eja: add another non-element subalgebra example.

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 024dfbe72ee6fb0f6f7fe2c00648b79a121d13a5..0be85616678d4f7f7ffa276ddcd13ab907c6e116 100644 (file)
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -85,7 +85,28 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
     SETUP::
 
         sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
-        ....:                                  JordanSpinEJA)
+        ....:                                  JordanSpinEJA,
+        ....:                                  RealSymmetricEJA)
+        sage: from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra
+
+    EXAMPLES:
+
+    The following Peirce subalgebras of the 2-by-2 real symmetric
+    matrices do not contain the superalgebra's identity element::
+
+        sage: J = RealSymmetricEJA(2)
+        sage: E11 = matrix(QQ, [ [1,0],
+        ....:                    [0,0] ])
+        sage: E22 = matrix(QQ, [ [0,0],
+        ....:                    [0,1] ])
+        sage: K1 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E11),))
+        sage: K1.one().natural_representation()
+        [1 0]
+        [0 0]
+        sage: K2 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E22),))
+        sage: K2.one().natural_representation()
+        [0 0]
+        [0 1]
 
     TESTS: