ABSTRACT
Just as systems of linear equations are the subject of linear algebra, systems of arbitrary polynomial equations are studied in algebraic geometry. Geometrically, to solve a system of linear equations means to find the points of intersection of lines, planes, and higher-dimensional affine spaces. Similarly, to solve a system of polynomial equations means to study intersections of circles, parabolas and other curves, but also higher-dimensional objects which we will call “affine varieties”. Let us give the general definition of an affine variety as the solution set of a system of polynomial equations.
