Improperly parametrized rational curves
Computer Aided Geometric Design
A course in computational algebraic number theory
A course in computational algebraic number theory
A rational function decomposition algorithm by near-separated polynomials
Journal of Symbolic Computation
A relatively optimal rational space curve reparametrization algorithm through canonical divisors
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Base field restriction techniques for parametric curves
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Algebraic factoring and rational function integration
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Inversion of parameterized hypersurfaces by means of subresultants
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
On the simplification of the coefficients of a parametrization
Journal of Symbolic Computation
Proper real reparametrization of rational ruled surfaces
Computer Aided Geometric Design
Optimal affine reparametrization of rational curves
Journal of Symbolic Computation
Original article: Algorithmic detection of hypercircles
Mathematics and Computers in Simulation
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Let K be a field of characteristic zero and let @a be an algebraic element of degree n over K. Given a proper parametrization @j of a rational curve C with coefficients in K(@a), we present a new algorithm to compute the hypercircle associated to the parametrization @j. As a consequence, we can decide if C is defined over K and, if not, we can compute the minimum field of definition of C containing K. The algorithm exploits the structure of the conjugate curves of C but avoids computing in the normal closure of K(@a) over K.