TITLE: Coercions and Categories in Sage SPEAKER: David Roe, Postdoc, University of Washington ABSTRACT: Sage includes a lot of infrastructure to support the creation of algebraic structures and to fit them into the existing ecosystem of rings, fields, modules, matrix spaces. Parents in Sage are objects modeling a set with additional structure, such as the ring of integers or a finite field of size 9. The coercion system supports arithmetic with elements in different parents: ZZ['x'].gen() + 1/2 for example. And the category framework allows you to specify mathematical properties of the parents you define and get access to generic code applying to objects of that type. Both parts of Sage have evolved over time: I'll give some brief history as well as best practices if you want to implement a new algebraic structure within Sage.