From fd6618bf82173916b9a35bb3f114d31b4604f456 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Fri, 13 Nov 2020 09:05:55 -0500 Subject: [PATCH] eja: add projections for DirectSumEJA. --- mjo/eja/eja_algebra.py | 54 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 54 insertions(+) diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py index b9389da..3f91ee3 100644 --- a/mjo/eja/eja_algebra.py +++ b/mjo/eja/eja_algebra.py @@ -2324,6 +2324,7 @@ class DirectSumEJA(FiniteDimensionalEuclideanJordanAlgebra): """ def __init__(self, J1, J2, field=AA, **kwargs): + self._factors = (J1, J2) n1 = J1.dimension() n2 = J2.dimension() n = n1+n2 @@ -2345,3 +2346,56 @@ class DirectSumEJA(FiniteDimensionalEuclideanJordanAlgebra): check_axioms=False, **kwargs) self.rank.set_cache(J1.rank() + J2.rank()) + + + def factors(self): + r""" + Return the pair of this algebra's factors. + + SETUP:: + + sage: from mjo.eja.eja_algebra import (HadamardEJA, + ....: JordanSpinEJA, + ....: DirectSumEJA) + + EXAMPLES:: + + sage: J1 = HadamardEJA(2,QQ) + sage: J2 = JordanSpinEJA(3,QQ) + sage: J = DirectSumEJA(J1,J2) + sage: J.factors() + (Euclidean Jordan algebra of dimension 2 over Rational Field, + Euclidean Jordan algebra of dimension 3 over Rational Field) + + """ + return self._factors + + def projections(self): + r""" + Return a pair of projections onto this algebra's factors. + + SETUP:: + + sage: from mjo.eja.eja_algebra import (JordanSpinEJA, + ....: ComplexHermitianEJA, + ....: DirectSumEJA) + + EXAMPLES:: + + sage: J1 = JordanSpinEJA(2) + sage: J2 = ComplexHermitianEJA(2) + sage: J = DirectSumEJA(J1,J2) + sage: (pi_left, pi_right) = J.projections() + sage: J.one().to_vector() + (1, 0, 1, 0, 0, 1) + sage: pi_left(J.one()).to_vector() + (1, 0) + sage: pi_right(J.one()).to_vector() + (1, 0, 0, 1) + + """ + (J1,J2) = self.factors() + n = J1.dimension() + pi_left = lambda x: J1.from_vector(x.to_vector()[:n]) + pi_right = lambda x: J2.from_vector(x.to_vector()[n:]) + return (pi_left, pi_right) -- 2.44.2