mjo/eja/TODO

   1 Trace inner product tests:
   2
   3             TESTS:
   4
   5             The trace inner product is commutative::
   6
   7             sage: set_random_seed()
   8             sage: J = random_eja()
   9             sage: x = J.random_element(); y = J.random_element()
  10             sage: x.trace_inner_product(y) == y.trace_inner_product(x)
  11             True
  12
  13             The trace inner product is bilinear::
  14
  15             sage: set_random_seed()
  16             sage: J = random_eja()
  17             sage: x = J.random_element()
  18             sage: y = J.random_element()
  19             sage: z = J.random_element()
  20             sage: a = QQ.random_element();
  21             sage: actual = (a*(x+z)).trace_inner_product(y)
  22             sage: expected = a*x.trace_inner_product(y) + a*z.trace_inner_product(y)
  23             sage: actual == expected
  24             True
  25             sage: actual = x.trace_inner_product(a*(y+z))
  26             sage: expected = a*x.trace_inner_product(y) +  a*x.trace_inner_product(z)
  27             sage: actual == expected
  28             True
  29
  30             The trace inner product is associative::
  31
  32             sage: pass
  33
  34             The trace inner product satisfies the compatibility
  35             condition in the definition of a Euclidean Jordan algebra:
  36
  37             sage: set_random_seed()
  38             sage: J = random_eja()
  39             sage: x = J.random_element()
  40             sage: y = J.random_element()
  41             sage: z = J.random_element()
  42             sage: (x*y).trace_inner_product(z) == y.trace_inner_product(x*z)
  43             True
  44