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Gröbner bases over Tate algebras

Abstract : Tate algebras are fundamental objects in the context of analytic geometry over the p-adics. Roughly speaking, they play the same role as polynomial algebras play in classical algebraic geometry. In the present article, we develop the formalism of Gröbner bases for Tate algebras. We prove an analogue of the Buchberger criterion in our framework and design a Buchberger-like and a F4-like algorithm for computing Gröbner bases over Tate algebras. An implementation in SM is also discussed.
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https://hal.archives-ouvertes.fr/hal-01995881
Contributor : Xavier Caruso Connect in order to contact the contributor
Submitted on : Monday, May 6, 2019 - 4:00:10 PM
Last modification on : Friday, January 21, 2022 - 3:12:01 AM
Long-term archiving on: : Tuesday, October 1, 2019 - 1:19:51 PM

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Xavier Caruso, Tristan Vaccon, Thibaut Verron. Gröbner bases over Tate algebras. ISSAC 2019 - International Symposium on Symbolic and Algebraic Computation, Jul 2019, Beijing, China. ⟨10.1145/3326229.3326257⟩. ⟨hal-01995881v2⟩

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