-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. Add dimension bounds on any tests over AA that compute element
+ subalgebras.
-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.
-
-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.
-
-8. Pre-cache charpoly for some small algebras?
-
-9. Compute the scalar in the general natural_inner_product() for
- matrices, so no overrides are necessary.
-
-10. Eliminate "natural representation" for non-matrix algebras.
-
-11. The main EJA element constructor is happy to convert between
- e.g. HadamardEJA(3) and JordanSpinEJA(3).
+5. The rational_algebra() stuff doesn't really belong in classes that
+ don't dervice from RationalBasisEJA or its as-yet-nonexistent
+ element class.