HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Computing Chebyshev knot diagrams

Abstract : A Chebyshev curve $\mathcal{C}(a,b,c,\phi)$ has a parametrization of the form $ x(t)=T_a(t)$; \ $y(t)=T_b(t)$; $z(t)= T_c(t + \phi)$, where $a,b,c$ are integers, $T_n(t)$ is the Chebyshev polynomial of degree $n$ and $\phi \in \mathbb{R}$. When $\mathcal{C}(a,b,c,\phi)$ is nonsingular, it defines a polynomial knot. We determine all possible knot diagrams when $\phi$ varies. Let $a,b,c$ be integers, $a$ is odd, $(a,b)=1$, we show that one can list all possible knots $\mathcal{C}(a,b,c,\phi)$ in $\tilde{\mathcal{O}}(n^2)$ bit operations, with $n=abc$.
Document type :
Journal articles
Complete list of metadata

Cited literature [22 references]  Display  Hide  Download

https://hal.inria.fr/hal-01232181
Contributor : Fabrice Rouillier Connect in order to contact the contributor
Submitted on : Friday, May 12, 2017 - 10:51:43 AM
Last modification on : Thursday, February 3, 2022 - 11:18:42 AM
Long-term archiving on: : Sunday, August 13, 2017 - 12:27:50 PM

Files

kprt_noels3.pdf
Files produced by the author(s)

Identifiers

Citation

Pierre-Vincent Koseleff, Daniel Pecker, Fabrice Rouillier, Cuong Tran. Computing Chebyshev knot diagrams. Journal of Symbolic Computation, Elsevier, 2018, 86, pp.21. ⟨10.1016/j.jsc.2017.04.001⟩. ⟨hal-01232181v2⟩

Share

Metrics

Record views

273

Files downloads

223