E-Book Overview
-------------------Description-------------------- The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics.
The Handbook of Computational Group Theory offers the first complete treatment of all the fundamental methods and algorithms in CGT presented at a level accessible even to advanced undergraduate students. It develops the theory of algorithms in full detail and highlights the connections between the different aspects of CGT and with other areas of computer algebra. While acknowledging the importance of the complexity analysis of CGT algorithms, the authors' primary focus is on algorithms that perform well in practice rather than on those with the best theoretical complexity.
Throughout the book, applications of all the key topics and algorithms to areas both within and outside of mathematics demonstrate how CGT fits into the wider world of mathematics and science. The authors include detailed pseudocode for all of the fundamental algorithms, and provide detailed worked examples that bring the theorems and algorithms to life. ---------------------Features--------------------- · Provides the first reasonably accessible, comprehensive presentation of computational group theory · Summarizes state-of-the-art methods and results, including pointers to the literature for the principal areas of CGT · Incorporates the full underlying theory and correctness proofs of basic algorithms, and presents those algorithms in pseudocode · Includes a chapter on the precomputed stored libraries and databases of groups and character tables now publicly available ---------------------Contents--------------------- History of Computational Group Theory
BACKGROUND MATERIALS Fundamentals Group Actions Series Presentation of Groups Presentation of Subgrou