This textual content covers issues in algebraic geometry and commutative algebra with a powerful point of view towards useful and computational features. the 1st 4 chapters shape the center of the publication. A complete chart within the Preface illustrates numerous how one can continue with the cloth as soon as those chapters are coated. as well as the basics of algebraic geometry—the removal theorem, the extension theorem, the closure theorem and the Nullstellensatz—this re-creation contains numerous big adjustments, all of that are indexed within the Preface. the biggest revision includes a new bankruptcy (ten), which provides many of the necessities of growth remodeled the final a long time in computing Gröbner bases. The publication additionally contains present desktop algebra fabric in Appendix C and up to date self reliant tasks (Appendix D).

The ebook could function a primary or moment path in undergraduate summary algebra and with a few supplementation possibly, for starting graduate point classes in algebraic geometry or computational algebra. necessities for the reader contain linear algebra and a proof-oriented course. It is believed that the reader has entry to a working laptop or computer algebra process. Appendix C describes positive factors of Maple™, Mathematica® and Sage, in addition to different platforms which are so much correct to the textual content. Pseudocode is utilized in the textual content; Appendix B conscientiously describes the pseudocode used.

From the studies of past editions:

 “…The booklet offers an advent to Buchberger’s set of rules with purposes to syzygies, Hilbert polynomials, basic decompositions. there's an advent to classical algebraic geometry with functions to the appropriate club challenge, fixing polynomial equations and removal conception. …The publication is well-written. …The reviewer is bound that it'll be a very good consultant to introduce extra undergraduates within the algorithmic point of commutative algebra and algebraic geometry.”

 —Peter Schenzel, zbMATH, 2007

 “I give some thought to the ebook to be great. ... The exposition is especially transparent, there are numerous priceless photos and there are an exceptional many instructive routines, a few really hard ... deals the guts and soul of recent commutative and algebraic geometry.”

 —The American Mathematical Monthly