Computational Commutative Algebra 1Martin Kreuzer and Lorenzo RobbianoSpringer Verlag, Heidelberg 2000 (Corr. 2nd Printing 2008) 

Fields: Symbolic Computation, Computer Algebra; Computational Mathematics and Scientific Computing; Algebra  Keywords: Groebner Bases, Commutative Algebra, Computer Algebra, CoCoA, Polynomial Systems.  
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Table of Contents (pdffile) 
Pictures of the Authors (pic1) (pic2) 

Errors and misprints: For the second printing (July 2008), no errors or misprints are known. For the first printing: (pdf file) 
The palindrome (close up) 
The main topic of this book is that of Groebner bases and their applications. The main purpose of this book is that of bridging the current gap in the literature between theory and real computation. The book can be used by teachers and students alike as a comprehensive guide to both the theory and the practice of Computational Commutative Algebra. It has been made as selfcontained as possible, and thus is ideally suited as a textbook for graduate or advanced undergraduate courses. 
Numerous applications are described, covering fields as disparate as algebraic geometry and financial markets. To aid a deeper understanding of these applications there are 44 tutorials aimed at illustrating how the theory can be used in these cases. The computational aspects of the tutorials can be carried out with the computer algebra system CoCoA, an introduction to which appears in an appendix. Besides the tutorials there are plenty of exercises, some of a theoretical nature and others more practical. 