Continuously Parameterized Symmetries and Buchberger’s Algorithm

Systems of polynomial equations often have symmetries. In solving such a system using Buchberger’s algorithm, the symmetries are neglected. Incorporating symmetries into the solution process enables us to solve larger problems than with Buchberger’s algorithm alone. This paper presents a method that shows how this can be achieved and also gives an algorithm that brings together continuously parameterized symmetries with Buchberger’s algorithm.