DMS Linear Algebra/Algebra Seminar

Speaker: Douglas A. Leonard

Title:  Using Computer Algebra Systems to improve mathematical theory

Abstract:  Mathematicians seem adverse to putting examples in their research papers, higher level textbooks, or even course notes. (My intro to commutative algebra was a slick definition-theorem-proof course from which I learned nothing about the topic but something about proofs instead.) This is compounded when others write code to implement theory in some CAS (computer algebra system). Mathematical theory, can be wrong, misguided, too general, or too complicated. The code can be wrong, misguided, too general, or too complicated as well, even when the underlying math is at least not wrong. If one can work through reasonable examples of the theory (so non-trivial, but not hopelessly pathological) using a CAS, then one is forced to think very hard about programming each step. This can lead to alternative viewpoints and maybe even an overhauling of the theory. I’ll probably concentrate on resolving singularities, starting with the example described by \(y^3 + yx + x^5 = 0\), using Macaulay2 and/or Singular.