Exploring the Dynamic Buchberger Algorithm
John Weir Perry · 2017
Abstract "Static" Buchberger algorithms to compute a Gröbner basis require as input both a set of polynomials and a term ordering. "Dynamic" Buchberger algorithms do not require an ordering as input, but compute instead a Gröbner basis with respect to a "discovered" ordering. A good heuristic usually results in a basis that is relatively small, a desirable property for many applications. This article uses a new C++ implementation to explore variants of the original algorithm. While the implementation is preliminary, and in general much slower than well-known static implementations, it still succeeds at computing some bases more quickly.