The notion of weakly relatively prime and W-Gr6bner basis in K[x1, x2,…, xn] are given. The following results are obtained： for polynomials fl, f2, ..., fm, {f1^λ1, f2^λ2,…, fm^λm} is a GrSbner basis if and only...The notion of weakly relatively prime and W-Gr6bner basis in K[x1, x2,…, xn] are given. The following results are obtained： for polynomials fl, f2, ..., fm, {f1^λ1, f2^λ2,…, fm^λm} is a GrSbner basis if and only if f1, f2, …, fm are pairwise weakly relatively prime with λ1, λ2, …, λm arbitrary non-negative integers; polynomial composition by θ = （θ1,θ2, …, θn） commutes with monomial-Grobner bases computation if and only if θ1, θ2, , θm are pairwise weakly relatively prime.展开更多
基金Supported by the NSFC (10771058, 11071062, 10871205), NSFH (10JJ3065)Scientific Research Fund of Hunan Provincial Education Department (10A033)Hunan Provincial Degree and Education of Graduate Student Foundation (JG2009A017)
文摘The notion of weakly relatively prime and W-Gr6bner basis in K[x1, x2,…, xn] are given. The following results are obtained： for polynomials fl, f2, ..., fm, {f1^λ1, f2^λ2,…, fm^λm} is a GrSbner basis if and only if f1, f2, …, fm are pairwise weakly relatively prime with λ1, λ2, …, λm arbitrary non-negative integers; polynomial composition by θ = （θ1,θ2, …, θn） commutes with monomial-Grobner bases computation if and only if θ1, θ2, , θm are pairwise weakly relatively prime.
