eja: declare a utf-8 encoding and use it to write Korányi.

[sage.d.git] / mjo / eja / eja_element.py

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index c2f9fe652851fa4dc2ce519856160efc221debcc..eee8f69bd76ddfba49e3cb4531f55d0e970ebd1d 100644 (file)
--- 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")