grobner 中文意思是什麼
grobner
解釋
格勒布納-
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，將求域上塊循環矩陣的極小多項式轉化為求一個環同態的核的簡化gr （ -
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
?給出了準確計算域上有限群的群代數上的多項式環的理想的gr （ ? ） bner基的演算法。 -
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基理論在求矩陣極小多項式，判定矩陣可逆性和求逆矩陣等方面的應用，並討論了多項式環的分次自對偶問題。 -
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在域上的多項式環的單項式的集合中引入項序，並利用s -多項式，給出了一種演算法，使得對多項式環中的任意給定的理想，從它的一組生成元，可計算得到一組被稱為簡化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基的應用研究包括代數方程組求解，多項式的因子分解，素理想的檢驗，代數流形的分解，糾錯碼中循環碼和代數幾何碼的譯碼，密碼學中高維線性遞歸陣列的分析與綜合，多維系統理論，信號處理和求解整數規劃等諸多領域。
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