Approximate Parametrization of Plane Algebraic Curves by Linear Systems of Curves

Details Approximate Parametrization of Plane Algebraic Curves by Linear Systems of Curves Approximate Parametrization of Plane Algebraic Curves by Linear Systems of Curves

2009-01-03

arxiv.org/abs/0901.0320v1

Mathematics

Algebraic Geometry

Scientific paper

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 $\epsilon>0$ and an $\epsilon$-irreducible algebraic affine plane curve $\mathcal C$ of proper degree $d$, we introduce the notion of $\epsilon$-rationality, and we provide an algorithm to parametrize approximately affine $\epsilon$-rational plane curves, without exact singularities at infinity, by means of linear systems of $(d-2)$-degree curves. The algorithm outputs a rational parametrization of a rational curve $\bar{\mathcal C}$ of degree at most $d$ which has the same points at infinity as $\mathcal C$. Moreover, although we do not provide a theoretical analysis, our empirical analysis shows that $\bar{\mathcal C}$ and $\mathcal C$ are close in practice.

Affiliated with

Also associated with

No associations

Rating

Approximate Parametrization of Plane Algebraic Curves by Linear Systems of Curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Approximate Parametrization of Plane Algebraic Curves by Linear Systems of Curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximate Parametrization of Plane Algebraic Curves by Linear Systems of Curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-288848