Hi Jason,
Thank you! Actually, following a suggestion from Nicolas, I have now
also written the following (minimally tested) function assuming the
base field is over QQ and assuming the function is symmetric (which
is not tested):
def from_polynomial(f):
exp = [list(x) for x in f.exponents()]
s = lambda x : sum(i for i in x)
exp = [Partition(x) for x in exp if x in Partitions(s(x),min_part=0)]
m=SFAMonomial(QQ)
return sum(m(la) for la in exp)
Best,
Anne
Jason Bandlow wrote:
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
--
Anne Schilling E-mail: a...@math.ucdavis.edu
Professor Web: http://www.math.ucdavis.edu/~anne
Department of Mathematics Office: MSB 3222
University of California Phone: (530) 554 2326
One Shields Ave Fax: (530) 752 6635
Davis, CA 95616
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