C.6.3 The Buchberger algorithm for toric ideals

Toric ideals have a very special structure that allows us to improve the Buchberger algorithm in many respects: They are prime ideals and generated by binomials. Pottier used this fact to describe all operations of the Buchberger algorithm on the ideal generators in terms of vector additions and subtractions. Some other strategies like multiple reduction (see [CoTr91]) or the use of bit vectors to represent the support of a monomial (see [Big97]) may be applied to more general ideals, but show to be especially useful in the toric case.