-Trace inner product tests:
+1. Add references and start citing them.
- TESTS:
+2. Pre-cache charpoly for some more algebras.
- The trace inner product is commutative::
+3. Profile the construction of "large" matrix algebras (like the
+ 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+ they're so slow.
- 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
+4. What the ever-loving fuck is this shit?
- The trace inner product is bilinear::
+ sage: O = Octonions(QQ)
+ sage: e0 = O.monomial(0)
+ sage: e0*[[[[]]]]
+ [[[[]]]]*e0
- 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
+5. Every once in a long while, the test
- The trace inner product is associative::
+ sage: set_random_seed()
+ sage: x = random_eja().random_element()
+ sage: x.is_invertible() == (x.det() != 0)
- 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
+ in eja_element.py returns False.