Border bases and kernels of homomorphisms and of derivations
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Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations on border bases are presented. Namely; the case of a restriction of an ideal to a polynomial ring (in a smaller number of variables), the case of the intersection of two ideals, and the case of the kernel of a homomorphism of polynomial rings. These constructions are applied to the ideal of relations and to factorizable derivations.
KeywordsBorder basis Gröbner basis Factorizable derivation Ideal of relations
MSC13N15 13P10 68W30 12Y05 12H05
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- Chen Y.F., Meng X.H., Border bases of positive dimensional polynomial ideals, In: Proceedings of the 2007 International Workshop on Symbolic-Numeric Computation, London, Ontario, July 25–27, ACM, New York, 2007, 65–71Google Scholar