From 4e52be210372144c8db44ddb1aeb5cb304438629 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Thu, 28 Nov 2024 19:26:55 -0500 Subject: [PATCH] mjo/eja/eja_operator.py: permutation test for is_isomorphism() --- mjo/eja/eja_operator.py | 22 ++++++++++++++++++++++ 1 file changed, 22 insertions(+) diff --git a/mjo/eja/eja_operator.py b/mjo/eja/eja_operator.py index 7b40b90..19bcf96 100644 --- a/mjo/eja/eja_operator.py +++ b/mjo/eja/eja_operator.py @@ -896,6 +896,28 @@ class EJAOperator(Map): TESTS: + Permuting factors is always a Jordan isomorphism:: + + sage: J1 = random_eja(field=QQ, orthonormalize=False) + sage: J2 = random_eja(field=QQ, orthonormalize=False) + sage: J3 = random_eja(field=QQ, orthonormalize=False) + sage: J = cartesian_product([J1,J1,J3,J2,J2]) + sage: I1 = J1.one().operator().matrix() + sage: I2 = J2.one().operator().matrix() + sage: I3 = J3.one().operator().matrix() + sage: M = block_matrix(5, 5, [[ 0, 0, 0, 0, I2 ], + ....: [ 0, I1, 0, 0, 0 ], + ....: [ 0, 0, 0, I2, 0 ], + ....: [I1, 0, 0, 0, 0 ], + ....: [ 0, 0, I3, 0, 0 ]]) + sage: L = EJAOperator(J,J,M) + sage: L.is_isomorphism() + True + sage: L.inverse().is_isomorphism() + True + sage: (L^2).is_isomorphism() + True + The identity operator is always a Jordan isomorphism:: sage: J = random_eja() -- 2.49.0