X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_operator.py;h=c32ff1ed7c2ba0aa87c842e5545f9bf204f43fac;hb=251d80b3473331d895be87f736b688f57963a9bb;hp=7c3b2a6a4721848caaaf4d30cecbb08d0eab587f;hpb=208bc5d64bd206684e59f757d932768552e9f7ba;p=sage.d.git diff --git a/mjo/eja/eja_operator.py b/mjo/eja/eja_operator.py index 7c3b2a6..c32ff1e 100644 --- a/mjo/eja/eja_operator.py +++ b/mjo/eja/eja_operator.py @@ -13,6 +13,8 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): F = domain_eja.base_ring() if not (F == codomain_eja.base_ring()): raise ValueError("domain and codomain must have the same base ring") + if not (F == mat.base_ring()): + raise ValueError("domain and matrix must have the same base ring") # We need to supply something here to avoid getting the # default Homset of the parent FiniteDimensionalAlgebra class, @@ -81,19 +83,18 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): [2 0 0] [0 2 0] [0 0 2] - Domain: Euclidean Jordan algebra of dimension 3 over - Rational Field - Codomain: Euclidean Jordan algebra of dimension 3 over - Rational Field + Domain: Euclidean Jordan algebra of dimension 3 over... + Codomain: Euclidean Jordan algebra of dimension 3 over... If you try to add two identical vector space operators but on different EJAs, that should blow up:: sage: J1 = RealSymmetricEJA(2) + sage: id1 = identity_matrix(J1.base_ring(), 3) sage: J2 = JordanSpinEJA(3) - sage: id = identity_matrix(QQ, 3) - sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J1,J1,id) - sage: g = FiniteDimensionalEuclideanJordanAlgebraOperator(J2,J2,id) + sage: id2 = identity_matrix(J2.base_ring(), 3) + sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J1,J1,id1) + sage: g = FiniteDimensionalEuclideanJordanAlgebraOperator(J2,J2,id2) sage: f + g Traceback (most recent call last): ... @@ -179,10 +180,8 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): [1 0 0] [0 1 0] [0 0 1] - Domain: Euclidean Jordan algebra of dimension 3 over - Rational Field - Codomain: Euclidean Jordan algebra of dimension 3 over - Rational Field + Domain: Euclidean Jordan algebra of dimension 3 over... + Codomain: Euclidean Jordan algebra of dimension 3 over... """ return FiniteDimensionalEuclideanJordanAlgebraOperator( @@ -215,30 +214,31 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): sage: x.operator() Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: - [ 2 4 0] + [ 2 2 0] [ 2 9 2] - [ 0 4 16] - Domain: Euclidean Jordan algebra of dimension 3 over - Rational Field - Codomain: Euclidean Jordan algebra of dimension 3 over - Rational Field + [ 0 2 16] + Domain: Euclidean Jordan algebra of dimension 3 over... + Codomain: Euclidean Jordan algebra of dimension 3 over... sage: x.operator()*(1/2) Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: - [ 1 2 0] + [ 1 1 0] [ 1 9/2 1] - [ 0 2 8] - Domain: Euclidean Jordan algebra of dimension 3 over - Rational Field - Codomain: Euclidean Jordan algebra of dimension 3 over - Rational Field + [ 0 1 8] + Domain: Euclidean Jordan algebra of dimension 3 over... + Codomain: Euclidean Jordan algebra of dimension 3 over... """ - if other in self.codomain().base_ring(): - return FiniteDimensionalEuclideanJordanAlgebraOperator( - self.domain(), - self.codomain(), - self.matrix()*other) + try: + if other in self.codomain().base_ring(): + return FiniteDimensionalEuclideanJordanAlgebraOperator( + self.domain(), + self.codomain(), + self.matrix()*other) + except NotImplementedError: + # This can happen with certain arguments if the base_ring() + # is weird and doesn't know how to test membership. + pass # This should eventually delegate to _composition_ after performing # some sanity checks for us. @@ -266,10 +266,8 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): [-1 0 0] [ 0 -1 0] [ 0 0 -1] - Domain: Euclidean Jordan algebra of dimension 3 over - Rational Field - Codomain: Euclidean Jordan algebra of dimension 3 over - Rational Field + Domain: Euclidean Jordan algebra of dimension 3 over... + Codomain: Euclidean Jordan algebra of dimension 3 over... """ return FiniteDimensionalEuclideanJordanAlgebraOperator( @@ -301,10 +299,8 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): [3 0 0] [0 3 0] [0 0 3] - Domain: Euclidean Jordan algebra of dimension 3 over - Rational Field - Codomain: Euclidean Jordan algebra of dimension 3 over - Rational Field + Domain: Euclidean Jordan algebra of dimension 3 over... + Codomain: Euclidean Jordan algebra of dimension 3 over... """ if (n == 1): @@ -380,10 +376,8 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): [-1 0 0] [ 0 -1 0] [ 0 0 -1] - Domain: Euclidean Jordan algebra of dimension 3 over - Rational Field - Codomain: Euclidean Jordan algebra of dimension 3 over - Rational Field + Domain: Euclidean Jordan algebra of dimension 3 over... + Codomain: Euclidean Jordan algebra of dimension 3 over... """ return (self + (-other)) @@ -432,3 +426,43 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): """ # The matrix method returns a polynomial in 'x' but want one in 't'. return self.matrix().minimal_polynomial().change_variable_name('t') + + + def spectral_decomposition(self): + """ + Return the spectral decomposition of this operator as a list of + (eigenvalue, orthogonal projector) pairs. + + SETUP:: + + sage: from mjo.eja.eja_algebra import RealSymmetricEJA + + EXAMPLES:: + + sage: J = RealSymmetricEJA(4,AA) + sage: x = sum(J.gens()) + sage: A = x.subalgebra_generated_by(orthonormalize_basis=True) + sage: L0x = A(x).operator() + sage: Ps = [ P*l for (l,P) in L0x.spectral_decomposition() ] + sage: Ps[0] + Ps[1] == L0x + True + + """ + if not self.matrix().is_symmetric(): + raise ValueError('algebra basis is not orthonormal') + + D,P = self.matrix().jordan_form(subdivide=False,transformation=True) + eigenvalues = D.diagonal() + us = P.columns() + projectors = [] + for i in range(len(us)): + # they won't be normalized, but they have to be + # for the spectral theorem to work. + us[i] = us[i]/us[i].norm() + mat = us[i].column()*us[i].row() + Pi = FiniteDimensionalEuclideanJordanAlgebraOperator( + self.domain(), + self.codomain(), + mat) + projectors.append(Pi) + return zip(eigenvalues, projectors)