From 9b6acc401eb02e9565db6212698662c9844c4239 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Thu, 25 Jul 2019 20:41:40 -0400 Subject: [PATCH] eja: add tests for more quadratic representation properties. --- mjo/eja/euclidean_jordan_algebra.py | 71 ++++++++++++++++++++++------- 1 file changed, 55 insertions(+), 16 deletions(-) diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py index 920ecc9..da3f600 100644 --- a/mjo/eja/euclidean_jordan_algebra.py +++ b/mjo/eja/euclidean_jordan_algebra.py @@ -1086,38 +1086,77 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra): sage: J = random_eja() sage: x = J.random_element() sage: y = J.random_element() + sage: Lx = x.operator_matrix() + sage: Lxx = (x*x).operator_matrix() + sage: Qx = x.quadratic_representation() + sage: Qy = y.quadratic_representation() + sage: Qxy = x.quadratic_representation(y) + sage: Qex = J.one().quadratic_representation(x) + sage: n = ZZ.random_element(10) + sage: Qxn = (x^n).quadratic_representation() Property 1: - sage: actual = x.quadratic_representation(y) - sage: expected = ( (x+y).quadratic_representation() - ....: -x.quadratic_representation() - ....: -y.quadratic_representation() ) / 2 - sage: actual == expected + sage: 2*Qxy == (x+y).quadratic_representation() - Qx - Qy True Property 2: sage: alpha = QQ.random_element() - sage: actual = (alpha*x).quadratic_representation() - sage: expected = (alpha^2)*x.quadratic_representation() - sage: actual == expected + sage: (alpha*x).quadratic_representation() == (alpha^2)*Qx + True + + Property 3: + + sage: not x.is_invertible() or ( + ....: Qx*x.inverse().vector() == x.vector() ) + True + + sage: not x.is_invertible() or ( + ....: Qx.inverse() + ....: == + ....: x.inverse().quadratic_representation() ) + True + + sage: Qxy*(J.one().vector()) == (x*y).vector() + True + + Property 4: + + sage: not x.is_invertible() or ( + ....: x.quadratic_representation(x.inverse())*Qx + ....: == Qx*x.quadratic_representation(x.inverse()) ) + True + + sage: not x.is_invertible() or ( + ....: x.quadratic_representation(x.inverse())*Qx + ....: == + ....: 2*x.operator_matrix()*Qex - Qx ) + True + + sage: 2*x.operator_matrix()*Qex - Qx == Lxx True Property 5: - sage: Qy = y.quadratic_representation() - sage: actual = J(Qy*x.vector()).quadratic_representation() - sage: expected = Qy*x.quadratic_representation()*Qy - sage: actual == expected + sage: J(Qy*x.vector()).quadratic_representation() == Qy*Qx*Qy True Property 6: - sage: k = ZZ.random_element(1,10) - sage: actual = (x^k).quadratic_representation() - sage: expected = (x.quadratic_representation())^k - sage: actual == expected + sage: Qxn == (Qx)^n + True + + Property 7: + + sage: not x.is_invertible() or ( + ....: Qx*x.inverse().operator_matrix() == Lx ) + True + + Property 8: + + sage: not x.operator_commutes_with(y) or ( + ....: J(Qx*y.vector())^n == J(Qxn*(y^n).vector()) ) True """ -- 2.43.2