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").

The Table of Contents of *
Ideals, Varieties, and Algorithms* gives a more detailed picture of
what the book covers.

Lists of typographical errors are available for the third edition. There are two lists, depending on which printing you have.

- 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. 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.

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

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.

- 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 .

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 dac@cs.amherst.edu. 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:

- 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:

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