eja: start adding precomputed charpoly coeffs to the TODO.

[sage.d.git] / mjo / eja / TODO

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 3c63d3b97796031de5ecf914f3051d8e47b93967..fa05841e38f6ec6f8c51970ac4981bb2d4b2ef67 100644 (file)
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -14,7 +14,7 @@
 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.
 
@@ -30,9 +30,18 @@
    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):
 
-10. Compute the scalar in the general natural_inner_product() for
-    matrices, so no overrides are necessary.
\ No newline at end of file
+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().