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.
+
+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. Use charpoly for inverse itself?
+
+9. Pre-cache charpoly for some small algebras?
+
+10. Compute the scalar in the general natural_inner_product() for
+ matrices, so no overrides are necessary.
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