1. Add CartesianProductEJA.
-2. Check the axioms in the constructor when check != False?
+2. Add references and start citing them.
-3. Add references and start citing them.
+3. Implement the octonion simple EJA.
-4. Implement the octonion simple EJA.
+4. Factor out the unit-norm basis (and operator symmetry) tests once
+ all of the algebras pass.
-5. Factor out the Jordan axiom and norm tests once all of the
- algebras pass.
+5. Override inner_product(), _max_test_case_size(), et cetera in
+ DirectSumEJA.
-6. Create Element subclasses for the matrix EJAs, and then override
- their characteristic_polynomial() method to create a new algebra
- over the rationals (with a non-normalized basis). We can then
- compute the charpoly quickly by passing the natural representation
- of the given element into the new algebra and computing its charpoly
- there. (Relies on the theory to ensure that the charpolys are equal.)
\ No newline at end of file
+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.
+
+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.
+
+ This may require supporting "basis" as a list of basis vectors
+ (as opposed to superalgebra elements) in the subalgebra constructor.
+
+8. Implement random_instance() for general algebras as random_eja().
+ Copy/paste the "general" construction into the other classes that
+ can use it. The general construction can be something like "call
+ random_instance() on something that inherits me and return the
+ result."
projects / sage.d.git / blobdiff