Fourth Edition, 2015

Springer

Amherst College

John B. Little,

College of the Holy Cross

Don O'Shea,

New College of Florida

- What's in the Book
- Typographical Errors
- Solutions to Selected Exercises
- Computer Algebra Programs
- Remarks on Earliers Editions of IVA
- Using Algebraic Geometry
- Contacting Springer-Verlag
- Contacting the Authors

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").

In 2016, *
Ideals, Varieties, and Algorithms* was awarded the Leroy P. Steele Prize for Mathematical Exposition by the American Mathematical Society. The article *The Story of Ideals, Varieties, and Algorithms* tells how the book came to be written.

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 Because of the fourth edition, the typo list for the third edition is no longer being updated.

- Typos in the first printing corrected in the second printing: pdf or postscript .
- Typos present in the first and second printings: pdf or postscript .

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. Because of the fourth edition, the typo list for the second edition is no longer being updated.

- Typos for the first printing: pdf or postscript .
- Typos for the second, third and fourth printings: pdf or postscript .

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. Because of the fourth edition, the typo list for the first edition is no longer being updated.

- Typos for the first printing: text file .
- Typos for the second printing: TeX source or postscript .
- Typos for the third printing: TeX source or postscript .

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.

A complete solutions manual for *Ideals, Varieties, and Algorithms* has been written up by David Cox and Ying Li of St. Francis University.

The solutions are not posted here because having open access to the solutions would diminish the value of the text. *Ideals, Varieties, and Algorithms* is a book where you learn by doing. If you are
teaching from *Ideals, Varieties, and Algorithms* or are studying
the book on your own, you may obtain a pdf copy of the solutions by
sending email to dacox@amherst.edu.

The book describes the computer algebra systems
*Maple*, *Mathematica* and *Sage* in some detail. *Maple* and *Mathematica* are commercial products, while *Sage* is freely available. at

- Appendix C of first edition of IVA describes the
obsolete
**grobner package**for Maple, while subsequent editions describe the**Groebner package**now used in Maple. - In the 5th printing of the second edition of IVA, a production error caused plus signs to appear as minus signs on many pages. Hence the 5th printing of the second edition is defective.
- The first three editions of IVA mention the existence of computer packages for Maple and Mathematica. These packages are no longer supported and are not available.
- Our earlier practice of paying $1 US for each new typographical error has been discontinued, though we are always grateful when readers notify us about errors they find in the book.

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:

dacox@amherst.edu little@math.holycross.edu doshea@ncf.edu