Discovering Mathematics with Magma

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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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.

• Magma
• Permutation
• Signatur
• algebra
• algorithms
• code
• computer
• computer algebra
• computer algebra system
• geometry
• graphs
• number theory
• programming
• programming language
• symbolic computation

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

  Wieb Bosma

• Department Pure Mathematics, University Sydney, Sydney, Australia

  John Cannon

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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