X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=3659694fe27625939b76de434c8a882a60e6faef;hp=1cf6fa51dd2626df1e75dcaeab95fc743000130f;hb=3105d9a726d9fd18569ed733d16078be7160362e;hpb=8ccf1d8af20cea17897aed21426b17872fd0fca3

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 1cf6fa5..3659694 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -2586,7 +2586,40 @@ class QuaternionHermitianEJA(ConcreteEJA, QuaternionMatrixEJA):
         return cls(n, **kwargs)
 
 class OctonionHermitianEJA(FiniteDimensionalEJA, MatrixEJA):
+    r"""
+
+    SETUP::
 
+        sage: from mjo.eja.eja_algebra import OctonionHermitianEJA
+
+    EXAMPLES:
+
+    The 3-by-3 algebra satisfies the axioms of an EJA::
+
+        sage: OctonionHermitianEJA(3,                    # long time
+        ....:                      field=QQ,             # long time
+        ....:                      orthonormalize=False, # long time
+        ....:                      check_axioms=True)    # long time
+        Euclidean Jordan algebra of dimension 27 over Rational Field
+
+    TESTS::
+
+        sage: J = OctonionHermitianEJA(3,                    # long time
+        ....:                          field=QQ,             # long time
+        ....:                          orthonormalize=False) # long time
+        sage: J.one.clear_cache()                            # long time
+        sage: J.one()                                        # long time
+        b0 + b9 + b26
+        sage: J.one().to_matrix()                            # long time
+        +----+----+----+
+        | e0 | 0  | 0  |
+        +----+----+----+
+        | 0  | e0 | 0  |
+        +----+----+----+
+        | 0  | 0  | e0 |
+        +----+----+----+
+
+    """
     def __init__(self, n, field=AA, **kwargs):
         if n > 3:
             # Otherwise we don't get an EJA.
@@ -2599,6 +2632,7 @@ class OctonionHermitianEJA(FiniteDimensionalEJA, MatrixEJA):
         super().__init__(self._denormalized_basis(n,field),
                          self.jordan_product,
                          self.trace_inner_product,
+                         field=field,
                          **kwargs)
 
         # TODO: this could be factored out somehow, but is left here
@@ -2621,7 +2655,7 @@ class OctonionHermitianEJA(FiniteDimensionalEJA, MatrixEJA):
 
         EXAMPLES::
 
-            sage: B = OctonionHermitianEJA._denormalized_basis(3)
+            sage: B = OctonionHermitianEJA._denormalized_basis(3,QQ)
             sage: all( M.is_hermitian() for M in B )
             True
             sage: len(B)