Graduate Texts in Mathematics

Volume 185

Springer, 2005

Amherst College

John B. Little,

College of the Holy Cross

Don O'Shea,

Mount Holyoke College

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.

For more information about the book, see the publications page of John Little.

A list of typographical errors is available for the **first
edition** of *Using Algebraic Geometry*: pdf or postscript .

A list of typographical errors is available for the **second
edition** of *Using Algebraic Geometry*: pdf or postscript .

** First Edition:** The Maple code for the first edition of *Using Algebraic
Geometry* was written for Releases 3 and 4 of Maple V. Some of the
code in the text uses commands from the *grobner* package, such
as "gbasis" and "finite".

In Release 5 of Maple V, the *grobner* package was
replaced with the *Groebner*
package. In this package, some commands (such as "gbasis") have a
different syntax, while other (such as "finite") have different
names. Hence, the Maple code in the first edition will need to be modified if
a reader wants to run it under more recent versions of Maple.

** Second Edition:** In the second edition of *Using Algebraic Geometry*, the
Maple code was rewritten to be consistent with the
*Groebner* package that came with Release 5 of Maple V.

Starting with Maple 11, the *Groebner* package was updated,
so that some commands have different names ("gbasis" is now "Basis")
and some of the syntax is slighlty different. Hence the Maple code in
the second edition will need to be modified if a reader wants to run
it under more recent versions of Maple. A document describing some of
these changes is available as
either pdf
or postscript .

The
catalog entry for * Using Algebraic Geometry* 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@mhc.mtholyoke.edu