-1. Add cartesian products to random_eja().
+1. Add references and start citing them.
-2. Add references and start citing them.
+2. Profile (and fix?) any remaining slow operations.
-3. Implement the octonion simple EJA.
+3. Every once in a long while, the test
-4. Pre-cache charpoly for some small algebras?
+ sage: set_random_seed()
+ sage: x = random_eja().random_element()
+ sage: x.is_invertible() == (x.det() != 0)
-RealSymmetricEJA(4):
+ in eja_element.py returns False. Example:
-sage: F = J.base_ring()
-sage: a0 = (1/4)*X[4]**2*X[6]**2 - (1/2)*X[2]*X[5]*X[6]**2 - (1/2)*X[3]*X[4]*X[6]*X[7] + (F(2).sqrt()/2)*X[1]*X[5]*X[6]*X[7] + (1/4)*X[3]**2*X[7]**2 - (1/2)*X[0]*X[5]*X[7]**2 + (F(2).sqrt()/2)*X[2]*X[3]*X[6]*X[8] - (1/2)*X[1]*X[4]*X[6*X[8] - (1/2)*X[1]*X[3]*X[7]*X[8] + (F(2).sqrt()/2)*X[0]*X[4]*X[7]*X[8] + (1/4)*X[1]**2*X[8]**2 - (1/2)*X[0]*X[2]*X[8]**2 - (1/2)*X[2]*X[3]**2*X[9] + (F(2).sqrt()/2)*X[1]*X[3]*X[4]*X[9] - (1/2)*X[0]*X[4]**2*X[9] - (1/2)*X[1]**2*X[5]*X[9] + X[0]*X[2]*X[5]*X[9]
+ sage: J1 = ComplexHermitianEJA(2)
+ sage: J2 = TrivialEJA()
+ sage: J = cartesian_product([J1,J2])
+ sage: x = J.from_vector(vector(QQ, [-1, -1/2, -1/2, -1/2]))
+ sage: x.is_invertible()
+ True
+ sage: x.det()
+ 0
-5. Profile the construction of "large" matrix algebras (like the
- 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
- they're so slow.
-
-6. We should compute whether or not the algebra is associative if it
- is unknown. I guess the "associative" argument should be ternary
- (True, False, None)? We should also figure out the correct
- True/False values for the example classes, and of course add an
- _is_associative() method.
-
-7. When field=RDF, subalgebra construction is failing because the
- inner product isn't associative? Actually, it's the combination
- of field=RDF and orthonormalize=True.
-
-8. Set check_axioms=False for element-subalgebras outside of once or
- twice in the test suite.
+4. When we take a Cartesian product involving a trivial algebra, we
+ could easily cache the identity and charpoly coefficients using
+ the nontrivial factor. On the other hand, it's nice that we can
+ test out some alternate code paths...