-1. Add CartesianProductEJA.
+1. Add references and start citing them.
-2. Check the axioms in the constructor when check != False?
+2. Profile (and fix?) any remaining slow operations.
-3. Add references and start citing them.
+3. Every once in a long while, the test
-4. Implement the octonion simple EJA.
+ sage: set_random_seed()
+ sage: x = random_eja().random_element()
+ sage: x.is_invertible() == (x.det() != 0)
-5. Factor out the Jordan axiom and norm tests once all of the
- algebras pass.
+ in eja_element.py returns False. Example:
-6. Create Element subclasses for the matrix EJAs, and then override
- their characteristic_polynomial() method to create a new algebra
- over the rationals (with a non-normalized basis). We can then
- compute the charpoly quickly by passing the natural representation
- of the given element into the new algebra and computing its charpoly
- there. (Relies on the theory to ensure that the charpolys are equal.)
\ No newline at end of file
+ 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