-1. Finish CartesianProductEJA: add to_matrix(), random_instance(),...
- methods. I guess we should create a separate class hierarchy for
- Cartesian products of RationalBasisEJA? That way we get fast
- charpoly and random_instance() defined...
+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]
-
-5. The main EJA element constructor is happy to convert between
- e.g. HadamardEJA(3) and JordanSpinEJA(3).
-
-6. Profile the construction of "large" matrix algebras (like the
- 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
- they're so slow.
-
-7. Printing of Cartesian product subalgebrasis wrong (it prints the
- superalgebra).
+ 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