+ A subalgebra of an EJA with a given basis.
+
+ SETUP::
+
+ sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
+ ....: 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(AA, [ [1,0],
+ ....: [0,0] ])
+ sage: E22 = matrix(AA, [ [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:
+
+ Ensure that our generator names don't conflict with the superalgebra::
+
+ sage: J = JordanSpinEJA(3)
+ sage: J.one().subalgebra_generated_by().gens()
+ (f0,)
+ sage: J = JordanSpinEJA(3, prefix='f')
+ sage: J.one().subalgebra_generated_by().gens()
+ (g0,)
+ sage: J = JordanSpinEJA(3, prefix='b')
+ sage: J.one().subalgebra_generated_by().gens()
+ (c0,)
+
+ Ensure that we can find subalgebras of subalgebras::
+
+ sage: A = ComplexHermitianEJA(3).one().subalgebra_generated_by()
+ sage: B = A.one().subalgebra_generated_by()
+ sage: B.dimension()
+ 1
+