Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6861213 | Journal of Symbolic Computation | 2018 | 22 Pages |
Abstract
A Chebyshev curve C(a,b,c,Ï) has a parametrization of the form x(t)=Ta(t); y(t)=Tb(t); z(t)=Tc(t+Ï), where a,b,c are integers, Tn(t) is the Chebyshev polynomial of degree n and ÏâR. When C(a,b,c,Ï) is nonsingular, it defines a polynomial knot. We determine all possible knot diagrams when Ï varies. When a,b,c are integers, (a,b)=1, we show that one can list all possible knots C(a,b,c,Ï) in OË(n2) bit operations, with n=abc. We give the parameterizations of minimal degree for all two-bridge knots with 10 crossings and fewer.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
P.-V. Koseleff, D. Pecker, F. Rouillier, C. Tran,