X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_subalgebra.py;h=9e5b010145b99f9442b5a86df8db3cd7d25048ad;hb=0ac5b5a3c8eb960b0f3c20a28c4d4bc0e33e5294;hp=7451e47bdbbbf2d58ce598aa3bb4e17ec42d5dae;hpb=ec7dbfb6ce0054f55280412e43870b4019abc40c;p=sage.d.git

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 7451e47..9e5b010 100644
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -71,6 +71,33 @@ class FiniteDimensionalEuclideanJordanElementSubalgebraElement(FiniteDimensional
 class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclideanJordanAlgebra):
     """
     The subalgebra of an EJA generated by a single element.
+
+    SETUP::
+
+        sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA,
+        ....:                                  JordanSpinEJA)
+
+    TESTS:
+
+    Ensure that our generator names don't conflict with the superalgebra::
+
+        sage: J = JordanSpinEJA(3)
+        sage: J.one().subalgebra_generated_by().gens()
+        (f0,)
+        sage: J = JordanSpinEJA(3, prefix='f')
+        sage: J.one().subalgebra_generated_by().gens()
+        (g0,)
+        sage: J = JordanSpinEJA(3, prefix='b')
+        sage: J.one().subalgebra_generated_by().gens()
+        (c0,)
+
+    Ensure that we can find subalgebras of subalgebras::
+
+        sage: A = ComplexHermitianEJA(3).one().subalgebra_generated_by()
+        sage: B = A.one().subalgebra_generated_by()
+        sage: B.dimension()
+        1
+
     """
     def __init__(self, elt):
         superalgebra = elt.parent()
@@ -79,11 +106,14 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         # the given element.
         V = superalgebra.vector_space()
         superalgebra_basis = [superalgebra.one()]
-        basis_vectors = [superalgebra.one().to_vector()]
+        # If our superalgebra is a subalgebra of something else, then
+        # superalgebra.one().to_vector() won't have the right
+        # coordinates unless we use V.from_vector() below.
+        basis_vectors = [V.from_vector(superalgebra.one().to_vector())]
         W = V.span_of_basis(basis_vectors)
         for exponent in range(1, V.dimension()):
             new_power = elt**exponent
-            basis_vectors.append( new_power.to_vector() )
+            basis_vectors.append( V.from_vector(new_power.to_vector()) )
             try:
                 W = V.span_of_basis(basis_vectors)
                 superalgebra_basis.append( new_power )
@@ -104,10 +134,24 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         for i in range(n):
             for j in range(n):
                 product = superalgebra_basis[i]*superalgebra_basis[j]
-                mult_table[i][j] = W.coordinate_vector(product.to_vector())
-
-        # TODO: We'll have to redo this and make it unique again...
-        prefix = 'f'
+                # product.to_vector() might live in a vector subspace
+                # if our parent algebra is already a subalgebra. We
+                # use V.from_vector() to make it "the right size" in
+                # that case.
+                product_vector = V.from_vector(product.to_vector())
+                mult_table[i][j] = W.coordinate_vector(product_vector)
+
+        # A half-assed attempt to ensure that we don't collide with
+        # the superalgebra's prefix (ignoring the fact that there
+        # could be super-superelgrbas in scope). If possible, we
+        # try to "increment" the parent algebra's prefix, although
+        # this idea goes out the window fast because some prefixen
+        # are off-limits.
+        prefixen = [ 'f', 'g', 'h', 'a', 'b', 'c', 'd' ]
+        try:
+            prefix = prefixen[prefixen.index(superalgebra.prefix()) + 1]
+        except ValueError:
+            prefix = prefixen[0]
 
         # The rank is the highest possible degree of a minimal
         # polynomial, and is bounded above by the dimension. We know
@@ -157,6 +201,12 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         ::
 
         """
+        if elt == 0:
+            # Just as in the superalgebra class, we need to hack
+            # this special case to ensure that random_element() can
+            # coerce a ring zero into the algebra.
+            return self.zero()
+
         if elt in self.superalgebra():
             coords = self.vector_space().coordinate_vector(elt.to_vector())
             return self.from_vector(coords)