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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Published in:2017 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) pp. 39 - 48
Main Authors: Kluesner, John, Monagan, Michael
Format: Conference Proceeding
Language:English
Published: IEEE 01.09.2017
Subjects:
Complexity theory
Hensel Lifting
Image reconstruction
Modular Algorithms
Polynomial GCD
Radical Ideals
Scientific computing
Testing
Triangular Sets
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Abstract 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.
AbstractList 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.
Author Monagan, Michael
Kluesner, John
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Snippet 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...
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StartPage 39
SubjectTerms Complexity theory
Hensel Lifting
Image reconstruction
Modular Algorithms
Polynomial GCD
Radical Ideals
Scientific computing
Testing
Triangular Sets
Title Resolving Zero Divisors Using Hensel Lifting
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