X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=c92cfc9a62c2424e7ae2ab3be37d7f17f3954630;hb=86ec96a9ff510b4b3d178998d63b0ce9a374c444;hp=87a162c73ab3ccf86623496dee39064e8b96bfb7;hpb=2a3ec0787b28bc35b3624594d921a995c9425d3a;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 87a162c..c92cfc9 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,31 +1,20 @@
-1. Add CartesianProductEJA.
+1. Add cartesian products to random_eja().
 
 2. Add references and start citing them.
 
 3. Implement the octonion simple EJA.
 
-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 random_instance(), one(), 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. The _rational_algebra for a cartesian product should be a cartesian product.
 
-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. Use super() where it works.