eja: add random_instance() method for algebras.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index dd671c5fd7ab847a4c635748923bf0cba12a63ad..f6d7743782613d241c50e05eee665d59278bd4b4 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,44 +1,21 @@
-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. Check the axioms in the constructor when check != False?
+
+3. Add references and start citing them.
+
+4. Implement the octonion simple EJA.
+
+5. Factor out the unit-norm basis (and operator symmetry) tests once
+   all of the algebras pass.
+
+6. Refactor the current ungodly fast charpoly hack (relies on the
+   theory to ensure that the charpolys are equal.)
+
+7. If we factor out a "matrix algebra" class, then it would make sense
+   to replace the custom embedding/unembedding functions with static
+   _real_embedding() and _real_unembedding() methods.
+
+8. Implement random_instance() for the main EJA class.
+
+9. Implement random_instance() for the subalgebra class.