Fast computation of Gröbner bases of ideals of F[x, y]

Authors:
Yindong Chen;Yao Lu;Peizhong Lu
Affiliations:
School of Computer Science, Fudan University, Shanghai, China;School of Electronic and Information Engineering, Tongji University, Shanghai, China;School of Computer Science, Fudan University, Shanghai, China
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Year:
2009

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Abstract

This paper provides a fast algorithm for Gröbner bases of ideals of F[x, y] over a field F. We show that only the S-polynomials of neighbor pairs of a strictly ordered finite generating set are needed in the computing of a Gröbner bases of the ideal. It reduces dramatically the number of unnecessary S-polynomials that are processed. Although the complexity of the algorithm is hard to evaluated, it obviously has a great improvement from Buchberger's Algorithm.