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.
the usual one. Then for the basis to be orthonormal, we would need
to divide e.g. (1,0,0) by <(1,0,0),(1,0,0)> = 2 to normalize it.
-8. Use charpoly for inverse itself?
+8. Pre-cache charpoly for some small algebras?
-9. 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. 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.