beginning of implemantation for general algebras

sagemath · Jul 25, 2014 · b2bb566 · b2bb566
1 parent 8aa7db9
commit b2bb566
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diff --git a/src/sage/categories/algebras.py b/src/sage/categories/algebras.py
@@ -119,6 +119,34 @@ def _div_(self, y):
 
     class Quotients(QuotientsCategory):
 
+        class ElementMethods:
+
+            def _lift_idempotent(self):
+                r"""
+                Lift an idempotent of parent of ``self`` into an indempotent of
+                parent of ``self.lift()``
+
+                EXAMPLES::
+
+                    sage: A3 = SymmetricGroup(3).algebra(QQ)
+                    sage: Z3 = A3.center()
+                    sage: Z3._refine_category_(SemisimpleAlgebras(QQ))
+                    sage: orth = Z3.orthogonal_idempotents()
+                    sage: x = orth[2]._lift_idempotent()
+                    sage: x not in Z3 and x in A3
+                    True
+
+                TODO: better documentation.
+                """
+                idempOld = None
+                idemp = self.lift()
+                p = idemp.parent()
+                while idemp <> idempOld:
+                    tmp = idemp
+                    idemp = (p.one() - (p.one() - idemp**2)**2)
+                    idempOld = tmp
+                return idemp
+
         class ParentMethods:
 
             def algebra_generators(self):
@@ -241,29 +269,3 @@ def _mul_(self, right):
                 """
                 p = self.parent()
                 return p.retract( self.lift() * right.lift())
-
-            def _lift_idempotent(self):
-                r"""
-                Lift an idempotent of parent of ``self`` into an indempotent of
-                parent of ``self.lift()``
-
-                EXAMPLES::
-
-                    sage: A3 = SymmetricGroup(3).algebra(QQ)
-                    sage: Z3 = A3.center()
-                    sage: Z3._refine_category_(SemisimpleAlgebras(QQ))
-                    sage: orth = Z3.orthogonal_idempotents()
-                    sage: x = orth[2]._lift_idempotent()
-                    sage: x not in Z3 and x in A3
-                    True
-
-                TODO: better documentation.
-                """
-                idempOld = None
-                idemp = self.lift()
-                p = idemp.parent()
-                while idemp <> idempOld:
-                    tmp = idemp
-                    idemp = (p.one() - (p.one() - idemp**2)**2)
-                    idempOld = tmp
-                return idemp
diff --git a/src/sage/categories/finite_dimensional_algebras_with_basis.py b/src/sage/categories/finite_dimensional_algebras_with_basis.py
@@ -346,6 +346,18 @@ def center(self):
             center.rename("Center of {}".format(self))
             return center
 
+        def orthogonal_idempotent(self):
+            r"""
+            Return a maximal family of orthogonal idempotents of ``self``.
+
+            INPUT:
+
+            - ``self`` -- a finite dimensional algebra
+            """
+            Aquo = self.semisimple_quotient()
+            orth_quo = Aquo.orthogonal_idempotents()
+            return [x._lift_idempotent() for x in orth_quo]
+
     class ElementMethods:
 
         def to_matrix(self, base_ring=None, action=operator.mul, side='left'):