On FGLM Algorithms with Tate Algebras
CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]
Lithe and fast algorithmic number theory [LFANT]
CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]
Lithe and fast algorithmic number theory [LFANT]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Centre National de la Recherche Scientifique [CNRS]
Lithe and fast algorithmic number theory [LFANT]
Language
en
Communication dans un congrès
This item was published in
International Symposium on Symbolic and Algebraic Computation — ISSAC 2021, 2021-07-18, Virtual event.
ACM
English Abstract
Tate introduced in [Ta71] the notion of Tate algebras to serve, in the context of analytic geometry over the-adics, as a counterpart of polynomial algebras in classical algebraic geometry. In [CVV19, CVV20] the formalism ...Read more >
Tate introduced in [Ta71] the notion of Tate algebras to serve, in the context of analytic geometry over the-adics, as a counterpart of polynomial algebras in classical algebraic geometry. In [CVV19, CVV20] the formalism of Gröbner bases over Tate algebras has been introduced and advanced signature-based algorithms have been proposed. In the present article, we extend the FGLM algorithm of [FGLM93] to Tate algebras. Beyond allowing for fast change of ordering, this strategy has two other important benefits. First, it provides an efficient algorithm for changing the radii of convergence which, in particular, makes effective the bridge between the polynomial setting and the Tate setting and may help in speeding up the computation of Gröbner basis over Tate algebras. Second, it gives the foundations for designing a fast algorithm for interreduction, which could serve as basic primitive in our previous algorithms and accelerate them significantly.Read less <
English Keywords
Algorithms
Gröbner bases
Tate algebra
FGLM algorithm
p-adic precision
ANR Project
Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026
Origin
Hal imported