Elimination Theory

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


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.


Singular Point Partial Solution Tangent Line Computer Algebra System Extension Theorem 
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Copyright information

© Springer Science+Business Media New York 1997

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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