A New Algorithm for Computing Gröbner Bases

Polynomial systems are ubiquitous in Mathematics, Sciences and Engineerings, and Gröbner basis theory is one of the most powerful tools for solving polynomial systems. Buchberger introduced in 1965 the first algorithm for computing Gröbner bases and it has been implemented in most computer algebra systems (e.g. Maple, Mathematica, Magma, etc). Faugere presented two new algorithms: F4 (1999) and F5 (2002), with the latter being the faster algorithm known. In this talk, I shall first give a brief overview on Gröbner bases then present a new algorithm that matches Buchberger's algorithm in simplicity yet is several times faster F5. The talk will be accessible to a general audience.

Joint work with Yinhua Guan (Clemson), Frank Volny (Clemson), and Mingsheng Wang (Chinese Academy of Sciences).