CS 915 - Constructive Commutative Algebra

University of Western Ontario
Computer Science Department

Date: September 7, 2009

This reading course introduces the student to fundamental and modern tools for computing with polynomial ideals and affine varieties. The aim is to give fundamental notions and also to show to the student how to navigate in the latest discoveries of the field. This proceeds in three steps
  • First we study in detail the fundamental notions of one of these tools from constructive commutative algebra. This year we study Gröbner bases based on the The Ideals, Varieties, and Algorithms book
  • Then we study in a seminar format some recent adavances on another tool and let the student get the fundamental notions by herself. This year we study fast technqiues for computing characteristic sets.
  • Finally, the student is given a little research project where she has to reuse recent ideas of one topic into another area. This year the student has to adapt the fast computation techniques of characteristic sets to Gröbner bases. The goal is not necessarily to make new discoveries but to show investigation techniques to the student.

These are links to some books and software related to the course.