eja: improve a gram_schmidt() error message.

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

diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index 832dcef1fac0baa573b4883bc4e2ddd3fbfd55a8..d4e9990ecc6749057905d3b1d5ac700bd34cdc71 100644 (file)
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -46,9 +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])
@@ -65,15 +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())
@@ -186,7 +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