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Signature-based algorithms for Gröbner bases over Tate algebras

Abstract : Introduced by Tate in [Ta71], Tate algebras play a major role in the context of analytic geometry over the-adics, where they act as a counterpart to the use of polynomial algebras in classical algebraic geometry. In [CVV19] the formalism of Gröbner bases over Tate algebras has been introduced and effectively implemented. One of the bottleneck in the algorithms was the time spent on reduction , which are significantly costlier than over polynomials. In the present article, we introduce two signature-based Gröbner bases algorithms for Tate algebras, in order to avoid many reductions. They have been implemented in SageMath. We discuss their superiority based on numerical evidences.
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https://hal.archives-ouvertes.fr/hal-02473665
Contributor : Thibaut Verron Connect in order to contact the contributor
Submitted on : Monday, May 10, 2021 - 11:02:13 AM
Last modification on : Thursday, January 20, 2022 - 5:29:02 PM

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Xavier Caruso, Tristan Vaccon, Thibaut Verron. Signature-based algorithms for Gröbner bases over Tate algebras. ISSAC 2021 - International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata / Virtual, Greece. ⟨10.1145/3373207.3404035⟩. ⟨hal-02473665v2⟩

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