Papers › On Two Signature Variants Of Buchberger's Algorithm Over Principal Ideal Domains
On Two Signature Variants Of Buchberger's Algorithm Over Principal Ideal Domains
Maria Francis, Thibaut Verron
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Signature-based algorithms have brought large improvements in the performances of Gr\"obner bases algorithms for polynomial systems over fields. Furthermore, they yield additional data which can be used, for example, to compute the module of syzygies of an ideal or to compute coefficients in terms of the input generators. In this paper, we examine two variants of Buchberger's algorithm to compute Gr\"obner bases over principal ideal domains, with the addition of signatures. The first one is adapted from Kandri-Rody and Kapur's algorithm, whereas the second one uses the ideas developed in the algorithms by L. Pan (1989) and D. Lichtblau (2012). The differences in constructions between the algorithms entail differences in the operations which are compatible with the signatures, and in the criteria which can be used to discard elements. We prove that both algorithms are correct and discuss their relative performances in a prototype implementation in Magma.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections