X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2FTODO;h=fa05841e38f6ec6f8c51970ac4981bb2d4b2ef67;hb=9a30998022fdc8eccaf724833a4cd88e545e4f0e;hp=65a9bd9da94604b3e2145ab513623f17187fed05;hpb=0dc72dd20f8386f5ff0716e4f266ca2eea0a47f6;p=sage.d.git

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index 65a9bd9..fa05841 100644
--- 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.
 
@@ -32,7 +32,16 @@
 
 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().