eja: add another TODO item.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index dd671c5fd7ab847a4c635748923bf0cba12a63ad..b27f2f12875e317fd2b088a74d7395c84ab8e454 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,44 +1,32 @@
-Trace inner product tests:
-
-            TESTS:
-
-            The trace inner product is commutative::
-
-            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
-
-            The trace inner product is bilinear::
-
-            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
+1. Add CartesianProductEJA.
+
+2. Add references and start citing them.
+
+3. Implement the octonion simple EJA.
+
+4. Factor out the unit-norm basis (and operator symmetry) tests once
+   all of the algebras pass.
+
+5. Override inner_product(), _max_test_case_size(), et cetera in
+   DirectSumEJA.
+
+6. 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.
+
+7. 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.
+
+   This may require supporting "basis" as a list of basis vectors
+   (as opposed to superalgebra elements) in the subalgebra constructor.
+
+8. Implement random_instance() for general algebras as random_eja().
+   Copy/paste the "general" construction into the other classes that
+   can use it. The general construction can be something like "call
+   random_instance() on something that inherits me and return the
+   result."