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Mathematics of Computation

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Efficient solution of rational conics

Authors: J. E. Cremona and D. Rusin
Journal: Math. Comp. 72 (2003), 1417-1441
MSC (2000): Primary 11G30, 11D41
Published electronically: December 18, 2002
MathSciNet review: 1972744
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Abstract: We present efficient algorithms for solving Legendre equations over $\mathbb Q$ (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.

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Additional Information

J. E. Cremona
Affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
MR Author ID: 52705
ORCID: 0000-0002-7212-0162

D. Rusin
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115

Received by editor(s): September 5, 2001
Published electronically: December 18, 2002
Article copyright: © Copyright 2002 American Mathematical Society