Computing in Algebraic Geometry A Quick Start using SINGULAR [Hardcover]

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.

Introductory Remarks on Computer Algebra.- 1 Basic Notations and Ideas: A Historical Account.- 2 Basic Computational Problems and Their Solution.- 3 An Introduction to SINGULAR.- Practical Session I .- Practical Session II .- 4 Homological Algebra I .- 5 Homological Algebra II .- Practical Session III .- 6 Solving Systems of Polynomial Equations .- 7 Primary Decomposition and Normalization .- Practical Session .- 8 Algorithms for Invariant .- 9 Computing in Local Rings .- Practical Session V .- Appendix A Sheaf Cohomology and Beilinson Monads .- Appendix B Solutions to Exercises .- References .- Index

From the reviews:

Algebraic geometry generally studies the properties of solution sets of systems of polynomial equations without direct reference to the actual polynomials used in these systems. & This is especially desirable for classwork where the development of the abstract machinery generally outlasts the patience of the students, except possibly the most motivated ones. & However, the book can & be used in an introductory algebraic geometry course where the students will have the advantage of experimenting with examples as their knowledge grows. (A. Sinan Sert?z, Mathematical Reviews, Issue 2007 b)

Wolfram Decker is professor of mathematics at the Universit?t des Saarlandes, Saarbr?cken, Germany. His fields of interest are algebraic geometry and computer algebra. From 1996-2004, he was the responsible overall organizer of the slC>