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Computing in quotients of rings of integers

Published online by Cambridge University Press:  01 August 2014

Claus Fieker
Affiliation:
Fachbereich Mathematik, Technische Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany email fieker@mathematik.uni-kl.de
Tommy Hofmann
Affiliation:
Fachbereich Mathematik, Technische Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany email thofmann@mathematik.uni-kl.de

Abstract

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We develop algorithms to turn quotients of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and their behavior under certain quotients. We illustrate the power of our ideas in a new modular normal form algorithm for modules over rings of integers, vastly outperforming classical algorithms.

Type
Research Article
Copyright
© The Author(s) 2014 

References

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