eja: add a comment about sub-subalgebra representations.

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

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index ac77f22a691e7cc04138e34cae46f148909de0f8..85ada0705fe8073fa80500d4719c38a5ea16a576 100644 (file)
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -130,7 +130,7 @@ 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 +153,11 @@ 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):
@@ -175,12 +179,13 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
 
 
         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)
 
 
 
@@ -215,8 +220,12 @@ 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))