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Hensel Lifting via Gröbner bases

Daniel Lichtblau
Organization: Wolfram Research, Inc.

ACA 2005
Conference location

Nara Women's University, Nara, Japan

A talk from the Conference on Applications of Computer Algebra (ACA) 2005 on a method of Hensel (August 1, 2005, Nara, Japan).


In this talk I will show how one may use Gröbner bases over Euclidean domains to perform Hensel lifting in some polynomial rings. The algorithm is quite simple. Moreover, for the ring of univariate polynomials over the integers, dedicated polynomial arithmetic code of around two dozen lines can implement this method quite efficiently (it compares well to tree lifting, which appears to be the most effective approach known). We will also see how the Gröbner basis approach to lifting may be applied to bivariate polynomials over finite fields.

*Mathematics > Algebra > Field and Ring Theory
*Mathematics > Algebra > Polynomials

Hensel lifting, Gröbner bases, polynomial algebra
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ACA2005_Hensel.pdf (57.1 KB) - PDF Document
ACA2005_Hensel.nb (153.3 KB) - Mathematica Notebook