Vol. 1, No. 1, 2013

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Solving quadratic equations in dimension $5$ or more without factoring

Pierre Castel

Vol. 1 (2013), No. 1, 213–233
Abstract

Let Q be a 5 × 5 symmetric matrix with integral entries and with detQ0, but neither positive nor negative definite. We describe a probabilistic algorithm which solves the equation txQx = 0 over without factoring detQ. The method can easily be generalized to forms of higher dimensions by reduction to a suitable subspace.

Keywords
general quadratic forms, factorization, general quadratic equations, isotropic spaces, algorithmic number theory, Cebotarev density theorem
Mathematical Subject Classification 2010
Primary: 11E20
Secondary: 11D09
Milestones
Published: 14 November 2013
Authors
Pierre Castel
Laboratoire de Mathématiques Nicolas Oresme
Université de Caen Basse-Normandie
UMR CNRS 6139
14032 Caen
France