Abstract
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.
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© 1992 Springer Science+Business Media New York
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Cox, D., Little, J., O’Shea, D. (1992). Elimination Theory. In: Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2181-2_3
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DOI: https://doi.org/10.1007/978-1-4757-2181-2_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2183-6
Online ISBN: 978-1-4757-2181-2
eBook Packages: Springer Book Archive