I don't see a natural way to define it depending on the basis. I think it would be weird to make a special case for the Schur basis. Also, isn't it easy to get rid of the partitions that are too long afterwards, if this is necessary for your application?
Best wishes, Martin On Friday, 31 October 2025 at 15:57:21 UTC+1 Trevor Karn wrote: > 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/55b57c38-50c1-43bf-a493-af308b2b8dc6n%40googlegroups.com.
