On the complexity and parallel implementation of Hensel's lemma and Weierstrass preparation

DOI10.1007/978-3-030-85165-1_6zbMath1506.13001arXiv2105.10798OpenAlexW3197461373MaRDI QIDQ831966

Alexander Brandt, Marc Moreno Maza

Publication date: 24 March 2022

Full work available at URL: https://arxiv.org/abs/2105.10798

zbMATH Keywords

parallel processingformal power seriesHensel's lemmaWeierstrass preparationHensel factorizationparallel pipeline

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Software, source code, etc. for problems pertaining to commutative algebra (13-04) Formal power series rings (13F25)

Uses Software

• gmp
• IBM Scratchpad
• Maple
• NTL
• SageMath
• MultivariatePowerSeries

Cites Work

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• Relax, but don't be too lazy
• Power series arithmetic with the BPAS library
• On the extended Hensel construction and its application to the computation of real limit points
• Polynomial root finding over local rings and application to error correcting codes
• Enhancing the Extended Hensel Construction by Using Gröbner Bases
• Faster relaxed multiplication
• Lazy and Forgetful Polynomial Arithmetic and Applications
• All Algebraic Functions Can Be Computed Fast
• Fast Computation of the Roots of Polynomials Over the Ring of Power Series
• On the parallelization of triangular decompositions
• Infinite structures in scratchpad II

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