Border bases of positive dimensional polynomial ideals

Authors:
Yufu Chen;Xiaohui Meng
Affiliations:
Graduate University of China Academy of Sciences, Beijing, China;Graduate University of China Academy of Sciences, Beijing, China
Venue:
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Year:
2007

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Abstract

The border bases were generalized to general polynomial ideals (zero and positive dimensional ideals). A new algorithm to compute a border basis for a given polynomial system w.r.t. a specified term order was presented. This algorithm computes a border basis, as well as a reduced Gröbner basis for the polynomial system. A particular eigenvector method to find some components of positive dimensional polynomial systems was sketched too.