Hi Mateusz and all,
refine_root() doesn't work with non-squarefree polynomials. Unfortunately
it's not written in the documentation. Remove root multiplicities with
sqf() and then proceed with your original approach, e.g.:
In [8]: sqf_list(f)
Out[8]:
⎛ ⎡⎛ 2 ⎞⎤⎞
⎝1, ⎣⎝x -
Hi smichr and all,
Thank you for your quick response.
Does that mean that the method 'refine_root()' of class 'Poly' is not
capable of finding isolation intervals for all real roots of an arbitrary
polynomial?
If so, this would, unfortunately, render the method 'refine_root()' useless
for my
Hi,
On 18 June 2013 09:35, Heiner Kirchhoffer heiner.kirchhof...@gmail.comwrote:
Hi smichr and all,
Thank you for your quick response.
Does that mean that the method 'refine_root()' of class 'Poly' is not
capable of finding isolation intervals for all real roots of an arbitrary
polynomial?
There is still a potential problem here:
Consider an unfactorable polynomial
eq = x**5-x**3+1
factor(_)
x**5 - x**3 + 1
find where it has zeros
df = eq.diff(x)
solve(df)
[0, -sqrt(15)/5, sqrt(15)/5]
shift the polynomial to put one of the zeros on the x axis
eq.subs(x,_[1])
Hi,
On 18 June 2013 12:26, Chris Smith smi...@gmail.com wrote:
There is still a potential problem here:
Consider an unfactorable polynomial
eq = x**5-x**3+1
factor(_)
x**5 - x**3 + 1
find where it has zeros
df = eq.diff(x)
solve(df)
[0, -sqrt(15)/5, sqrt(15)/5]
shift the
Hello,
method 'refine_root()' of class 'Poly' seems to unexpectedly raise an
exception.
The following code produces the exception:
x = Symbol( x )
p = Poly( x**4 - 6*x**3 + 11*x**2 - 6*x + 1 )
p.refine_root( 0, 1 ) # raises: sympy.polys.polyerrors.RefinementFailed:
there should be exactly one
I suppose this could be called a feature since the routine will fail if you
comment out the error since it needs a sign change to find the root. But
perhaps the refine_root could check return the evaluated root in that range
if it can be found explicitly.
Perhaps it would be better to evaluate
