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Communication Dans Un Congrès Année : 2012

Relaxed p-adic Hensel lifting for algebraic systems

Résumé

In a previous article, an implementation of lazy p-adic integers with a multiplication of quasi-linear complexity, the so-called relaxed product, was presented. Given a ring R and an element p in R, we design a relaxed Hensel lifting for algebraic systems from R/(p) to the p-adic completion R_p of R. Thus, any root of linear and algebraic regular systems can be lifted with a quasi-optimal complexity. We report our implementations in C++ within the computer algebra system Mathemagix and compare them with Newton operator. As an application, we solve linear systems over the integers and compare the running times with Linbox and IML
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hal-00660566 , version 1 (17-01-2012)
hal-00660566 , version 2 (20-02-2012)

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Jérémy Berthomieu, Romain Lebreton. Relaxed p-adic Hensel lifting for algebraic systems. 37th International Symposium on Symbolic and Algebraic Computation, Jul 2012, Grenoble, France. pp.59-66, ⟨10.1145/2442829.2442842⟩. ⟨hal-00660566v2⟩
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