|Title||Effective set membership in computer algebra and beyond.|
|Author(s)|| James H. Davenport|
|Type||Book, Chapter in Book, Conference Proceeding|
|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’.