+ sage: from mjo.eja.eja_algebra import OctonionHermitianEJA
+
+ EXAMPLES:
+
+ The 3-by-3 algebra satisfies the axioms of an EJA::
+
+ sage: OctonionHermitianEJA(3, # long time
+ ....: field=QQ, # long time
+ ....: orthonormalize=False, # long time
+ ....: check_axioms=True) # long time
+ Euclidean Jordan algebra of dimension 27 over Rational Field
+
+ TESTS::
+
+ sage: J = OctonionHermitianEJA(3, # long time
+ ....: field=QQ, # long time
+ ....: orthonormalize=False) # long time
+ sage: J.one.clear_cache() # long time
+ sage: J.one() # long time
+ b0 + b9 + b26
+ sage: J.one().to_matrix() # long time
+ +----+----+----+
+ | e0 | 0 | 0 |
+ +----+----+----+
+ | 0 | e0 | 0 |
+ +----+----+----+
+ | 0 | 0 | e0 |
+ +----+----+----+
+
+ """