-1. Add CartesianProductEJA.
+1. Add cartesian products to random_eja().
2. Add references and start citing them.
3. Implement the octonion simple EJA.
-4. Override random_instance(), one(), et cetera in DirectSumEJA.
+4. Pre-cache charpoly for some small algebras?
-5. Switch to QQ in *all* algebras for _charpoly_coefficients().
- This only works when we know that the basis can be rationalized...
- which is the case at least for the concrete EJAs we provide,
- but not in general.
+RealSymmetricEJA(4):
-6. Pass already_echelonized (default: False) and echelon_basis
- (default: None) into the subalgebra constructor. The value of
- already_echelonized can be passed to V.span_of_basis() to save
- some time, and usinf e.g. FreeModule_submodule_with_basis_field
- we may somehow be able to pass the echelon basis straight in to
- save time.
+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]
- This may require supporting "basis" as a list of basis vectors
- (as opposed to superalgebra elements) in the subalgebra constructor.
+5. Profile the construction of "large" matrix algebras (like the
+ 15-dimensional QuaternionHermitianAlgebra(3)) to find out why
+ they're so slow.
-7. Use charpoly for inverse stuff if it's cached.
+6. The _rational_algebra for a cartesian product should be a cartesian product.
+
+7. Use super() where it works.
projects / sage.d.git / blobdiff