Resolving Zero Divisors Using Hensel Lifting

Algorithms which compute modulo triangular sets must respect zero divisors. We present Hensel lifting as a tool for resolving them. We give an application: a modular algorithm for computing gcds of univariate polynomials with coefficients modulo a radical triangular set over the rational numbers. We...

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Vydáno v:2017 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) s. 39 - 48
Hlavní autoři: Kluesner, John, Monagan, Michael
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 01.09.2017
Témata:
Complexity theory
Hensel Lifting
Image reconstruction
Modular Algorithms
Polynomial GCD
Radical Ideals
Scientific computing
Testing
Triangular Sets
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Shrnutí:Algorithms which compute modulo triangular sets must respect zero divisors. We present Hensel lifting as a tool for resolving them. We give an application: a modular algorithm for computing gcds of univariate polynomials with coefficients modulo a radical triangular set over the rational numbers. We have implemented our algorithm using Maple's RECDEN package. We compare our implementation with the procedure RegularGcd in the RegularChains package.
DOI:10.1109/SYNASC.2017.00017