X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=fe18d5634835c97dcc1ee635c4fadecab25787ea;hb=d9bf7b27a9a595ee4566da8f1df753ba9122a033;hp=f09191e3890ea4589ccc5fae3da3e27c2a23b6b8;hpb=db5226c4f5478db40d844b99077a5b164ef6d714;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index f09191e..fe18d56 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,24 +1,25 @@
-1. Add CartesianProductEJA.
+1. Finish CartesianProductEJA: add to_matrix(), random_instance(),
+   one()... methods. This will require rethinking what a "matrix
+   representation" and "matrix space" means for a cartesian product
+   algebra. Do we want our matrix basis to consist of ordered pairs
+   (or triples, or...)? Should the matrix_space() of the algebra be
+   the cartesian product of the factors' matrix spaces? Can we just
+   fix the matrix basis/space after we call the FDEJA initializer?
 
 2. Add references and start citing them.
 
 3. Implement the octonion simple EJA.
 
-4. Override random_instance(), one(), et cetera in DirectSumEJA.
+4. Pre-cache charpoly for some small algebras?
 
-5. 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.
+RealSymmetricEJA(4):
 
-6. 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.
+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]
 
-   This may require supporting "basis" as a list of basis vectors
-   (as opposed to superalgebra elements) in the subalgebra constructor.
+5. The main EJA element constructor is happy to convert between
+   e.g. HadamardEJA(3) and JordanSpinEJA(3).
 
-7. Use charpoly for inverse stuff if it's cached.
+6. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.