Abstract

Gröbner bases are a central tool in computational algebra, but it is well-known that their ease of computation rapidly deteriorates with increasing number of variables and/or degree of the input generators. Due to the connection between polyhedral geometry and Gröbner bases through the Gröbner fan, one can attempt an incremental approach to compute Gröbner bases. First computing a Gröbner basis with respect to an “easy” term ordering and transforming that result to a Gröbner basis with respect to the desired term ordering by using information about this polyhedral fan is done by a family of algorithms termed as Gröbner walk. We implemented two variants of the Gröbner walk in the computer algebra system OSCAR and compared their performance with classical Gröbner basis methods already found in OSCAR.

Keywords

Mathematical Subject Classification

Supplementary material

Implementation of two Groebner walk varients in OSCAR.

Milestones

Authors