X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=310e3073c667fb42b7591c0b8a989f590455e4fa;hb=197e8fdf8737fabde9003bd093cf45527afd4568;hp=b8ceda8fa3defcb3df1a5641ab03eed28c910ee9;hpb=0ed6dd869beb5fecd91e3653243e9c899b12c36b;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index b8ceda8..310e307 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,19 +1,38 @@
-A. Add tests for orthogonality in the Peirce decomposition.
+1. Add references and start citing them.
 
-B. Add support for a symmetric positive-definite bilinear form in
-   the JordanSpinEJA.
+2. Pre-cache charpoly for some small algebras?
 
-1. Add CartesianProductEJA.
+RealSymmetricEJA(4):
 
-2. Check the axioms in the constructor when check != False?
+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]
 
-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. 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?
 
-5. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+5. What the ever-loving fuck is this shit?
 
-6. Can we make the minimal and characteristic polynomial tests work
-   for trivial algebras, too? Then we wouldn't need the "nontrivial"
-   argument to random_eja().
+       sage: O = Octonions(QQ)
+       sage: e0 = O.monomial(0)
+       sage: e0*[[[[]]]]
+       [[[[]]]]*e0
+
+6. Can we convert the complex/quaternion algebras to avoid real-
+   (un)embeddings? Quaternions would need their own
+   QuaternionMatrixAlgebra, since Sage matrices have to have entries
+   in a commutative ring.
+
+7. 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.