Relaxed algorithms for \(p\)-adic numbers

DOI10.5802/jtnb.777zbMath1247.11152OpenAlexW1987316492MaRDI QIDQ449711

Jérémy Berthomieu, Grégoire Lecerf, Joris van der Hoeven

Publication date: 31 August 2012

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/219803

zbMATH Keywords

algorithmspower series\(p\)-adic numbers

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40)

Related Items (7)

Solving p-adic polynomial systems via iterative eigenvector algorithms ⋮ On the complexity exponent of polynomial system solving ⋮ Polynomial root finding over local rings and application to error correcting codes ⋮ Relaxed Hensel lifting of triangular sets ⋮ Exact \(p\)-adic computation in Magma ⋮ A simple and fast online power series multiplication and its analysis ⋮ Tracking -adic precision

Uses Software

• FLINT
• gmp
• Kronecker
• Mathemagix
• PARI/GP
• SageMath

Cites Work

• Newton's method and FFT trading
• On fast multiplication of polynomials over arbitrary algebras
• Fast evaluation of holonomic functions
• Relax, but don't be too lazy
• A concise proof of the Kronecker polynomial system solver from scratch
• Efficient accelero-summation of holonomic functions
• New algorithms for relaxed multiplication
• Fast multiplication of large numbers
• Effective procedures in field theory
• Hensel and Newton Methods in Valuation Rings
• Fast Algorithms for Manipulating Formal Power Series
• Fast evaluation of holonomic functions near and in regular singularities
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