+class ConcreteEuclideanJordanAlgebra:
+ r"""
+ A class for the Euclidean Jordan algebras that we know by name.
+
+ These are the Jordan algebras whose basis, multiplication table,
+ 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 basis is normalized with respect to the algebra's 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 basis is orthonormal with respect to the algebra's 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().is_self_adjoint()
+ True
+ """
+