A better failure example for _test_generated_by_degree_one and some m…

…ore doc.
sagemath · Aug 21, 2018 · 8b3c585 · 8b3c585
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Showing 2 changed files with 15 additions and 10 deletions.
diff --git a/src/sage/categories/finite_dimensional_graded_lie_algebras_with_basis.py b/src/sage/categories/finite_dimensional_graded_lie_algebras_with_basis.py
@@ -111,7 +111,9 @@ class Stratified(CategoryWithAxiom_over_base_ring):
         Category of finite dimensional stratified Lie algebras with a basis.
 
         A stratified Lie algebra is a graded Lie algebra that is generated
-        as a Lie algebra by its homogeneous component of degree 1.
+        as a Lie algebra by its homogeneous component of degree 1. That is
+        to say, For a graded Lie algebra `L = \bigoplus_{k=0}^M L_k`,
+        we have `L_{k+1} = [L_1, L_k]`.
 
         TESTS::
 
@@ -121,12 +123,13 @@ class Stratified(CategoryWithAxiom_over_base_ring):
         class ParentMethods:
             def _test_generated_by_degree_one(self, **options):
                 r"""
-                Tests that the Lie algebra is generated by the homogeneous component
-                of degree one.
+                Tests that the Lie algebra is generated by the homogeneous
+                component of degree one.
 
                 INPUT:
 
-                - ``options`` -- any keyword arguments accepted by :meth:`_tester`.
+                - ``options`` -- any keyword arguments accepted by
+                  :meth:`_tester`
 
                 EXAMPLES::
 
@@ -137,15 +140,13 @@ def _test_generated_by_degree_one(self, **options):
                     sage: L.<x,y,z> = NilpotentLieAlgebra(QQ, sc, category=C)
                     sage: L._test_generated_by_degree_one()
 
-                We modify ``L`` with a different grading::
-
-                    sage: L._basis_degrees = {x: 1, y: 2, z: 3}
-                    sage: L.homogeneous_component_as_submodule.clear_cache()
+                    sage: sc = {('x','y'): {'z': 1}, ('a','b'): {'c':1}, ('z','c'): {'m':1}}
+                    sage: L.<a,b,c,m,x,y,z> = NilpotentLieAlgebra(QQ, sc, category=C)
                     sage: L._test_generated_by_degree_one()
                     Traceback (most recent call last):
                     ...
-                    AssertionError: [x] does not generate Nilpotent Lie algebra on
-                    3 generators (x, y, z) over Rational Field
+                    AssertionError: [a, b, x, y] does not generate Nilpotent Lie algebra
+                     on 7 generators (a, b, c, m, x, y, z) over Rational Field
 
                 See the documentation for :class:`TestSuite` for more information.
                 """

diff --git a/src/sage/categories/graded_lie_algebras.py b/src/sage/categories/graded_lie_algebras.py
@@ -47,6 +47,10 @@ class Stratified(CategoryWithAxiom_over_base_ring):
         r"""
         Category of stratified Lie algebras.
 
+        A graded Lie algebra `L = \bigoplus_{k=0}^M L_k` (where
+        possibly `M = \infty`) is called *stratified* if it is generated
+        by `L_1`; in other words, we have `L_{k+1} = [L_1, L_k]`.
+
         TESTS::
 
             sage: C = LieAlgebras(QQ).Graded().Stratified()