-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. Factor out the unit-norm basis (and operator symmetry) tests once
- all of the algebras pass.
+4. Can we hit "x" with the deortho matrix and delegate to the
+ _rational_algebra to speed up minimal_polynomial?
-5. Override inner_product(), _max_test_case_size(), et cetera in
- DirectSumEJA.
+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. Switch to QQ in *all* algebras for _charpoly_coefficients().
-
-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.
+6. Figure out how to remove Unital() from subalgebras.