1. Add references and start citing them.
-2. Pre-cache charpoly for some more algebras.
+2. Profile (and fix?) any remaining slow operations.
-3. Profile the construction of "large" matrix algebras (like the
- 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
- they're so slow.
-
-4. What the ever-loving fuck is this shit?
-
- sage: O = Octonions(QQ)
- sage: e0 = O.monomial(0)
- sage: e0*[[[[]]]]
- [[[[]]]]*e0
-
-5. Every once in a long while, the test
+3. Every once in a long while, the test
sage: set_random_seed()
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...