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Algorithmic Algebra and Number Theory

Selected Papers From a Conference Held at the University of Heidelberg in October 1997

  • Conference proceedings
  • © 1999

Overview

Editors:
  1. B. Heinrich Matzat

    1. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, der Universität Heidelberg, Heidelberg, Germany

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  2. Gert-Martin Greuel

    1. Fachbereich Mathematik, Universität Kaiserslautern, Kaiserslautern, Germany

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  3. Gerhard Hiss

    1. Lehrstuhl D für Mathematik, RWTH Aachen, Aachen, Germany

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  • The book contains contributions by many top class researchers in algorithmic number theory.

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Table of contents (22 papers)

  1. Front Matter

    Pages I-VIII
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  2. Algorithmic Algebraic Number Theory

    1. Front Matter

      Pages 1-1
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    2. Sieving Methods for Class Group Computation

      • Johannes Buchmann, Michael J. Jacobson Jr., Stefan Neis, Patrick Theobald, Damian Weber
      Pages 3-10

    3. Arithmetic of Modular Curves and Applications

      • Gerhard Frey, Michael Müller
      Pages 11-48

    4. Local and Global Ramification Properties of Elliptic Curves

      • Ernst-Ulrich Gekeler
      Pages 49-64

    5. Techniques for the Computation of Galois Groups

      • Alexander Hulpke
      Pages 65-77

    6. Fortschritte in der inversen Galoistheorie

      • B. Heinrich Matzat
      Pages 79-102

    7. From Class Groups to Class Fields

      • Michael E. Pohst
      Pages 103-119

    8. A Gross-Zagier Formula for Function Fields

      • Hans-Georg Rück, Ulrich Tipp
      Pages 121-137

    9. Extremal Lattices

      • Rudolf Scharlau, Rainer Schulze-Pillot
      Pages 139-170

  3. Algorithmic Commutative Algebra and Algebraic Geometry

    1. Front Matter

      Pages 171-171
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    2. On the Real Nullstellensatz

      • Eberhard Becker, Joachim Schmid
      Pages 173-185

    3. Primary Decomposition: Algorithms and Comparisons

      • Wolfram Decker, Gert-Martin Greuel, Gerhard Pfister
      Pages 187-220

    4. Real Quantifier Elimination in Practice

      • Andreas Dolzmann, Thomas Sturm, Volker Weispfenning
      Pages 221-247

    5. Hilbert Series and Degree Bounds in Invariant Theory

      • Gregor Kemper
      Pages 249-263

    6. Invariant Rings and Fields of Finite Groups

      • Gregor Kemper, Gunter Malle
      Pages 265-281

    7. Computing Versal Deformations with Singular

      • Bernd Martin
      Pages 283-293

    8. Algorithms for the Computation of Free Resolutions

      • Thomas Siebert
      Pages 295-310

  4. Algorithmic Group and Representation Theory

    1. Front Matter

      Pages 311-311
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    2. Computational Aspects of the Isomorphism Problem

      • Frauke M. Bleher, Wolfgang Kimmerle, Klaus W. Roggenkamp, Martin Wursthor
      Pages 313-329
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Keywords

About this book

This book contains 22 lectures presented at the final conference of the Ger­ man research program (Schwerpunktprogramm) Algorithmic Number The­ ory and Algebra 1991-1997, sponsored by the Deutsche Forschungsgemein­ schaft. The purpose of this research program and of the meeting was to bring together developers of computer algebra software and researchers using com­ putational methods to gain insight into experimental problems and theoret­ ical questions in algebra and number theory. The book gives an overview on algorithmic methods and on results ob­ tained during this period. This includes survey articles on the main research projects within the program: • algorithmic number theory emphasizing class field theory, constructive Galois theory, computational aspects of modular forms and of Drinfeld modules • computational algebraic geometry including real quantifier elimination and real algebraic geometry, and invariant theory of finite groups • computational aspects of presentations and representations of groups, especially finite groups of Lie type and their Heeke algebras, and of the isomorphism problem in group theory. Some of the articles illustrate the current state of computer algebra sys­ tems and program packages developed with support by the research pro­ gram, such as KANT and LiDIA for algebraic number theory, SINGULAR, RED LOG and INVAR for commutative algebra and invariant theory respec­ tively, and GAP, SYSYPHOS and CHEVIE for group theory and representation theory.

Editors and Affiliations

  • Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, der Universität Heidelberg, Heidelberg, Germany

    B. Heinrich Matzat

  • Fachbereich Mathematik, Universität Kaiserslautern, Kaiserslautern, Germany

    Gert-Martin Greuel

  • Lehrstuhl D für Mathematik, RWTH Aachen, Aachen, Germany

    Gerhard Hiss

Bibliographic Information

  • Book Title: Algorithmic Algebra and Number Theory

  • Book Subtitle: Selected Papers From a Conference Held at the University of Heidelberg in October 1997

  • Editors: B. Heinrich Matzat, Gert-Martin Greuel, Gerhard Hiss

  • DOI: https://doi.org/10.1007/978-3-642-59932-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Softcover ISBN: 978-3-540-64670-9Published: 20 October 1998

  • eBook ISBN: 978-3-642-59932-3Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: VIII, 434

  • Number of Illustrations: 3 b/w illustrations

  • Topics: Mathematics of Computing, Algorithms, Algebraic Geometry, Number Theory

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