X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=bb2b7f30069dda7ba5b1c63ec7062f1ab397c596;hb=0430a8642776e71ef0c26ab5e186f5a98a5a7433;hp=94fb172aba0dda1d601e7c70ccf4f991749a6fcc;hpb=f02d09e53017ba3b3b5592a45be84487c580379d;p=sage.d.git diff --git a/mjo/eja/TODO b/mjo/eja/TODO index 94fb172..bb2b7f3 100644 --- a/mjo/eja/TODO +++ b/mjo/eja/TODO @@ -1,31 +1,17 @@ -1. Add CartesianProductEJA. +1. Add references and start citing them. -2. Add references and start citing them. +2. Profile (and fix?) any remaining slow operations. -3. Implement the octonion simple EJA. +3. When we take a Cartesian product involving a trivial algebra, we + could easily cache the identity and charpoly coefficients using + the nontrivial factor. On the other hand, it's nice that we can + test out some alternate code paths... -4. Override random_instance(), one(), et cetera in DirectSumEJA. +4. Can we hit "x" with the deortho matrix and delegate to the + _rational_algebra to speed up minimal_polynomial? -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. +5. In CartesianProductEJA we already know the multiplication table and + inner product matrix. Refactor things until it's no longer + necessary to duplicate that work. -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. - - This may require supporting "basis" as a list of basis vectors - (as opposed to superalgebra elements) in the subalgebra constructor. - -7. The inner product should be an *argument* to the main EJA - constructor. Afterwards, the basis normalization step should be - optional (and enabled by default) for ALL algebras, since any - algebra can have a nonstandard inner-product and its basis can be - normalized with respect to that inner- product. For example, the - HadamardEJA could be equipped with an inner- product that is twice - the usual one. Then for the basis to be orthonormal, we would need - to divide e.g. (1,0,0) by <(1,0,0),(1,0,0)> = 2 to normalize it. +6. Eliminate the matrix_space() override in CartesianProductEJA.