eja: refactor _all2list to support forthcoming matrix algebras.

diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index 832dcef1fac0baa573b4883bc4e2ddd3fbfd55a8..430113d5cddaede7074ca9798f7f3f920a3e93ab 100644 (file)
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -46,9 +46,18 @@ def _all2list(x):
     Flatten a vector, matrix, or cartesian product of those things
     into a long list.
 
-    EXAMPLES::
+    If the entries of the matrix themselves belong to a real vector
+    space (such as the complex numbers which can be thought of as
+    pairs of real numbers), they will also be expanded in vector form
+    and flattened into the list.
+
+    SETUP::
 
         sage: from mjo.eja.eja_utils import _all2list
+        sage: from mjo.octonions import Octonions, OctonionMatrixAlgebra
+
+    EXAMPLES::
+
         sage: V1 = VectorSpace(QQ,2)
         sage: V2 = MatrixSpace(QQ,2)
         sage: x1 = V1([1,1])
@@ -65,15 +74,35 @@ def _all2list(x):
         sage: _all2list(M((x2,y2)))
         [1, -1, 0, 1, 1, 0]
 
+    ::
+
+        sage: _all2list(Octonions().one())
+        [1, 0, 0, 0, 0, 0, 0, 0]
+        sage: _all2list(OctonionMatrixAlgebra(1).one())
+        [1, 0, 0, 0, 0, 0, 0, 0]
+
     """
-    if hasattr(x, 'list'):
-        # Easy case...
-        return x.list()
-    else:
-        # But what if it's a tuple or something else? This has to
-        # handle cartesian products of cartesian products, too; that's
-        # why it's recursive.
-        return sum( map(_all2list,x), [] )
+    if hasattr(x, 'to_vector'):
+        # This works on matrices of e.g. octonions directly, without
+        # first needing to convert them to a list of octonions and
+        # then recursing down into the list. It also avoids the wonky
+        # list(x) when x is an element of a CFM. I don't know what it
+        # returns but it aint the coordinates. This will fall through
+        # to the iterable case the next time around.
+        return _all2list(x.to_vector())
+
+    try:
+        xl = list(x)
+    except TypeError: # x is not iterable
+        return [x]
+
+    if len(xl) == 1:
+        # Avoid the retardation of list(QQ(1)) == [1].
+        return xl
+
+    return sum(list( map(_all2list, xl) ), [])
+
+
 
 def _mat2vec(m):
         return vector(m.base_ring(), m.list())