Efficient solution of rational conics

Authors:
J. E. Cremona;D. Rusin
Affiliations:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom;Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois
Venue:
Mathematics of Computation
Year:
2003

Citing 3
Cited 8

On the Number of Divisions of the Euclidean Algorithm Applied to Gaussian Integers

Journal of Symbolic Computation
An efficient solution of the congruence x2+ky2=m (modn)

IEEE Transactions on Information Theory
A course in computational algebraic number theory

A course in computational algebraic number theory

An Algorithm for Computing Weierstrass Points

ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Near-optimal parameterization of the intersection of quadrics

Proceedings of the nineteenth annual symposium on Computational geometry
Trivializing a central simple algebra of degree 4 over the rational numbers

Journal of Symbolic Computation
Algorithms for quadratic forms

Journal of Symbolic Computation
Near-optimal parameterization of the intersection of quadrics: III. Parameterizing singular intersections

Journal of Symbolic Computation
A Variant of Boneh-Gentry-Hamburg's Pairing-Free Identity Based Encryption Scheme

Information Security and Cryptology
Brauer groups of diagonal quartic surfaces

Journal of Symbolic Computation
Optimal affine reparametrization of rational curves

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present efficient algorithms for solving Legendre equations over Q (equivalently, for finding rational points on rational conics) and parametrizing all solutions. Unlike existing algorithms, no integer factorization is required, provided that the prime factors of the discriminant are known.