eja: add a TODO for tomorrow.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index dd671c5fd7ab847a4c635748923bf0cba12a63ad..bb2b7f30069dda7ba5b1c63ec7062f1ab397c596 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,44 +1,17 @@
-Trace inner product tests:
+1. Add references and start citing them.
 
-            TESTS:
+2. Profile (and fix?) any remaining slow operations.
 
-            The trace inner product is commutative::
+3. When we take a Cartesian product involving a trivial algebra, we
+   could easily cache the identity and charpoly coefficients using
+   the nontrivial factor. On the other hand, it's nice that we can
+   test out some alternate code paths...
 
-            sage: set_random_seed()
-            sage: J = random_eja()
-            sage: x = J.random_element(); y = J.random_element()
-            sage: x.trace_inner_product(y) == y.trace_inner_product(x)
-            True
+4. Can we hit "x" with the deortho matrix and delegate to the
+   _rational_algebra to speed up minimal_polynomial?
 
-            The trace inner product is bilinear::
+5. In CartesianProductEJA we already know the multiplication table and
+   inner product matrix. Refactor things until it's no longer
+   necessary to duplicate that work.
 
-            sage: set_random_seed()
-            sage: J = random_eja()
-            sage: x = J.random_element()
-            sage: y = J.random_element()
-            sage: z = J.random_element()
-            sage: a = QQ.random_element();
-            sage: actual = (a*(x+z)).trace_inner_product(y)
-            sage: expected = a*x.trace_inner_product(y) + a*z.trace_inner_product(y)
-            sage: actual == expected
-            True
-            sage: actual = x.trace_inner_product(a*(y+z))
-            sage: expected = a*x.trace_inner_product(y) +  a*x.trace_inner_product(z)
-            sage: actual == expected
-            True
-
-            The trace inner product is associative::
-
-            sage: pass
-
-            The trace inner product satisfies the compatibility
-            condition in the definition of a Euclidean Jordan algebra:
-
-            sage: set_random_seed()
-            sage: J = random_eja()
-            sage: x = J.random_element()
-            sage: y = J.random_element()
-            sage: z = J.random_element()
-            sage: (x*y).trace_inner_product(z) == y.trace_inner_product(x*z)
-            True
-           
\ No newline at end of file
+6. Eliminate the matrix_space() override in CartesianProductEJA.