Ideals, Varieties, and Algorithms pp 1-46 | Cite as

# Geometry, Algebra, and Algorithms

Chapter

## Abstract

This chapter will introduce some of the basic themes of the book. 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 Computer Algebra System Implicit Representation Great Common Divisor Affine Space
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## Copyright information

© Springer Science+Business Media New York 1997