Invariant G2V algorithm for computing SAGBI-Gröbner bases

• Published in: Science China. Mathematics Vol. 56; no. 9; pp. 1781 - 1794
• Main Authors: Hashemi, Amir, M.-Alizadeh, Benyamin, Riahi, Monireh
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2013
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; invariant F; invariant G; 68W30; G; V algorithm; 13P10; SAGBI-Gröbner bases; algorithm
• ISSN: 1674-7283; 1869-1862
• DOI: 10.1007/s11425-012-4506-8

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.