#8259: Conversion from symmetric polynomials to basis of monomial symmetric
functions
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Reporter: aschilling | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone:
Component: combinatorics | Keywords: symmetric functions
Author: Anne Schilling | Upstream: N/A
Reviewer: Jason Bandlow | Merged:
Work_issues: |
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Changes (by newvalueoldvalue):
* status: new => needs_review
* reviewer: => Jason Bandlow
* author: => Anne Schilling
Old description:
> Currently a function that converts a symmetric polynomial into the
> monomial basis is missing in sage. Jason Bandlow wrote a first version
> which should be integrated into sage:
>
> 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
New description:
Currently a function that converts a symmetric polynomial into a symmetric
function is missing in sage.
-Added method to convert symmetric polynomial to a symmetric function in
monomial basis
-Added shortcut to symmetric functions
-Small fix in crystals
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8259#comment:2>
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