From a0360717be0553d801a972c0cda6effe657f894a Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sat, 6 Mar 2021 13:35:33 -0500 Subject: [PATCH] eja: remove the (completed) Cartesian product TODO. --- mjo/eja/TODO | 18 ++++++++---------- 1 file changed, 8 insertions(+), 10 deletions(-) diff --git a/mjo/eja/TODO b/mjo/eja/TODO index f2e71c8..0624ddb 100644 --- a/mjo/eja/TODO +++ b/mjo/eja/TODO @@ -1,40 +1,38 @@ -1. Add cartesian products to random_eja(). +1. Add references and start citing them. -2. Add references and start citing them. - -3. Implement the octonion simple EJA. We don't actually need octonions +2. 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? +3. Pre-cache charpoly for some small algebras? RealSymmetricEJA(4): sage: F = J.base_ring() 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]*X[7] + (F(2).sqrt()/2)*X[1]*X[5]*X[6]*X[7] + (1/4)*X[3]**2*X[7]**2 - (1/2)*X[0]*X[5]*X[7]**2 + (F(2).sqrt()/2)*X[2]*X[3]*X[6]*X[8] - (1/2)*X[1]*X[4]*X[6*X[8] - (1/2)*X[1]*X[3]*X[7]*X[8] + (F(2).sqrt()/2)*X[0]*X[4]*X[7]*X[8] + (1/4)*X[1]**2*X[8]**2 - (1/2)*X[0]*X[2]*X[8]**2 - (1/2)*X[2]*X[3]**2*X[9] + (F(2).sqrt()/2)*X[1]*X[3]*X[4]*X[9] - (1/2)*X[0]*X[4]**2*X[9] - (1/2)*X[1]**2*X[5]*X[9] + X[0]*X[2]*X[5]*X[9] -5. Profile the construction of "large" matrix algebras (like the +4. Profile the construction of "large" matrix algebras (like the 15-dimensional QuaternionHermitianAlgebra(3)) to find out why they're so slow. -6. Instead of storing a basis multiplication matrix, just make +5. 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? +6. 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 +7. 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. Every once in a long while, the test +8. Every once in a long while, the test sage: set_random_seed() sage: x = random_eja().random_element() -- 2.43.2