X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=e6aba200a90a0317150bde9093f6a28569d2db74;hb=3f49e3bf2b85b1918c1abb0e8973a6f203dabc86;hp=ee2b52665e8a7d73b50fb4e159430627bcf8b36b;hpb=63d9a1be5861241fb7f02838a74589cf56c2548e;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index ee2b526..e6aba20 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -347,14 +347,19 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         # its own set of non-ambient coordinates (in terms of the
         # supplied basis).
         vector_basis = tuple( V(_all2list(b)) for b in basis )
-        W = V.span_of_basis( vector_basis, check=check_axioms)
+
+        # Save the span of our matrix basis (when written out as long
+        # vectors) because otherwise we'll have to reconstruct it
+        # every time we want to coerce a matrix into the algebra.
+        self._matrix_span = V.span_of_basis( vector_basis, check=check_axioms)
 
         if orthonormalize:
-            # Now "W" is the vector space of our algebra coordinates. The
-            # variables "X1", "X2",...  refer to the entries of vectors in
-            # W. Thus to convert back and forth between the orthonormal
-            # coordinates and the given ones, we need to stick the original
-            # basis in W.
+            # Now "self._matrix_span" is the vector space of our
+            # algebra coordinates. The variables "X1", "X2",...  refer
+            # to the entries of vectors in self._matrix_span. Thus to
+            # convert back and forth between the orthonormal
+            # coordinates and the given ones, we need to stick the
+            # original basis in self._matrix_span.
             U = V.span_of_basis( deortho_vector_basis, check=check_axioms)
             self._deortho_matrix = matrix.column( U.coordinate_vector(q)
                                                   for q in vector_basis )
@@ -378,7 +383,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
                 # The jordan product returns a matrixy answer, so we
                 # have to convert it to the algebra coordinates.
                 elt = jordan_product(q_i, q_j)
-                elt = W.coordinate_vector(V(_all2list(elt)))
+                elt = self._matrix_span.coordinate_vector(V(_all2list(elt)))
                 self._multiplication_table[i][j] = self.from_vector(elt)
 
                 if not orthonormalize:
@@ -685,8 +690,8 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
 
     def _element_constructor_(self, elt):
         """
-        Construct an element of this algebra from its vector or matrix
-        representation.
+        Construct an element of this algebra or a subalgebra from its
+        EJA element, vector, or matrix representation.
 
         This gets called only after the parent element _call_ method
         fails to find a coercion for the argument.
@@ -725,6 +730,16 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             sage: J( (J1.matrix_basis()[1], J2.matrix_basis()[2]) )
             b1 + b5
 
+        Subalgebra elements are embedded into the superalgebra::
+
+            sage: J = JordanSpinEJA(3)
+            sage: J.one()
+            b0
+            sage: x = sum(J.gens())
+            sage: A = x.subalgebra_generated_by()
+            sage: J(A.one())
+            b0
+
         TESTS:
 
         Ensure that we can convert any element back and forth
@@ -749,6 +764,7 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             Traceback (most recent call last):
             ...
             ValueError: not an element of this algebra
+
         """
         msg = "not an element of this algebra"
         if elt in self.base_ring():
@@ -758,13 +774,16 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
             # that the integer 3 belongs to the space of 2-by-2 matrices.
             raise ValueError(msg)
 
-        try:
-            # Try to convert a vector into a column-matrix...
+        if hasattr(elt, 'superalgebra_element'):
+            # Handle subalgebra elements
+            if elt.parent().superalgebra() == self:
+                return elt.superalgebra_element()
+
+        if hasattr(elt, 'sparse_vector'):
+            # Convert a vector into a column-matrix. We check for
+            # "sparse_vector" and not "column" because matrices also
+            # have a "column" method.
             elt = elt.column()
-        except (AttributeError, TypeError):
-            # and ignore failure, because we weren't really expecting
-            # a vector as an argument anyway.
-            pass
 
         if elt not in self.matrix_space():
             raise ValueError(msg)
@@ -781,15 +800,10 @@ class FiniteDimensionalEJA(CombinatorialFreeModule):
         # is that we're already converting everything to long vectors,
         # and that strategy works for tuples as well.
         #
-        # We pass check=False because the matrix basis is "guaranteed"
-        # to be linearly independent... right? Ha ha.
-        elt = _all2list(elt)
-        V = VectorSpace(self.base_ring(), len(elt))
-        W = V.span_of_basis( (V(_all2list(s)) for s in self.matrix_basis()),
-                             check=False)
+        elt = self._matrix_span.ambient_vector_space()(_all2list(elt))
 
         try:
-            coords = W.coordinate_vector(V(elt))
+            coords = self._matrix_span.coordinate_vector(elt)
         except ArithmeticError:  # vector is not in free module
             raise ValueError(msg)