On 20 Mrz., 22:50, Ondrej Certik <[email protected]> wrote:
> On Sat, Mar 20, 2010 at 2:47 PM, Ondrej Certik <[email protected]> wrote:
> > Thanks Aaron!
>
> > It may be, that the new polynomials can't handle floating point
> > numbers (for some algorithmic reasons), in which case imho we should
> > provide the user with the following options:
>
> > a) convert floating point numbers to Rational and run solve(), and at
> > the end, convert all roots to floating point numbers again, it has the
> > advantage of finding all the roots (I mean as long as they can be
> > found analytically)
> > b) use some numerical algorithms
>
> > Maybe for polynomial equations, there are numerical algorithms that
> > return (find) all roots automatically? nsolve() currently needs an
> > initial guess.
>
> Wolfram alpha seems to be able to find all 4 roots numerically (and
> automatically):
>
> http://www.wolframalpha.com/input/?i=solve(-12*(2*sqrt(3)+%2B+9)+*+12...)
>
> so we should do it too.

For polynomials we could use mpmath.polyroots to determine all roots
numerically. Didn't actually Mateusz implement something like this?
nsolve() is more general, so I'm not sure whether it should special-
case polynomials.

Vinzent

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