Invariant G2V algorithm for computing SAGBI-Gröbner bases - Hashemi, Amir; M.-Alizadeh, Benyamin; Riahi, Monireh (Science China. Mathematics, 2013)
Faugère and Rahmany have presented the invariant F 5 algorithm to compute SAGBI-Gröbner bases of ideals of invariant rings. This algorithm has an incremental structure, and it is based on the matrix version of F5 algorithm to use F5 criterion to remove a part of useless reductions. Although this algorithm is more efficient than the Buchberger-like algorithm, however it does not use all the existing criteria (for an incremental structure) to detect superfluous reductions. In this paper, we consider a new algorithm, namely, invariant G 2 V algorithm , to compute SAGBI-Gröbner bases of ideals of invariant rings using more criteria. This algorithm has a new structure and it is based on the G 2 V algorithm; a variant of the F 5 algorithm to compute Gröbner bases. We have implemented our new algorithm in Maple, and we give experimental comparison, via some examples, of performance of this algorithm with the invariant F 5 algorithm.