eja: add automatic associativity detection.

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

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 67f390ba24f06e6d0f419609ddb8654afd0a65bf..c92cfc9a62c2424e7ae2ab3be37d7f17f3954630 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,17 +1,20 @@
-1. Add CartesianProductEJA.
+1. Add cartesian products to random_eja().
 
-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. Create Element subclasses for the matrix EJAs, and then override
-   their characteristic_polynomial() method to create a new algebra
-   over the rationals (with a non-normalized basis). We can then
-   compute the charpoly quickly by passing the natural representation
-   of the given element into the new algebra and computing its charpoly
-   there. (Relies on the theory to ensure that the charpolys are equal.)
\ No newline at end of file
+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. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.
+
+6. The _rational_algebra for a cartesian product should be a cartesian product.
+
+7. Use super() where it works.