1 1. Add references and start citing them.
3 2. Pre-cache charpoly for some small algebras?
7 sage: F = J.base_ring()
8 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]
10 3. Profile the construction of "large" matrix algebras (like the
11 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
14 4. What the ever-loving fuck is this shit?
16 sage: O = Octonions(QQ)
17 sage: e0 = O.monomial(0)
21 5. Every once in a long while, the test
23 sage: set_random_seed()
24 sage: x = random_eja().random_element()
25 sage: x.is_invertible() == (x.det() != 0)
27 in eja_element.py returns False.