eja: factor out some common tests.

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index d9a3abc7508e69424d4432ed64875cf17c01cac8..3b5828fed55098dfd3f4c95bf2354ac4e38efc87 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -1061,6 +1061,33 @@ class ConcreteEuclideanJordanAlgebra:
     rank, and so on are known a priori. More to the point, they are
     the Euclidean Jordan algebras for which we are able to conjure up
     a "random instance."
+
+    SETUP::
+
+        sage: from mjo.eja.eja_algebra import ConcreteEuclideanJordanAlgebra
+
+    TESTS:
+
+    Our natural basis is normalized with respect to the natural inner
+    product unless we specify otherwise::
+
+        sage: set_random_seed()
+        sage: J = ConcreteEuclideanJordanAlgebra.random_instance()
+        sage: all( b.norm() == 1 for b in J.gens() )
+        True
+
+    Since our natural basis is normalized with respect to the natural
+    inner product, and since we know that this algebra is an EJA, any
+    left-multiplication operator's matrix will be symmetric because
+    natural->EJA basis representation is an isometry and within the EJA
+    the operator is self-adjoint by the Jordan axiom::
+
+        sage: set_random_seed()
+        sage: J = ConcreteEuclideanJordanAlgebra.random_instance()
+        sage: x = J.random_element()
+        sage: x.operator().matrix().is_symmetric()
+        True
+
     """
 
     @staticmethod
@@ -1335,25 +1362,6 @@ class RealSymmetricEJA(RealMatrixEuclideanJordanAlgebra,
         sage: RealSymmetricEJA(3, prefix='q').gens()
         (q0, q1, q2, q3, q4, q5)
 
-    Our natural basis is normalized with respect to the natural inner
-    product unless we specify otherwise::
-
-        sage: set_random_seed()
-        sage: J = RealSymmetricEJA.random_instance()
-        sage: all( b.norm() == 1 for b in J.gens() )
-        True
-
-    Since our natural basis is normalized with respect to the natural
-    inner product, and since we know that this algebra is an EJA, any
-    left-multiplication operator's matrix will be symmetric because
-    natural->EJA basis representation is an isometry and within the EJA
-    the operator is self-adjoint by the Jordan axiom::
-
-        sage: set_random_seed()
-        sage: x = RealSymmetricEJA.random_instance().random_element()
-        sage: x.operator().matrix().is_symmetric()
-        True
-
     We can construct the (trivial) algebra of rank zero::
 
         sage: RealSymmetricEJA(0)
@@ -1623,25 +1631,6 @@ class ComplexHermitianEJA(ComplexMatrixEuclideanJordanAlgebra,
         sage: ComplexHermitianEJA(2, prefix='z').gens()
         (z0, z1, z2, z3)
 
-    Our natural basis is normalized with respect to the natural inner
-    product unless we specify otherwise::
-
-        sage: set_random_seed()
-        sage: J = ComplexHermitianEJA.random_instance()
-        sage: all( b.norm() == 1 for b in J.gens() )
-        True
-
-    Since our natural basis is normalized with respect to the natural
-    inner product, and since we know that this algebra is an EJA, any
-    left-multiplication operator's matrix will be symmetric because
-    natural->EJA basis representation is an isometry and within the EJA
-    the operator is self-adjoint by the Jordan axiom::
-
-        sage: set_random_seed()
-        sage: x = ComplexHermitianEJA.random_instance().random_element()
-        sage: x.operator().matrix().is_symmetric()
-        True
-
     We can construct the (trivial) algebra of rank zero::
 
         sage: ComplexHermitianEJA(0)
@@ -1937,25 +1926,6 @@ class QuaternionHermitianEJA(QuaternionMatrixEuclideanJordanAlgebra,
         sage: QuaternionHermitianEJA(2, prefix='a').gens()
         (a0, a1, a2, a3, a4, a5)
 
-    Our natural basis is normalized with respect to the natural inner
-    product unless we specify otherwise::
-
-        sage: set_random_seed()
-        sage: J = QuaternionHermitianEJA.random_instance()
-        sage: all( b.norm() == 1 for b in J.gens() )
-        True
-
-    Since our natural basis is normalized with respect to the natural
-    inner product, and since we know that this algebra is an EJA, any
-    left-multiplication operator's matrix will be symmetric because
-    natural->EJA basis representation is an isometry and within the EJA
-    the operator is self-adjoint by the Jordan axiom::
-
-        sage: set_random_seed()
-        sage: x = QuaternionHermitianEJA.random_instance().random_element()
-        sage: x.operator().matrix().is_symmetric()
-        True
-
     We can construct the (trivial) algebra of rank zero::
 
         sage: QuaternionHermitianEJA(0)