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’.
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Davenport, J.H. (2008). Effective Set Membership in Computer Algebra and Beyond. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds) Intelligent Computer Mathematics. CICM 2008. Lecture Notes in Computer Science(), vol 5144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85110-3_22
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DOI: https://doi.org/10.1007/978-3-540-85110-3_22
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