eja: cache one() for Cartesian product algebras.

[sage.d.git] / mjo / eja / TODO

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 0c3bd156662e20247bdc2206a304e4acadf55ec2..03bf40459e26805a2b2d6e3bae114779f0de57d3 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,15 +1,25 @@
-1. Add CartesianProductEJA.
+1. Finish CartesianProductEJA: add to_matrix(),
+   random_instance(),... methods. This will require rethinking what a
+   "matrix representation" and "matrix space" means for a cartesian
+   product algebra. Do we want our matrix basis to consist of ordered
+   pairs (or triples, or...)? Should the matrix_space() of the algebra
+   be the cartesian product of the factors' matrix spaces? Can we just
+   fix the matrix basis/space after we call the FDEJA initializer?
 
-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. Override inner_product(), _max_test_case_size(), et cetera in
-   DirectSumEJA.
+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]
 
-7. Switch to QQ in *all* algebras for _charpoly_coefficients().
+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.