Xavier Caruso, Tristan Vaccon, Thibaut Verron,
"Gröbner Bases Over Tate Algebras"
: ISSAC '19: Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, Seite(n) 74-81, 7-2019
Original Titel:
Gröbner Bases Over Tate Algebras
Sprache des Titels:
Englisch
Original Buchtitel:
ISSAC '19: Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation
Original Kurzfassung:
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.
Forschungs-