RT info:eu-repo/semantics/article
T1 Detecting Symmetries of Rational Plane Curves
A1 Alcázar Arribas, Juan Gerardo
A1 Hermoso Ortíz, Carlos
K1 Rational planar curve
K1 Rational space curve
K1 Symmetry
K1 Central symmetry
K1 Mirror symmetry
K1 Rotation symmetry
K1 Symmetry center
K1 Symmetry axis
K1 Involution
K1 Ciencia
K1 Matemáticas
K1 Science
K1 Mathematics
AB Given a rational algebraic curve defined by means of a rational parametrization, we address here the problem of deterministically detecting whether the curve exhibits some kind of symmetry (central, mirror, rotation), and of computing the elements of the symmetry in the affirmative case. We provide effective methods for solving these questions without any conversion to implicit form. The underlying idea is the existing relationship between two proper parametrizations of a same curve, which in turn leads to algorithms where only univariate polynomials are involved. These methods have been implemented and tested in the computer algebra system Maple 15; evidence of their applicability, as well as a detailed theoretical analysis, is given.
PB Elsevier
SN 0167-8396
YR 2013
FD 2013
LK http://hdl.handle.net/10017/20452
UL http://hdl.handle.net/10017/20452
LA eng
NO Ministerio de Ciencia e Innovación
DS MINDS@UW
RD 13-abr-2024