Computing Chebyshev knot diagrams

Pierre-Vincent Koseleff (1) , Daniel Pecker (2) , Fabrice Rouillier (1)

1 SALSA - Solvers for Algebraic Systems and Applications
2 UPMC - Université Pierre et Marie Curie - Paris 6

A Chebyshev curve C(a,b,c,\phi) has a parametrization of the form x(t)=Ta(t); y(t)=T_b(t) ; z(t)= Tc(t + \phi), where a,b,c are integers, Tn(t) is the Chebyshev polynomial of degree n and \phi \in \RR. When C(a,b,c,\phi) has no double points, it defines a polynomial knot. We determine all possible knots when a, b and c are given.

Mots clés: factorization of Chebyshev polynomials; minimal polynomial; Zero dimensional systems; Chebyshev curves; Lissajous knots; polynomial knots

Domaines: Topologie géométrique [math.GT]

Pierre-Vincent Koseleff, Daniel Pecker, Fabrice Rouillier. Computing Chebyshev knot diagrams. 2010. ⟨hal-00451221v2⟩