Trac #34673: change iterator for ordered set partitions

as suggested by

https://gitlab.com/modulispaces/admcycles/-/issues/100

URL: https://trac.sagemath.org/34673
Reported by: chapoton
Ticket author(s): Frédéric Chapoton
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/combinat/chas/wqsym.py

@@ -69,9 +69,12 @@ def __init__(self, alg, graded=True):
             sage: M = algebras.WQSym(QQ).M()
             sage: TestSuite(M).run()  # long time
         """
+        def sorting_key(X):
+            return (sum(map(len, X)), X)
         CombinatorialFreeModule.__init__(self, alg.base_ring(),
                                          OrderedSetPartitions(),
                                          category=WQSymBases(alg, graded),
+                                         sorting_key=sorting_key,
                                          bracket="", prefix=self._prefix)
 
     def _repr_term(self, osp):
@@ -574,7 +577,7 @@ class Monomial(WQSymBasis_abstract):
             sage: M = WQSym.M(); M
             Word Quasi-symmetric functions over Rational Field in the Monomial basis
             sage: sorted(M.basis(2))
-            [M[{1, 2}], M[{2}, {1}], M[{1}, {2}]]
+            [M[{1}, {2}], M[{2}, {1}], M[{1, 2}]]
         """
         _prefix = "M"
         _basis_name = "Monomial"
@@ -625,6 +628,7 @@ def product_on_basis(self, x, y):
 
             def union(X, Y):
                 return X.union(Y)
+
             return self.sum_of_monomials(ShuffleProduct_overlapping(x, yshift,
                                                                     K, union))
 
@@ -975,12 +979,15 @@ def _C_to_X(self, P):
                         temp = temp[:j]
                         break
 
+            def union(X, Y):
+                return X.union(Y)
+
             # Perform the quasi-shuffle product
             cur = {data[0]: 1}
             for B in data[1:]:
                 ret = {}
                 for A in cur:
-                    for C in ShuffleProduct_overlapping(A, B, element_constructor=OSP):
+                    for C in ShuffleProduct_overlapping(A, B, element_constructor=OSP, add=union):
                         if C in ret:
                             ret[C] += cur[A]
                         else: