SymPy factoring of polynomials

[Sebastian]

Hey guys, just a quick question.

I'm using SymPy to factorize polynomials, but I stumbled upon a certain polynomial that it wouldn't factorize.
I have P(x) = x**3 - 3*x, which should be factorized to x*(x-sqrt(3))*(x+sqrt(3)).
Using sympy.factor('x**3-3*x'), I get x*(x**2 - 3).

Any ideas why SymPy can't factorize this polynomial?

[ccc]

You should try to post this question to stackoverflow.com

[JonB]

Reading the help of factor shows that factor will only factor rationals, unless you tell it what extensions to use. sqrt(3) is not rational. You could generate such a list from roots, see below.

expr='(x**3-3*x)'
# find extensions needed for factor.
# of course, we could also simply use the roots directly and form a poly
# extension=True here lets it detect sqrt, etc 
r=set([abs(x) for x in list(roots(expr,extension=True).keys()) if not x==0])

f=factor(expr,extension=r,deep=True)
print(f)

I suspect it is also possible to directly take the output of roots, and generate a factored polynomial. I didnt see that in the docs, so this does it:

f=1
x=symbols('x')
for k,v in roots(expr,extension=True).items():
    f=f*(x-k)**v    

[Sebastian]

@JonB this is exactly what I'm looking for, thank you! Since I learned mathematics with Norwegian terms, I didn't really know what to search for in English 😂