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’.
|Title of host publication||Intelligent Computer Mathematics: Proc. AISC/Calculemus/MKM 2008|
|Editors||S Autexier, J Campbell, J Rubio, V Sorge, M Suzuki, F Wiedijk|
|Place of Publication||Berlin, Heidelberg|
|Number of pages||15|
|Publication status||Published - 2008|
|Name||Lecture Notes in Computer Science|