Conversion from symmetric polynomials to basis of monomial symmetric functions

[anneschilling]

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

CC: @jbandlow @sagetrac-sage-combinat

Component: combinatorics

Keywords: symmetric functions

Author: Anne Schilling

Reviewer: Jason Bandlow

Merged: sage-4.3.4.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/8259

[anneschilling]

Author: Anne Schilling

[anneschilling]

Reviewer: Jason Bandlow

[anneschilling]

Description changed:

--- 
+++ 
@@ -1,20 +1,6 @@
-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:
+Currently a function that converts a symmetric polynomial into a symmetric function is missing in 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
+-Added method to convert symmetric polynomial to a symmetric function in monomial basis
+-Added shortcut to symmetric functions
+-Small fix in crystals
 

[anneschilling]

Description changed:

--- 
+++ 
@@ -1,6 +1,8 @@
 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
 

[sagetrac-drkirkby]

comment:4

Has this been checked on Solaris?

There's general information about building on Solaris at

http://wiki.sagemath.org/solaris

Information specifically for 't2' at

http://wiki.sagemath.org/devel/Building-Sage-on-the-T5240-t2

Both the source (4.3.0.1 is the latest to build on Solaris) and a binary which will run on any SPARC can be found at http://www.sagemath.org/download-source.html

Dave

[anneschilling]

comment:5

Dave,

Are you sure you posted this comment to the correct ticket?

If so, could you please comment on the relevance of Solaris to
the code?

Thanks,

Anne

Replying to @sagetrac-drkirkby:

Has this been checked on Solaris?

There's general information about building on Solaris at

http://wiki.sagemath.org/solaris

Information specifically for 't2' at

http://wiki.sagemath.org/devel/Building-Sage-on-the-T5240-t2

Both the source (4.3.0.1 is the latest to build on Solaris) and a binary which will run on any SPARC can be found at http://www.sagemath.org/download-source.html

Dave

[jbandlow]

comment:6

Hi Anne,

The fix to crystals.py doesn't apply to either sage 4.3.2 or sage 4.3.3. Can it be removed from this patch?

Thanks,
Jason

[jbandlow]

comment:7

One more thing. I would really like to have an option to verify that the input actually is a symmetric function. In fact I think this should be true by default. So the key function would look something like this:

def from_polynomial(self, f, check=True):        
    assert(self.base_ring() == f.base_ring()
    d = dict([(e,c) for e,c in f.dict().iteritems() if tuple(sorted(e)) == tuple(reversed(e))]) 
    if not check:
        return self.sum(d[la]*self(Partition(la)) for la in d.keys())
    out = self.sum(d[la]*self(Partition(la)) for la in d.keys())
    assert( out.expand(f.parent().ngens(),f.parent().gens()) == f )
    return out

[anneschilling]

comment:8

Hi Jason,

I attached a revised patch which includes your suggestion to add the option to test
whether the polynomial is symmetric.

For me the patch applied to sage-4.3.3. It depends on trac tickets #7978 and #8154
which have been merged in sage-4.3.3. Hence it might not apply cleanly to sage-4.3.2.

Anne