Gr\"obner bases over polytopal affinoid algebras
<|reference_start|>Gr\"obner bases over polytopal affinoid algebras: Polyhedral affinoid algebras have been introduced by Einsiedler, Kapranov and Lind to connect rigid analytic geometry (analytic geometry over non-archimedean fields) and tropical geometry.In this article, we present a theory of Gr{\"o}bner bases for polytopal affinoid algebras that extends both Caruso et al.'s theory of Gr{\"o}bner bases on Tate algebras and Pauer et al.'s theory of Gr{\"o}bner bases on Laurent polynomials.We provide effective algorithms to compute Gr{\"o}bner bases for both ideals of Laurent polynomials and ideals in polytopal affinoid algebras. Experiments with a Sagemath implementation are provided.<|reference_end|>
@article{barkatou2024gr{\"o}bner,
    title={Gr{\"o}bner bases over polytopal affinoid algebras},
    author={Moulay A. Barkatou (XLIM-MATHIS, XLIM), Lucas Legrand (XLIM-MATHIS,
  XLIM), Tristan Vaccon (XLIM, XLIM-MATHIS)},
    journal={arXiv preprint arXiv:2403.13382},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.13382},
    primaryClass={cs.SC math.AC math.NT}
}