Computational Algebra and Number Theory

1. Front Matter

   Pages i-xiv

   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

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.

• Category theory
• Group theory
• algebra
• algorithms
• automata
• computer
• computer science
• number theory
• combinatorics

• 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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