-A. Add tests for orthogonality in the Peirce decomposition.
+1. Add CartesianProductEJA.
-B. Add support for a symmetric positive-definite bilinear form in
- the JordanSpinEJA.
+2. Add references and start citing them.
-1. Add CartesianProductEJA.
+3. Implement the octonion simple EJA.
-2. Check the axioms in the constructor when check != False?
+4. Factor out the unit-norm basis (and operator symmetry) tests once
+ all of the algebras pass.
-3. Add references and start citing them.
+5. Override inner_product(), _max_test_case_size(), et cetera in
+ DirectSumEJA.
-4. Implement the octonion simple EJA.
+6. 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. Factor out the unit-norm basis (and operator symmetry) tests once
- all of the algebras pass.
+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. 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().
+ This may require supporting "basis" as a list of basis vectors
+ (as opposed to superalgebra elements) in the subalgebra constructor.