X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=3c63d3b97796031de5ecf914f3051d8e47b93967;hb=39d8d3190b721ea21e0e86618d774437bc1eeb35;hp=f09191e3890ea4589ccc5fae3da3e27c2a23b6b8;hpb=db5226c4f5478db40d844b99077a5b164ef6d714;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index f09191e..3c63d3b 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -21,4 +21,18 @@
    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. 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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