From: Michael Orlitzky Date: Fri, 28 Jan 2022 02:12:11 +0000 (-0500) Subject: eja: test the nonnegativity of trace() for squares. X-Git-Url: http://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=607ba10dfea185af919a1f60b3ec7c7432d93b2b;hp=1d6c0d98ea24be9bcfec236ad94d6d125dabd8f4;p=sage.d.git eja: test the nonnegativity of trace() for squares. --- 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()