eja: get a rudimentary spectral decomposition for operators working.

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

diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index d486b4c604723b2a3e8544c2cf2644edb733d713..cf75e325697dcefb3bf682b855f8d83e3e4f89e2 100644 (file)
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -26,11 +26,11 @@ def gram_schmidt(v):
         sage: u = gram_schmidt(v)
         sage: all( u_i.inner_product(u_i).sqrt() == 1 for u_i in u )
         True
-        sage: u[0].inner_product(u[1]) == 0
+        sage: bool(u[0].inner_product(u[1]) == 0)
         True
-        sage: u[0].inner_product(u[2]) == 0
+        sage: bool(u[0].inner_product(u[2]) == 0)
         True
-        sage: u[1].inner_product(u[2]) == 0
+        sage: bool(u[1].inner_product(u[2]) == 0)
         True
 
     TESTS:
@@ -67,29 +67,10 @@ def gram_schmidt(v):
     # And now drop all zero vectors again if they were "orthogonalized out."
     v = [ v_i for v_i in v if not v_i.is_zero() ]
 
-    # Now pretend to normalize, building a new ring R that contains
-    # all of the necessary square roots.
-    norms_squared = [0]*len(v)
-
-    for i in xrange(len(v)):
-        norms_squared[i] = v[i].inner_product(v[i])
-        ns = [norms_squared[i].numerator(), norms_squared[i].denominator()]
-
-        # Do the numerator and denominator separately so that we
-        # adjoin e.g. sqrt(2) and sqrt(3) instead of sqrt(2/3).
-        for j in xrange(len(ns)):
-            PR = PolynomialRing(R, 'z')
-            z = PR.gen()
-            p = z**2 - ns[j]
-            if p.is_irreducible():
-                R = NumberField(p,
-                                'sqrt' + str(ns[j]),
-                                embedding=RLF(ns[j]).sqrt())
-
-    # When we're done, we have to change every element's ring to the
-    # extension that we wound up with, and then normalize it (which
-    # should work, since "R" contains its norm now).
+    # Just normalize. If the algebra is missing the roots, we can't add
+    # them here because then our subalgebra would have a bigger field
+    # than the superalgebra.
     for i in xrange(len(v)):
-        v[i] = v[i].change_ring(R) / R(norms_squared[i]).sqrt()
+        v[i] = v[i] / v[i].norm()
 
     return v