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
+ 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.
8. 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]
+
9. Compute the scalar in the general natural_inner_product() for
matrices, so no overrides are necessary.
-10. Eliminate "natural representation" for non-matrix algebras.
+10. The main EJA element constructor is happy to convert between
+ e.g. HadamardEJA(3) and JordanSpinEJA(3).
+
+11. Figure out if CombinatorialFreeModule's use of IndexedGenerators
+ can be used to replace the matrix_basis().
+
+12. Don't pass in an n-by-n multiplication/i-p table since only the
+ lower-left half is used.