X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=45a9ac06bf2c86020dee102143393e486fa408c5;hb=cf5e64b70869df65c7bb38888de54b1083e60d45;hp=db02b276e9a8a427afd3ad2a3e0b9fb77020fb50;hpb=778835152f5d5408017c47b0c1e74db19ab70a69;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index db02b27..45a9ac0 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,37 +1,22 @@
-1. Finish DirectSumEJA: add to_matrix(), random_instance(),
-   one()... methods. Make it subclass RationalBasisEuclideanJordanAlgebra.
-   This is not a general direct sum / cartesian product implementation,
-   it's used only with the other rationalbasis algebras (to make non-
-   simple EJAs out of the simple ones).
+1. Add references and start citing them.
 
-2. Add references and start citing them.
+2. Pre-cache charpoly for some more algebras.
 
-3. Implement the octonion simple EJA.
+3. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.
 
-4. 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 using e.g. FreeModule_submodule_with_basis_field
-   we may somehow be able to pass the echelon basis straight in to
-   save time.
+4. What the ever-loving fuck is this shit?
 
-   This may require supporting "basis" as a list of basis vectors
-   (as opposed to superalgebra elements) in the subalgebra constructor.
+       sage: O = Octonions(QQ)
+       sage: e0 = O.monomial(0)
+       sage: e0*[[[[]]]]
+       [[[[]]]]*e0
 
-5. Pre-cache charpoly for some small algebras?
+5. Every once in a long while, the test
 
-RealSymmetricEJA(4):
+       sage: set_random_seed()
+       sage: x = random_eja().random_element()
+       sage: x.is_invertible() == (x.det() != 0)
 
-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]
-
-6. Compute the scalar in the general natural_inner_product() for
-   matrices, so no overrides are necessary.
-
-7. The main EJA element constructor is happy to convert between
-   e.g. HadamardEJA(3) and JordanSpinEJA(3).
-
-8. Figure out if CombinatorialFreeModule's use of IndexedGenerators
-   can be used to replace the matrix_basis().
-
-9. Move the "field" argument to a keyword after basis, jp, and ip.
+   in eja_element.py returns False.