mjo/eja/TODO

   1 1. Add CartesianProductEJA.
   2
   3 2. Add references and start citing them.
   4
   5 3. Implement the octonion simple EJA.
   6
   7 4. Override random_instance(), one(), et cetera in DirectSumEJA.
   8
   9 5. Switch to QQ in *all* algebras for _charpoly_coefficients().
  10    This only works when we know that the basis can be rationalized...
  11    which is the case at least for the concrete EJAs we provide,
  12    but not in general.
  13
  14 6. Pass already_echelonized (default: False) and echelon_basis
  15    (default: None) into the subalgebra constructor. The value of
  16    already_echelonized can be passed to V.span_of_basis() to save
  17    some time, and usinf e.g. FreeModule_submodule_with_basis_field
  18    we may somehow be able to pass the echelon basis straight in to
  19    save time.
  20
  21    This may require supporting "basis" as a list of basis vectors
  22    (as opposed to superalgebra elements) in the subalgebra constructor.
  23
  24 7. The inner product should be an *argument* to the main EJA
  25    constructor.  Afterwards, the basis normalization step should be
  26    optional (and enabled by default) for ALL algebras, since any
  27    algebra can have a nonstandard inner-product and its basis can be
  28    normalized with respect to that inner- product. For example, the
  29    HadamardEJA could be equipped with an inner- product that is twice
  30    the usual one. Then for the basis to be orthonormal, we would need
  31    to divide e.g. (1,0,0) by <(1,0,0),(1,0,0)> = 2 to normalize it.
  32
  33 8. Pre-cache charpoly for some small algebras?
  34
  35 9. Compute the scalar in the general natural_inner_product() for
  36    matrices, so no overrides are necessary.