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Tracking $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}p$-adic precision

Published online by Cambridge University Press:  01 August 2014

Xavier Caruso ,
David Roe  and
Tristan Vaccon
Xavier Caruso
Affiliation:
Institut de recheche en mathématiques de Rennes (IRMAR), Université Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France email xavier.caruso@normalesup.org
David Roe
Affiliation:
Department of Mathematics, University of Calgary, 2500 University Dr NW, Calgary, AB T2N 1N4, Canada email roed.math@gmail.com
Tristan Vaccon
Affiliation:
Institut de recheche en mathématiques de Rennes (IRMAR), Université Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France email tristan.vaccon@univ-rennes1.fr

Abstract

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We present a new method to propagate $p$-adic precision in computations, which also applies to other ultrametric fields. We illustrate it with some examples and give a toy application to the stable computation of the SOMOS 4 sequence.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Special Issue A: Algorithmic Number Theory Symposium XI , 2014 , pp. 274 - 294
Copyright
© The Author(s) 2014 

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