Sorry - I forgot to include the example I had in mind.
sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.s()
sage: s[3].expand(2)(1+x,1+y)
x^3 + x^2*y + x*y^2 + y^3 + 4*x^2 + 4*x*y + 4*y^2 + 6*x + 6*y + 4
sage: f = s[3].expand(2)(1+x,1+y)
sage: s.from_polynomial(f).expand(2)(x,y) == f
True
sage: s.from_polynomial(f)
4*s[] + 6*s[1] - s[1, 1, 1] + 4*s[2] + s[3]
On Thursday, October 30, 2025 at 4:32:47 PM UTC-4 Trevor Karn wrote:
> Hi all,
>
> I have a question about a design decision for working with symmetric
> functions.
>
> I was doing some computations passing back and forth between symmetric
> polynomials (finitely many variables) and symmetric functions (infinitely
> many variables). When converting between a symmetric polynomial in 2
> variables and one in infinitely many variables in the s-basis, I obtained a
> term of -s_{111}. I understand why this is happening under the hood, but my
> question is about the desired behavior. To me, it seems like
> `.from_polynomial()` should only return Schur functions indexed by
> partitions with at most the number of rows equal to the number of variables
> in the polynomial or in the ambient ring. On the other hand, creating the
> polynomial and then expanding back in terms of two variables is the
> identity.
>
> Does anyone else have any opinions on this matter? If the consensus is
> that length should be bounded by number of polynomial generators, then I
> can open the ticket and make the fix, but I wanted to hear some input from
> others.
>
> Thanks,
> Trevor
>
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