X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_utils.py;h=29edf5b8a339b073e1426a12a98a6143e7af5069;hb=667e0df9c07589c03616ad8cf42eebe5c86de50b;hp=4d70e062c44e98ba90584fb0f97d3bbfef91e491;hpb=3c1c9170143a6412b050602cd79a383e3da6c821;p=sage.d.git

diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index 4d70e06..29edf5b 100644
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -1,9 +1,22 @@
 from sage.functions.other import sqrt
 from sage.matrix.constructor import matrix
 from sage.modules.free_module_element import vector
-from sage.rings.number_field.number_field import NumberField
-from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.real_lazy import RLF
+
+def _all2list(x):
+    r"""
+    Flatten a vector, matrix, or cartesian product of those things
+    into a long list.
+    """
+    if hasattr(x, 'list'):
+        # Easy case...
+        return x.list()
+    if hasattr(x, 'cartesian_factors'):
+        # If it's a formal cartesian product space element, then
+        # we also know what to do...
+        return sum(( x_i.list() for x_i in x ), [])
+    else:
+        # But what if it's a tuple or something else?
+        return sum( map(_all2list,x), [] )
 
 def _mat2vec(m):
         return vector(m.base_ring(), m.list())
@@ -64,6 +77,23 @@ def gram_schmidt(v, inner_product=None):
         sage: ip(u[1],u[2]).is_zero()
         True
 
+    This Gram-Schmidt routine can be used on matrices as well, so long
+    as an appropriate inner-product is provided::
+
+        sage: E11 = matrix(QQ, [ [1,0],
+        ....:                    [0,0] ])
+        sage: E12 = matrix(QQ, [ [0,1],
+        ....:                    [1,0] ])
+        sage: E22 = matrix(QQ, [ [0,0],
+        ....:                    [0,1] ])
+        sage: I = matrix.identity(QQ,2)
+        sage: trace_ip = lambda X,Y: (X*Y).trace()
+        sage: gram_schmidt([E11,E12,I,E22], inner_product=trace_ip)
+        [
+        [1 0]  [          0 1/2*sqrt(2)]  [0 0]
+        [0 0], [1/2*sqrt(2)           0], [0 1]
+        ]
+
     TESTS:
 
     Ensure that zero vectors don't get in the way::