-1. Add CartesianProductEJA.
+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).
-2. Check the axioms in the constructor when check != False?
+2. Add references and start citing them.
-3. Add references and start citing them.
+3. Implement the octonion simple EJA.
-4. Implement the octonion simple EJA.
+4. Pre-cache charpoly for some small algebras?
-5. Factor out the unit-norm basis (and operator symmetry) tests once
- all of the algebras pass.
+RealSymmetricEJA(4):
-6. Add a TrivialEJA class and use it in the tests for is_trivial().
- The random_eja() function should also be able to return these.
+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().
+
+9. Add back the check_field=False and check_axioms=False parameters
+ for the EJAs we've constructed ourselves.
projects / sage.d.git / blobdiff