The SyCo Maple package

Symmetry and Computation - Multivariate Interplation, Symmetry Adapted Bases of Polynomial Rings & Fundamental Equivariants

The SyCo package is a collection of routines to preserve and exploit symmetry in algebraic computation, like interpolation. It includes the computation of symmetry adapted bases, fundamental invariants and equivariants. If you use, or want to use, the SyCo package for your research, I would love to hear about it (email).

Download the SyCo directory. You'll find there

The library SyCo.mla to be filed with your other Maple libraries; otherwise adapt your libname variable to its location.

Maple worksheets with examples of use in place of a manual.

The SyCo package was created and developed by Erick Rodriguez Bazan during his PhD (2020). Whether you use it as a central tool or for exploration, please acknowledge it by refering to this web page and the related publications below.

Worksheets Illustrating the Bibliography

Multivariate Interpolation with Symmetry in SyCo :

This worksheet covers all the computations made for the examples in the articles

E. Rodriguez Bazan, E. Hubert; Multivariate interpolation: Preserving and exploiting symmetry. Journal of Symbolic Computation 107:1-22 (2021) [doi:10.1016/j.jsc.2021.01.004] [hal-03123418]

E. Rodriguez Bazan, E. Hubert; Symmetry Preserving Interpolation. ISSAC'19. Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, Pages 34-41, ACM Press (2019) . [doi:10.1145/3326229.3326247] [hal-01994016]

Ideal Interpolation with Symmetry in SyCo :

This worksheet covers all the computations made for the examples in the articles

E. Rodriguez Bazan, E. Hubert; Symmetry in Multivariate Ideal Interpolation. Journal of Symbolic Computation 115:174-200 (2023) [doi:10.1016/j.jsc.2022.08.014] [hal-03129766]

E. Rodriguez Bazan, E. Hubert; Ideal interpolation, H-bases, and Symmetry. ISSAC 2020. Proceedings of the 2020 on International Symposium on Symbolic and Algebraic Computation, Pages 402-409, ACM Press (2020). [doi:10.1145/3373207.3404057] [hal-02482098]

Computing Fundamental Invariants and Equivariant of finite groups with SyCo :

This worksheet covers all the computations made for the examples in the articles

E. Rodriguez Bazan, E. Hubert; Algorithms for fundamental invariants and equivariants (of finite groups). Mathematics of Computation, volume 91 number 337 pages 2459-2488 (2022) [doi:10.1090/mcom/3749] [hal-03209117]

E. Hubert