Trac #34470: categories of lazy series

We should check the categories of our lazy rings:
{{{
sage: L = LazyTaylorSeriesRing(QQ, "x, y") ; L in DiscreteValuationRings
True
sage: L in PrincipalIdealDomains
True
}}}
is wrong.  It is not even a 'valuation ring' , see
https://en.wikipedia.org/wiki/Valuation_ring, because neither `x/y` not
`y/x` is in `L`.  I doubt it should be in `UniqueFactorizationDomains`,
because this category is reserved for constructive UFD's.

In the univariate case, the uniformizer is the generator "x", but this
is not yet implemented:
{{{
sage: L = LazyTaylorSeriesRing(QQ, "x")
sage: L.uniformizer()
...
NotImplementedError: <abstract method uniformizer at 0x7ff26e85acb0>
}}}

Similarly, we have
{{{
sage: LazySymmetricFunctions(SymmetricFunctions(QQ).p()) in
DiscreteValuationRings
True
sage: LazySymmetricFunctions(SymmetricFunctions(QQ).p()) in
PrincipalIdealDomains
True
}}}
which is also wrong.

URL: https://trac.sagemath.org/34470
Reported by: mantepse
Ticket author(s): Martin Rubey
Reviewer(s): Travis Scrimshaw

src/sage/combinat/sf/sfa.py

@@ -1722,6 +1722,24 @@ def degree_zero_coefficient(self):
             """
             return self.coefficient([])
 
+        def is_unit(self):
+            """
+            Return whether this element is a unit in the ring.
+
+            EXAMPLES::
+
+                sage: m = SymmetricFunctions(ZZ).monomial()
+                sage: (2*m[2,1] + m[[]]).is_unit()
+                False
+
+                sage: m = SymmetricFunctions(QQ).monomial()
+                sage: (3/2*m([])).is_unit()
+                True
+            """
+            m = self.monomial_coefficients(copy=False)
+            return len(m) <= 1 and self.coefficient([]).is_unit()
+
+
 #SymmetricFunctionsBases.Filtered = FilteredSymmetricFunctionsBases
 #SymmetricFunctionsBases.Graded = GradedSymmetricFunctionsBases
 

src/sage/combinat/species/generating_series.py

@@ -143,8 +143,11 @@ def __init__(self, base_ring):
         TESTS::
 
             sage: from sage.combinat.species.generating_series import OrdinaryGeneratingSeriesRing
+            sage: OrdinaryGeneratingSeriesRing.options.halting_precision(15)
             sage: R = OrdinaryGeneratingSeriesRing(QQ)
-            sage: TestSuite(R).run(skip=["_test_associativity", "_test_distributivity", "_test_elements"])
+            sage: TestSuite(R).run()
+
+            sage: OrdinaryGeneratingSeriesRing.options._reset()  # reset options
         """
         super().__init__(base_ring, names="z")
 
@@ -264,8 +267,11 @@ def __init__(self, base_ring):
         TESTS::
 
             sage: from sage.combinat.species.generating_series import ExponentialGeneratingSeriesRing
+            sage: ExponentialGeneratingSeriesRing.options.halting_precision(15)
             sage: R = ExponentialGeneratingSeriesRing(QQ)
-            sage: TestSuite(R).run(skip=["_test_associativity", "_test_distributivity", "_test_elements"])
+            sage: TestSuite(R).run()
+
+            sage: ExponentialGeneratingSeriesRing.options._reset()  # reset options
         """
         super().__init__(base_ring, names="z")
 
@@ -546,8 +552,11 @@ def __init__(self, base_ring, sparse=True):
         TESTS::
 
             sage: from sage.combinat.species.generating_series import CycleIndexSeriesRing
+            sage: CycleIndexSeriesRing.options.halting_precision(12)
             sage: R = CycleIndexSeriesRing(QQ)
-            sage: TestSuite(R).run(skip=["_test_elements", "_test_quo_rem"])
+            sage: TestSuite(R).run()
+
+            sage: CycleIndexSeriesRing.options._reset()  # reset options
         """
         p = SymmetricFunctions(base_ring).power()
         super().__init__(p)
@@ -659,4 +668,3 @@ def LogarithmCycleIndexSeries(R=QQ):
     """
     CIS = CycleIndexSeriesRing(R)
     return CIS(_cl_term)
-