+
+ SETUP::
+
+ sage: from mjo.eja.eja_algebra import (random_eja,
+ ....: JordanSpinEJA,
+ ....: TrivialEJA)
+
+ EXAMPLES:
+
+ A Jordan frame for the trivial algebra has to be empty
+ (zero-length) since its rank is zero. More to the point, there
+ are no non-zero idempotents in the trivial EJA. This does not
+ cause any problems so long as we adopt the convention that the
+ empty sum is zero, since then the sole element of the trivial
+ EJA has an (empty) spectral decomposition::
+
+ sage: J = TrivialEJA()
+ sage: J.a_jordan_frame()
+ ()
+
+ A one-dimensional algebra has rank one (equal to its dimension),
+ and only one primitive idempotent, namely the algebra's unit
+ element::
+
+ sage: J = JordanSpinEJA(1)
+ sage: J.a_jordan_frame()
+ (e0,)
+
+ TESTS::
+
+ sage: J = random_eja()
+ sage: c = J.a_jordan_frame()
+ sage: all( x^2 == x for x in c )
+ True
+ sage: r = len(c)
+ sage: all( c[i]*c[j] == c[i]*(i==j) for i in range(r)
+ ....: for j in range(r) )
+ True
+