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arXiv · 1612.09176

Computing in quotients of rings of integers

Tommy Hofmann·Claus Fieker
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Abstract

We develop algorithms to turn quotients of rings 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.

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Tommy Hofmann, Claus Fieker. 2016-12-29. Computing in quotients of rings of integers. https://doi.org/10.1112/s1461157014000291

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