Automatic parameterization of rational curves and surfaces III: Algebraic plane curves

We consider algorithms to compute the genus and rational parametric equations, for implicitly defined irreducible rational plane algebraic curves of arbitrary degree. Rational panuneterizations exist for all irreducible algebraic curves of genus O. The genus is compuled by a complete analysis of the singularities of plane algebraic curves, using affine quadratic transformations. The rational parameterization techniques. essentially, reduce to solving symbolically systems of homogeneous linear equations and the computation of resultants. t Research suppoItCd in part by NSF grant DMS 85-00491 and ONR grantN 00014-86-0689 under URI. :1= Research suppoItCd in part by NSF grant MIP 85-21356.