Make is_symmetric method for polynomials or where else useful

[kcrisman]

This is a little vague - should it also be for SR, not just polynomial rings? But it seems like a reasonable request on sage-support:

Hi, 
I would like to know if there are any function that says if a 
polynomial is or not symmetric (like: 'is_symmetric'), so Mathematica 
have this kind of function. 
http://en.wikipedia.org/wiki/Symmetric_polynomial 
Thanks! 

CC: @sagetrac-sage-combinat

Component: combinatorics

Issue created by migration from https://trac.sagemath.org/ticket/9558

[jbandlow]

comment:1

The following works (at least in sage-4.4.4):

sage: R.<x,y,z> = QQ[]
sage: SF = SymmetricFunctions(QQ)
sage: SF.from_polynomial(x^2 + y^2 + z^2)
m[2]
sage: SF.from_polynomial(x^2 + y^2)
...
ValueError: x^2 + y^2 is not a symmetric polynomial

If someone wants to make a top level function like that suggested in the initial post, a design discussion should probably happen on sage.devel or sage.combinat.devel first.

I'm changing the component to combinatorics since that's where tickets related to symmetric functions usually live.