Springer Discovering Mathematics with Magma: Reducing the Abstract to the Concrete: 19 (Algorithms and Computation in Mathematics, 19)

Based on the ontology and semantics of algebra, the computer algebra system Magma enables users to rapidly formulate and perform calculations in abstract parts of mathematics. Edited by the principal designers of the program, this book explores Magma. Coverage ranges from number theory and algebraic geometry, through representation theory and group theory to discrete mathematics and graph theory. Includes case studies describing computations underpinning new theoretical results. From the Back Cover 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 Author 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