X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=1f6112ca188124b114da9892d6a8aed283681161;hb=1c7418a9b9a3f6f41c95b785c9e4ec18c168d962;hp=07c49473a044411374583b60a15127096c355c2c;hpb=4e1d889fa70b660e789f31adb13f449c9f3a2fb1;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 07c4947..1f6112c 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -135,13 +135,17 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             return self.zero()
 
         natural_basis = self.natural_basis()
-        if elt not in natural_basis[0].matrix_space():
+        basis_space = natural_basis[0].matrix_space()
+        if elt not in basis_space:
             raise ValueError("not a naturally-represented algebra element")
 
-        # Thanks for nothing! Matrix spaces aren't vector
-        # spaces in Sage, so we have to figure out its
-        # natural-basis coordinates ourselves.
-        V = VectorSpace(elt.base_ring(), elt.nrows()*elt.ncols())
+        # Thanks for nothing! Matrix spaces aren't vector spaces in
+        # Sage, so we have to figure out its natural-basis coordinates
+        # ourselves. We use the basis space's ring instead of the
+        # element's ring because the basis space might be an algebraic
+        # closure whereas the base ring of the 3-by-3 identity matrix
+        # could be QQ instead of QQbar.
+        V = VectorSpace(basis_space.base_ring(), elt.nrows()*elt.ncols())
         W = V.span_of_basis( _mat2vec(s) for s in natural_basis )
         coords =  W.coordinate_vector(_mat2vec(elt))
         return self.from_vector(coords)
@@ -800,6 +804,19 @@ def random_eja():
 def _real_symmetric_basis(n, field):
     """
     Return a basis for the space of real symmetric n-by-n matrices.
+
+    SETUP::
+
+        sage: from mjo.eja.eja_algebra import _real_symmetric_basis
+
+    TESTS::
+
+        sage: set_random_seed()
+        sage: n = ZZ.random_element(1,5)
+        sage: B = _real_symmetric_basis(n, QQbar)
+        sage: all( M.is_symmetric() for M in  B)
+        True
+
     """
     # The basis of symmetric matrices, as matrices, in their R^(n-by-n)
     # coordinates.