Titlebook: Using Algebraic Geometry; David Cox,John Little,Donal O’Shea Textbook 19981st edition Springer Science+Business Media New York 1998 Combin

MORT

Free Resolutions,sive syzygy modules of .. In this chapter, we will study resolutions and the information they encode about .. Throughout this chapter, . will denote the polynomial ring .[..,..., ..] or one of its localizations.

BROTH

0072-5285 e computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applica

BABY

Resultants,tant and explore its generalization to several polynomials in several variables. This . can be used to eliminate variables from three or more equations and, as we will see at the end of the chapter, it is a surprisingly powerful tool for finding solutions of equations.

CODA

傻瓜

诱骗

Algebraic Coding Theory, this structure to develop good encoding and decoding algorithms. Finally, we will introduce the Reed-Muller and geometric Goppa codes, where algebraic geometry is used in the construction of the code itself.

恸哭

Introduction,ion of coordinates to describe points in Euclidean space and his idea of describing curves and surfaces by algebraic equations. Over the long history of the subject, both powerful general theories and detailed knowledge of many specific examples have been developed. Recently, with the development of

小官

Solving Polynomial Equations,n the elimination properties of lexicographic Gröbner bases. Combining elimination with numerical root-finding for one-variable polynomials we get a conceptually simple method that generalizes the usual techniques used to solve systems of linear equations. However, there are potentially severe diffi

单色

Resultants,tant of two polynomials is well known and is implemented in many computer algebra systems. In this chapter, we will review the properties of the resultant and explore its generalization to several polynomials in several variables. This . can be used to eliminate variables from three or more equation

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