sage: x = random_eja().random_element()
sage: x.is_invertible() == (x.det() != 0)
- in eja_element.py returns False.
+ in eja_element.py returns False. Example:
+
+ sage: J1 = ComplexHermitianEJA(2)
+ sage: J2 = TrivialEJA()
+ sage: J = cartesian_product([J1,J2])
+ sage: x = J.from_vector(vector(QQ, [-1, -1/2, -1/2, -1/2]))
+ sage: x.is_invertible()
+ True
+ sage: x.det()
+ 0
+
+4. When we take a Cartesian product involving a trivial algebra, we
+ could easily cache the identity and charpoly coefficients using
+ the nontrivial factor. On the other hand, it's nice that we can
+ test out some alternate code paths...