#8899: Implement non commutative symmetric functions
--------------------------------------------------------------------------------+
Reporter: nthiery
| Owner: sage-combinat
Type: enhancement
| Status: needs_review
Priority: major
| Milestone: sage-wishlist
Component: combinatorics
| Resolution:
Keywords: sd40
| Work issues:
Report Upstream: N/A
| Reviewers:
Authors: Jason Bandlow, Chris Berg, Franco Saliola, Nicolas M. Thiéry
| Merged in:
Dependencies: #12953, #12956, #12959, #13238, #13243
| Stopgaps:
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Old description:
> This patch includes quasi symmetric functions as well (see #11929).
>
> Each algebra is implemented as a Hopf algebra with realizations (the
> realizations being the various bases of the algebras).
>
> - Bases implemented for NCSF, and change of bases between them:
>
> - Complete
> - Ribbon
> - Elementary
> - Psi (power sums)
> - Phi (power sums)
>
> - Bases implemented for QSym, and change of bases between them:
>
> - Monomial
> - Fundamental
>
> There is also a method a_realization that returns a particular
> realization of the algebra. Computations that are not yet implemented in
> basis are performed by converting to a_realization(). Current
> implementation:
>
> - NCSF.a_realization() returns the Complete basis
> - QSym.a_realization() returns the Monomial basis
>
> Dependencies:
>
> - #12959 : provides the machinery for converting to a_realization for
> default implementations
> - #13238 : integer matrices (required for the internal product in NCSF)
> - #13243 : new methods for compositions
>
> '''Apply''':
> * [attachment:trac_11929_8899-antipode_by_coercion_in_category-
> fs.patch]
> * [attachment:coproduct_with_realizations-fs.patch]
> * [attachment:trac_11929_8899-ncsf-qsym-fs.patch]
> * [attachment:trac_11929_8899-fix_skewby-fs.patch]
> * [attachment:trac_11929_8899-add_degree_to_elementmethods-fs.patch]
> * [attachment:trac_11929_8899-include_doc_in_reference_manual-
> fs.patch]
> * [attachment:trac_11929_8899-modify_duality_method_names-fs.patch]
> * [attachment:trac_11929_8899-is_symmetric-fs.patch]
> * [attachment:trac_11929_8899-internal_product_fix-fs.patch]
New description:
This patch includes quasi symmetric functions as well (see #11929).
Each algebra is implemented as a Hopf algebra with realizations (the
realizations being the various bases of the algebras).
- Bases implemented for NCSF, and change of bases between them:
- Complete
- Ribbon
- Elementary
- Psi (power sums)
- Phi (power sums)
- Bases implemented for QSym, and change of bases between them:
- Monomial
- Fundamental
There is also a method a_realization that returns a particular realization
of the algebra. Computations that are not yet implemented in basis are
performed by converting to a_realization(). Current implementation:
- NCSF.a_realization() returns the Complete basis
- QSym.a_realization() returns the Monomial basis
Dependencies:
- #12959 : provides the machinery for converting to a_realization for
default implementations
- #13238 : integer matrices (required for the internal product in NCSF)
- #13243 : new methods for compositions
'''Apply''':
* [attachment:trac_11929_8899-antipode_by_coercion_in_category-
fs.patch]
* [attachment:coproduct_with_realizations-fs.patch]
* [attachment:trac_11929_8899-ncsf-qsym-fs.patch]
* [attachment:trac_11929_8899-fix_skewby-fs.patch]
* [attachment:trac_11929_8899-add_degree_to_elementmethods-fs.patch]
* [attachment:trac_11929_8899-include_doc_in_reference_manual-
fs.patch]
* [attachment:trac_11929_8899-modify_duality_method_names-fs.patch]
* [attachment:trac_11929_8899-is_symmetric-fs.patch]
* [attachment:trac_11929_8899-internal_product_fix-fs.patch]
* [attachment:trac_11929_8899-additional_documentation-mz.patch]
--
Comment (by zabrocki):
Minor changes to documentation plus the addition of a tutorial for quasi-
symmetric function and additional doc tests and examples. The doc tests
added use functionality that is in sage-5.3.beta2.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8899#comment:22>
Sage <http://www.sagemath.org>
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