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» Computing singular points of plane rational curves
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AISC
1998
Springer
13 years 11 months ago
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....
J. Rafael Sendra, Franz Winkler
ANTS
2006
Springer
118views Algorithms» more  ANTS 2006»
13 years 8 months ago
Construction of Rational Points on Elliptic Curves over Finite Fields
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...
Andrew Shallue, Christiaan van de Woestijne
CAD
1999
Springer
13 years 6 months ago
The intersection of two ruled surfaces
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 ...
Hee-Seok Heo, Myung-Soo Kim, Gershon Elber
CORR
2010
Springer
110views Education» more  CORR 2010»
13 years 7 months ago
Construction of Rational Surfaces Yielding Good Codes
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...
Alain Couvreur
FOCS
2006
IEEE
14 years 26 days ago
Points on Computable Curves
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...
Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo