Documentation and Learning Material for Basic Structures and the CategoryObject class

[Nehal Patel]

Hello -- I am interested in learning how one goes about modeling the abstract concepts of modern mathematics such as Groups, Rings, Ideals, Fields, etc. in an object oriented way (as well as learning a bit about Category Theory along the way). I seems like a pretty tricky software engineering problem and there must be all sorts of lessons people have learned along the way. Given the openness of Sage, I figured this was a great place to start. I'm reading through the Basic Structures section of the Reference Manual and intend to browse through some of the code, but I thought I would ask the lists as well.

++ Is there any documentation that describes how the Sage developers decided to design their class hierarchy?

++ How similar is it to what is used in Magma?

++ Are there good resources that discuss the software design issues (rather than just algorithms) related to CAS

Ideally there would be something equivalent to the section in William Stein's overview video in which he discusses the history and implementation of the Calculus functionality.

thanks!

[JamesHDavenport]

Although not SAGE-specific, some of the issues are discussed in our
Davenport,J.H. & Trager,B.M.,
Scratchpad's View of Algebra I: Basic Commutative Algebra.
Proc. DISCO '90 (Springer Lecture Notes in Computer Science Vol.
429, ed. A. Miola) pp. 40-54.
http://opus.bath.ac.uk/32336/.

Davenport,J.H., Gianni,P. & Trager,B.M.,
Scratchpad's View of Algebra II:
A Categorical View of Factorization.
Proc. ISSAC 1991 (ed. S.M. Watt), ACM, New York, pp. 32--38.
http://opus.bath.ac.uk/32335/.