X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=ca3df5fea55949225a51f8255a2c13a33c37d9f2;hb=7f55521ab4652d3ca10cd085f8e9d41bf149e8e5;hp=43f8021706fdeaa20033043ae31d808b00bc007a;hpb=f8a4f27fc914955d6dd38108f7cdebbdc2103a8d;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 43f8021..ca3df5f 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -36,17 +36,21 @@ for these simple algebras:
 
 In addition to these, we provide two other example constructions,
 
+  * :class:`JordanSpinEJA`
   * :class:`HadamardEJA`
+  * :class:`AlbertEJA`
   * :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 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.
+of one-dimensional spin algebras. The Albert EJA is simply a special
+case of the :class:`OctonionHermitianEJA` where the matrices are
+three-by-three and the resulting space has dimension 27. And
+last/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::
 
@@ -58,8 +62,6 @@ EXAMPLES::
     Euclidean Jordan algebra of dimension...
 """
 
-from itertools import repeat
-
 from sage.algebras.quatalg.quaternion_algebra import QuaternionAlgebra
 from sage.categories.magmatic_algebras import MagmaticAlgebras
 from sage.categories.sets_cat import cartesian_product
@@ -1542,7 +1544,7 @@ 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::
 
@@ -2584,7 +2586,7 @@ 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::
 
@@ -2667,7 +2669,23 @@ 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.
@@ -2754,6 +2772,28 @@ class OctonionHermitianEJA(FiniteDimensionalEJA, MatrixEJA):
         """
         return (X*Y).trace().real().coefficient(0)
 
+
+class AlbertEJA(OctonionHermitianEJA):
+    r"""
+    The Albert algebra is the algebra of three-by-three Hermitian
+    matrices whose entries are octonions.
+
+    SETUP::
+
+        from mjo.eja.eja_algebra import AlbertEJA
+
+    EXAMPLES::
+
+        sage: AlbertEJA(field=QQ, orthonormalize=False)
+        Euclidean Jordan algebra of dimension 27 over Rational Field
+        sage: AlbertEJA() # long time
+        Euclidean Jordan algebra of dimension 27 over Algebraic Real Field
+
+    """
+    def __init__(self, *args, **kwargs):
+        super().__init__(3, *args, **kwargs)
+
+
 class HadamardEJA(ConcreteEJA, RationalBasisEJA):
     """
     Return the Euclidean Jordan Algebra corresponding to the set
@@ -3641,7 +3681,9 @@ class RationalBasisCartesianProductEJA(CartesianProductEJA,
 
     SETUP::
 
-        sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
+        sage: from mjo.eja.eja_algebra import (HadamardEJA,
+        ....:                                  JordanSpinEJA,
+        ....:                                  OctonionHermitianEJA,
         ....:                                  RealSymmetricEJA)
 
     EXAMPLES:
@@ -3658,15 +3700,32 @@ 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