from sage.matrix.matrix_space import MatrixSpace
from sage.misc.table import table
-from mjo.matrix_algebra import MatrixAlgebra
+from mjo.matrix_algebra import HurwitzMatrixAlgebra
class Octonion(IndexedFreeModuleElement):
def conjugate(self):
-class OctonionMatrixAlgebra(MatrixAlgebra):
+class OctonionMatrixAlgebra(HurwitzMatrixAlgebra):
r"""
The algebra of ``n``-by-``n`` matrices with octonion entries over
(a subfield of) the real numbers.
| e2 - e6 | e3 - e7 |
+---------+---------+
+ ::
+
+ sage: A1 = OctonionMatrixAlgebra(1,QQ)
+ sage: A2 = OctonionMatrixAlgebra(1,QQ)
+ sage: cartesian_product([A1,A2])
+ Module of 1 by 1 matrices with entries in Octonion algebra with
+ base ring Rational Field over the scalar ring Rational Field (+)
+ Module of 1 by 1 matrices with entries in Octonion algebra with
+ base ring Rational Field over the scalar ring Rational Field
+
TESTS::
sage: set_random_seed()