Computing the multiplicative group of residue class rings

Authors:
Florian Heß;Sebastian Pauli;Michael E. Pohst
Affiliations:
Department of Computer Science, University of Bristol, BS8 1UB, England;Institut für Mathematik, MA 8-1, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany;Institut für Mathematik, MA 8-1, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany
Venue:
Mathematics of Computation
Year:
2003

Citing 7
Cited 2

A course in computational algebraic number theory

A course in computational algebraic number theory
Hermite and Smith normal form algorithms over Dedekind domains

Mathematics of Computation
KANT V4

Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Computing ray class groups, conductors and discriminants

Mathematics of Computation
Computing class fields via the Artin map

Mathematics of Computation
Discrete Logarithms: The Effectiveness of the Index Calculus Method

ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Computing Ray Class Groups, Conductors and Discriminants

ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory

KASH: recent developments

ICMS'06 Proceedings of the Second international conference on Mathematical Software
Generalised jacobians in cryptography and coding theory

WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let k be a global field with maximal order 0k and let m0 be an ideal of 0k. We present algorithms for the computation of the multiplicative group (0k/m0)* of the residue class ring 0k/m0 and the discrete logarithm therein based on the explicit representation of the group of principal units. We show how these algorithms can be combined with other methods in order to obtain more efficient algorithms. They are applied to the computation of the ray class group Clkm modulo m = m0m∞, where m∞ denotes a formal product of real infinite places, and also to the computation of conductors of ideal class groups and of discriminants and genera of class fields.