eja: expand an existing subalgebra test.

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

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 0be85616678d4f7f7ffa276ddcd13ab907c6e116..292c770c8b2bb8d52ecc38c25c1170a36ded59bc 100644 (file)
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -56,6 +56,14 @@ class FiniteDimensionalEuclideanJordanSubalgebraElement(FiniteDimensionalEuclide
             f1
             sage: A(x).superalgebra_element()
             e0 + e1 + e2 + e3 + e4 + e5
+            sage: y = sum(A.gens())
+            sage: y
+            f0 + f1
+            sage: B = y.subalgebra_generated_by()
+            sage: B(y)
+            g1
+            sage: B(y).superalgebra_element()
+            f0 + f1
 
         TESTS:
 
@@ -70,10 +78,17 @@ class FiniteDimensionalEuclideanJordanSubalgebraElement(FiniteDimensionalEuclide
             sage: y = A.random_element()
             sage: A(y.superalgebra_element()) == y
             True
+            sage: B = y.subalgebra_generated_by()
+            sage: B(y).superalgebra_element() == y
+            True
 
         """
-        return self.parent().superalgebra().linear_combination(
-          zip(self.parent()._superalgebra_basis, self.to_vector()) )
+        W = self.parent().vector_space()
+        V = self.parent().superalgebra().vector_space()
+        A = W.basis_matrix().transpose()
+        W_coords = A*self.to_vector()
+        V_coords = V.coordinate_vector(W_coords)
+        return self.parent().superalgebra().from_vector(V_coords)
 
 
 
@@ -95,9 +110,9 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
     matrices do not contain the superalgebra's identity element::
 
         sage: J = RealSymmetricEJA(2)
-        sage: E11 = matrix(QQ, [ [1,0],
+        sage: E11 = matrix(AA, [ [1,0],
         ....:                    [0,0] ])
-        sage: E22 = matrix(QQ, [ [0,0],
+        sage: E22 = matrix(AA, [ [0,0],
         ....:                    [0,1] ])
         sage: K1 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E11),))
         sage: K1.one().natural_representation()
@@ -130,7 +145,7 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         1
 
     """
-    def __init__(self, superalgebra, basis, rank=None, category=None):
+    def __init__(self, superalgebra, basis, category=None, check_axioms=True):
         self._superalgebra = superalgebra
         V = self._superalgebra.vector_space()
         field = self._superalgebra.base_ring()
@@ -153,7 +168,11 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         superalgebra_basis = [ self._superalgebra.from_vector(b)
                                for b in basis_vectors ]
 
+        # 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.
         W = V.span_of_basis( V.from_vector(v) for v in basis_vectors )
+
         n = len(superalgebra_basis)
         mult_table = [[W.zero() for i in range(n)] for j in range(n)]
         for i in range(n):
@@ -171,16 +190,15 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
 
 
         self._vector_space = W
-        self._superalgebra_basis = superalgebra_basis
-
 
         fdeja = super(FiniteDimensionalEuclideanJordanSubalgebra, self)
-        return fdeja.__init__(field,
-                              mult_table,
-                              rank,
-                              prefix=prefix,
-                              category=category,
-                              natural_basis=natural_basis)
+        fdeja.__init__(field,
+                       mult_table,
+                       prefix=prefix,
+                       category=category,
+                       natural_basis=natural_basis,
+                       check_field=False,
+                       check_axioms=check_axioms)
 
 
 
@@ -198,7 +216,7 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         EXAMPLES::
 
             sage: J = RealSymmetricEJA(3)
-            sage: X = matrix(QQ, [ [0,0,1],
+            sage: X = matrix(AA, [ [0,0,1],
             ....:                  [0,1,0],
             ....:                  [1,0,0] ])
             sage: x = J(X)
@@ -215,8 +233,12 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         if elt not in self.superalgebra():
             raise ValueError("not an element of this subalgebra")
 
-        coords = self.vector_space().coordinate_vector(elt.to_vector())
-        return self.from_vector(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(elt.to_vector(),
+                                 self.superalgebra().vector_space().basis()) )
+        return self.from_vector(self.vector_space().coordinate_vector(coords))
 
 
 
@@ -249,10 +271,10 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         EXAMPLES::
 
             sage: J = RealSymmetricEJA(3)
-            sage: E11 = matrix(QQ, [ [1,0,0],
+            sage: E11 = matrix(ZZ, [ [1,0,0],
             ....:                    [0,0,0],
             ....:                    [0,0,0] ])
-            sage: E22 = matrix(QQ, [ [0,0,0],
+            sage: E22 = matrix(ZZ, [ [0,0,0],
             ....:                    [0,1,0],
             ....:                    [0,0,0] ])
             sage: b1 = J(E11)