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.
Ondrej
On Sat, Mar 20, 2010 at 2:39 PM, Aaron S. Meurer <asmeu...@gmail.com> wrote:
> I bisected it down to this commit:
>
> 2686805263d86639420ae56414666d38f0efaa8c is the first bad commit
> commit 2686805263d86639420ae56414666d38f0efaa8c
> Author: Mateusz Paprocki <matt...@gmail.com>
> Date: Sun Mar 14 21:18:04 2010 +0100
>
> Fixed and improved solve(x**4 + x**3 + x**2 + x + 1)
>
> :040000 040000 76beac15724bf74859d6a156f965434016a29680
> e7e966361cfd8b1fefaa96fbc2430ab8f234d6ad M sympy
>
> Hope that helps.
>
> Aaron Meurer
> On Mar 20, 2010, at 3:25 PM, Ondrej Certik wrote:
>
>> Hi Mateusz,
>>
>> what is the way to use solve with floating point coefficients, e.g.
>> this used to work:
>>
>> In [1]: solve(x**2+x+1, x)
>> Out[1]:
>> ⎡ ⎽⎽⎽ ⎽⎽⎽⎤
>> ⎢ ⅈ⋅╲╱ 3 ⅈ⋅╲╱ 3 ⎥
>> ⎢-1/2 - ───────, -1/2 + ───────⎥
>> ⎣ 2 2 ⎦
>>
>> In [2]: solve(x**2+x+1.0, x)
>> Out[2]: [-1/2 - 0.866025403784439⋅ⅈ, -1/2 + 0.866025403784439⋅ⅈ]
>>
>>
>> But now it doesn't:
>>
>> In [1]: solve(x**2+x+1, x)
>> Out[1]:
>> ⎡ ⎽⎽⎽ ⎽⎽⎽⎤
>> ⎢ ⅈ⋅╲╱ 3 ⅈ⋅╲╱ 3 ⎥
>> ⎢-1/2 - ───────, -1/2 + ───────⎥
>> ⎣ 2 2 ⎦
>>
>> In [2]: solve(x**2+x+1.0, x)
>> ---------------------------------------------------------------------------
>> DomainError Traceback (most recent call last)
>>
>> /home/ondrej/repos/sympy/<ipython console> in <module>()
>>
>> /home/ondrej/repos/sympy/sympy/solvers/solvers.pyc in solve(f,
>> *symbols, **flags)
>> 237 if poly.degree > 2:
>> 238 flags['simplified'] = flags.get('simplified', False)
>> --> 239 result = roots(poly, cubics=True, quartics=True).keys()
>> 240
>> 241 elif strategy == GS_RATIONAL:
>>
>> /home/ondrej/repos/sympy/sympy/polys/polyroots.pyc in roots(f, *gens,
>> **flags)
>> 326 raise PolynomialError('multivariate polynomials
>> are not supported')
>> 327
>> --> 328 f, x = f.to_field(), f.gen
>> 329
>> 330 def _update_dict(result, root, k):
>>
>> /home/ondrej/repos/sympy/sympy/polys/polytools.pyc in to_field(f)
>> 771 """Make the ground domain a field. """
>> 772 try:
>> --> 773 result = f.rep.to_field()
>> 774 except AttributeError: # pragma: no cover
>> 775 raise OperationNotSupported(f, 'to_field')
>>
>> /home/ondrej/repos/sympy/sympy/polys/polyclasses.pyc in to_field(f)
>> 1151 def to_field(f):
>> 1152 """Make the ground domain a field. """
>> -> 1153 return f.convert(f.dom.get_field())
>> 1154
>> 1155 def convert(f, dom):
>>
>> /home/ondrej/repos/sympy/sympy/polys/algebratools.pyc in get_field(self)
>> 1186 def get_field(self):
>> 1187 """Returns a field associated with `self`. """
>> -> 1188 raise DomainError('there is no field associated with %s' %
>> self)
>> 1189
>> 1190 def get_exact(self):
>>
>> DomainError: there is no field associated with RR
>>
>>
>> We need to fix this.
>>
>> Ondrej
>>
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