Computation of Pommaret Bases Using Syzygies

Co-author(s): Bentolhoda Binaei and Amir Hashemi

Reference: Computer Algebra in Scientific Computing - CASC 2018, V.P. Gerdt, W. Koepf, W.M. Seiler, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2018, Lecture Notes in Computer Science 11077, pp. 51-66

Description: We consider the problem of computing simultaneously involutive bases of an ideal and its syzygy module. The first approach presented modifies the classical TQ algorithm for computing Janet bases such that it also determines a basis of the syzygy module of the Janet basis. This new algorithm is then applied for computing Pommaret bases. The second approach presented adapts to involutive bases a recent algorithm of Gao, Volny and Wang (GVW) which computes in addition a basis of the syzygy module of the input basis.

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