From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 26 Nov 2020 02:59:28 +0000 (-0500)
Subject: eja: start adding precomputed charpoly coeffs to the TODO.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=3bbd8df6759e00a29a2df95a1479ea16e24bc3dc;p=sage.d.git

eja: start adding precomputed charpoly coeffs to the TODO.
---

diff --git a/mjo/eja/TODO b/mjo/eja/TODO
index f0901ca..fa05841 100644
--- a/mjo/eja/TODO
+++ b/mjo/eja/TODO
@@ -32,6 +32,11 @@
 
 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.