From 607ba10dfea185af919a1f60b3ec7c7432d93b2b Mon Sep 17 00:00:00 2001 From: Michael Orlitzky 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