X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=81c2b54fca757f0696468b5c450a6dda674a0f7a;hb=78bee5c30c1cd2828d9834fc7d652db21331d4fe;hp=9044860b8b8674c4110bde49edc2d46e9c999bfa;hpb=667e0df9c07589c03616ad8cf42eebe5c86de50b;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 9044860..81c2b54 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):
     """
@@ -664,7 +664,7 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         element should always be in terms of minimal idempotents::
 
             sage: J = JordanSpinEJA(4)
-            sage: x = sum( i*J.gens()[i] for i in range(len(J.gens())) )
+            sage: x = sum( i*J.monomial(i) for i in range(len(J.gens())) )
             sage: x.is_regular()
             True
             sage: [ c.is_primitive_idempotent()
@@ -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.
         #
@@ -1077,7 +1077,9 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         SETUP::
 
             sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
-            ....:                                  QuaternionHermitianEJA)
+            ....:                                  HadamardEJA,
+            ....:                                  QuaternionHermitianEJA,
+            ....:                                  RealSymmetricEJA)
 
         EXAMPLES::
 
@@ -1123,14 +1125,13 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         B = self.parent().matrix_basis()
         W = self.parent().matrix_space()
 
-        if self.parent()._matrix_basis_is_cartesian:
+        if hasattr(W, 'cartesian_factors'):
             # Aaaaand linear combinations don't work in Cartesian
-            # product spaces, even though they provide a method
-            # with that name.
+            # product spaces, even though they provide a method with
+            # that name. This is hidden behind an "if" 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 ),
-                        W.zero())
+            return W.sum( _scale(b, alpha) for (b,alpha) in pairs )
         else:
             # This is just a manual "from_vector()", but of course
             # matrix spaces aren't vector spaces in sage, so they
@@ -1401,7 +1402,20 @@ 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:
 
@@ -1435,7 +1449,11 @@ 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