eja: add a TODO with some tests that fail for now.

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
new file mode 100644 (file)
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+++ b/mjo/eja/TODO
@@ -0,0 +1,44 @@
+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
+           
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