A Gröbner free alternative for polynomial system solving
Journal of Complexity
Efficient isolation of polynomial's real roots
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
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A Chebyshev knot C(a,b,c,@f) 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+@f), where a,b,c are integers, T"n(t) is the Chebyshev polynomial of degree n and @f@?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,@f). We deduce the list of minimal Chebyshev representations of rational knots with 10 or fewer crossings.