Oops, small typo. Let me try again:
def toSF(f):
""" Input is a symmetric polynomial in a polynomial ring in finitely
many variables. Output is a symmetric function in the monomial
basis of the ring of symmetric functions over the same base ring.
"""
X = f.parent().gens()
n = f.parent().ngens()
SF = SymmetricFunctions(f.base_ring())
m = SF.monomial()
out = m(0)
while f != 0:
lt = f.lt()
c = lt.monomial_coefficient(lt)
p = Partition(lt.exponents()[0])
f += -c*m(p).expand(n,X)
out += c*m(p)
return out
-Jason
Jason Bandlow wrote:
> Hi Anne,
>
> Nicolas M. Thiery wrote:
>> On Sat, Feb 13, 2010 at 09:53:27AM -0800, Anne Schilling wrote:
>>> I would like to write a symmetric polynomial (not function)
>>> in terms of one of the usual bases (like Schur polynomials).
>
>> That's a quite basic feature, that we ought to have (that was fromPoly
>> in MuPAD-Combinat). But I fear we don't. At least I could not find it
>> browsing through the sources.
>
> I don't know of the existence of such a function. I've written a very
> quick-and-dirty (and very minimally tested) function below. If someone
> opens a ticket, I will try to get a proper version of this into sage at
> some point.
>
> Cheers,
> Jason
>
> def toSF(f):
> """ Input is a symmetric polynomial in a polynomial ring in finitely
> many variables. Output is a symmetric function in the monomial
> basis of the ring of symmetric functions over the same base ring.
> """
> X = f.parent().gens()
> n = f.parent().ngens()
> SF = SymmetricFunctions(f.base_ring())
> m = SF.monomial()
> out = m(0)
> while f != 0:
> lt = f.lt()
> c = lt.monomial_coefficient(lt)
> p = Partition(lt.exponents()[0])
> f += -m(p).expand(n,X)
> out += c*m(p)
> return out
>
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