X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=8af3b77698457486af3d5b64eb52bf6f6e7b5ea8;hb=c38ce6eab53954221d4f944ea0ad4ac27f323023;hp=235047a153f0594bf450987ae2988a5873d92f36;hpb=ec4c9a49813109790d461da06d4f64219fa4bf8c;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 235047a..8af3b77 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -3,11 +3,11 @@ from sage.misc.cachefunc import cached_method
 from sage.modules.free_module import VectorSpace
 from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement
 
-from mjo.eja.eja_operator import FiniteDimensionalEJAOperator
+from mjo.eja.eja_operator import EJAOperator
 from mjo.eja.eja_utils import _scale
 
 
-class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
+class EJAElement(IndexedFreeModuleElement):
     """
     An element of a Euclidean Jordan algebra.
     """
@@ -1162,7 +1162,7 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         P = self.parent()
         left_mult_by_self = lambda y: self*y
         L = P.module_morphism(function=left_mult_by_self, codomain=P)
-        return FiniteDimensionalEJAOperator(P, P, L.matrix() )
+        return EJAOperator(P, P, L.matrix() )
 
 
     def quadratic_representation(self, other=None):
@@ -1722,19 +1722,18 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         return self.trace_inner_product(self).sqrt()
 
 
-class CartesianProductEJAElement(FiniteDimensionalEJAElement):
-    def det(self):
-        r"""
-        Compute the determinant of this product-element using the
-        determianants of its factors.
-
-        This result Follows from the spectral decomposition of (say)
-        the pair `(x,y)` in terms of the Jordan frame `\left\{ (c_1,
-        0),(c_2, 0),...,(0,d_1),(0,d_2),... \right\}.
-        """
-        from sage.misc.misc_c import prod
-        return prod( f.det() for f in self.cartesian_factors() )
+class CartesianProductParentEJAElement(EJAElement):
+    r"""
+    An intermediate class for elements that have a Cartesian
+    product as their parent algebra.
 
+    This is needed because the ``to_matrix`` method (which gives you a
+    representation from the superalgebra) needs to do special stuff
+    for Cartesian products. Specifically, an EJA subalgebra of a
+    Cartesian product EJA will not itself be a Cartesian product (it
+    has its own basis) -- but we want ``to_matrix()`` to be able to
+    give us a Cartesian product representation.
+    """
     def to_matrix(self):
         # An override is necessary to call our custom _scale().
         B = self.parent().matrix_basis()
@@ -1742,7 +1741,20 @@ class CartesianProductEJAElement(FiniteDimensionalEJAElement):
 
         # Aaaaand linear combinations don't work in Cartesian
         # product spaces, even though they provide a method with
-        # that name. This is hidden behind an "if" because the
+        # that name. This is hidden in a subclass because the
         # _scale() function is slow.
         pairs = zip(B, self.to_vector())
         return W.sum( _scale(b, alpha) for (b,alpha) in pairs )
+
+class CartesianProductEJAElement(CartesianProductParentEJAElement):
+    def det(self):
+        r"""
+        Compute the determinant of this product-element using the
+        determianants of its factors.
+
+        This result Follows from the spectral decomposition of (say)
+        the pair `(x,y)` in terms of the Jordan frame `\left\{ (c_1,
+        0),(c_2, 0),...,(0,d_1),(0,d_2),... \right\}.
+        """
+        from sage.misc.misc_c import prod
+        return prod( f.det() for f in self.cartesian_factors() )