On Sun, Aug 24, 2008 at 2:03 PM, Joshua Kantor <[EMAIL PROTECTED]> wrote:
>
> 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 is written in ADA.
> it might be better suited to your problem.
>
> http://www.math.uic.edu/~jan/download.html
It is good when the zero locus is maybe not 0-dimensional,
i.e., when there are infinitely many solutions and you want
to understand them.
> 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.
It's best to just do
RealNumber = float; Integer = int
first.
Thanks Josh!
>
>
> 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
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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