-A. Add tests for orthogonality in the Peirce decomposition.
+1. Add cartesian products to random_eja().
-B. Add support for a symmetric positive-definite bilinear form in
- the JordanSpinEJA.
+2. Add references and start citing them.
-1. Add CartesianProductEJA.
+3. Implement the octonion simple EJA.
-2. Check the axioms in the constructor when check != False?
+4. Pre-cache charpoly for some small algebras?
-3. Add references and start citing them.
+RealSymmetricEJA(4):
-4. Implement the octonion simple EJA.
+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. Factor out the unit-norm basis (and operator symmetry) tests once
- all of the algebras pass.
-
-6. Can we make the minimal and characteristic polynomial tests work
- for trivial algebras, too? Then we wouldn't need the "nontrivial"
- argument to random_eja().
-
-7. Solve the charpoly system with A_of_x.solve_right(x_powers[r])
- rather than dumbass Cramer's rule.
+5. Profile the construction of "large" matrix algebras (like the
+ 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+ they're so slow.