1. I would recommend looking at phcpack, it is designed to exploit the special nature of large polynomial systems, however, supposedly I believe it is sometimes difficult to compile, I've never used it but it might be better suited to your problem.
http://www.math.uic.edu/~jan/download.html 2. The optimize.fsolve routine may be able to do what you want, though I'm not sure how it will deal with that large a system sage: import scipy sage: from scipy import optimize sage: def f(x): return [float(x[0]**2-x[0]*x[1]-1),float(x[1]**2+x[0]*x[1]-2)] ....: sage: optimize.fsolve(f,[0.1r,0.1r]) array([-0.46821319, 1.66756601]) Note the float and 0.1r. scipy is not happy with sage floats or ints, so you need to make sure everything is really python types and not sage types. The initial guess is very important if you give it a starting point of [0,0] it won't converge. Also, you can give it a jacobian which for that large a system is probably a good idea. do sage: optimize.fsolve? for the arguments. On Aug 24, 12:24 pm, "William Stein" <[EMAIL PROTECTED]> wrote: > On Sun, Aug 24, 2008 at 12:16 PM, Michael <[EMAIL PROTECTED]> wrote: > > > I have a polynomial system of 50 equations in 50 unknowns. I would > > like > > to numerically solve this system (I'm interested in complex zeros). > > Seems to me that if I use sage's solve, it will sttempt to solve these > > algebraically. > > > Are there any funcitons in sage for solving a polynomial or non-linear > > system > > numerically. > > You're probably going to want to use scipy.optimize. It has a large > range of sophisticated numerical optimization routines. Maybe > they can be used for what you want. I've hardly used them, so I > can't easily say more -- hopefully somebody who has can. > > sage: import scipy > scisagimport scipy.optimize > sage: scipy.optimize. > scipy.optimize.NumpyTest scipy.optimize.broyden2 > scipy.optimize.fmin_ncg scipy.optimize.moduleTNC > scipy.optimize.anderson scipy.optimize.broyden3 > scipy.optimize.fmin_powell scipy.optimize.newton > scipy.optimize.anderson2 scipy.optimize.broyden_generalized > scipy.optimize.fmin_tnc scipy.optimize.nonlin > scipy.optimize.anneal scipy.optimize.brute > scipy.optimize.fminbound scipy.optimize.optimize > scipy.optimize.approx_fprime scipy.optimize.check_grad > scipy.optimize.fsolve scipy.optimize.ridder > scipy.optimize.bisect scipy.optimize.cobyla > scipy.optimize.golden scipy.optimize.rosen > scipy.optimize.bisection scipy.optimize.fixed_point > scipy.optimize.lbfgsb scipy.optimize.rosen_der > scipy.optimize.bracket scipy.optimize.fmin > scipy.optimize.leastsq scipy.optimize.rosen_hess > scipy.optimize.brent scipy.optimize.fmin_bfgs > scipy.optimize.line_search scipy.optimize.rosen_hess_prod > scipy.optimize.brenth scipy.optimize.fmin_cg > scipy.optimize.linesearch scipy.optimize.test > scipy.optimize.brentq scipy.optimize.fmin_cobyla > scipy.optimize.minpack scipy.optimize.tnc > scipy.optimize.broyden1 scipy.optimize.fmin_l_bfgs_b > scipy.optimize.minpack2 scipy.optimize.zeros --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
