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

[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

[anneschilling]

Attachment: trac_8259-from_poly_to_sym-as.patch.gz

[anneschilling]

comment:9

Hi Jason,

As we just discussed on the phone, I did revert the indentation of class Element
in /combinat/sf/monomial.py back to the same level as
class SymmetricFunctionAlgebra_monomial

However, I did change the indentation to be multiples of 4 rather than multiples
of 3. I sent an e-mail to sage-combinat-devel to ask about the indentation issues
in sf.

Anne

[jbandlow]

comment:10

Thanks Anne! This looks good to me. Positive review.

-Jason

[nthiery]

comment:11

Just two tiny remarks:

• One can write assert a==b instead of assert(a==b)
• One could be a bit more specific: `assert a==b, "not a symmetric polynomial"
• Assertion are not always checked (see http://docs.python.org/reference/simple_stmts.html).
  So I am not sure it is the appropriate idiom here.

That's minor, so I let you see if you want to add a quick review patch, or just leave things as is.

Thanks!

[anneschilling]

comment:12

Attachment: trac_8259-from_poly_to_sym-review-as.patch.gz

Replying to @nthiery:

Just two tiny remarks:

• One can write assert a==b instead of assert(a==b)
• One could be a bit more specific: `assert a==b, "not a symmetric polynomial"
• Assertion are not always checked (see http://docs.python.org/reference/simple_stmts.html).
  So I am not sure it is the appropriate idiom here.

That's minor, so I let you see if you want to add a quick review patch, or just leave things as is.

Thanks!

Done! Please review the review of the review of the review ... oops! Infinite loop!

[nthiery]

comment:13

Replying to @anneschilling:

Replying to @nthiery:

Just two tiny remarks:

• One can write assert a==b instead of assert(a==b)
• One could be a bit more specific: `assert a==b, "not a symmetric polynomial"
• Assertion are not always checked (see http://docs.python.org/reference/simple_stmts.html).
  So I am not sure it is the appropriate idiom here.

That's minor, so I let you see if you want to add a quick review patch, or just leave things as is.

Thanks!

Done! Please review the review of the review of the review ... oops! Infinite loop!

Thanks! I haven't rerun the tests, but the review patch looks good to me.

[sagetrac-mvngu]

Merged: sage-4.3.4.alpha0

[sagetrac-mvngu]

comment:14

Merged in this order:

1. trac_8259-from_poly_to_sym-as.patch
2. trac_8259-from_poly_to_sym-review-as.patch