@Article{         0a4b2eb5-c7ca-3ff5-bffa-19c4fa412815,
  Author        = "von zur Gathen, Joachim",
  Abstract      = "We give a computational description of Hensel's method for lifting approximate factorizations of polynomials. The general setting of valuation rings provides the framework for this and the other results of the paper. We describe a Newton method for solving algebraic and differential equations. Finally, we discuss a fast algorithm for factoring polynomials via computing short vectors in modules.",
  date-added    = "2023-07-10 11:01:21 +0200",
  date-modified = "2023-07-10 11:01:21 +0200",
  ISSN          = "00255718, 10886842",
  Journal       = "Mathematics of Computation",
  Number        = "166",
  Pages         = "637--661",
  Publisher     = "American Mathematical Society",
  Title         = "Hensel and Newton Methods in Valuation Rings",
  URL           = "http://www.jstor.org/stable/2007608",
  URLDate       = "2023-07-10",
  Volume        = "42",
  Year          = "1984",
  bdsk-url-1    = "http://www.jstor.org/stable/2007608",
  File          = "Hensel and Newton Methods in Valuation Rings - Gathen-HenselNewtonMethods-1984.pdf"
}

@Article{ 0a4b2eb5-c7ca-3ff5-bffa-19c4fa412815, Author = "von zur Gathen, Joachim", Abstract = "We give a computational description of Hensel's method for lifting approximate factorizations of polynomials. The general setting of valuation rings provides the framework for this and the other results of the paper. We describe a Newton method for solving algebraic and differential equations. Finally, we discuss a fast algorithm for factoring polynomials via computing short vectors in modules.", date-added = "2023-07-10 11:01:21 +0200", date-modified = "2023-07-10 11:01:21 +0200", ISSN = "00255718, 10886842", Journal = "Mathematics of Computation", Number = "166", Pages = "637--661", Publisher = "American Mathematical Society", Title = "Hensel and Newton Methods in Valuation Rings", URL = "http://www.jstor.org/stable/2007608", URLDate = "2023-07-10", Volume = "42", Year = "1984", bdsk-url-1 = "http://www.jstor.org/stable/2007608", File = "Hensel and Newton Methods in Valuation Rings - Gathen-HenselNewtonMethods-1984.pdf" }