X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=f34fc34701a214afd3d086a675844b44619e5d9a;hb=23ced4147cf68d9e5d7a00be958ad3c579436f50;hp=b27f2f12875e317fd2b088a74d7395c84ab8e454;hpb=bfaac3f5d42f31fabb37a5260fd5b870f639ea59;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index b27f2f1..f34fc34 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,32 +1,46 @@
-1. Add CartesianProductEJA.
+1. Add cartesian products to random_eja().
 
 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. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+4. Pre-cache charpoly for some small algebras?
 
-5. Override inner_product(), _max_test_case_size(), et cetera in
-   DirectSumEJA.
+RealSymmetricEJA(4):
 
-6. Switch to QQ in *all* algebras for _charpoly_coefficients().
-   This only works when we know that the basis can be rationalized...
-   which is the case at least for the concrete EJAs we provide,
-   but not in general.
+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]
 
-7. Pass already_echelonized (default: False) and echelon_basis
-   (default: None) into the subalgebra constructor. The value of
-   already_echelonized can be passed to V.span_of_basis() to save
-   some time, and usinf e.g. FreeModule_submodule_with_basis_field
-   we may somehow be able to pass the echelon basis straight in to
-   save time.
+5. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.
 
-   This may require supporting "basis" as a list of basis vectors
-   (as opposed to superalgebra elements) in the subalgebra constructor.
+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?
 
-8. Implement random_instance() for general algebras as random_eja().
-   Copy/paste the "general" construction into the other classes that
-   can use it. The general construction can be something like "call
-   random_instance() on something that inherits me and return the
-   result."
+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.