eja: dropp the already_echelonized TODO.

We generally orthonormalize things now, but having an orthonormal
basis is not the same as having a basis in RREF form.

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index db02b276e9a8a427afd3ad2a3e0b9fb77020fb50..ccd0b5ae507312c68d7a5e61d5094cfab617b7c5 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -8,30 +8,20 @@
 
 3. Implement the octonion simple EJA.
 
-4. 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 using e.g. FreeModule_submodule_with_basis_field
-   we may somehow be able to pass the echelon basis straight in to
-   save time.
-
-   This may require supporting "basis" as a list of basis vectors
-   (as opposed to superalgebra elements) in the subalgebra constructor.
-
-5. Pre-cache charpoly for some small algebras?
+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]
 
-6. Compute the scalar in the general natural_inner_product() for
+5. Compute the scalar in the general natural_inner_product() for
    matrices, so no overrides are necessary.
 
-7. The main EJA element constructor is happy to convert between
+6. The main EJA element constructor is happy to convert between
    e.g. HadamardEJA(3) and JordanSpinEJA(3).
 
-8. Figure out if CombinatorialFreeModule's use of IndexedGenerators
+7. Figure out if CombinatorialFreeModule's use of IndexedGenerators
    can be used to replace the matrix_basis().
 
-9. Move the "field" argument to a keyword after basis, jp, and ip.
+8. Move the "field" argument to a keyword after basis, jp, and ip.