This book is an introduction to computational algebraic geometry and commutative algebra at the undergraduate level. It discusses systems of polynomial equations ("ideals"), their solutions ("varieties"), and how these objects can be manipulated ("algorithms").
The Table of Contents of Ideals, Varieties, and Algorithms gives a more detailed picture of what the book covers.
Typos in the fourth edition are available in pdf .
Lists of typographical errors are available for the third edition. There are two lists, depending on which printing you have. Because of the fourth edition, the typo list for the third edition is no longer being updated.
To find out which printing you have, check the second line from the bottom on the copyright page; the last digit displayed is the printing number. If you have the first printing, you will need to download both lists; if you have the second printing, you only need the second.
Lists of typographical errors are available for the second edition. There is a separate list for each printing. To find out which printing you have, check the second line from the bottom on the copyright page; the last digit displayed is the printing number.
Lists of typographical errors are also available for the first edition. There is a separate list for each printing. To find out which printing you have, check the third line from the bottom on the copyright page; the last digit displayed is the printing number.
Solutions to various exercises from the first four chapters have been written up by Fred Woodward under the direction of Michael Singer of North Carolina State University. We are grateful to Fred and Michael for allowing us to use their solutions.
Solutions to selected exercises from the whole book have been written up by Hyeyoun Chung for a seminar supervised by Steven Kleiman of MIT. We are grateful to Hyeyoun and Steve for allowing us to use their solutions.
The solutions are not posted here because some instructors don't want their students to have access to solutions. However, if you are teaching from Ideals, Varieties, and Algorithms or are studying the book on your own, you may obtain a copy of the solutions by sending email to email@example.com. When requesting a copy, please let us know whether you would prefer the solutions sent in a LaTeX file, a postscript file, or a pdf file. Hardcopy is also available if for some reason the electronic versions aren't suitable.
The book describes the computer algebra systems AXIOM, Maple, Mathematica and REDUCE in some detail. In addition, here are some other computer algebra programs which can do Gröbner basis calculations:
Click here for the web page for our book Using Algebraic Geometry. This book is an introduction to Gröbner bases and resultants, which are two of the main tools used in computational algebraic geometry and commutative algebra. It also discusses local methods and syzygies, and gives applications to integer programming, polynomial splines and algebraic coding theory. The second edition was published by Springer in the summer of 2005. It is available in both hardcover and paperback.
The catalog entry for Ideals, Varieties, and Algorithms in the Springer-Verlag on-line catalog contains a brief description of the book and also includes ordering information.
You can contact the authors at the following email addresses:firstname.lastname@example.org email@example.com firstname.lastname@example.org