eja: add some tests for new utility functions.

diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index 803ec636520515543c873ecc59669475a0048a3c..38e75761dab0394f3aa5e6e3016aed7c0edebbc8 100644 (file)
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -6,6 +6,26 @@ def _all2list(x):
     r"""
     Flatten a vector, matrix, or cartesian product of those things
     into a long list.
+
+    EXAMPLES::
+
+        sage: from mjo.eja.eja_utils import _all2list
+        sage: V1 = VectorSpace(QQ,2)
+        sage: V2 = MatrixSpace(QQ,2)
+        sage: x1 = V1([1,1])
+        sage: x2 = V1([1,-1])
+        sage: y1 = V2.one()
+        sage: y2 = V2([0,1,1,0])
+        sage: _all2list((x1,y1))
+        [1, 1, 1, 0, 0, 1]
+        sage: _all2list((x2,y2))
+        [1, -1, 0, 1, 1, 0]
+        sage: M = cartesian_product([V1,V2])
+        sage: _all2list(M((x1,y1)))
+        [1, 1, 1, 0, 0, 1]
+        sage: _all2list(M((x2,y2)))
+        [1, -1, 0, 1, 1, 0]
+
     """
     if hasattr(x, 'list'):
         # Easy case...
@@ -92,6 +112,28 @@ def gram_schmidt(v, inner_product=None):
         [0 0], [1/2*sqrt(2)           0], [0 1]
         ]
 
+    It even works on Cartesian product spaces whose factors are vector
+    or matrix spaces::
+
+        sage: V1 = VectorSpace(AA,2)
+        sage: V2 = MatrixSpace(AA,2)
+        sage: M = cartesian_product([V1,V2])
+        sage: x1 = V1([1,1])
+        sage: x2 = V1([1,-1])
+        sage: y1 = V2.one()
+        sage: y2 = V2([0,1,1,0])
+        sage: z1 = M((x1,y1))
+        sage: z2 = M((x2,y2))
+        sage: def ip(a,b):
+        ....:     return a[0].inner_product(b[0]) + (a[1]*b[1]).trace()
+        sage: U = gram_schmidt([z1,z2], inner_product=ip)
+        sage: ip(U[0],U[1])
+        0
+        sage: ip(U[0],U[0])
+        1
+        sage: ip(U[1],U[1])
+        1
+
     TESTS:
 
     Ensure that zero vectors don't get in the way::
@@ -102,7 +144,6 @@ def gram_schmidt(v, inner_product=None):
         sage: v = [v1,v2,v3]
         sage: len(gram_schmidt(v)) == 2
         True
-
     """
     if inner_product is None:
         inner_product = lambda x,y: x.inner_product(y)