gh-38108: Implicit function solver for lazy series
    
This pull request provides a method `define_implicitly` for lazy rings
that allows to produce lazy power series solutions for systems of
functional equations, in relatively great generality, superseding
#37033.

We use a special action to make sure that coercion between
`CoefficientRing` and its base ring works as desired. However, it is a
local change, if the current approach eventually shows its shortcomings.
(Alternative approach previously considered: Using a special functor to
control the pushout behaviors. The action approach was chosen as a way
to prevent potential conflicts with other construction functors that may
appear in the future.)

Dependencies: #38729
    
URL: #38108
Reported by: Martin Rubey
Reviewer(s): Martin Rubey, Travis Scrimshaw

Author: Release Manager

src/sage/combinat/sf/orthotriang.py

@@ -103,7 +103,7 @@ def __init__(self, Sym, base, scalar, prefix, basis_name, leading_coeff):
         TESTS::
 
             sage: TestSuite(s).run(elements=[s[1,1]+2*s[2], s[1]+3*s[1,1]])
-            sage: TestSuite(s).run(skip=["_test_associativity", "_test_prod", '_test_construction'])  # long time (7s on sage.math, 2011)
+            sage: TestSuite(s).run(skip=["_test_associativity", "_test_prod"])  # long time (7s on sage.math, 2011)
 
         Note: ``s.an_element()`` is of degree 4; so we skip
         ``_test_associativity`` and ``_test_prod`` which involve

src/sage/combinat/sf/sf.py

@@ -845,7 +845,6 @@ class function on the symmetric group where the elements
         - Devise a mechanism so that pickling bases of symmetric
           functions pickles the coercions which have a cache.
     """
-
     def __init__(self, R):
         r"""
         Initialization of ``self``.

src/sage/combinat/species/generating_series.py

@@ -141,7 +141,7 @@ def __init__(self, base_ring):
             sage: from sage.combinat.species.generating_series import OrdinaryGeneratingSeriesRing
             sage: OrdinaryGeneratingSeriesRing.options.halting_precision(15)
             sage: R = OrdinaryGeneratingSeriesRing(QQ)
-            sage: TestSuite(R).run()
+            sage: TestSuite(R).run(skip="_test_construction")
 
             sage: OrdinaryGeneratingSeriesRing.options._reset()  # reset options
         """
@@ -268,7 +268,7 @@ def __init__(self, base_ring):
             sage: from sage.combinat.species.generating_series import ExponentialGeneratingSeriesRing
             sage: ExponentialGeneratingSeriesRing.options.halting_precision(15)
             sage: R = ExponentialGeneratingSeriesRing(QQ)
-            sage: TestSuite(R).run()
+            sage: TestSuite(R).run(skip="_test_construction")
 
             sage: ExponentialGeneratingSeriesRing.options._reset()  # reset options
         """

src/sage/combinat/species/species.py

@@ -376,7 +376,7 @@ def structures(self, labels, structure_class=None):
             sage: F.structures([1,2,3]).list()
             Traceback (most recent call last):
             ...
-            NotImplementedError
+            ValueError: Stream is not yet defined
         """
         return StructuresWrapper(self, labels, structure_class)
 
@@ -388,7 +388,7 @@ def isotypes(self, labels, structure_class=None):
             sage: F.isotypes([1,2,3]).list()
             Traceback (most recent call last):
             ...
-            NotImplementedError
+            ValueError: Stream is not yet defined
         """
         return IsotypesWrapper(self, labels, structure_class=structure_class)