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....
Abstract. We give a deterministic polynomial-time algorithm that computes a nontrivial rational point on an elliptic curve over a finite field, given a Weierstrass equation for the...
This article presents an efficient and robust algorithm that computes the intersection curve of two ruled surfaces. The surface intersection problem is reformulated as a zero-set ...
In the present article, we consider algebraic geometry codes on some rational surfaces. The estimate of the minimum distance is translated into a point counting problem on plane cu...
The “analyst’s traveling salesman theorem” of geometric measure theory characterizes those subsets of Euclidean space that are contained in curves of finite length. This re...