Synopsis
I Introducing Macaulay 2.- Ideals, Varieties and Macaulay 2.- Projective Geometry and Homological Algebra.- Data Types, Functions, and Programming.- Teaching the Geometry of Schemes.- II Mathematical Computations.- Monomial Ideals.- From Enumerative Geometry to Solving Systems of Polynomial Equations.- Resolutions and Cohomology over Complete Intersections.- Algorithms for the Toric Hilbert Scheme.- Sheaf Algorithms Using the Exterior Algebra.- Needles in a Haystack: Special Varieties via Small Fields.- D-modules and Cohomology of Varieties.
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