eja: speed up det() for Cartesian product elements.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 693e8e2d03c0e2aadeb5cf52034fa112a2208f4b..47f6ff080c1d48a1a32b4903991aa0ec5bd0a502 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -6,6 +6,7 @@ from sage.modules.with_basis.indexed_element import IndexedFreeModuleElement
 from mjo.eja.eja_operator import FiniteDimensionalEJAOperator
 from mjo.eja.eja_utils import _scale
 
+
 class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
     """
     An element of a Euclidean Jordan algebra.
@@ -1121,18 +1122,10 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
         B = self.parent().matrix_basis()
         W = self.parent().matrix_space()
 
-        if hasattr(W, 'cartesian_factors'):
-            # 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
-            # _scale() function is slow.
-            pairs = zip(B, self.to_vector())
-            return W.sum( _scale(b, alpha) for (b,alpha) in pairs )
-        else:
-            # This is just a manual "from_vector()", but of course
-            # matrix spaces aren't vector spaces in sage, so they
-            # don't have a from_vector() method.
-            return W.linear_combination( zip(B, self.to_vector()) )
+        # This is just a manual "from_vector()", but of course
+        # matrix spaces aren't vector spaces in sage, so they
+        # don't have a from_vector() method.
+        return W.linear_combination( zip(B, self.to_vector()) )
 
 
 
@@ -1650,3 +1643,29 @@ 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() )
+
+    def to_matrix(self):
+        # An override is necessary to call our custom _scale().
+        B = self.parent().matrix_basis()
+        W = self.parent().matrix_space()
+
+        # 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
+        # _scale() function is slow.
+        pairs = zip(B, self.to_vector())
+        return W.sum( _scale(b, alpha) for (b,alpha) in pairs )