-1. Finish DirectSumEJA: add to_matrix(), random_instance(),
- one()... methods. Make it subclass RationalBasisEuclideanJordanAlgebra.
- This is not a general direct sum / cartesian product implementation,
- it's used only with the other rationalbasis algebras (to make non-
- simple EJAs out of the simple ones).
+1. Add cartesian products to random_eja().
2. Add references and start citing them.
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. Compute the scalar in the general natural_inner_product() for
- matrices, so no overrides are necessary.
-
-6. The main EJA element constructor is happy to convert between
- e.g. HadamardEJA(3) and JordanSpinEJA(3).
-
-7. Figure out if CombinatorialFreeModule's use of IndexedGenerators
- can be used to replace the matrix_basis().
-
-8. Move the "field" argument to a keyword after basis, jp, and ip.
-
-9. Add back the check_field=False and check_axioms=False parameters
- for the EJAs we've constructed ourselves. We can probably pass
- the value of "check_axioms" to <whatever>.span_of_basis() to skip
- the linear-independence check.
+5. Profile the construction of "large" matrix algebras (like the
+ 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+ they're so slow.
projects / sage.d.git / blobdiff