[Sans titre]
CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
< Réduire
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Langue
en
Communication dans un congrès
Ce document a été publié dans
ISSAC 2019 - International Symposium on Symbolic and Algebraic Computation, 2019-07-15, Beijing.
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
Mots clés en anglais
p-adic precision
Gröbner bases
F4 algorithm
Power series
Tate algebra
Origine
Importé de halUnités de recherche