+
+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() )