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.

Depends on #32367

CC: @tscrim

Component: categories

Keywords: LazyPowerSeries

Author: Martin Rubey

Branch/Commit: 56cef07

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/34470