X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=cea1476f1eef34df7db63a231c9b1ff54efe5224;hb=26ca01fdf8ab74e5cc443e83d96843a5bc272871;hp=53f61511ed480a242df760d6a1808d91ce2f4607;hpb=1c7c3eb6e1861e6293ea2d92a1aa0ae52c35ab20;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 53f6151..cea1476 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -5,7 +5,7 @@ are used in optimization, and have some additional nice methods beyond
 what can be supported in a general Jordan Algebra.
 """
 
-from itertools import repeat
+from itertools import izip, repeat
 
 from sage.algebras.quatalg.quaternion_algebra import QuaternionAlgebra
 from sage.categories.magmatic_algebras import MagmaticAlgebras
@@ -938,7 +938,7 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
             (_,x,_,_) = J._charpoly_matrix_system()
             p = J._charpoly_coeff(i)
             # p might be missing some vars, have to substitute "optionally"
-            pairs = zip(x.base_ring().gens(), self._basis_normalizers)
+            pairs = izip(x.base_ring().gens(), self._basis_normalizers)
             substitutions = { v: v*c for (v,c) in pairs }
             return p.subs(substitutions)
 
@@ -1022,24 +1022,16 @@ class RealMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
     @staticmethod
     def real_embed(M):
         """
-        Embed the matrix ``M`` into a space of real matrices.
-
-        The matrix ``M`` can have entries in any field at the moment:
-        the real numbers, complex numbers, or quaternions. And although
-        they are not a field, we can probably support octonions at some
-        point, too. This function returns a real matrix that "acts like"
-        the original with respect to matrix multiplication; i.e.
-
-          real_embed(M*N) = real_embed(M)*real_embed(N)
-
+        The identity function, for embedding real matrices into real
+        matrices.
         """
         return M
 
-
     @staticmethod
     def real_unembed(M):
         """
-        The inverse of :meth:`real_embed`.
+        The identity function, for unembedding real matrices from real
+        matrices.
         """
         return M