Hi all, When attempting to find the roots of a Legendre polynomial:
In [3]: from sympy import Poly, legendre_poly In [4]: lp = Poly(legendre_poly(5)) In [5]: [float(r.evalf()) for r in lp.all_roots()] Out[5]: [-0.5384693101056831, -0.5384693101056831, 0.0, 0.5384693101056831, 0.906179845938664] Observe now the first root, which should be -0.906, gets found as -0.538. I /suspect/ this is because the RootOf.evalf() method uses nsolve -- or something analogous -- which requires an initial guess. mpmath.polysolve does the job (and on account of the method used does not have any trouble finding all of the roots) but has a less direct syntax. (Specifically, if one tries to pass the output from .all_coeffs() as the coeffs parameter to mpmath.polysolve the method enters an infinite loop; it is necessary to explicitly run: mpmath.polysolve([float(c) for c in lp.all_coeffs()]) Regards, Freddie.
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