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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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