In article <[EMAIL PROTECTED]>, "Carl Banks" <[EMAIL PROTECTED]> wrote:
> Just wrote: > > While googling for a non-linear equation solver, I found > > Math::Polynomial::Solve in CPAN. It seems a great little module, > except > > it's not Python... I'm especially looking for its poly_root() > > functionality (which solves arbitrary polynomials). Does anyone know > of > > a Python module/package that implements that? > > If you don't have a great need for speed, you can accomplish this > easily with the linear algebra module of Numeric/numarray. Suppose > your quintic polynomial's in the form > > a + b*x + c*x**2 + d*x**3 + e*x**4 + x**5 > > The roots of it are equal to the eigenvalues of the companion matrix: > > 0 1 0 0 0 > 0 0 1 0 0 > 0 0 0 1 0 > 0 0 0 0 1 > -a -b -c -d -e > > It should be pretty easy to set up a Numeric matrix and call > LinearAlgebra.eigenvalues. For example, here is a simple quintic > solver: > > . from Numeric import * > . from LinearAlgebra import * > . > . def quinticroots(p): > . cm = zeros((5,5),Float32) > . cm[0,1] = cm[1,2] = cm[2,3] = cm[3,4] = 1.0 > . cm[4,0] = -p[0] > . cm[4,1] = -p[1] > . cm[4,2] = -p[2] > . cm[4,3] = -p[3] > . cm[4,4] = -p[4] > . return eigenvalues(cm) > > > now-you-can-find-all-five-Lagrange-points-ly yr's, Wow, THANKS. This was the answer I was secretly hoping for... "Great need for speed", no, not really, but this Numeric-based version is about 9 times faster than what I translated from Perl code yesterday, so from where I'm standing your version is blazingly fast... Thanks again, Just -- http://mail.python.org/mailman/listinfo/python-list
