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, Two-bridge knots, Chebyshev curves, Real root isolation, Computer algebra, Algorithms | | ISSN | 0747-7171 |
| 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 |
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