Bøger i Algorithms and Computation in Mathematics serien

One of the most remarkable theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. This book develops a new theory which is powerful enough to include all the earlier generalizations. It is also in part an extensive encyclopedia listing the different types of self-dual codes and their properties.

This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation.

This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity;

This acclaimed book examines the topic of symbolic integration in comprehensive detail, incorporating new results along the way. The second edition offers a new chapter on parallel integration, and a number of other improvements including additional exercises.

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. Coverage ranges from number theory and algebraic geometry, through representation theory and group theory to discrete mathematics and graph theory.

This text offers an introduction to error-correcting linear codes. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The book is based on the successful German edition.

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations.