Status: Valid
Owner: ----
Labels: Type-Defect Priority-Medium Solvers Polynomial WrongResult
New issue 3551 by ronan.l...@gmail.com: solve() doesn't find the root of a
polynomial when solving over the reals
http://code.google.com/p/sympy/issues/detail?id=3551
In [5]: x = Symbol('x', real=True)
In [6]: solve(x**5 + x**3 + 1, x)
Out[6]: []
This polynomial has odd order, so has obviously at least one real root.
However, solving for a complex variable finds all roots:
In [8]: solve(z**5 + z**3 + 1, z)
Out[8]:
⎡ ⎛ 5 3 ⎞ ⎛ 5 3 ⎞ ⎛ 5 3
⎞ ⎛ 5 3 ⎞ ⎛ 5 3 ⎞⎤
⎣RootOf⎝z + z + 1, 0⎠, RootOf⎝z + z + 1, 1⎠, RootOf⎝z + z + 1, 2⎠,
RootOf⎝z + z + 1, 3⎠, RootOf⎝z + z + 1, 4⎠⎦
In [9]: _[0].is_real
Out[9]: True
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