Parametrization of algebraic curves

Algebraic geometry is the study of geometric objects defined as the zeros of polynomial equations. So it is not surprising that many of the techniques in algebraic geometry become computationally feasible once we have algorithmic solutions for the relevant problems in commutative algebra, i.e., the algebra of polynomial rings. We take a look at one particular problem in algebraic geometry, the rational parametrization of algebraic curves. For an introduction to algebraic curves we refer to Walker (1950) or Fulton (1969).