This paper will prove that f≡g(modI) iff N F(f)=N F(g) for f,g∈K[x,],obtain a basis for the K vector space K[x,]/I,give the method for finding a Grbner basis of intersection of the left ideals I and J.
The aim of this paper is to given an algebraic computational method for finding maximal independent sets as well as the independent number of an arbitrary finite graph of n vertices G by strengthening the problem of f...The aim of this paper is to given an algebraic computational method for finding maximal independent sets as well as the independent number of an arbitrary finite graph of n vertices G by strengthening the problem of finding maximal independent sets of G to the problem of finding k-independent sets in G for. It is shown that the existence of k-independent sets in G is equivalent to the existence of solutions of a system of multivariate polynomial equations. It follows that the problem of finding k-independent sets can be realized by using Gröbner bases of polynomial ideals. Since the number of k-independent sets is finite, the triangular equations composed by Gröbner bases are easier to be solved. Consequently, the maximal independent sets and the independent number of G are obtained after solving at most n such equations. Finally, the numerical example is presented to illustrate the effectiveness of this algebraic computational method.展开更多
Improved algorithm for Grbner basis is a new way to solve Grbner basis by adopting the locally analytic method,which is based on GrbnerNew algorithm The process consists of relegating the leading terms of generator of...Improved algorithm for Grbner basis is a new way to solve Grbner basis by adopting the locally analytic method,which is based on GrbnerNew algorithm The process consists of relegating the leading terms of generator of the polynomial in the idea according to correlated expressions of leading terms and then analyzing every category.If a polynomial can be reduced to a remainder polynomial by a polynomial in the idea,then it can be replaced by the remainder polynomial as generator In the solving process,local reduction and local puwer decrease are employed to prevent the number of middle terms from increasing too fast and the degrees of polynomial from being too high so as to reduce the amount of展开更多
采用Grbner基方法,可以把一个在有限群作用下不变的多项式写成不变环的生成元的多项式.核心问题是如何有效地计算这个正维不变理想的Grbner基.本文引入一个有效提升算法来计算这组Grbner基.当用straight line program模型对整个...采用Grbner基方法,可以把一个在有限群作用下不变的多项式写成不变环的生成元的多项式.核心问题是如何有效地计算这个正维不变理想的Grbner基.本文引入一个有效提升算法来计算这组Grbner基.当用straight line program模型对整个计算过程进行复杂度分析时,可以把计算开销控制在多项式时间内.展开更多
文摘This paper will prove that f≡g(modI) iff N F(f)=N F(g) for f,g∈K[x,],obtain a basis for the K vector space K[x,]/I,give the method for finding a Grbner basis of intersection of the left ideals I and J.
文摘The aim of this paper is to given an algebraic computational method for finding maximal independent sets as well as the independent number of an arbitrary finite graph of n vertices G by strengthening the problem of finding maximal independent sets of G to the problem of finding k-independent sets in G for. It is shown that the existence of k-independent sets in G is equivalent to the existence of solutions of a system of multivariate polynomial equations. It follows that the problem of finding k-independent sets can be realized by using Gröbner bases of polynomial ideals. Since the number of k-independent sets is finite, the triangular equations composed by Gröbner bases are easier to be solved. Consequently, the maximal independent sets and the independent number of G are obtained after solving at most n such equations. Finally, the numerical example is presented to illustrate the effectiveness of this algebraic computational method.
文摘Improved algorithm for Grbner basis is a new way to solve Grbner basis by adopting the locally analytic method,which is based on GrbnerNew algorithm The process consists of relegating the leading terms of generator of the polynomial in the idea according to correlated expressions of leading terms and then analyzing every category.If a polynomial can be reduced to a remainder polynomial by a polynomial in the idea,then it can be replaced by the remainder polynomial as generator In the solving process,local reduction and local puwer decrease are employed to prevent the number of middle terms from increasing too fast and the degrees of polynomial from being too high so as to reduce the amount of
文摘采用Grbner基方法,可以把一个在有限群作用下不变的多项式写成不变环的生成元的多项式.核心问题是如何有效地计算这个正维不变理想的Grbner基.本文引入一个有效提升算法来计算这组Grbner基.当用straight line program模型对整个计算过程进行复杂度分析时,可以把计算开销控制在多项式时间内.
