class Element(FiniteDimensionalAlgebraElement):
"""
An element of a Euclidean Jordan algebra.
+
+ Since EJAs are commutative, the "right multiplication" matrix is
+ also the left multiplication matrix and must be symmetric::
+
+ sage: set_random_seed()
+ sage: J = eja_ln(5)
+ sage: J.random_element().matrix().is_symmetric()
+ True
+
"""
def __pow__(self, n):
sage: (e0 - e1).degree()
2
+ In the spin factor algebra (of rank two), all elements that
+ aren't multiples of the identity are regular::
+
+ sage: set_random_seed()
+ sage: n = ZZ.random_element(1,10).abs()
+ sage: J = eja_ln(n)
+ sage: x = J.random_element()
+ sage: x == x.coefficient(0)*J.one() or x.degree() == 2
+ True
+
"""
return self.span_of_powers().dimension()