From b9e93ee540d22480315f1d0d4a28004869b633ed Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Fri, 5 Jul 2019 19:19:49 -0400 Subject: [PATCH] eja: add a TODO with some tests that fail for now. --- mjo/eja/TODO | 44 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 44 insertions(+) create mode 100644 mjo/eja/TODO diff --git a/mjo/eja/TODO b/mjo/eja/TODO new file mode 100644 index 0000000..dd671c5 --- /dev/null +++ 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 + \ No newline at end of file -- 2.44.2