Computations in algebraic geometry with Macaulay 2

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes detailsof the mathematics. . INDICE: Part I. Introducing Macaulay 2: 1. Ideals, Varieties and Macaulay 2 by Bernd Sturmfels.- 2. Projective Geometry and Homological Algebra by DavidEisenbud.- 3. Data Types, Functions, and Programming by Daniel R. Grayson andMichael E. Stillman.- 4. Teaching the Geometry of Schemes by Gregory G. Smithand Bernd Sturmfels.- Part II. Mathematical Computations: 5. Monomial Ideals by Serkan Hosten and Gregory G. Smith.- 6. From Enumerative Geometry to Solving Systems of Polynomial Equations by Frank Sottile.- 7. Resolutions and Cohomology over Complete Intersections by Luchezar L. Avramov and Daniel R. Grayson.- 8. Algorithms for the Toric Hilbert Scheme by Stillman, Bernd Sturmfels, andRekha Thomas.- 9. Sheaf Algorithms Using the Exterior Algebra by Wolfram Decker and David Eisenbud.- 10. Needles in a Haystack: Special Varieties via SmallFields by Frank-Olaf Schreyer and Fabio Tonoli.- 11.D-modules and Cohomology of Varieties by Uli Walther.

• ISBN: 978-3-642-07592-6
• Editorial: Springer
• Encuadernacion: Rústica
• Fecha Publicación: 31/03/2012
• Nº Volúmenes: 1
• Idioma: Inglés