X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=ed15aa3dd5443c18195d9548c44e4a208a601dd7;hb=b44ddab3076cc3b01c95bf6eb3b5f7b20dfd7913;hp=207c06d9156b38ac485f2de3a4d836089aa68d0b;hpb=c96719c121e67d47e635f47a23ec0271cc149c77;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 207c06d..ed15aa3 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,16 +1,49 @@
-A. 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.
+
+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 using 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. Pre-cache charpoly for some small algebras?
+
+RealSymmetricEJA(4):
+
+sage: F = J.base_ring()
+sage: a0 = (1/4)*X[4]**2*X[6]**2 - (1/2)*X[2]*X[5]*X[6]**2 - (1/2)*X[3]*X[4]*X[6]*X[7] + (F(2).sqrt()/2)*X[1]*X[5]*X[6]*X[7] + (1/4)*X[3]**2*X[7]**2 - (1/2)*X[0]*X[5]*X[7]**2 + (F(2).sqrt()/2)*X[2]*X[3]*X[6]*X[8] - (1/2)*X[1]*X[4]*X[6*X[8] - (1/2)*X[1]*X[3]*X[7]*X[8] + (F(2).sqrt()/2)*X[0]*X[4]*X[7]*X[8] + (1/4)*X[1]**2*X[8]**2 - (1/2)*X[0]*X[2]*X[8]**2 - (1/2)*X[2]*X[3]**2*X[9] + (F(2).sqrt()/2)*X[1]*X[3]*X[4]*X[9] - (1/2)*X[0]*X[4]**2*X[9] - (1/2)*X[1]**2*X[5]*X[9] + X[0]*X[2]*X[5]*X[9]
 
-3. Add references and start citing them.
+9. Compute the scalar in the general natural_inner_product() for
+   matrices, so no overrides are necessary.
 
-4. Implement the octonion simple EJA.
+10. The main EJA element constructor is happy to convert between
+    e.g. HadamardEJA(3) and JordanSpinEJA(3).
 
-5. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
+11. Figure out if CombinatorialFreeModule's use of IndexedGenerators
+    can be used to replace the matrix_basis().
 
-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().
+12. Move the "field" argument to a keyword after basis, jp, and ip.