eja: fix cartesian products of cartesian product EJAs.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index fcba1c0ea2e38a6e4dc9dbb8ba7c860179c08c20..93aa9fb42e6ec6cdba6963db8dacfddd116ba762 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,5 +1,22 @@
-1. Add CartesianProductEJA.
+1. Finish CartesianProductEJA: add to_matrix(), random_instance(),...
+   methods. I guess we should create a separate class hierarchy for
+   Cartesian products of RationalBasisEJA? That way we get fast
+   charpoly and random_instance() defined...
 
-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. Pre-cache charpoly for some small algebras?
+
+RealSymmetricEJA(4):
+
+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. 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.