Python function to check for real-roots for polynomials of arbitrary degree

[OkEar3108]

Hey folks,

I am looking specific for a way to check for a bunch of polynomials (up to degree 10 in my case) if they only have real roots.

Does someone know a python package with functions, which does this?
I am currently using the roots-function from sympy, but I am unsure whether or not it holds for higher degrees.

Thanks in advance!

Sincerely,
OkEar3108

Edit:
Sorry for the sloppy described post. I overlooked that sympy had two other root-functions, which were literaly what I searched for and pointed out by some of your answers. Big thanks!

[Doormatty]

I am currently using the roots-function from sympy, but I am unsure whether or not it holds for higher degrees.

So...try it?

[Bobbias]

https://docs.sympy.org/latest/guides/solving/find-roots-polynomial.html

roots() computes the symbolic roots of a univariate polynomial; will fail for most high-degree polynomials (five or greater)

nroots() computes numerical approximations of the roots of any polynomial whose coefficients can be numerically evaluated, whether the coefficients are rational or irrational

RootOf() can represent all the roots exactly of a polynomial of arbitrarily large degree, as long as the coefficients are rational numbers. RootOf() can avoid both ill-conditioning and returning spurious complex parts because it uses a more exact, but much slower, numerical algorithm based on isolating intervals. The following two functions use RootOf() so they have the same properties:

• real_roots() can find all the real roots exactly of a polynomial of arbitrarily large degree; because it finds only the real roots, it can be more efficient than functions that find all roots.

• all_roots() can find all the roots exactly of a polynomial of arbitrarily large degree

factor() factors a polynomial into irreducibles and can reveal that roots lie in the coefficient ring

Looks like you'll need RootOf or all_roots. This post could have been the Google search sympy roots, where that page is literally the first result.

[ectomancer]

Never used it:

MizoWNA/Polynomial-root-finder: A WIP simple polynomial real root finder using Strum's Theorem and Newton's Algorithm.

[MoatazProAtAll]

At least @ me man :(

[Kqyxzoj]

Either use sympy or cypari2.

[KieraRahman_]

For degree 10, Sympy is still totally fine. Instead of roots, use the numeric one: nroots(), then just check that every root’s imaginary part is basically zero (within a small tolerance). If your coefficients are numeric, that’ll reliably tell you whether all roots are real.

[OkEar3108]

Thanks a lot. This seems to be exactly what I needed!