Langbeschreibung
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.
Inhaltsverzeichnis
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