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Computational Algebra and Number Theory

  • Book
  • © 1995

Overview

Editors:
  1. Wieb Bosma

    1. School of Mathematics and Statistics, University of Sydney, Sydney, Australia

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    You can also search for this editor in PubMed   Google Scholar

  2. Alf Poorten

    1. CeNTRe for Number Theory Research, Macquarie University, Sydney, Australia

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 325)

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Calculating Growth Functions for Groups Using Automata

    • Marcus Brazil
    Pages 1-18

  3. The Minimal Faithful Degree of a Finite Commutative Inverse Semigroup

    • S. Byleveld, D. Easdown
    Pages 19-27

  4. Generalisations of the Todd-Coxeter Algorithm

    • S. A. Linton
    Pages 29-51

  5. Computing Left Kan Extensions Using the Todd-Coxeter Procedure

    • M. Leeming, R. F. C. Walters
    Pages 53-73

  6. Computing Finite Soluble Quotients

    • Alice C. Niemeyer
    Pages 75-82

  7. Computing Automorphism Groups of p-Groups

    • E. A. O’Brien
    Pages 83-90

  8. The Art and Science of Computing in Large Groups

    • S. A. Linton
    Pages 91-109

  9. Does the Set of Points of an Elliptic Curve Determine the Group?

    • H. W. Lenstra Jr., J. Pila
    Pages 111-118

  10. An Implementation of the Elliptic Curve Integer Factorization Method

    • Wieb Bosma, Arjen K. Lenstra
    Pages 119-136

  11. Continued Fractions of Algebraic Numbers

    • Enrico Bombieri, Alfred J. van der Poorten
    Pages 137-152

  12. Bounds for Class Numbers of Quadratic Orders

    • Stéphane Louboutin, Richard A. Mollin
    Pages 153-158

  13. Short Representation of Quadratic Integers

    • Johannes Buchmann, Christoph Thiel, Hugh Williams
    Pages 159-185

  14. A Density Conjecture for the Negative Pell Equation

    • Peter Stevenhagen
    Pages 187-200

  15. Computing Aurifeuillian Factors

    • Richard P. Brent
    Pages 201-212

  16. Computation of Cyclotomic Polynomials with Magma

    • Wieb Bosma
    Pages 213-225

  17. On Some Characteristics of Uniformity of Distribution and Their Applications

    • Igor E. Shparlinski
    Pages 227-241

  18. Recent Progress on Consistency Testing for Polynomial Systems

    • Scott McCallum
    Pages 243-253

  19. A New Generalisation of the Kummer Congruence

    • H. Sunil Gunaratne
    Pages 255-265

  20. Series Expansions of Algebraic Functions

    • Deryn Griffiths
    Pages 267-277
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Keywords

About this book

Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few.
Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed.
Audience: Students, experts, and those performing current research in any of the topics mentioned above.

Editors and Affiliations

  • School of Mathematics and Statistics, University of Sydney, Sydney, Australia

    Wieb Bosma

  • CeNTRe for Number Theory Research, Macquarie University, Sydney, Australia

    Alf Poorten

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