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派博传思国际中心 »期刊书目

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Titlebook: Ideals, Varieties, and Algorithms; An Introduction to C David Cox,John Little,Donal O’Shea Textbook 20073rd edition Springer-Verlag New Yor

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书目名称Ideals, Varieties, and Algorithms
副标题An Introduction to C
编辑David Cox,John Little,Donal O’Shea
视频videohttp://file.papertrans.cn/461/460768/460768.mp4
概述Covers important topics such as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.Includes a significantly updated section on Maple in Appendi
丛书名称Undergraduate Texts in Mathematics
图书封面Titlebook: Ideals, Varieties, and Algorithms; An Introduction to C David Cox,John Little,Donal O’Shea Textbook 20073rd edition Springer-Verlag New Yor
描述.Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? ..The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory...The algorithms to answer questions such as those posed above are an important part of algebraic geometry. Although the algorithmic roots of algebraic geometry are old, it is only in the last forty years that computational methods have regainedtheir earlier prominence. New algorithms, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in geometric theorem proving...In ad
出版日期Textbook 20073rd edition
关键词Maple; Mathematica; addition; algebra; commutative property; computer algebra system; proof
版次3
doihttps://doi.org/10.1007/978-0-387-35651-8
isbn_ebook978-0-387-35651-8Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightSpringer-Verlag New York 2007
The information of publication is updating

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Undergraduate Texts in Mathematicshttp://image.papertrans.cn/i/image/460768.jpg
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Elimination Theory,This chapter will study systematic methods for eliminating variables from systems of polynomial equations. The basic strategy of elimination theory will be given in two main theorems: the Elimination Theorem and the Extension Theorem. We will prove these results using Groebner bases and the classic theory of resultants.
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Invariant Theory of Finite Groups,Invariant theory has had a profound effect on the development of algebraic geometry. For example, the Hilbert Basis Theorem and Hilbert Nullstellensatz, which play a central role in the earlier chapters in this book, were proved by Hilbert in the course of his investigations of invariant theory.
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Geometry, Algebra, and Algorithms,her dimensional objects) defined by polynomial equations. To understand affine varieties, we will need some algebra, and in particular, we will need to study . in the polynomial ring .[.1.]. Finally, we will discuss polynomials in one variable to illustrate the role played by .
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Polynomial and Rational Functions on a Variety,se objects, and especially the mappings which preserve some property of interest. For instance, in linear algebra after studying vector spaces, you also studied the properties of . between vector spaces (mappings that preserve the vector space operations of sum and scalar product).
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Springer-Verlag New York 2007
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