I think it boils down to the question whether `basis.from_polynomial`
should depend on the basis or not. Currently, it does not, since basis is
always the monomial basis, right? What would you want it to do in the h
basis?
Martin
On Thursday, 30 October 2025 at 21:33:59 UTC+1 Trevor Karn wrote:
> 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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