X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=eee8f69bd76ddfba49e3cb4531f55d0e970ebd1d;hb=bbd6d4c6e39870b0936949b510e70af2b5358f9e;hp=070501852ae4efa8d6845d74240d4495695f42a9;hpb=b05705ab04692f738a57a6ef387662ba5ea46ceb;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 0705018..eee8f69 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -1,3 +1,5 @@
+# -*- coding: utf-8 -*-
+
 from itertools import izip
 
 from sage.matrix.constructor import matrix
@@ -34,7 +36,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         Return ``self`` raised to the power ``n``.
 
         Jordan algebras are always power-associative; see for
-        example Faraut and Koranyi, Proposition II.1.2 (ii).
+        example Faraut and Korányi, Proposition II.1.2 (ii).
 
         We have to override this because our superclass uses row
         vectors instead of column vectors! We, on the other hand,
@@ -375,7 +377,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             True
 
         Ensure that the determinant is multiplicative on an associative
-        subalgebra as in Faraut and Koranyi's Proposition II.2.2::
+        subalgebra as in Faraut and Korányi's Proposition II.2.2::
 
             sage: set_random_seed()
             sage: J = random_eja().random_element().subalgebra_generated_by()
@@ -460,6 +462,17 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             ...
             ValueError: element is not invertible
 
+        Proposition II.2.3 in Faraut and Korányi 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 +1024,7 @@ 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 +1063,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             0
 
         """
-        return FiniteDimensionalEuclideanJordanElementSubalgebra(self)
+        return FiniteDimensionalEuclideanJordanElementSubalgebra(self, orthonormalize_basis)
 
 
     def subalgebra_idempotent(self):