On p-adic differential equations with separation of variables - Archive ouverte HAL Access content directly
Conference Papers Year :

On p-adic differential equations with separation of variables

Pierre Lairez
Tristan Vaccon
  • Function : Author
  • PersonId : 975861

Abstract

Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This raises precision concerns: how much precision do we need on the input to compute the output accurately? In the case of ordinary differential equations with separation of variables, we make use of the recent technique of differential precision to obtain optimal bounds on the stability of the Newton iteration. The results apply, for example, to algorithms for manipulating algebraic numbers over finite fields, for computing isogenies between elliptic curves or for deterministically finding roots of polynomials in finite fields. The new bounds lead to significant speedups in practice.
Fichier principal
Vignette du fichier
padicdeq.pdf (446.95 Ko) Télécharger le fichier
speedup.pdf (70.61 Ko) Télécharger le fichier
timings.pdf (53.17 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)

Dates and versions

hal-01265226 , version 1 (31-01-2016)
hal-01265226 , version 2 (10-05-2016)

Identifiers

Cite

Pierre Lairez, Tristan Vaccon. On p-adic differential equations with separation of variables. ISSAC 2016, Jul 2016, Waterloo, Ontario, Canada. ⟨10.1145/2930889.2930912⟩. ⟨hal-01265226v2⟩
112 View
306 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More