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By concrete polynomial, I mean something like (x1+x2)(x1+x3)(x2+x3) What I tried didn't work here:

R.<x0,x1,x2>=PolynomialRing(QQ,3); R Sym=SymmetricFunctions(QQ) s = SymmetricFunctions(QQ).s() f=x0^2x1 + x0x1^2 + x0^2x2 + 2x0x1x2 + x1^2x2 + x0x2^2 + x1*x2^2 s(f)

It gives a long error message

By concrete polynomial, I mean something like (x1+x2)(x1+x3)like

$$ (x1+x2) (x1+x3) (x2+x3) $$

What I tried didn't work here:

sage: R.<x0,x1,x2> = PolynomialRing(QQ, 3)
sage: Sym = SymmetricFunctions(QQ)
sage: s = SymmetricFunctions(QQ).s()
f=x0^2x1 sage: f = x0^2*x1 + x0x1^2 x0*x1^2 + x0^2x2 x0^2*x2 + 2x0x1x2 2*x0*x1*x2 + x1^2x2 x1^2*x2 + x0x2^2 x0*x2^2 + x1*x2^2
s(f)
sage: s(f)