This book, written in two volumes, is an introductory manual for Magma, a programming language designed for the investigation of algebraic, geometric and combinatorial structures, or "magmas". It presumes no knowledge of computer programming, and its examples are chosen to illustrate language and algorithmic features as simply as possible. Magma is a sophisticated tool for experimentation, education, and computer-aided proof, useful for both students and professional mathematicians. Volume I explains the language and user environment in detail, whereas Volume II deals with the major algebraic, geometrical and combinatorial structures implemented in the system.
Volume II: Part V. Rings and Fields: Overview of Rings and Fields.- The Ring of Integers. Univariate Polynomial Rings.- Multivariate Polynomial Rings.- Power Series and Laurent Series.- Finite Fields.- Number Fields.- The Real and Complex Fields.- Part VI. Modules and Algebras: Vector Spaces and Matrix Spaces.- Matrix Algebras.- Part VII. Groups: Overview of Groups.- Finitely-Presented Groups.- Abelian Groups.- Permutation Groups.- Matrix Groups.- Part VIII. Algebraic Geometry: Elliptic Curves.- Part IX. Geometric and Combinatorial Structures: Enumerative Combinatorics.- Overview of Incidence Structures.- Graphs.- Designs.- Finite Planes.- Error-Correcting Codes.- References.- Index
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- ID: 9783540627470
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