X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=blobdiff_plain;f=mjo%2Foctonions.py;h=2850545280b122cb8109324f4b6431ed0f5076ec;hp=073765ccf1ef934ab6d9f6fc59435384bf832f36;hb=d006c2e856b970d2f8e77d738030ef2e63ec5b78;hpb=282312431417150844934782b2431602704d8b89

diff --git a/mjo/octonions.py b/mjo/octonions.py
index 073765c..2850545 100644
--- a/mjo/octonions.py
+++ b/mjo/octonions.py
@@ -7,7 +7,7 @@ from sage.rings.all import AA, ZZ
 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):
@@ -141,6 +141,11 @@ class Octonion(IndexedFreeModuleElement):
         """
         return self._norm_squared().sqrt()
 
+    # The absolute value notation is typically used for complex numbers...
+    # and norm() isn't supported in AA, so this lets us use abs() in all
+    # of the division algebras we need.
+    abs = norm
+
     def inverse(self):
         r"""
         Return the inverse of this element if it exists.
@@ -342,7 +347,7 @@ class Octonions(CombinatorialFreeModule):
 
 
 
-class OctonionMatrixAlgebra(MatrixAlgebra):
+class OctonionMatrixAlgebra(HurwitzMatrixAlgebra):
     r"""
     The algebra of ``n``-by-``n`` matrices with octonion entries over
     (a subfield of) the real numbers.
@@ -369,14 +374,24 @@ class OctonionMatrixAlgebra(MatrixAlgebra):
         sage: O = Octonions(QQ)
         sage: e0,e1,e2,e3,e4,e5,e6,e7 = O.gens()
         sage: MS = OctonionMatrixAlgebra(2)
-        sage: MS.from_list([ [e0+e4, e1+e5],
-        ....:                [e2-e6, e3-e7] ])
+        sage: MS([ [e0+e4, e1+e5],
+        ....:      [e2-e6, e3-e7] ])
         +---------+---------+
         | e0 + e4 | e1 + e5 |
         +---------+---------+
         | 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()