Abstract
In this paper, we describe improved algorithms to compute Janet and Pommaret bases. To this end, based on the method proposed by Möller et al. [20], we present a more efficient variant of Gerdt’s algorithm (than the algorithm presented in [16]) to compute minimal involutive bases. Furthermore, by using an involutive version of the Hilbert driven technique along with the new variant of Gerdt’s algorithm, we modify the algorithm given in [23] to compute a linear change of coordinates for a given homogeneous ideal so that the new ideal (after performing this change) possesses a finite Pommaret basis. All the proposed algorithms have been implemented in Maple and their efficiency is discussed via a set of benchmark polynomials.
A. Hashemi—The research of the second author was in part supported by a grant from IPM (No. 94550420).
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Notes
- 1.
The Maple code of the implementations of our algorithms and examples are available at http://amirhashemi.iut.ac.ir/softwares.
- 2.
See http://invo.jinr.ru.
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Binaei, B., Hashemi, A., Seiler, W.M. (2016). Improved Computation of Involutive Bases. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2016. Lecture Notes in Computer Science(), vol 9890. Springer, Cham. https://doi.org/10.1007/978-3-319-45641-6_5
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