X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=9a770ae5f68b3e19f3946ca7716f299a3ff82685;hb=9efefa3e54fc3e69e3f2c78457d50127a7a10131;hp=660cbb5c2d98d4135d465533a92ddba84720abdd;hpb=a0e9fb9e4c56781b9dad824bac517ca3e56ef461;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 660cbb5..9a770ae 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -4,7 +4,7 @@ from sage.modules.free_module import VectorSpace
 from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement
 
 from mjo.eja.eja_operator import FiniteDimensionalEJAOperator
-from mjo.eja.eja_utils import _mat2vec
+from mjo.eja.eja_utils import _mat2vec, _scale
 
 class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
     """
@@ -910,7 +910,7 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         M = matrix([(self.parent().one()).to_vector()])
         old_rank = 1
 
-        # Specifying the row-reduction algorithm can e.g.  help over
+        # Specifying the row-reduction algorithm can e.g. help over
         # AA because it avoids the RecursionError that gets thrown
         # when we have to look too hard for a root.
         #
@@ -1128,10 +1128,10 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         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.
+            # with that name. This is special-cased because the
+            # _scale() function is slow.
             pairs = zip(B, self.to_vector())
-            return sum( ( W(tuple(alpha*b_i for b_i in b))
-                          for (b,alpha) in pairs ),
+            return sum( ( _scale(b, alpha) for (b,alpha) in pairs ),
                         W.zero())
         else:
             # This is just a manual "from_vector()", but of course
@@ -1403,7 +1403,20 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         SETUP::
 
-            sage: from mjo.eja.eja_algebra import random_eja
+            sage: from mjo.eja.eja_algebra import (random_eja,
+            ....:                                  HadamardEJA,
+            ....:                                  RealSymmetricEJA)
+
+        EXAMPLES:
+
+        We can create subalgebras of Cartesian product EJAs that are not
+        themselves Cartesian product EJAs (they're just "regular" EJAs)::
+
+            sage: J1 = HadamardEJA(3)
+            sage: J2 = RealSymmetricEJA(2)
+            sage: J = cartesian_product([J1,J2])
+            sage: J.one().subalgebra_generated_by()
+            Euclidean Jordan algebra of dimension 1 over Algebraic Real Field
 
         TESTS:
 
@@ -1437,7 +1450,11 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
 
         """
         powers = tuple( self**k for k in range(self.degree()) )
-        A = self.parent().subalgebra(powers, associative=True, **kwargs)
+        A = self.parent().subalgebra(powers,
+                                     associative=True,
+                                     check_field=False,
+                                     check_axioms=False,
+                                     **kwargs)
         A.one.set_cache(A(self.parent().one()))
         return A