X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=9044860b8b8674c4110bde49edc2d46e9c999bfa;hb=667e0df9c07589c03616ad8cf42eebe5c86de50b;hp=c2f2b7c12ff92dbc0a57036057afad55acd63ddd;hpb=a4f0908c2216ff989161d33873102805d1c6aabd;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index c2f2b7c..9044860 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -1107,14 +1107,36 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
             [0 0 0 0 0 0 1 0]
             [0 0 0 0 0 0 0 1]
 
+        This also works in Cartesian product algebras::
+
+            sage: J1 = HadamardEJA(1)
+            sage: J2 = RealSymmetricEJA(2)
+            sage: J = cartesian_product([J1,J2])
+            sage: x = sum(J.gens())
+            sage: x.to_matrix()[0]
+            [1]
+            sage: x.to_matrix()[1]
+            [                  1 0.7071067811865475?]
+            [0.7071067811865475?                   1]
+
         """
         B = self.parent().matrix_basis()
         W = self.parent().matrix_space()
 
-        # This is just a manual "from_vector()", but of course
-        # matrix spaces aren't vector spaces in sage, so they
-        # don't have a from_vector() method.
-        return W.linear_combination( zip(B, self.to_vector()) )
+        if self.parent()._matrix_basis_is_cartesian:
+            # Aaaaand linear combinations don't work in Cartesian
+            # product spaces, even though they provide a method
+            # with that name.
+            pairs = zip(B, self.to_vector())
+            return sum( ( W(tuple(alpha*b_i for b_i in b))
+                          for (b,alpha) in pairs ),
+                        W.zero())
+        else:
+            # This is just a manual "from_vector()", but of course
+            # matrix spaces aren't vector spaces in sage, so they
+            # don't have a from_vector() method.
+            return W.linear_combination( zip(B, self.to_vector()) )
+
 
 
     def norm(self):
@@ -1412,12 +1434,8 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
             True
 
         """
-        from mjo.eja.eja_subalgebra import FiniteDimensionalEJASubalgebra
         powers = tuple( self**k for k in range(self.degree()) )
-        A = FiniteDimensionalEJASubalgebra(self.parent(),
-                                           powers,
-                                           associative=True,
-                                           **kwargs)
+        A = self.parent().subalgebra(powers, associative=True, **kwargs)
         A.one.set_cache(A(self.parent().one()))
         return A