Ideals, Varieties, and AlgorithmsThird Edition, 2007
Springer
Ideals, Varieties, and Algorithms
The third edition of IVA is now available.
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.
On pages 522 and 524 of the third edition (= pages 510 and 512 of the second edition), Appendix C mentions computer packages for Maple and Mathematica. The packages were written for teaching purposes and tend to be very slow. Thus you can use them only on very simple problems.
For Releases 2, 3 and 4 of Maple V, the following versions of the Maple package are available:
For Release 5 of Maple V, an expanded version of the Maple package is available. This version includes commands for computing Gröbner bases which give intermediate steps as well as tutorial and reference worksheets. The files involved are:
WARNING: The IVA Maple package for Release 5 of Maple V is incompatible with Maple 6 and Maple 7. For Maple 6 and 7, you should download the following files:
For Mathematica, the following versions of the Mathematica package are available:
When using these Mathematica packages and notebooks, the following should be kept in mind:
In general, if you have difficulties with either of the packages or suggestions for improvements, please let us know! (Thanks to David Vella and his students at Skidmore for letting me know that the 4.0 version of the package doesn't work with Mathematica 5.0. They also suggested the solution implemented in the 5.0 version of the package.)
Lists of typographical errors are available for the third 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 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 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.
Releases 3 and 4 of Maple V contained the grobner package for doing Gröbner basis computations, and Appendix C of the first and second editions of the book described this package. Starting with Release 5 of Maple V, the grobner package was replaced with the new Groebner package, which has many improvements.
The third edition of the book includes an updated the Maple section of Appendix C by including a description of the Groebner package in Maple V Release 5 and Maple 6, 7, 8, 9 and 10.
For readers who have the first or second editions of the book, the new version of this section is available as either TeX source or postscript .
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:
Of these, all are free except for Magma.
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@cs.amherst.edu little@math.holycross.edu doshea@mhc.mtholyoke.edu