In my mind it should depend on the basis. I see your point about the h basis but in my mind since I am already choosing a basis and a number of variables to substitute there is no reason to want something canonical. What do you think, Martin?
Best, Trevor On Fri, Oct 31, 2025 at 5:14 AM 'Martin R' via sage-devel < [email protected]> wrote: > 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 >>> >> -- > You received this message because you are subscribed to a topic in the > Google Groups "sage-devel" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sage-devel/vwDhGB5Q5uI/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/sage-devel/7d70e726-64b5-4fef-9d7d-05656e5dc900n%40googlegroups.com > <https://groups.google.com/d/msgid/sage-devel/7d70e726-64b5-4fef-9d7d-05656e5dc900n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/sage-devel/CAJ6VCMC2ydk1G3rWiQAncC63XB3ikFJyaKKL%2BVpn4%2Bm%2BWE1hLQ%40mail.gmail.com.
