eja: add another test for element inverses.

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index c2f9fe652851fa4dc2ce519856160efc221debcc..5944c0779a8b7a63b1fa41897947cef4dbee83bb 100644 (file)
--- 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")