Computing in Algebraic Geometry

A Quick Start using SINGULAR

By: Wolfram Decker, Christoph Lossen

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Paperback | 12 February 2010

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344 Pages

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23.39 x 15.6 x 1.83

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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

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"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 Sertoez, Mathematical Reviews, Issue 2007 b)

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