**Proceedings of Symposia in Applied Mathematics**

Volume: 53;
1998;
172 pp;
Hardcover

MSC: Primary 13; 14;
Secondary 05; 68; 90; 94

Print ISBN: 978-0-8218-0750-7

Product Code: PSAPM/53

List Price: $46.00

AMS Member Price: $36.80

MAA member Price: $41.40

**Electronic ISBN: 978-0-8218-9268-8
Product Code: PSAPM/53.E**

List Price: $46.00

AMS Member Price: $36.80

MAA member Price: $41.40

# Applications of Computational Algebraic Geometry

Share this page *Edited by *
*David A. Cox; Bernd Sturmfels*

This book introduces readers to key ideas and applications of computational
algebraic geometry. Beginning with the discovery of Gröbner bases and fueled by the
advent of modern computers and the rediscovery of resultants, computational
algebraic geometry has grown rapidly in importance. The fact that
“crunching equations” is now as easy as “crunching numbers” has had a profound impact
in recent years. At the same time, the mathematics used in computational
algebraic geometry is unusually elegant and accessible, which makes the subject
easy to learn and easy to apply.

This book begins with an introduction to Gröbner bases and resultants, then discusses some of the more recent methods for solving systems of polynomial equations. A sampler of possible applications follows, including computer-aided geometric design, complex information systems, integer programming, and algebraic coding theory. The lectures in the book assume no previous acquaintance with the material.

#### Readership

Graduate students and research mathematicians interested in commutative rings and algebras.

# Table of Contents

## Applications of Computational Algebraic Geometry

- Contents vii8 free
- Preface ix10 free
- Introduction to Gröbner bases 112 free
- Introduction to resultants 2536
- Numerical methods for solving polynomial equations 4152
- Applications to computer aided geometric design 6780
- Combinatorial homotopy of simplicial complexes and complex information systems 91104
- Applications to integer programming 119132
- Applications to coding theory 143156
- Index 169182