-1. Add CartesianProductEJA.
+1. Add references and start citing them.
-2. Check the axioms in the constructor when check != False?
+2. Pre-cache charpoly for some more algebras.
-3. Add references and start citing them.
+3. Profile the construction of "large" matrix algebras (like the
+ 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+ they're so slow.
-4. Implement the octonion simple EJA.
+4. What the ever-loving fuck is this shit?
-5. Factor out the unit-norm basis (and operator symmetry) tests once
- all of the algebras pass.
+ sage: O = Octonions(QQ)
+ sage: e0 = O.monomial(0)
+ sage: e0*[[[[]]]]
+ [[[[]]]]*e0
-6. Implement spectral projector decomposition for EJA operators
- using jordan_form() or eigenmatrix_right(). I suppose we can
- ignore the problem of base rings for now and just let it crash
- if we're not using AA as our base field.
+5. Every once in a long while, the test
-7. Do we really need to orthonormalize the basis in a subalgebra?
- So long as we can decompose the operator (which is invariant
- under changes of basis), who cares?
+ sage: set_random_seed()
+ sage: x = random_eja().random_element()
+ sage: x.is_invertible() == (x.det() != 0)
-8. Ensure that we can construct all algebras over both AA and RR.
-
-9. Check that our field is a subring of RLF.
+ in eja_element.py returns False.