1992 | Supplement | Buchkapitel
Elimination Theory
verfasst von : David Cox, John Little, Donal O’Shea
Erschienen in: Ideals, Varieties, and Algorithms
Verlag: Springer New York
Enthalten in: Professional Book Archive
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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 classical theory of resultants. The geometric interpretation of elimination will also be explored when we discuss the Closure Theorem. Of the many applications of elimination theory, we will treat two in detail: the implicitization problem and the envelope of a family of curves.