X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=1407ebdbe83bafab1ef79d881d25d2cf4912e18e;hb=ee9ac102b8b392793466c13039a6e50b1e3c4c01;hp=38aa85bfe7a5c5ecc4b97c880c05533e42b5ad69;hpb=09298a6b80a44847f506961e0eeccb8cdf2ad9d3;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 38aa85b..1407ebd 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -1,22 +1,19 @@
-A. Add tests for orthogonality in the Peirce decomposition.
+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...
 
-B. Add support for a symmetric positive-definite bilinear form in
-   the JordanSpinEJA.
+2. Add references and start citing them.
 
-1. Add CartesianProductEJA.
+3. Implement the octonion simple EJA.
 
-2. Check the axioms in the constructor when check != False?
+4. Pre-cache charpoly for some small algebras?
 
-3. Add references and start citing them.
+RealSymmetricEJA(4):
 
-4. Implement the octonion simple EJA.
+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. Factor out the unit-norm basis (and operator symmetry) tests once
-   all of the algebras pass.
-
-6. Can we make the minimal and characteristic polynomial tests work
-   for trivial algebras, too? Then we wouldn't need the "nontrivial"
-   argument to random_eja().
-
-7. Solve the charpoly system with A_of_x.solve_right(x_powers[r])
-   rather than dumbass Cramer's rule.
+5. Profile the construction of "large" matrix algebras (like the
+   15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+   they're so slow.