Characteristic polynomials of p-adic matrices

Xavier Caruso; David Roe; Tristan Vaccon

Characteristic polynomials of p-adic matrices

Xavier Caruso ¹ David Roe ² Tristan Vaccon ³

1 IRMAR - Institut de Recherche Mathématique de Rennes

2 PITT - University of Pittsburgh [Pittsburg]

3 XLIM-MATHIS - Mathématiques & Sécurité de l'information

XLIM - XLIM : MATHIS

Abstract : We analyze the precision of the characteristic polynomial of an n×n p-adic matrix A using differential precision methods developed previously. When A is integral with precision O(p^N), we give a criterion (checkable in time O˜(n^omega)) for χ(A) to have precision exactly O(p^N). We also give a O˜(n^3) algorithm for determining the optimal precision when the criterion is not satisfied, and give examples when the precision is larger than O(p^N).

Keywords : Algorithms characteristic polynomial p-adic precision eigenvalue

Document type :

Conference papers

Domain :

Mathematics [math] / Number Theory [math.NT]

Computer Science [cs] / Symbolic Computation [cs.SC]

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https://hal.archives-ouvertes.fr/hal-01458027
Contributor : Xavier Caruso <>
Submitted on : Monday, February 6, 2017 - 4:25:26 PM
Last modification on : Monday, February 18, 2019 - 2:13:03 PM
Document(s) archivé(s) le : Sunday, May 7, 2017 - 2:36:50 PM

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Characteristic polynomials of p-adic matrices

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