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Discovering Mathematics with Magma

Reducing the Abstract to the Concrete

  • Book
  • © 2006

Overview

Editors:
  1. Wieb Bosma

    1. Vakgroep Wiskunde, Katholieke Univ. Nijmegen, Nijmegen, Netherlands

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  2. John Cannon

    1. Department Pure Mathematics, University Sydney, Sydney, Australia

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    You can also search for this editor in PubMed   Google Scholar

  • First book on the well-known MAGMA symbolic computation system

Part of the book series: Algorithms and Computation in Mathematics (AACIM, volume 19)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-XXIV
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  2. Some computational experiments in number theory

    • Wieb Bosma
    Pages 1-30

  3. Applications of the class field theory of global fields

    • Claus Fieker
    Pages 31-62

  4. Some ternary Diophantine equations of signature (n, n, 2)

    • Nils Bruin
    Pages 63-91

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

    • William Stein
    Pages 93-116

  6. Computing with the analytic Jacobian of a genus 2 curve

    • Paul B. van Wamelen
    Pages 117-135

  7. Graded rings and special K3 surfaces

    • Gavin Brown
    Pages 137-159

  8. Constructing the split octonions

    • Donald E. Taylor
    Pages 161-185

  9. Support varieties for modules

    • Jon F. Carlson
    Pages 187-204

  10. When is projectivity detected on subalgebras?

    • Jon F. Carlson
    Pages 205-220

  11. Cohomology and group extensions in Magma

    • Derek F. Holt
    Pages 221-241

  12. Computing the primitive permutation groups of degree less than 1000

    • Colva M. Roney-Dougal, William R. Unger
    Pages 243-260

  13. Computer aided discovery of a fast algorithm for testing conjugacy in braid groups

    • Volker Gebhardt
    Pages 261-285

  14. Searching for linear codes with large minimum distance

    • Markus Grassl
    Pages 287-313

  15. Colouring planar graphs

    • Paulette Lieby
    Pages 315-330

  16. Appendix: The Magma language

    • Geoff Bailey
    Pages 331-356

  17. Back Matter

    Pages 356-374
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Keywords

About this book

The appearance of this volume celebrates the ?rst decade of Magma, a new computeralgebrasystemlaunchedattheFirstMagmaConferenceonCom- tational Algebra held at Queen Mary and West?eld College, London, August 1993. This book introduces the reader to the role Magma plays in advanced mathematical research. Each paper examines how the computer can be used to gain insight into either a single problem or a small group of closely related problems. The intention is to present su?cient detail so that a reader can (a), gain insight into the mathematical questions that are the origin of the problems,and(b),developanunderstandingastohowsuchcomputations are speci?edinMagma.Itishopedthatthereaderwillcometoarealisationofthe important rolethatcomputational algebracanplayinmathematical research. Readers not primarily interested in using Magma will easily acquire the skills needed to undertake basic programming in Magma, while experienced Magma users can learn both mathematics and advanced computational methods in areas related to their own. The core of the volume comprises 14 papers. The authors were invited to submit articles on designated topics and these articles were then reviewed by referees. Although by no means exhaustive, the topics range over a consid- ablepartofMagma’scoverageofalgorithmicalgebra:fromnumbertheoryand algebraicgeometry,viarepresentationtheoryandcomputationalgrouptheory to some branches of discrete mathematics and graph theory. The papers are preceded by an outline of the Magma project, a brief summary of the papers and some instructions on reading the Magma code. A basic introduction to the Magma language is given in an appendix. Theeditorsexpresstheirgratitudetothecontributorstothisvolume,both for the work put into producing the papers and for theirpatience.

Editors and Affiliations

  • Vakgroep Wiskunde, Katholieke Univ. Nijmegen, Nijmegen, Netherlands

    Wieb Bosma

  • Department Pure Mathematics, University Sydney, Sydney, Australia

    John Cannon

About the editors

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

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