+
+ # Assuming associativity is wrong here, but it works to
+ # temporarily trick the Jordan algebra constructor into using the
+ # multiplication table.
+ return FiniteDimensionalEuclideanJordanAlgebra(field,Qs)
+
+
+def eja_ln(dimension, field=QQ):
+ """
+ Return the Jordan algebra corresponding to the Lorentz "ice cream"
+ cone of the given ``dimension``.
+
+ EXAMPLES:
+
+ This multiplication table can be verified by hand::
+
+ sage: J = eja_ln(4)
+ sage: e0,e1,e2,e3 = J.gens()
+ sage: e0*e0
+ e0
+ sage: e0*e1
+ e1
+ sage: e0*e2
+ e2
+ sage: e0*e3
+ e3
+ sage: e1*e2
+ 0
+ sage: e1*e3
+ 0
+ sage: e2*e3
+ 0
+
+ In one dimension, this is the reals under multiplication::
+
+ sage: J1 = eja_ln(1)
+ sage: J2 = eja_rn(1)
+ sage: J1 == J2
+ True
+
+ """
+ Qs = []
+ id_matrix = identity_matrix(field,dimension)
+ for i in xrange(dimension):
+ ei = id_matrix.column(i)
+ Qi = zero_matrix(field,dimension)
+ Qi.set_row(0, ei)
+ Qi.set_column(0, ei)
+ Qi += diagonal_matrix(dimension, [ei[0]]*dimension)
+ # The addition of the diagonal matrix adds an extra ei[0] in the
+ # upper-left corner of the matrix.
+ Qi[0,0] = Qi[0,0] * ~field(2)
+ Qs.append(Qi)
+
+ return FiniteDimensionalEuclideanJordanAlgebra(field,Qs)