If R = k[x] with k a field, then determining whether or not a polynomial is in a particular ideal of R can be done with (polynomial) long division. However, what happens when R is a polynomial ring in multiple variables? In this talk, we'll introduce Gröbner bases and discuss how they can be used to solve this problem. Along the way, we'll discuss monomial orders, a division algorithm for polynomials in multiple variables, and Buchberger's algorithm.

Speaker(s): Teresa Yu (UM)