Merge remote-tracking branch 'trac/public/lie_algebras/base_class_nilponent-26074' into u/gh-ehaka/free_nilpotent_lie_algebras-26076

Author: ehaka

src/sage/categories/category_with_axiom.py

@@ -1679,14 +1679,15 @@ class ``Sets.Finite``), or in a separate file (typically in a class
                "WellGenerated",
                "Facade", "Finite", "Infinite","Enumerated",
                "Complete",
+               "Nilpotent",
                "FiniteDimensional", "Connected", "WithBasis",
                "Irreducible",
                "Commutative", "Associative", "Inverse", "Unital", "Division", "NoZeroDivisors", "Cellular",
                "AdditiveCommutative", "AdditiveAssociative", "AdditiveInverse", "AdditiveUnital",
                "Distributive",
                "Endset",
                "Pointed",
-               "Stratified", "Nilpotent"
+               "Stratified",
               )
 
 def uncamelcase(s,separator=" "):
@@ -2268,6 +2269,14 @@ def _repr_object_names_static(category, axioms):
                 result = result.replace("graded ", "graded connected ", 1)
             elif axiom == "Connected" and "filtered " in result:
                 result = result.replace("filtered ", "filtered connected ", 1)
+            elif axiom == "Stratified" and "graded " in result:
+                result = result.replace("graded ", "stratified ", 1)
+            elif axiom == "Nilpotent" and "finite dimensional " in result:
+                # We need to put nilpotent before finite dimensional in the
+                #   axioms ordering so we do not (unnecessarily) display
+                #   'nilpotent' in 'finite dimensional nilpotent stratified'.
+                # So we need to swap the order here.
+                result = result.replace("finite dimensional ", "finite dimensional nilpotent ", 1)
             elif axiom == "Endset" and "homsets" in result:
                 # Without the space at the end to handle Homsets().Endset()
                 result = result.replace("homsets", "endsets", 1)

src/sage/categories/finite_dimensional_graded_lie_algebras_with_basis.py

@@ -114,9 +114,20 @@ class Stratified(CategoryWithAxiom_over_base_ring):
         to say, for a graded Lie algebra `L = \bigoplus_{k=1}^M L_k`,
         we have `L_{k+1} = [L_1, L_k]`.
 
+        EXAMPLES::
+
+            sage: C = LieAlgebras(QQ).WithBasis().Graded().Stratified().FiniteDimensional()
+            sage: C
+            Category of finite dimensional stratified lie algebras with basis over Rational Field
+
+        A finite-dimensional stratified Lie algebra is nilpotent::
+
+            sage: C is C.Nilpotent()
+            True
+
         TESTS::
 
-            sage: C = LieAlgebras(QQ).Graded().FiniteDimensional().WithBasis().Stratified()
+            sage: C = LieAlgebras(QQ).WithBasis().Graded().FiniteDimensional().Stratified()
             sage: TestSuite(C).run()
         """
         class ParentMethods:

src/sage/categories/finite_dimensional_lie_algebras_with_basis.py

@@ -38,7 +38,7 @@ class FiniteDimensionalLieAlgebrasWithBasis(CategoryWithAxiom_over_base_ring):
         Many of these tests should use non-abelian Lie algebras and need to
         be added after :trac:`16820`.
     """
-    _base_category_class_and_axiom = [LieAlgebras.FiniteDimensional, "WithBasis"]
+    _base_category_class_and_axiom = (LieAlgebras.FiniteDimensional, "WithBasis")
 
     def example(self, n=3):
         """

src/sage/categories/finite_dimensional_nilpotent_lie_algebras_with_basis.py

@@ -45,7 +45,7 @@ class FiniteDimensionalNilpotentLieAlgebrasWithBasis(CategoryWithAxiom_over_base
         True
         sage: TestSuite(C1).run()
     """
-    _base_category_class_and_axiom = [LieAlgebras.FiniteDimensional.WithBasis, "Nilpotent"]
+    _base_category_class_and_axiom = (LieAlgebras.FiniteDimensional.WithBasis, "Nilpotent")
 
     class ParentMethods:
         def _test_nilpotency(self, **options):

src/sage/categories/graded_lie_algebras.py

@@ -39,7 +39,7 @@ def Stratified(self):
             EXAMPLES::
 
                 sage: LieAlgebras(QQ).Graded().Stratified()
-                Category of stratified graded Lie algebras over Rational Field
+                Category of stratified Lie algebras over Rational Field
             """
             return self._with_axiom("Stratified")
 
@@ -60,6 +60,11 @@ class FiniteDimensional(CategoryWithAxiom_over_base_ring):
             r"""
             Category of finite dimensional stratified Lie algebras.
 
+            EXAMPLES::
+
+                sage: LieAlgebras(QQ).Graded().Stratified().FiniteDimensional()
+                Category of finite dimensional stratified Lie algebras over Rational Field
+
             TESTS::
 
                 sage: C = LieAlgebras(QQ).Graded().Stratified().FiniteDimensional()

src/sage/categories/lie_algebras_with_basis.py

@@ -25,7 +25,7 @@ class LieAlgebrasWithBasis(CategoryWithAxiom_over_base_ring):
     """
     Category of Lie algebras with a basis.
     """
-    _base_category_class_and_axiom = [LieAlgebras, "WithBasis"]
+    _base_category_class_and_axiom = (LieAlgebras, "WithBasis")
 
     def example(self, gens=None):
         """