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 classic 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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Cox, D., Little, J., O’Shea, D. (1997). Elimination Theory. In: Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-41154-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-662-41154-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-7-5062-6598-0
Online ISBN: 978-3-662-41154-4
eBook Packages: Springer Book Archive