Algorithms and Computation in Mathematics • Volume 19 Editors Arjeh M. Cohen Henri Cohen David Eisenbud Bernd Sturmfels Wieb Bosma John Cannon (Eds.) Discovering Mathematics with Magma Reducing the Abstract to the Concrete With 9 Figures and 16 Tables ABC Editors Dr. Wieb Bosma Professor Dr. John Cannon Katholieke Univ. Nijmegen Vakgroep Wiskunde Postbus 9010, 6500 GL Nijmegen, Netherlands E-mail:
[email protected] University Sydney Department Pure Mathematics F07 2006 Sydney, Australia E-mail:
[email protected] Library of Congress Control Number: 2006931477 Mathematics Subject Classification (2000): 68W30, 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05 ISSN 1431-1550 ISBN-10 3-540-37632-1 Springer Berlin Heidelberg New York ISBN-13 978-3-540-37632-3 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2006 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: by the authors and techbooks using a Springer LATEX macro package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper SPIN: 11693079 17/techbooks 543210 Preface The appearance of this volume celebrates the first decade of Magma, a new computer algebra system launched at the First Magma Conference on Computational Algebra held at Queen Mary and Westfield 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 sufficient detail so that a reader can (a), gain insight into the mathematical questions that are the origin of the problems, and (b), develop an understanding as to how such computations are specified in Magma. It is hoped that the reader will come to a realisation of the important role that computational algebra can play in mathematical 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 t