Abstract
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 ϵ > 0 and an ϵ-irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of ϵ-rationality, and we provide an algorithm to parametrize approximately affine ϵ-rational plane curves by means of linear systems of ( d − 2 ) -degree curves. The algorithm outputs a rational parametrization of a rational curve C ¯ of degree d which has the same points at infinity as C . Moreover, although we do not provide a theoretical analysis, our empirical analysis shows that C ¯ and C are close in practice.
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