X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=266015647f50bf17e7546fe4d191b99d9e3655ba;hb=1b6878559ad75aa0064503a962c8c183e13ab91a;hp=f09191e3890ea4589ccc5fae3da3e27c2a23b6b8;hpb=db5226c4f5478db40d844b99077a5b164ef6d714;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index f09191e..2660156 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -21,4 +21,21 @@
    This may require supporting "basis" as a list of basis vectors
    (as opposed to superalgebra elements) in the subalgebra constructor.
 
-7. Use charpoly for inverse stuff if it's cached.
+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.
+
+10. Eliminate "natural representation" for non-matrix algebras.
+
+11. The main EJA element constructor is happy to convert between
+    e.g. HadamardEJA(3) and JordanSpinEJA(3).