-0. Add tests for orthogonality in the Peirce decomposition.
-
1. Add CartesianProductEJA.
-2. Check the axioms in the constructor when check != False?
+2. Add references and start citing them.
+
+3. Implement the octonion simple EJA.
+
+4. Override random_instance(), one(), et cetera in DirectSumEJA.
-3. Add references and start citing them.
+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.
-4. Implement the octonion simple EJA.
+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.
-5. Factor out the unit-norm basis (and operator symmetry) tests once
- all of the algebras pass.
+ This may require supporting "basis" as a list of basis vectors
+ (as opposed to superalgebra elements) in the subalgebra constructor.
-6. Can we make the minimal and characteristic polynomial tests work
- for trivial algebras, too? Then we wouldn't need the "nontrivial"
- argument to random_eja().
+7. Use charpoly for inverse stuff if it's cached.