LI Ting1; SUN Yao1; HUANG Zhenyu1; WANG Dingkang3; LIN Dongdai1
Source Publication系统科学与复杂性学报英文版
AbstractThe GVW algorithm is an efficient signature-based algorithm for computing GrSbner bases. In this paper,the authors consider the implementation of the GVW algorithm by using Hnear algebra, and speed up GVW via a substituting method.As it is well known that,most of the computing time of a GrSbner basis is spent on reductions of polynomials.Thus,linear algebraic techniques,such as matrix operations,have been used extensively to speed up the implementations.Particularly,one-direction (also called signature-safe)reduction is used in signature-based algorithms,because polynomials (or rows in matrices)with larger signatures can only be reduced by polynomials (rows)with smaller signatures.The authors propose a new method to construct sparser matrices for signature-based algorithms via a substituting method.Specifically,instead of only storing the original polynomials in GVW,the authors also record many equivalent but sparser polynomials at the same time.In matrix construction,denser polynomials are substituted by sparser equivalent ones.As the matrices get sparser,they can be eliminated more efficiently.Two specifical algorithms,Block-GVW and LM-GVW,are presented,and their combination is the Sub-GVW algorithm.The correctness of the new proposed method is proved,and the experimental results demonstrate the efficiency of this new method.
Document Type期刊论文
Affiliation1.SKLOIS,Institute of Information Engineering,Chinese Academy of Sciences
3.KLMM,Academy of Mathematics and Systems Science,Chinese Academy of Sciences
Recommended Citation
GB/T 7714
LI Ting,SUN Yao,HUANG Zhenyu,et al. speedingupthegvwalgorithmviaasubstitutingmethod[J]. 系统科学与复杂性学报英文版,2019,032(001):205.
APA LI Ting,SUN Yao,HUANG Zhenyu,WANG Dingkang,&LIN Dongdai.(2019).speedingupthegvwalgorithmviaasubstitutingmethod.系统科学与复杂性学报英文版,032(001),205.
MLA LI Ting,et al."speedingupthegvwalgorithmviaasubstitutingmethod".系统科学与复杂性学报英文版 032.001(2019):205.
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