Trac #34414: Implement Key polynomials

Implement the Key polynomials as an algebra with basis indexed by
compositions.

URL: https://trac.sagemath.org/34414
Reported by: tkarn
Ticket author(s): Trevor K. Karn
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/doc/en/reference/combinat/module_list.rst

@@ -145,6 +145,7 @@ Comprehensive Module List
     sage/combinat/k_regular_sequence
     sage/combinat/k_tableau
     sage/combinat/kazhdan_lusztig
+    sage/combinat/key_polynomial
     sage/combinat/knutson_tao_puzzles
     sage/combinat/matrices/all
     sage/combinat/matrices/dancing_links

src/sage/combinat/algebraic_combinatorics.py

@@ -41,6 +41,7 @@
 - :class:`~sage.combinat.symmetric_group_representations.SymmetricGroupRepresentation`
 - :ref:`sage.combinat.yang_baxter_graph`
 - :ref:`sage.combinat.hall_polynomial`
+- :ref:`sage.combinat.key_polynomial`
 
 Operads and their algebras
 --------------------------

src/sage/combinat/all.py

@@ -87,6 +87,7 @@
 from .debruijn_sequence import DeBruijnSequences
 
 from .schubert_polynomial import SchubertPolynomialRing
+lazy_import('sage.combinat.key_polynomial', 'KeyPolynomialBasis', as_='KeyPolynomials')
 from .symmetric_group_algebra import SymmetricGroupAlgebra, HeckeAlgebraSymmetricGroupT
 from .symmetric_group_representations import SymmetricGroupRepresentation, SymmetricGroupRepresentations
 from .yang_baxter_graph import YangBaxterGraph