X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=80147dfa62ca0ab408d6da2f5a7ee047eb788f05;hb=1bae84b14cb9352727a670be01b5ef06dbcc7328;hp=51973d14822bdc5dd49065de77c1927883161ae9;hpb=19909f0fa338d79db1c003528eee3d1123713810;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 51973d1..80147df 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -694,7 +694,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             # not worry about it.
             raise NotImplementedError
 
-        n = ZZ.random_element(1, cls._max_test_case_size())
+        n = ZZ.random_element(cls._max_test_case_size()) + 1
         return cls(n, field, **kwargs)
 
 
@@ -899,7 +899,7 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
     def _max_test_case_size():
         # Play it safe, since this will be squared and the underlying
         # field can have dimension 4 (quaternions) too.
-        return 3
+        return 2
 
     @classmethod
     def _denormalized_basis(cls, n, field):
@@ -1138,7 +1138,7 @@ class RealSymmetricEJA(RealMatrixEuclideanJordanAlgebra):
 
     @staticmethod
     def _max_test_case_size():
-        return 5 # Dimension 10
+        return 4 # Dimension 10
 
 
 
@@ -1261,6 +1261,37 @@ class ComplexMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
         return matrix(F, n/2, elements)
 
 
+    @classmethod
+    def natural_inner_product(cls,X,Y):
+        """
+        Compute a natural inner product in this algebra directly from
+        its real embedding.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import ComplexHermitianEJA
+
+        TESTS:
+
+        This gives the same answer as the slow, default method implemented
+        in :class:`MatrixEuclideanJordanAlgebra`::
+
+            sage: set_random_seed()
+            sage: J = ComplexHermitianEJA.random_instance()
+            sage: x,y = J.random_elements(2)
+            sage: Xe = x.natural_representation()
+            sage: Ye = y.natural_representation()
+            sage: X = ComplexHermitianEJA.real_unembed(Xe)
+            sage: Y = ComplexHermitianEJA.real_unembed(Ye)
+            sage: expected = (X*Y).trace().vector()[0]
+            sage: actual = ComplexHermitianEJA.natural_inner_product(Xe,Ye)
+            sage: actual == expected
+            True
+
+        """
+        return RealMatrixEuclideanJordanAlgebra.natural_inner_product(X,Y)/2
+
+
 class ComplexHermitianEJA(ComplexMatrixEuclideanJordanAlgebra):
     """
     The rank-n simple EJA consisting of complex Hermitian n-by-n
@@ -1509,6 +1540,36 @@ class QuaternionMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
         return matrix(Q, n/4, elements)
 
 
+    @classmethod
+    def natural_inner_product(cls,X,Y):
+        """
+        Compute a natural inner product in this algebra directly from
+        its real embedding.
+
+        SETUP::
+
+            sage: from mjo.eja.eja_algebra import QuaternionHermitianEJA
+
+        TESTS:
+
+        This gives the same answer as the slow, default method implemented
+        in :class:`MatrixEuclideanJordanAlgebra`::
+
+            sage: set_random_seed()
+            sage: J = QuaternionHermitianEJA.random_instance()
+            sage: x,y = J.random_elements(2)
+            sage: Xe = x.natural_representation()
+            sage: Ye = y.natural_representation()
+            sage: X = QuaternionHermitianEJA.real_unembed(Xe)
+            sage: Y = QuaternionHermitianEJA.real_unembed(Ye)
+            sage: expected = (X*Y).trace().coefficient_tuple()[0]
+            sage: actual = QuaternionHermitianEJA.natural_inner_product(Xe,Ye)
+            sage: actual == expected
+            True
+
+        """
+        return RealMatrixEuclideanJordanAlgebra.natural_inner_product(X,Y)/4
+
 
 class QuaternionHermitianEJA(QuaternionMatrixEuclideanJordanAlgebra):
     """