X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=13b00ac6a3056eaf623ac5c2905be6c7d049706c;hp=67f390ba24f06e6d0f419609ddb8654afd0a65bf;hb=db1f7761ebf564221669137ae07476ea45d82a2c;hpb=33e3a4deff70731138dafc2857ba811b3c66f5b3 diff --git a/mjo/eja/TODO b/mjo/eja/TODO index 67f390b..13b00ac 100644 --- a/mjo/eja/TODO +++ b/mjo/eja/TODO @@ -1,17 +1,37 @@ -1. Add CartesianProductEJA. +1. Add cartesian products to random_eja(). -2. Check the axioms in the constructor when check != False? +2. Add references and start citing them. -3. Add references and start citing them. +3. Implement the octonion simple EJA. We don't actually need octonions + for this to work, only their real embedding (some 8x8 monstrosity). -4. Implement the octonion simple EJA. +4. Pre-cache charpoly for some small algebras? -5. Factor out the unit-norm basis (and operator symmetry) tests once - all of the algebras pass. +RealSymmetricEJA(4): -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: 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 + 15-dimensional QuaternionHermitianAlgebra(3)) to find out why + they're so slow. + +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. + +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.