From 607ba10dfea185af919a1f60b3ec7c7432d93b2b Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 27 Jan 2022 21:12:11 -0500
Subject: [PATCH] eja: test the nonnegativity of trace() for squares.

---
 mjo/eja/eja_element.py | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 0fd1c5f..bef1289 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -1512,6 +1512,12 @@ class FiniteDimensionalEJAElement(IndexedFreeModuleElement):
             sage: (alpha*x + y).trace() == alpha*x.trace() + y.trace()
             True
 
+        The trace of a square is nonnegative::
+
+            sage: x = random_eja().random_element()
+            sage: (x*x).trace() >= 0
+            True
+
         """
         P = self.parent()
         r = P.rank()
-- 
2.44.2