sympy solve and polynomial roots

[Alexandre Eudes]

Hello Everyone,

I have noted some stranges behaviours of solve for polynomial in my use of sympy.

In case of 4th degree polynomial with 2 two conjugates solutions, solve return only two of the four solutions.

The problem seems to appear only with real coefficients, integer polynomial solutions are fine.

On the other side, sympy roots always gives the good answer.

Example :

>>> import sympy as sy

>>> s = sy.S("s")

>>> expr =  4.0*s**4 + 3.0*s**3 + 3.0*s**2 - 4.0*s + 4.0

>>> rt= sy.roots(expr)

>>> sl= sy.solve(expr)

>>> print sl,"\n",rt

[0.490766420298022 - 0.526081774461482*I, 0.490766420298022 + 0.526081774461482*I] 

{-0.865766420298022 - 1.08737810369128*I: 1, 0.490766420298022 - 0.526081774461482*I: 1, -0.865766420298022 + 1.08737810369128*I: 1, 0.490766420298022 + 0.526081774461482*I: 1}

Similarly, solving for 5th degree polynomial return strange error :

>>> sy.solve(s**5+s**4-1.0)

Traceback (most recent call last):

  File "<stdin>", line 1, in <module>

  File "sympy/sympy/solvers/solvers.py", line 958, in solve

    solution = nfloat(solution, exponent=False)

  File "sympy/sympy/core/function.py", line 2219, in nfloat

    return type(expr)([nfloat(a, n, exponent) for a in expr])

  File "sympy/sympy/core/function.py", line 2235, in nfloat

    rv = rv.xreplace(dict(reps))

  File "sympy/sympy/core/basic.py", line 1106, in xreplace

    return self.func(*args)

  File "sympy/sympy/polys/rootoftools.py", line 62, in __new__

    raise PolynomialError("only univariate polynomials are allowed")

sympy.polys.polyerrors.PolynomialError: only univariate polynomials are allowed

Should I had an issue in the tracker or this problems are already known ?

Regards,

Alexandre.

[Ondřej Čertík]

Hi Alexandre,

On Sun, Sep 1, 2013 at 5:05 PM, Alexandre Eudes
<alexand...@gmail.com> wrote:
> Hello Everyone,
> I have noted some stranges behaviours of solve for polynomial in my use of
> sympy.
>
> In case of 4th degree polynomial with 2 two conjugates solutions, solve
> return only two of the four solutions.
> The problem seems to appear only with real coefficients, integer polynomial
> solutions are fine.

Is there a reason you need floating point coefficients? In my opinion,
one should use floating point only as a last resort.

Note that this works:

In [1]: solve(x**5+x**4-1)
Out[1]:
⎡ ⎛ 5 4 ⎞ ⎛ 5 4 ⎞ ⎛ 5 4 ⎞
⎣RootOf⎝x + x - 1, 0⎠, RootOf⎝x + x - 1, 1⎠, RootOf⎝x + x - 1, 2⎠, RootO

⎛ 5 4 ⎞ ⎛ 5 4 ⎞⎤
f⎝x + x - 1, 3⎠, RootOf⎝x + x - 1, 4⎠⎦

but this doesn't:

In [2]: solve(x**5+x**4-1.0)

yes, I think you should report it. I am attaching a pdf of what
Mathematica does in this case ---
the integer case work the same as in sympy, but the floating point
case returns numerical solution,
while SymPy fails.

Ondrej

[Aaron Meurer]

This is also a bug in the sense that the only exception that should
ever be raised by solve() should be NotImplementedError.

Aaron Meurer

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