X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_utils.py;h=d4e9990ecc6749057905d3b1d5ac700bd34cdc71;hb=8f3ba1d9473195c1cbafe967a127800d90fde3ee;hp=81b5634bc921736b0d007f3df04013d0dc6df265;hpb=2108ec57e32e5417f92c4ccbff9df6fdad8a819d;p=sage.d.git

diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index 81b5634..d4e9990 100644
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -2,57 +2,6 @@ from sage.functions.other import sqrt
 from sage.matrix.constructor import matrix
 from sage.modules.free_module_element import vector
 
-def _change_ring(x, R):
-    r"""
-    Change the ring of a vector, matrix, or a cartesian product of
-    those things.
-
-    SETUP::
-
-        sage: from mjo.eja.eja_utils import _change_ring
-
-    EXAMPLES::
-
-        sage: v = vector(QQ, (1,2,3))
-        sage: m = matrix(QQ, [[1,2],[3,4]])
-        sage: _change_ring(v, RDF)
-        (1.0, 2.0, 3.0)
-        sage: _change_ring(m, RDF)
-        [1.0 2.0]
-        [3.0 4.0]
-        sage: _change_ring((v,m), RDF)
-        (
-                         [1.0 2.0]
-        (1.0, 2.0, 3.0), [3.0 4.0]
-        )
-        sage: V1 = cartesian_product([v.parent(), v.parent()])
-        sage: V = cartesian_product([v.parent(), V1])
-        sage: V((v, (v, v)))
-        ((1, 2, 3), ((1, 2, 3), (1, 2, 3)))
-        sage: _change_ring(V((v, (v, v))), RDF)
-        ((1.0, 2.0, 3.0), ((1.0, 2.0, 3.0), (1.0, 2.0, 3.0)))
-
-    """
-    try:
-        return x.change_ring(R)
-    except AttributeError:
-        try:
-            from sage.categories.sets_cat import cartesian_product
-            if hasattr(x, 'element_class'):
-                # x is a parent and we're in a recursive call.
-                return cartesian_product( [_change_ring(x_i, R)
-                                           for x_i in x.cartesian_factors()] )
-            else:
-                # x is an element, and we want to change the ring
-                # of its parent.
-                P = x.parent()
-                Q = cartesian_product( [_change_ring(P_i, R)
-                                        for P_i in P.cartesian_factors()] )
-                return Q(x)
-        except AttributeError:
-            # No parent for x
-            return x.__class__( _change_ring(x_i, R) for x_i in x )
-
 def _scale(x, alpha):
     r"""
     Scale the vector, matrix, or cartesian-product-of-those-things
@@ -97,9 +46,23 @@ 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: _all2list([[1]])
+        [1]
+
+    ::
+
         sage: V1 = VectorSpace(QQ,2)
         sage: V2 = MatrixSpace(QQ,2)
         sage: x1 = V1([1,1])
@@ -116,15 +79,45 @@ 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]
+
+    ::
+
+        sage: V1 = VectorSpace(QQ,2)
+        sage: V2 = OctonionMatrixAlgebra(1,field=QQ)
+        sage: C = cartesian_product([V1,V2])
+        sage: x1 = V1([3,4])
+        sage: y1 = V2.one()
+        sage: _all2list(C( (x1,y1) ))
+        [3, 4, 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 xl == [x]:
+        # Avoid the retardation of list(QQ(1)) == [1].
+        return [x]
+
+    return sum(list( map(_all2list, xl) ), [])
+
+
 
 def _mat2vec(m):
         return vector(m.base_ring(), m.list())
@@ -237,7 +230,14 @@ def gram_schmidt(v, inner_product=None):
     """
     if inner_product is None:
         inner_product = lambda x,y: x.inner_product(y)
-    norm = lambda x: inner_product(x,x).sqrt()
+    def norm(x):
+        ip = inner_product(x,x)
+        # Don't expand the given field; the inner-product's codomain
+        # is already correct. For example QQ(2).sqrt() returns sqrt(2)
+        # in SR, and that will give you weird errors about symbolics
+        # when what's really going wrong is that you're trying to
+        # orthonormalize in QQ.
+        return ip.parent()(ip.sqrt())
 
     v = list(v) # make a copy, don't clobber the input