Approximate parametrization of plane algebraic curves by linear systems of curves

Approximate parametrization of plane algebraic curves by linear systems of curves

It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance ǫ > 0 and an ǫ-irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of ǫ-rationality, and we provide an algorithm to parametrize approximately affine ǫ-rational plane curves, without exact singularities at infinit...

Parametrization of approximate algebraic curves by lines

It is well known that irreducible algebraic plane curves having a singularity of maximum multiplicity are rational and can be parametrized by lines. In this paper, given a tolerance ¿ 0 and an -irreducible algebraic plane curve C of degree d having an -singularity of multiplicity d−1, we provide an algorithm that computes a proper parametrization of a rational curve that is exactly parametrizab...

Sparse Parametrization of Plane Curves

We present a new method for the rational parametrization of plane algebraic curves. The algorithm exploits the shape of the Newton polygon of the defining implicit equation and is based on methods of toric geometry.

Real Parametrization of Algebraic Curves

There are various algorithms known for deciding the parametrizability (rationality) of a plane algebraic curve, and if the curve is rational, actually computing a parametrization. Optimality criteria such as low degrees in the parametrization or low degree field extensions are met by some parametrization algorithms. In this paper we investigate real curves. Given a parametrizable plane curve ov...

Linear Systems of Plane Curves