Computational Commutative Algebra 1

This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical. "The main topic of this book is that of Groebner bases and their applications. The main purpose of this book is that of bridging the current gap in the literature between theory and real computation. The book can be used by teachers and students alike as a comprehensive guide to both the theory and the practice of Computational Commutative Algebra. It has been made as self-contained as possible, and thus is ideally suited as a textbook for graduate or advanced undergraduate courses. Numerous applications are described, covering fields as disparate as algebraic geometry and financial markets. To aid a deeper understanding of these applications, there are 44 tutorials aimed at illustrating how the theory can be used in these cases The computational aspects of the tutorials can be carried out with the computer algebra system CoCoA, an introduction to which appears in an appendix. Besides the tutorials there are plenty of exercises, some of a theoretical nature and others more practical."--Jacket This introduction to polynomial rings, Groebner bases and applications bridges the gap in the literature between theory and actual computation. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. This book is intended to bridge the gap between theoretical computer algebra and actual computation