A Sage package for computing congruence schemes

congruenceschemes

A Sage package for computing congruence schemes

This package accompanies the paper On congruence schemes for constant terms and their applications [S22].

The basic usage of this package is indicated in Section 4 of that paper.

Author

• Armin Straub (2021/10): Initial implementation

Contributions

• The underlying ideas and algorithms for computing congruence schemes were first described by Eric Rowland and Reem Yassawi [RY15] and extended by Eric Rowland and Doron Zeilberger [RZ14].
• As part of his 2019 master's thesis, Joel Henningsen (under the guidance of Armin Straub) implemented a subset of these algorithms in Sage. The performance and design lessons learned from Joel's work have benefitted the present code.

Changes

• 2023/09: Adjusted code to work with SageMath 10.1 (the implementation of PolyDict changed considerably), breaking compatibility with earlier versions of SageMath.

References

[RY15] Eric Rowland and Reem Yassawi (2015). Automatic congruences for diagonals of rational functions. Journal de Théorie des Nombres de Bordeaux, 27(1), 245-288. DOI

[RZ14] Eric Rowland and Doron Zeilberger (2014). A case study in meta-automation: automatic generation of congruence automata for combinatorial sequences. Journal of Difference Equations and Applications, 20(7), 973-988. DOI

[S22] Armin Straub (2022). On congruence schemes for constant terms and their applications. Research in Number Theory, 8(3), #42, 1-21. DOI

Download

This package is also available at https://github.com/arminstraub/congruenceschemes.

Note that the package is somewhat preliminary and likely has rough edges—please report any issues to mail@arminstraub.com.