X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=2a13855ac7f3fdfbb61db04adc7649cc200d5fcf;hb=72a8ca0572c2846170bde9e3e46f48979b3aa0b0;hp=b8ceda8fa3defcb3df1a5641ab03eed28c910ee9;hpb=a21b1f2bf9bba6386185812c2804b5c17f0dd84b;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index b8ceda8..2a13855 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,19 +1,43 @@
-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. Implement the octonion simple EJA. We don't actually need octonions
+   for this to work, only their real embedding (some 8x8 monstrosity).
 
-1. Add CartesianProductEJA.
+3. Pre-cache charpoly for some small algebras?
 
-2. Check the axioms in the constructor when check != False?
+RealSymmetricEJA(4):
 
-3. Add references and start citing them.
+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]
 
-4. Implement the octonion simple EJA.
+4. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.
 
-5. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+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?
 
-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().
+6. What the ever-loving fuck is this shit?
+
+       sage: O = Octonions(QQ)
+       sage: e0 = O.monomial(0)
+       sage: e0*[[[[]]]]
+       [[[[]]]]*e0
+
+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...
+
+8. 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.
+
+9. Add an alias for AlbertAlgebra.