X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=5944c0779a8b7a63b1fa41897947cef4dbee83bb;hb=5cbb93016e4b192d2a2d7be81014a55a33c9a8f9;hp=070501852ae4efa8d6845d74240d4495695f42a9;hpb=b05705ab04692f738a57a6ef387662ba5ea46ceb;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 0705018..5944c07 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -460,6 +460,17 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             ...
             ValueError: element is not invertible
 
+        Proposition II.2.3 in Faraut and Koranyi says that the inverse
+        of an element is the inverse of its left-multiplication operator
+        applied to the algebra's identity, when that inverse exists::
+
+            sage: set_random_seed()
+            sage: J = random_eja()
+            sage: x = J.random_element()
+            sage: (not x.operator().is_invertible()) or (
+            ....:    x.operator().inverse()(J.one()) == x.inverse() )
+            True
+
         """
         if not self.is_invertible():
             raise ValueError("element is not invertible")
@@ -1011,7 +1022,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
 
 
-    def subalgebra_generated_by(self):
+    def subalgebra_generated_by(self, orthonormalize_basis=False):
         """
         Return the associative subalgebra of the parent EJA generated
         by this element.
@@ -1050,7 +1061,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             0
 
         """
-        return FiniteDimensionalEuclideanJordanElementSubalgebra(self)
+        return FiniteDimensionalEuclideanJordanElementSubalgebra(self, orthonormalize_basis)
 
 
     def subalgebra_idempotent(self):