eja: refactor _all2list to support forthcoming matrix algebras.

[sage.d.git] / mjo / eja / eja_utils.py

diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index c25b81921e1be4f0d6a77580227cb8692e21605f..430113d5cddaede7074ca9798f7f3f920a3e93ab 100644 (file)
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -6,6 +6,32 @@ def _scale(x, alpha):
     r"""
     Scale the vector, matrix, or cartesian-product-of-those-things
     ``x`` by ``alpha``.
+
+    This works around the inability to scale certain elements of
+    Cartesian product spaces, as reported in
+
+      https://trac.sagemath.org/ticket/31435
+
+    ..WARNING:
+
+        This will do the wrong thing if you feed it a tuple or list.
+
+    SETUP::
+
+        sage: from mjo.eja.eja_utils import _scale
+
+    EXAMPLES::
+
+        sage: v = vector(QQ, (1,2,3))
+        sage: _scale(v,2)
+        (2, 4, 6)
+        sage: m = matrix(QQ, [[1,2],[3,4]])
+        sage: M = cartesian_product([m.parent(), m.parent()])
+        sage: _scale(M((m,m)), 2)
+        ([2 4]
+        [6 8], [2 4]
+        [6 8])
+
     """
     if hasattr(x, 'cartesian_factors'):
         P = x.parent()
@@ -14,14 +40,24 @@ def _scale(x, alpha):
     else:
         return x*alpha
 
+
 def _all2list(x):
     r"""
     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])
@@ -38,15 +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())