From 70411af8dc3f53d9126ca8b23a5ae83244cf2373 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sun, 28 Jul 2019 11:05:40 -0400 Subject: [PATCH] eja: move a bunch of operator_matrix() tests to operator(). --- mjo/eja/euclidean_jordan_algebra.py | 102 ++++++++++++++-------------- 1 file changed, 51 insertions(+), 51 deletions(-) diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py index f913030..750b6c1 100644 --- a/mjo/eja/euclidean_jordan_algebra.py +++ b/mjo/eja/euclidean_jordan_algebra.py @@ -962,6 +962,57 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra): sage: lhs == rhs True + Test the first polarization identity from my notes, Koecher Chapter + III, or from Baes (2.3):: + + sage: set_random_seed() + sage: J = random_eja() + sage: x = J.random_element() + sage: y = J.random_element() + sage: Lx = x.operator() + sage: Ly = y.operator() + sage: Lxx = (x*x).operator() + sage: Lxy = (x*y).operator() + sage: bool(2*Lx*Lxy + Ly*Lxx == 2*Lxy*Lx + Lxx*Ly) + True + + Test the second polarization identity from my notes or from + Baes (2.4):: + + sage: set_random_seed() + sage: J = random_eja() + sage: x = J.random_element() + sage: y = J.random_element() + sage: z = J.random_element() + sage: Lx = x.operator() + sage: Ly = y.operator() + sage: Lz = z.operator() + sage: Lzy = (z*y).operator() + sage: Lxy = (x*y).operator() + sage: Lxz = (x*z).operator() + sage: bool(Lx*Lzy + Lz*Lxy + Ly*Lxz == Lzy*Lx + Lxy*Lz + Lxz*Ly) + True + + Test the third polarization identity from my notes or from + Baes (2.5):: + + sage: set_random_seed() + sage: J = random_eja() + sage: u = J.random_element() + sage: y = J.random_element() + sage: z = J.random_element() + sage: Lu = u.operator() + sage: Ly = y.operator() + sage: Lz = z.operator() + sage: Lzy = (z*y).operator() + sage: Luy = (u*y).operator() + sage: Luz = (u*z).operator() + sage: Luyz = (u*(y*z)).operator() + sage: lhs = Lu*Lzy + Lz*Luy + Ly*Luz + sage: rhs = Luyz + Ly*Lu*Lz + Lz*Lu*Ly + sage: bool(lhs == rhs) + True + """ if not other in self.parent(): raise TypeError("'other' must live in the same algebra") @@ -1384,57 +1435,6 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra): EXAMPLES: - Test the first polarization identity from my notes, Koecher Chapter - III, or from Baes (2.3):: - - sage: set_random_seed() - sage: J = random_eja() - sage: x = J.random_element() - sage: y = J.random_element() - sage: Lx = x.operator_matrix() - sage: Ly = y.operator_matrix() - sage: Lxx = (x*x).operator_matrix() - sage: Lxy = (x*y).operator_matrix() - sage: bool(2*Lx*Lxy + Ly*Lxx == 2*Lxy*Lx + Lxx*Ly) - True - - Test the second polarization identity from my notes or from - Baes (2.4):: - - sage: set_random_seed() - sage: J = random_eja() - sage: x = J.random_element() - sage: y = J.random_element() - sage: z = J.random_element() - sage: Lx = x.operator_matrix() - sage: Ly = y.operator_matrix() - sage: Lz = z.operator_matrix() - sage: Lzy = (z*y).operator_matrix() - sage: Lxy = (x*y).operator_matrix() - sage: Lxz = (x*z).operator_matrix() - sage: bool(Lx*Lzy + Lz*Lxy + Ly*Lxz == Lzy*Lx + Lxy*Lz + Lxz*Ly) - True - - Test the third polarization identity from my notes or from - Baes (2.5):: - - sage: set_random_seed() - sage: J = random_eja() - sage: u = J.random_element() - sage: y = J.random_element() - sage: z = J.random_element() - sage: Lu = u.operator_matrix() - sage: Ly = y.operator_matrix() - sage: Lz = z.operator_matrix() - sage: Lzy = (z*y).operator_matrix() - sage: Luy = (u*y).operator_matrix() - sage: Luz = (u*z).operator_matrix() - sage: Luyz = (u*(y*z)).operator_matrix() - sage: lhs = Lu*Lzy + Lz*Luy + Ly*Luz - sage: rhs = Luyz + Ly*Lu*Lz + Lz*Lu*Ly - sage: bool(lhs == rhs) - True - Ensure that our operator's ``matrix`` method agrees with this implementation:: -- 2.44.2