Better mutliplication of PBW elements.

sagemath · Jun 18, 2017 · f61aae2 · f61aae2
1 parent e0f9c88
commit f61aae2
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Showing 2 changed files with 15 additions and 2 deletions.
diff --git a/src/sage/algebras/lie_algebras/lie_algebra.py b/src/sage/algebras/lie_algebras/lie_algebra.py
@@ -1105,7 +1105,7 @@ def monomial(self, i):
             sage: L.monomial(x.leading_support())
             x
         """
-        if i not in self.basis().keys():
+        if i not in self._assoc.basis().keys():
             #return self(self._assoc.monomial(i))
             raise ValueError("not an index")
         return self.element_class(self, self._assoc.monomial(i))
@@ -1121,7 +1121,7 @@ def term(self, i, c=None):
             sage: L.term(x.leading_support(), 4)
             4*x
         """
-        if i not in self.basis().keys():
+        if i not in self._assoc.basis().keys():
             #return self(self._assoc.term(i, c))
             raise ValueError("not an index")
         return self.element_class(self, self._assoc.term(i, c))

diff --git a/src/sage/algebras/lie_algebras/poincare_birkhoff_witt.py b/src/sage/algebras/lie_algebras/poincare_birkhoff_witt.py
@@ -345,6 +345,19 @@ def product_on_basis(self, lhs, rhs):
             sage: E * F * H * E
             PBW['E']^2*PBW['F']*PBW['H'] + 2*PBW['E']^2*PBW['F']
              - PBW['E']*PBW['H']^2 - 2*PBW['E']*PBW['H']
+
+        TESTS:
+
+        Check that :trac:`23268` is fixed::
+
+            sage: MS = MatrixSpace(QQ, 2,2)
+            sage: gl = LieAlgebra(associative=MS)
+            sage: Ugl = gl.pbw_basis()
+            sage: prod(Ugl.gens())
+            PBW[(0, 0)]*PBW[(0, 1)]*PBW[(1, 0)]*PBW[(1, 1)]
+            sage: prod(reversed(list(Ugl.gens())))
+            PBW[(0, 0)]*PBW[(0, 1)]*PBW[(1, 0)]*PBW[(1, 1)]
+             - PBW[(0, 0)]^2*PBW[(1, 1)] + PBW[(0, 0)]*PBW[(1, 1)]^2
         """
         # Some trivial base cases
         if lhs == self.one_basis():