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Titlebook: Computations in Algebraic Geometry with Macaulay 2; David Eisenbud,Michael Stillman,Bernd Sturmfels Textbook 2002 Springer-Verlag Berlin H

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书目名称Computations in Algebraic Geometry with Macaulay 2
编辑David Eisenbud,Michael Stillman,Bernd Sturmfels
视频videohttp://file.papertrans.cn/234/233266/233266.mp4
概述Only textbook using Macaulay as a tool.Computational algebraic geometry presented in the optimal way by top researchers.Includes supplementary material:
丛书名称Algorithms and Computation in Mathematics
图书封面Titlebook: Computations in Algebraic Geometry with Macaulay 2;  David Eisenbud,Michael Stillman,Bernd Sturmfels Textbook 2002 Springer-Verlag Berlin H
描述Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re­ cently developed algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorith­ mic approach to the subject has two principal aims: developing new tools for research within mathematics, and providing new tools for modeling and solv­ ing problems that arise in the sciences and engineering. A healthy synergy emerges, as new theorems yield new algorithms and emerging applications lead to new theoretical questions. This book presents algorithmic tools for algebraic geometry and experi­ mental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations
出版日期Textbook 2002
关键词Groebner bases; algebraic geometry; algorithms; commutative algebra; computer algebra system; symbolic al
版次1
doihttps://doi.org/10.1007/978-3-662-04851-1
isbn_softcover978-3-642-07592-6
isbn_ebook978-3-662-04851-1Series ISSN 1431-1550
issn_series 1431-1550
copyrightSpringer-Verlag Berlin Heidelberg 2002
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Needles in a Haystack: Special Varieties via Small Fields we develop a program that produces random curves of genus . ≤ 14. In the second part we use the program to test Green’s Conjecture on syzygies of canonical curves and compare it with the corresponding statement for Coble self-dual sets of points. In the third section we apply our techniques to prod
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1431-1550 , commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations978-3-642-07592-6978-3-662-04851-1Series ISSN 1431-1550
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Computations in Algebraic Geometry with Macaulay 2
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1431-1550 ry material: Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re­ cently developed algorithms have made theoretical aspect
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https://doi.org/10.1057/9780230509559d polynomial ring, so they can be represented in the computer, and can be used to compute Ext modules simultaneously in all homological degrees. It is shown how to write . code to implement the construction, and how to use the computer to determine invariants of modules over complete intersections that are difficult to obtain otherwise.
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Richard Sutton,David G. Bendittnected. In this chapter we illustrate the use of . for exploring the structure of toric Hilbert schemes. In the process we will encounter algorithms from commutative algebra, algebraic geometry, polyhedral theory and geometric combinatorics.
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