Details:
Title  The first rational Chebyshev knots  Author(s)  P.V. Koseleff, D. Pecker, Fabrice Rouillier  Type  Article in Journal  Abstract  A Chebyshev knot C ( a , b , c , φ ) is a knot which has a parametrization of the form x ( t ) = T_a ( t ) ; y ( t ) = T_b ( t ) ; z ( t ) = T_c ( t + φ ) , where a , b , c are integers, T n ( t ) is the Chebyshev polynomial of degree n and φ ∈ R . We show that any rational knot is a Chebyshev knot with a = 3 and also with a = 4 . For every a , b , c integers ( a = 3 , 4 and a , b coprime), we describe an algorithm that gives all Chebyshev knots C ( a , b , c , φ ) . We deduce the list of minimal Chebyshev representations of rational knots with 10 or fewer crossings.  Keywords  Polynomial curves, Rational knots, Twobridge knots, Chebyshev curves, Real root isolation, Computer algebra, Algorithms  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717110000945 
Language  English  Journal  Journal of Symbolic Computation  Volume  45  Number  12  Pages  1341  1358  Year  2010  Note  MEGA’2009  Edition  0  Translation 
No  Refereed 
No 
