eja: use cached charpoly for element inverse() if possible.

[sage.d.git] / mjo / eja / TODO

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 51c2a33b542569c431d986a0d165d8774b0d49eb..87cdcbcb57c781449590f999b0f14589da705d0e 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,21 +1,36 @@
 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. Override random_instance(), one(), et cetera in DirectSumEJA.
 
-5. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+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. Implement spectral projector decomposition for EJA operators
-   using jordan_form() or eigenmatrix_right(). I suppose we can
-   ignore the problem of base rings for now and just let it crash
-   if we're not using AA as our base field.
+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.
 
-7. Do we really need to orthonormalize the basis in a subalgebra?
-   So long as we can decompose the operator (which is invariant
-   under changes of basis), who cares?
+   This may require supporting "basis" as a list of basis vectors
+   (as opposed to superalgebra elements) in the subalgebra constructor.
 
-8. Check that our field is a subring of RLF.
+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. Pre-cache charpoly for some small algebras?
+
+9. Compute the scalar in the general natural_inner_product() for
+   matrices, so no overrides are necessary.
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