On rational triangles via algebraic curves

Acquisition of Rational Points on Algebraic Curves

Geometry of Rational Curves on Algebraic Varieties

Geometry of Rational Curves on Algebraic Varieties

Rational Algebraic Curves: A Computer Algebra Approach

Algebraic geometry is a central field within mathematics which is often viewed as difficult for outsiders to enter. Recent years have seen many books which present various topics of algebraic geometry from a computational viewpoint, thereby making the subject more accessible. The book under review, RAC for short, is part of this positive trend. Its main focus is parametrizing rational plane alg...

Algorithms for Rational Real Algebraic Curves

In this paper, we study fundamental properties of real curves, especially of rational real curves, and we derive several algorithms to decide the reality and rationality of curves in the complex plane. Furthermore, if the curve is real and rational, we determine a real parametrization. More precisely, we present a reality test algorithm for plane curves, and three different types of real parame...

Rational quadratic approximation to real algebraic curves

An algorithm is proposed to give a global approximation of an implicit real plane algebraic curve with rational quadratic B-spline curves. The algorithm consists of four steps: topology determination, curve segmentation, segment approximation and curve tracing. Due to the detailed geometric analysis, high accuracy of approximation may be achieved with a small number of quadratic segments. The f...