@inbook{6030218a7ade42eb9bd7a628195a63b4,

title = "Effective Set Membership in Computer Algebra and Beyond",

abstract = "In previous work, we showed the importance of distinguishing “I know that X ≠ Y{"} from “I don{\textquoteright}t know that X = Y”. In this paper we look at effective set membership, starting with Gr{\"o}bner bases, where the issues are well-expressed in algebra systems, and going on to integration and other questions of {\textquoteleft}computer calculus{\textquoteright}. In particular, we claim that a better recognition of the role of set membership would clarify some features of computer algebra systems, such as {\textquoteleft}what does an integral mean as output{\textquoteright}.",

author = "Davenport, {J H}",

note = "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",

year = "2008",

doi = "10.1007/978-3-540-85110-3_22",

language = "English",

isbn = "978-3-540-85109-7",

volume = "5144",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "266--280",

editor = "S Autexier and J Campbell and J Rubio and V Sorge and M Suzuki and F Wiedijk",

booktitle = "Intelligent Computer Mathematics: Proc. AISC/Calculemus/MKM 2008",

}