Skip to main content

Resolving Zero-Divisors of Radical Triangular Sets Using Hensel Lifting and Applications

Resource type
Thesis type
(Thesis) M.Sc.
Date created
This thesis aims to create efficient algorithms for computing in the ring R = Q[z1,...,zn]/T where T is a zero-dimensional triangular set. The presence of zero-divisors in R makes it a computational challenge to use modular algorithms. In particular, there has never been a proper modular algorithm for computing greatest common divisors of polynomials in R[x]. We present two new ways of resolving zero-divisors: Hensel lifting and fault tolerant rational reconstruction, which allows us to create a new modular gcd algorithm for R[x] as well as a new inversion algorithm for R. We have implemented our algorithms in Maple using the RECDEN library, and we show that they outperform the methods currently implemented in Maple's RegularChains package. The method of Hensel lifting for resolving zero-divisors should give rise to other new modular algorithms for computing modulo triangular sets and our applications show that this approach is fruitful.
Copyright statement
Copyright is held by the author.
This thesis may be printed or downloaded for non-commercial research and scholarly purposes.
Scholarly level
Supervisor or Senior Supervisor
Thesis advisor: Monagan, Michael
Member of collection
Download file Size
etd10318_JKluesner.pdf 609.08 KB

Views & downloads - as of June 2023

Views: 0
Downloads: 0