Fixes to symmetric functions

[anneschilling]

This patch implements the following fixes to symmetric functions:

• HL creation operator for k-Schur functions

• it fixes omega for k-Schur functions for generic t

• it changes the multiplication for k-Schur functions for generic t, so that
  the result stays in the k-bounded subspace if possible and lifts to symmetric functions otherwise

• it moves coproduct_by_coercion to SymmetricFunctionAlgebra_generic and
  inserts a coproduct function in KBoundedSubspaceBases, ElementMethods

• it fixes the coersion between the Jack P and Pq basis; this was previously extremely slow,
  for example for

      sage: Sym = SymmetricFunctions(FractionField(QQ['t']))
      sage: Qp = Sym.jack().Qp()
      sage: P = Sym.jack().P()
      sage: P(Qp[2,1])
      ((-192*t^3+192*t^2-192*t+192)/(-64*t^3-224*t^2-224*t-64))*JackP[1, 1, 1]
      + ((128*t^2-64*t+80)/(64*t^2+64*t+16))*JackP[2, 1] + ((8*t-8)/(8*t+4))*JackP[3]
  

• it fixes the coproduct for Jack symmetric functions

Apply:

• attachment: trac_13399-sf-as.3.patch

Depends on #13404

CC: @sagetrac-sage-combinat @zabrocki

Component: combinatorics

Keywords: symmetric functions

Author: Anne Schilling, Mike Zabrocki

Reviewer: Mike Zabrocki, Anne Schilling

Merged: sage-5.4.beta2

Issue created by migration from https://trac.sagemath.org/ticket/13399

[nthiery]

comment:2

Speaking of fixes/improvements for symmetric functions: the current code is not perfectly consistent for the naming of the bases:

sage: S = SymmetricFunctions(QQ['q,t'].fraction_field())
sage: S.s()
Symmetric Function Algebra over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field, Schur symmetric functions as basis
sage: S.macdonald().P()
Symmetric Functions over Fraction Field of Multivariate Polynomial Ring in q, t over Rational Field in the realization MacdonaldPolynomials_p

And indeed in the code, S.s().repr comes from SymmetricFunctionAlgebra_classical, where as
S.macdonald().P().repr comes from generic with_realization code.

What about moving (in this ticket, or later), the _repr_ from
SymmetricFunctionAlgebra_classical to SymmetricFunctionsBases?

A bit of fiddling with ._basis might be needed to get the string 'Macdonald P symmetric functions' right, but this should not be too bad.

Cheers,
Nicolas

PS: as a side effect, this would help me a bit with my functorial
construction patch, as it currently breaks the naming of the
macdo/llt/hl basis, and would not anymore with the changes above.

[anneschilling]

comment:4

Hi Mike,

I made all changes we discussed by e-mail. Could you have a look?

Anne

[zabrocki]

comment:5

All tests pass and the documentation looks good. Nicolas, we can address the !repr! changes in another patch. -Mike

[anneschilling]

comment:6

Thank you, Mike! Same comments as on 12140.

[anneschilling]

comment:7

Removed trailing white spaces.

[anneschilling]

Dependencies: #5457

[zabrocki]

comment:9

After discussion, another addition to make will be coproduct method on k-Schur bases.

[zabrocki]

comment:10

I implemented coproduct on k-Schur functions. This required moving coproduct_by_coercion to the class SymmetricFunctionAlgebra_generic. Please test and review.

[anneschilling]

Changed author from Anne Schilling to Anne Schilling, Mike Zabrocki

[anneschilling]

Changed reviewer from Mike Zabrocki to Mike Zabrocki, Anne Schilling

[anneschilling]

comment:12

Hi Mike,

Thanks for the addition! I made some more changes to the doc explanations (there was still a reference to monomial symmetric functions even though coproduct_by_coercion was moved to sfa.py). I also added some further tests for k-Schurs and LLTs. Both patches are now folded, so please only

Apply: trac_13399-sf-as.patch

All tests pass on sage_5.3.rc0 + two additional 5457 patches. No idea what the current version of sage is that we are supposed to test against!

Best,

Anne

[anneschilling]

Changed dependencies from #5457 to #13404

[anneschilling]

comment:14

Rebased with respect to #13404. More additions regarding Jack polynomials are pending!

[anneschilling]

comment:16

Hi Mike,

I folded the previous 13399 patch with the changes to jack.py. For me all tests pass and the documentation looks good. Please set a positive review if you are satisfied!

Anne

[zabrocki]

comment:17

I changed two minor things in the doc strings indicating that coercion was done through the homogeneous basis. All doc tests pass on sage-5.3.rc1 + dependency patches. It looks good and I give it a positive review.

[anneschilling]

comment:18

Apply: trac_13399-sf-as.3.patch

[jdemeyer]

Attachment: trac_13399-sf-as.3.patch.gz

same patch with minor doc changes

[jdemeyer]

Merged: sage-5.4.beta2