Implement non commutative symmetric functions #8899
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:
- Improvements to Sets.WithRealizations #12959 : provides the machinery for converting to a_realization for default implementations
- add functionality for counting, generating, and manipulating non-negative integer matrices #13238 : integer matrices (required for the internal product in NCSF)
- new methods for compositions #13243 : new methods for compositions
Apply:
- attachment: trac_11929_8899-ncsf-qsym-final.patch
- attachment: trac_11929_8899-ncsf-qsym-repr-fix-fs.patch
Depends on #12953
Depends on #12956
Depends on #12959
Depends on #13238
Depends on #13243
Depends on #5457
CC: @sagetrac-sage-combinat @sagetrac-chrisjamesberg @zabrocki @anneschilling
Component: combinatorics
Keywords: sd40, days38
Author: Jason Bandlow, Chris Berg, Franco Saliola, Nicolas M. Thiéry
Reviewer: Mike Zabrocki, Franco Saliola, Mike Hansen
Merged: sage-5.4.beta1
Issue created by migration from https://trac.sagemath.org/ticket/8899