Effective Set Membership in Computer Algebra and Beyond
Davenport, J. H., 2008. Effective Set Membership in Computer Algebra and Beyond. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M. and Wiedijk, F., eds. Intelligent Computer Mathematics: Proc. AISC/Calculemus/MKM 2008.Vol. 5144. Berlin, Heidelberg: Springer, pp. 266-280. (Lecture Notes in Computer Science)
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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’.
|Item Type||Book Sections|
|Creators||Davenport, J. H.|
|Editors||Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M. and Wiedijk, F.|
|Departments||Faculty of Science > Computer Science|
|Additional Information||Proceedings of the 9th International Conference, AISC 2008, 15th Symposium, Calculemus 2008, 7th International Conference, MKM 2008, Birmingham, UK, July 28 - August 1, 2008. ID number: 5144|
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