From 9866a99126ab5ec1e71b7a9c43ba5924ebfc6baf Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Fri, 26 Jul 2019 12:45:19 -0400 Subject: [PATCH] eja: add __invert__ method for morphisms. --- mjo/eja/euclidean_jordan_algebra.py | 44 +++++++++++++++++++++++++++-- 1 file changed, 42 insertions(+), 2 deletions(-) diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py index fa11aed..78fa6b7 100644 --- a/mjo/eja/euclidean_jordan_algebra.py +++ b/mjo/eja/euclidean_jordan_algebra.py @@ -16,8 +16,10 @@ from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_morphi class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMorphism): """ - A very thin wrapper around FiniteDimensionalAlgebraMorphism that - does only three things: + A linear map between two finite-dimensional EJAs. + + This is a very thin wrapper around FiniteDimensionalAlgebraMorphism + that does only a few things: 1. Avoids the ``unitary`` and ``check`` arguments to the constructor that will always be ``False``. This is necessary because these @@ -85,6 +87,44 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo check=False) + def __invert__(self): + """ + EXAMPLES:: + + sage: J = RealSymmetricEJA(2) + sage: x = J.linear_combination(zip(range(len(J.gens())), J.gens())) + sage: x.is_invertible() + True + sage: ~x.operator() + Morphism from Euclidean Jordan algebra of degree 3 over Rational + Field to Euclidean Jordan algebra of degree 3 over Rational Field + given by matrix + [-3/2 2 -1/2] + [ 1 0 0] + [-1/2 0 1/2] + sage: x.operator_matrix().inverse() + [-3/2 2 -1/2] + [ 1 0 0] + [-1/2 0 1/2] + + TESTS:: + + sage: set_random_seed() + sage: J = random_eja() + sage: x = J.random_element() + sage: not x.is_invertible() or ( + ....: (~x.operator()).matrix() == x.operator_matrix().inverse() ) + True + + """ + A = self.matrix() + if not A.is_invertible(): + raise ValueError("morphism is not invertible") + + P = self.parent() + return FiniteDimensionalEuclideanJordanAlgebraMorphism(self.parent(), + A.inverse()) + def _repr_(self): """ We override only the representation that is shown to the user, -- 2.44.2