Effective Set Membership in Computer Algebra and Beyond

Abstract

Abstract. In previous work, we showed the importance of distinguishing "I know that X = 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'.