From cc6ae0ea99de58b790e685440e3952b6b7406dd2 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sun, 18 Oct 2020 01:23:09 -0400 Subject: [PATCH] mjo/eja/eja_element.py: test spectral decomposition in subalgebras. --- mjo/eja/eja_element.py | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py index 1cf93cc..da4b123 100644 --- a/mjo/eja/eja_element.py +++ b/mjo/eja/eja_element.py @@ -1220,6 +1220,17 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement): sage: l0*c0 + l1*c1 == x True + The spectral decomposition should work in subalgebras, too:: + + sage: J = RealSymmetricEJA(4) + sage: (e0, e1, e2, e3, e4, e5, e6, e7, e8, e9) = J.gens() + sage: A = 2*e5 - 2*e8 + sage: (lambda1, c1) = A.spectral_decomposition()[1] + sage: (J0, J5, J1) = J.peirce_decomposition(c1) + sage: (f0, f1, f2) = J1.gens() + sage: f0.spectral_decomposition() + [(0, 1.000000000000000?*f2), (1, 1.000000000000000?*f0)] + """ A = self.subalgebra_generated_by(orthonormalize_basis=True) result = [] -- 2.44.2