X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=f34fc34701a214afd3d086a675844b44619e5d9a;hb=23ced4147cf68d9e5d7a00be958ad3c579436f50;hp=0d6edf2500664bbbad54e08b18f9e304765a7b6f;hpb=f8b068735ac7cb1d78c0166fbccdc3498f6b165a;p=sage.d.git diff --git a/mjo/eja/TODO b/mjo/eja/TODO index 0d6edf2..f34fc34 100644 --- a/mjo/eja/TODO +++ b/mjo/eja/TODO @@ -2,7 +2,8 @@ 2. Add references and start citing them. -3. Implement the octonion simple EJA. +3. Implement the octonion simple EJA. We don't actually need octonions + for this to work, only their real embedding (some 8x8 monstrosity). 4. Pre-cache charpoly for some small algebras? @@ -15,8 +16,31 @@ sage: a0 = (1/4)*X[4]**2*X[6]**2 - (1/2)*X[2]*X[5]*X[6]**2 - (1/2)*X[3]*X[4]*X[6 15-dimensional QuaternionHermitianAlgebra(3)) to find out why they're so slow. -6. We should compute whether or not the algebra is associative if it - is unknown. I guess the "associative" argument should be ternary - (True, False, None)? We should also figure out the correct - True/False values for the example classes, and of course add an - _is_associative() method. +6. Instead of storing a basis multiplication matrix, just make + product_on_basis() a cached method and manually cache its + entries. The cython cached method lookup should be faster than a + python-based matrix lookup anyway. NOTE: we should still be able + to recompute the table somehow. Is this worth it? + +7. What the ever-loving fuck is this shit? + + sage: O = Octonions(QQ) + sage: e0 = O.monomial(0) + sage: e0*[[[[]]]] + [[[[]]]]*e0 + +8. In fact, could my octonion matrix algebra be generalized for any + algebra of matrices over the reals whose entries are not real? Then + we wouldn't need real embeddings at all. They might even be fricking + vector spaces if I did that... + +9. Add HurwitzMatrixAlgebra subclass between MatrixAlgebra and + OctonionMatrixAlgebra. + +10. 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.