Check if function is symmetric

edit

You should do:

sage: f.is_symmetric()
True

Indeed, the source code of is_SymmetricFunction function is:

return isinstance(x, SymmetricFunctionAlgebra_generic.Element)

see:

sage: is_SymmetricFunction??

which means that it only tests the type of f. But f is just a polynomial:

sage: f.parent()
Multivariate Polynomial Ring in x1, x2, x3 over Rational Field

I guess that's because f is a not a function but polynomial. Whether f is symmetric can be seen from whether its conversion to a symmetric function succeeds - like in the code below:

R.<x1,x2,x3>=PolynomialRing(QQ,3); 
S = SymmetricFunctions(QQ)
s = S.schur();
f=s([2,1]).expand(3,'x1,x2,x3');
try:
    S.from_polynomial(f)
    print('f is symmetric')
except ValueError:
    print('f is not symmetric')