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Elimination Theory

  • David Cox
  • John Little
  • Donal O’Shea
Part of the Undergraduate Texts in Mathematics book series (UTM)

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.

Keywords

Singular Point Partial Solution Tangent Line Extension Theorem Unique Factorization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • David Cox
    • 1
  • John Little
    • 2
  • Donal O’Shea
    • 3
  1. 1.Department of Mathematics and Computer ScienceAmherst CollegeAmherstUSA
  2. 2.Department of MathematicsCollege of the Holy CrossWorcesterUSA
  3. 3.Department of Mathematics, Statistics, and Computer ScienceMount Holyoke CollegeSouth HadleyUSA

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