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  • The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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Section: New Results

Computing Chebyshev knot diagrams

A Chebyshev curve 𝒞(a,b,c,φ) has a parametrization of the form x(t)=Ta(t); y(t)=Tb(t); z(t)=Tc(t+φ), where a,b,c are integers, Tn(t) is the Chebyshev polynomial of degree n and φ. When 𝒞(a,b,c,φ) is nonsingular, it defines a polynomial knot. In [12], we determine all possible knot diagrams when φ varies. Let a,b,c be integers, a is odd, (a,b)=1, we show that one can list all possible knots 𝒞(a,b,c,φ) in O(n2) bit operations, with n=abc.