Hensel and Newton Methods in Valuation Rings

DOI10.2307/2007608zbMath0581.13001OpenAlexW4253657740MaRDI QIDQ3703974

Joachim von zur Gathen

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/2007608

zbMATH Keywords

factorization of polynomialsNewton methodunivariate polynomialsbivariate polynomialsHensel methodzeros of polynomials over

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Software, source code, etc. for problems pertaining to commutative algebra (13-04) Polynomials over commutative rings (13B25) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Algorithms in computer science (68W99)

Related Items

Factoring sparse multivariate polynomials ⋮ Discovering the Roots: Uniform Closure Results for Algebraic Classes Under Factoring ⋮ On lattice reduction for polynomial matrices ⋮ Fast separable factorization and applications ⋮ Relaxed algorithms for \(p\)-adic numbers ⋮ Polynomial root finding over local rings and application to error correcting codes ⋮ Nearly optimal solution of rational linear systems of equations with symbolic lifting and numerical initialization ⋮ On the \(\mathbb{F}_2\)-linear relations of Mersenne Twister pseudorandom number generators ⋮ Highly parallel computations modulo a number having only small prime factors ⋮ New recombination algorithms for bivariate polynomial factorization based on Hensel lifting ⋮ Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding ⋮ Factorization of polynomials given by arithmetic branching programs ⋮ Functional decomposition of polynomials: the wild case