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])
6*sqrt(15)/125 + 1
>>> eq=Poly(eq-_, x)
Now
1) intervals can't be used
>>> eq.intervals()
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "sympy\polys\polytools.py", line 2942, in intervals
all=all, eps=eps, inf=inf, sup=sup, fast=fast, sqf=sqf)
File "sympy\polys\polyclasses.py", line 749, in intervals
return dup_isolate_real_roots(f.rep, f.dom, eps=eps, inf=inf, sup=sup,
fast=
fast)
File "sympy\polys\rootisolation.py", line 512, in dup_isolate_real_roots
raise DomainError("isolation of real roots not supported over %s" % K)
sympy.polys.polyerrors.DomainError: isolation of real roots not supported
over E
X
2) solve doesn't even give RootOf solutions
>>> solve(eq)
[]
3) sqf doesn't do anything
>>> sqf(eq)
x**5 - x**3 - 6*sqrt(15)/125
But there are 2 roots
>>> nsolve(eq.as_expr(),x,-1)
mpf('-0.77459665120927842')
>>> nsolve(eq.as_expr(),x,1)
mpf('1.0726704244933239')
/c
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