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Real and complex pseudozero sets for polynomials with applications

Stef Graillat, Philippe Langlois (2007)

RAIRO - Theoretical Informatics and Applications

Pseudozeros are useful to describe how perturbations of polynomial coefficients affect its zeros. We compare two types of pseudozero sets: the complex and the real pseudozero sets. These sets differ with respect to the type of perturbations. The first set – complex perturbations of a complex polynomial – has been intensively studied while the second one – real perturbations of a real polynomial – seems to have received little attention. We present a computable formula for the real pseudozero...

Relaxed algorithms for p -adic numbers

Jérémy Berthomieu, Joris van der Hoeven, Grégoire Lecerf (2011)

Journal de Théorie des Nombres de Bordeaux

Current implementations of p -adic numbers usually rely on so called zealous algorithms, which compute with truncated p -adic expansions at a precision that can be specified by the user. In combination with Newton-Hensel type lifting techniques, zealous algorithms can be made very efficient from an asymptotic point of view.In the similar context of formal power series, another so called lazy technique is also frequently implemented. In this context, a power series is essentially a stream of coefficients,...

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