Effective Set Membership in Computer Algebra and Beyond

Authors:
James H. Davenport
Affiliations:
Department of Computer Science, University of Bath, Bath, United Kingdom BA2 7AY
Venue:
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Year:
2008

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Abstract

In previous work, we showed the importance of distinguishing "I know that $X\ne Y$" from "I don't know that X= Y". In this paper we look at effective set membership, starting with Gröbner bases, where the issues are well-expressed in algebra systems, and going on to integration and other questions of `computer calculus'.In particular, we claim that a better recognition of the role of set membership would clarify some features of computer algebra systems, such as `what does an integral mean as output'.