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Geometry, Algebra, and Algorithms

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

Abstract

This chapter will introduce some of the basic themes of the course. The geometry we are interested in concerns affine varieties, which are curves and surfaces (and higher dimensional objects) defined by polynomial equations. To understand affine varieties, we will need some algebra, and in particular, we will need to study ideals in the polynomial ring k[x l,...,x n]. Finally, we will discuss polynomials in one variable to illustrate the role played by algorithms.

Keywords

Tangent Line Parametric Representation Computer Algebra System Implicit Representation Great Common Divisor 
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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