> <\body> <\tmdoc-title> Univariate Continued Fraction solver \; The family of methods based on continued fraction expansion proceed as follows: <\framed-fragment> <\named-algorithm-old|solve_continued_fraction(f,>)> \; : Isolation of the roots of on the interval >. : A representation > where is a univariate polynomial expressed in the monomial basis and is an homography such that \h:x|)>=f:x|)>> and and 0,+\=>.\ <\itemize-dot> Compute an integer lower bound of the positive \ roots of =0>; Shift by : =p>; Compute the number of sign changes of the coefficients of >; if then output the corresponding isolation interval and stop; if stop also; Split the polynomial > in = |)>> whose positive roots correspond to the roots of > in >, => whose positive roots correspond to the roots of > in |[>>. Apply reccursively the algorithm on > and >. : list of rational intervals ,|q>|[>> where > and |q>> are consecutive continued fraction approximations of a root \ ]a,b[> of and such that all roots of \ \ ]a,b[> of is in one of these intervals. \; Such a solver computes the first terms of the continued fraction expansion of the roots of a univariate polynomial. Two variants are also available, depending wether we want to isolate or approximate the real roots. <\initial> <\collection>