Algorithms and Computation in Mathematics

Discovering Mathematics with Magma

Reducing the Abstract to the Concrete

Editors: Bosma, Wieb, Cannon, John (Eds.)

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  • ISBN 978-3-540-37634-7
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About this book

This volume celebrates the first decade of the Computer Algebra system Magma. With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the reader to the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning new theoretical results. The authors of the chapters were chosen both for their expertise in the particular field and for their innovative use of Magma. Although by no means exhaustive, the topics range over much of Magma's coverage of algorithmic algebra: from number theory and algebraic geometry, via representation theory and group theory to some branches of discrete mathematics and graph theory. A basic introduction to the Magma language is given in an appendix. The book is simultaneously an invitation to learn a new programming language in the context of contemporary research problems, and an exposition of the types of problem that can be investigated using computational algebra.

About the authors

Cannon:

1) Principal designer of the Magma system

2) Extensive contributions to the field of group theory algorithms

3) Awards:

  • 1993 CSIRO Medal (for Computer Algebra)
  • 2001 ATSE Clunies Ross Award (for Cryptography and Computer Algebra)
  • 2006 Richard D. Jenks Memorial Prize for Excellence in Software Engineering Applied to Computer Algebra.

 

Bosma: co-designer of Magma, active in computational number theory and computer algebra

Table of contents (15 chapters)

Table of contents (15 chapters)
  • Some computational experiments in number theory

    Pages 1-30

    Bosma, Wieb

  • Applications of the class field theory of global fields

    Pages 31-62

    Fieker, Claus

  • Some ternary Diophantine equations of signature (n, n, 2)

    Pages 63-91

    Bruin, Nils

  • Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma

    Pages 93-116

    Stein, William

  • Computing with the analytic Jacobian of a genus 2 curve

    Pages 117-135

    van Wamelen, Paul B.

Buy this book

eBook 96,29 €
price for Spain (gross)
  • ISBN 978-3-540-37634-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
  • Institutional customers should get in touch with their account manager
Hardcover 124,79 €
price for Spain (gross)
Softcover 124,79 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Discovering Mathematics with Magma
Book Subtitle
Reducing the Abstract to the Concrete
Editors
  • Wieb Bosma
  • John Cannon
Series Title
Algorithms and Computation in Mathematics
Series Volume
19
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-37634-7
DOI
10.1007/978-3-540-37634-7
Hardcover ISBN
978-3-540-37632-3
Softcover ISBN
978-3-642-07231-4
Series ISSN
1431-1550
Edition Number
1
Number of Pages
XXIV, 364
Topics