Computations in algebraic geometry with Macaulay 2
著者
書誌事項
Computations in algebraic geometry with Macaulay 2
（Algorithms and computation in mathematics, v. 8）
Springer, [2011], c2002
- : pbk
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注記
Originally published: 2002
"Softcover reprint of the hardcover 1st edition 2002"--T.p. verso
Includes bibliographical references and index
内容説明・目次
内容説明
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 details of the mathematics.
目次
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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