Gröbner Bases Over Tate Algebras

Xavier Caruso; Tristan Vaccon; Thibaut Verron

doi:10.1145/3326229.3326257

Gröbner Bases Over Tate Algebras

Xavier Caruso, Tristan Vaccon, Thibaut Verron

Institute for Algebra

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

Abstract

Tate algebras, introduced in [Tate, 1971], 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 SageMath is also discussed.

Original language	English
Title of host publication	ISSAC '19: Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation
Pages	74-81
Number of pages	8
DOIs	https://doi.org/10.1145/3326229.3326257
Publication status	Published - Jul 2019

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101013 Mathematical logic
102031 Theoretical computer science

JKU Focus areas

Digital Transformation

Access to Document

10.1145/3326229.3326257

Cite this

@inproceedings{401c7933801d47a5ba1dc4f39a86a48e,

title = "Gr{\"o}bner Bases Over Tate Algebras",

abstract = "Tate algebras, introduced in [Tate, 1971], 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 Gr{\"o}bner 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 Gr{\"o}bner bases over Tate algebras. An implementation in SageMath is also discussed.",

author = "Xavier Caruso and Tristan Vaccon and Thibaut Verron",

year = "2019",

month = jul,

doi = "10.1145/3326229.3326257",

language = "English",

pages = "74--81",

booktitle = "ISSAC '19: Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation",

}

TY - GEN

T1 - Gröbner Bases Over Tate Algebras

AU - Caruso, Xavier

AU - Vaccon, Tristan

AU - Verron, Thibaut

PY - 2019/7

Y1 - 2019/7

N2 - Tate algebras, introduced in [Tate, 1971], 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 SageMath is also discussed.

AB - Tate algebras, introduced in [Tate, 1971], 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 SageMath is also discussed.

UR - http://arxiv.org/abs/1901.09574

U2 - 10.1145/3326229.3326257

DO - 10.1145/3326229.3326257

M3 - Conference proceedings

SP - 74

EP - 81

BT - ISSAC '19: Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation

ER -

Gröbner Bases Over Tate Algebras

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Cite this