式，给出了一种算法，使得对多项式环中的任意给定的理想，从它的一组生成元，可计算得到一组被称为简化gr ( - Since 1980s , many mathematicians have been engaged in studying the applications of the grobner basis such as solving the system of algebraic equations , factoring polynomials , testing primary ideals , factoring algebraic manifolds , decoding circular codes in corrected codes and algebraically geometrical codes , analyzing and synthesizing high dimensional linear recurring arrays in cryptology , dealing with multidimensional systematic theory , signaling , solving integer programming and so on
) bner基的应用研究包括代数方程组求解，多项式的因子分解，素理想的检验，代数流形的分解，纠错码中循环码和代数几何码的译码，密码学中高维线性递归阵列的分析与综合，多维系统理论，信号处理和求解整数规划等诸多领域。