gh-37687: provide a construction functor using a single functor for families
    
We enable sage to find common parents also when symmetric functions are
involved. In particular, we provide a functorial construction that takes
a commutative (coefficient) ring and produces a (commutative) ring of
symmetric functions over this ring.

For Macdonald polynomials and other symmetric functions that involve
parameters we cheat a bit: the categories should actually be commutative
rings with distinguished elements (namely, the parameters). However,
having these is very likely overkill.

This is an alternative to #37220, relying on individual construction
functors instead of passing around strings, and #37686, which provides
an individual functor for each family.
    
URL: #37687
Reported by: Martin Rubey
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/combinat/sf/dual.py

@@ -293,7 +293,7 @@ def basis_name(self):
         Return the name of the basis of ``self``.
 
         This is used for output and, for the classical bases of
-        symmetric functions, to connect this basis with Symmetrica.
+        symmetric functions, to connect this basis with :ref:`Symmetrica <spkg_symmetrica>`.
 
         EXAMPLES::
 

src/sage/combinat/sf/sfa.py

@@ -642,7 +642,8 @@ def corresponding_basis_over(self, R):
                 sage: Sym = SymmetricFunctions(P)
                 sage: mj = Sym.macdonald().J()
                 sage: mj.corresponding_basis_over(Integers(13)['q','t'])
-                Symmetric Functions over Multivariate Polynomial Ring in q, t over Ring of integers modulo 13 in the Macdonald J basis
+                Symmetric Functions over Multivariate Polynomial Ring in q, t over
+                 Ring of integers modulo 13 in the Macdonald J basis
 
             TESTS:
 

src/sage/combinat/sf/witt.py

@@ -24,7 +24,6 @@
 from sage.arith.misc import divisors
 from sage.combinat.integer_lists.invlex import IntegerListsLex
 from sage.combinat.partitions import ZS1_iterator
-from sage.matrix.constructor import matrix
 from sage.misc.cachefunc import cached_method