X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=6750f228451b5ec2052efc3974ddee72cd0d0c12;hb=02cbbda68c8efd79b3c9735d5eca7e7162b24840;hp=f2d7ba70c82ae38375d3496521eef14463566897;hpb=2e4211deee2c4556f2c2b4dccc857106ce6bc89a;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index f2d7ba7..6750f22 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -32,22 +32,21 @@ for these simple algebras:
   * :class:`RealSymmetricEJA`
   * :class:`ComplexHermitianEJA`
   * :class:`QuaternionHermitianEJA`
+  * :class:`OctonionHermitianEJA`
 
-Missing from this list is the algebra of three-by-three octononion
-Hermitian matrices, as there is (as of yet) no implementation of the
-octonions in SageMath. In addition to these, we provide two other
-example constructions,
+In addition to these, we provide two other example constructions,
 
   * :class:`HadamardEJA`
   * :class:`TrivialEJA`
 
 The Jordan spin algebra is a bilinear form algebra where the bilinear
 form is the identity. The Hadamard EJA is simply a Cartesian product
-of one-dimensional spin algebras. And last but not least, the trivial
-EJA is exactly what you think. Cartesian products of these are also
-supported using the usual ``cartesian_product()`` function; as a
-result, we support (up to isomorphism) all Euclidean Jordan algebras
-that don't involve octonions.
+of one-dimensional spin algebras. And last but least, the trivial EJA
+is exactly what you think it is; it could also be obtained by
+constructing a dimension-zero instance of any of the other
+algebras. Cartesian products of these are also supported using the
+usual ``cartesian_product()`` function; as a result, we support (up to
+isomorphism) all Euclidean Jordan algebras.
 
 SETUP::
 
@@ -1543,7 +1542,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
 class RationalBasisEJA(FiniteDimensionalEJA):
     r"""
-    New class for algebras whose supplied basis elements have all rational entries.
+    Algebras whose supplied basis elements have all rational entries.
 
     SETUP::
 
@@ -2585,7 +2584,7 @@ class QuaternionHermitianEJA(ConcreteEJA,
         n = ZZ.random_element(cls._max_random_instance_size() + 1)
         return cls(n, **kwargs)
 
-class OctonionHermitianEJA(FiniteDimensionalEJA, MatrixEJA):
+class OctonionHermitianEJA(ConcreteEJA, MatrixEJA):
     r"""
     SETUP::
 
@@ -2668,7 +2667,23 @@ class OctonionHermitianEJA(FiniteDimensionalEJA, MatrixEJA):
         sage: J.rank.clear_cache()                           # long time
         sage: J.rank()                                       # long time
         2
+
     """
+    @staticmethod
+    def _max_random_instance_size():
+        r"""
+        The maximum rank of a random QuaternionHermitianEJA.
+        """
+        return 1 # Dimension 1
+
+    @classmethod
+    def random_instance(cls, **kwargs):
+        """
+        Return a random instance of this type of algebra.
+        """
+        n = ZZ.random_element(cls._max_random_instance_size() + 1)
+        return cls(n, **kwargs)
+
     def __init__(self, n, field=AA, **kwargs):
         if n > 3:
             # Otherwise we don't get an EJA.
@@ -3642,7 +3657,9 @@ class RationalBasisCartesianProductEJA(CartesianProductEJA,
 
     SETUP::
 
-        sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
+        sage: from mjo.eja.eja_algebra import (HadamardEJA,
+        ....:                                  JordanSpinEJA,
+        ....:                                  OctonionHermitianEJA,
         ....:                                  RealSymmetricEJA)
 
     EXAMPLES:
@@ -3659,15 +3676,32 @@ class RationalBasisCartesianProductEJA(CartesianProductEJA,
         sage: J.rank()
         5
 
+    TESTS:
+
+    The ``cartesian_product()`` function only uses the first factor to
+    decide where the result will live; thus we have to be careful to
+    check that all factors do indeed have a `_rational_algebra` member
+    before we try to access it::
+
+        sage: J1 = OctonionHermitianEJA(1) # no rational basis
+        sage: J2 = HadamardEJA(2)
+        sage: cartesian_product([J1,J2])
+        Euclidean Jordan algebra of dimension 1 over Algebraic Real Field
+        (+) Euclidean Jordan algebra of dimension 2 over Algebraic Real Field
+        sage: cartesian_product([J2,J1])
+        Euclidean Jordan algebra of dimension 2 over Algebraic Real Field
+        (+) Euclidean Jordan algebra of dimension 1 over Algebraic Real Field
+
     """
     def __init__(self, algebras, **kwargs):
         CartesianProductEJA.__init__(self, algebras, **kwargs)
 
         self._rational_algebra = None
         if self.vector_space().base_field() is not QQ:
-            self._rational_algebra = cartesian_product([
-                r._rational_algebra for r in algebras
-            ])
+            if all( hasattr(r, "_rational_algebra") for r in algebras ):
+                self._rational_algebra = cartesian_product([
+                    r._rational_algebra for r in algebras
+                ])
 
 
 RationalBasisEJA.CartesianProduct = RationalBasisCartesianProductEJA