eja: don't compute an unused vector space for the element subalgebra.

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

diff --git a/mjo/eja/eja_element_subalgebra.py b/mjo/eja/eja_element_subalgebra.py
index 7fbd0609d9578406cb3ce9a8683fc6e46c8a95e4..a26381b12dbe649d5dad9bc0cd056adbb1606f62 100644 (file)
--- a/mjo/eja/eja_element_subalgebra.py
+++ b/mjo/eja/eja_element_subalgebra.py
@@ -28,10 +28,6 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
 
             # Pick those out of the list of all powers.
             superalgebra_basis = tuple(map(powers.__getitem__, ind_rows))
-
-            # If our superalgebra is a subalgebra of something else, then
-            # these vectors won't have the right coordinates for
-            # V.span_of_basis() unless we use V.from_vector() on them.
             basis_vectors = map(power_vectors.__getitem__, ind_rows)
         else:
             # If we're going to orthonormalize the basis anyway, we
@@ -47,7 +43,11 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
             superalgebra_basis = [ self._superalgebra.from_vector(b)
                                    for b in basis_vectors ]
 
-        W = V.span_of_basis( V.from_vector(v) for v in basis_vectors )
+        fdeja = super(FiniteDimensionalEuclideanJordanElementSubalgebra, self)
+        fdeja.__init__(self._superalgebra,
+                       superalgebra_basis,
+                       category=category,
+                       check_axioms=False)
 
         # The rank is the highest possible degree of a minimal
         # polynomial, and is bounded above by the dimension. We know
@@ -55,37 +55,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         # polynomial has the same degree as the space's dimension
         # (remember how we constructed the space?), so that must be
         # its rank too.
-        rank = W.dimension()
-
-        fdeja = super(FiniteDimensionalEuclideanJordanElementSubalgebra, self)
-        return fdeja.__init__(self._superalgebra,
-                              superalgebra_basis,
-                              rank=rank,
-                              category=category)
-
-
-    def _a_regular_element(self):
-        """
-        Override the superalgebra method to return the one
-        regular element that is sure to exist in this
-        subalgebra, namely the element that generated it.
-
-        SETUP::
-
-            sage: from mjo.eja.eja_algebra import random_eja
-
-        TESTS::
-
-            sage: set_random_seed()
-            sage: J = random_eja().random_element().subalgebra_generated_by()
-            sage: J._a_regular_element().is_regular()
-            True
-
-        """
-        if self.dimension() == 0:
-            return self.zero()
-        else:
-            return self.monomial(1)
+        self.rank.set_cache(self.dimension())
 
 
     def one(self):
@@ -163,5 +133,10 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
             return self.zero()
         else:
             sa_one = self.superalgebra().one().to_vector()
-            sa_coords = self.vector_space().coordinate_vector(sa_one)
-            return self.from_vector(sa_coords)
+            # The extra hackery is because foo.to_vector() might not
+            # live in foo.parent().vector_space()!
+            coords = sum( a*b for (a,b)
+                          in zip(sa_one,
+                                 self.superalgebra().vector_space().basis()) )
+            return self.from_vector(self.vector_space().coordinate_vector(coords))
+