X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_operator.py;fp=mjo%2Feja%2Feja_operator.py;h=6ec335f7560f174cf205b1f814fc7a1438a35e6c;hb=4c8f9aac69d1cb4097b60b10e5b198b6372ec55e;hp=0b52f555d51f58341fe56f5b63984f88cdf99da0;hpb=795ac83cd78143e36d47fa267fe6ddf1ca8da111;p=sage.d.git diff --git a/mjo/eja/eja_operator.py b/mjo/eja/eja_operator.py index 0b52f55..6ec335f 100644 --- a/mjo/eja/eja_operator.py +++ b/mjo/eja/eja_operator.py @@ -2,14 +2,14 @@ from sage.matrix.constructor import matrix from sage.categories.all import FreeModules from sage.categories.map import Map -class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): +class FiniteDimensionalEJAOperator(Map): r""" An operator between two finite-dimensional Euclidean Jordan algebras. SETUP:: sage: from mjo.eja.eja_algebra import HadamardEJA - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator EXAMPLES: @@ -19,12 +19,12 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): sage: J = HadamardEJA(3) sage: V = VectorSpace(J.base_ring(), 3) sage: M = matrix.identity(J.base_ring(), 3) - sage: FiniteDimensionalEuclideanJordanAlgebraOperator(V,J,M) + sage: FiniteDimensionalEJAOperator(V,J,M) Traceback (most recent call last): ... TypeError: domain must be a finite-dimensional Euclidean Jordan algebra - sage: FiniteDimensionalEuclideanJordanAlgebraOperator(J,V,M) + sage: FiniteDimensionalEJAOperator(J,V,M) Traceback (most recent call last): ... TypeError: codomain must be a finite-dimensional Euclidean @@ -33,16 +33,14 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): """ def __init__(self, domain_eja, codomain_eja, mat): - from mjo.eja.eja_algebra import FiniteDimensionalEuclideanJordanAlgebra + from mjo.eja.eja_algebra import FiniteDimensionalEJA # I guess we should check this, because otherwise you could # pass in pretty much anything algebraish. - if not isinstance(domain_eja, - FiniteDimensionalEuclideanJordanAlgebra): + if not isinstance(domain_eja, FiniteDimensionalEJA): raise TypeError('domain must be a finite-dimensional ' 'Euclidean Jordan algebra') - if not isinstance(codomain_eja, - FiniteDimensionalEuclideanJordanAlgebra): + if not isinstance(codomain_eja, FiniteDimensionalEJA): raise TypeError('codomain must be a finite-dimensional ' 'Euclidean Jordan algebra') @@ -63,7 +61,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): # The Map initializer will set our parent to a homset, which # is explicitly NOT what we want, because these ain't algebra # homomorphisms. - super(FiniteDimensionalEuclideanJordanAlgebraOperator,self).__init__(parent) + super().__init__(parent) # Keep a matrix around to do all of the real work. It would # be nice if we could use a VectorSpaceMorphism instead, but @@ -78,7 +76,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import JordanSpinEJA EXAMPLES:: @@ -86,7 +84,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): sage: J = JordanSpinEJA(3) sage: x = J.linear_combination(zip(J.gens(),range(len(J.gens())))) sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id) + sage: f = FiniteDimensionalEJAOperator(J,J,id) sage: f(x) == x True @@ -100,7 +98,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import ( ....: JordanSpinEJA, ....: RealSymmetricEJA ) @@ -111,8 +109,8 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): sage: J = RealSymmetricEJA(2) sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id) - sage: g = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id) + sage: f = FiniteDimensionalEJAOperator(J,J,id) + sage: g = FiniteDimensionalEJAOperator(J,J,id) sage: f + g Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -129,15 +127,15 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): sage: id1 = identity_matrix(J1.base_ring(), 3) sage: J2 = JordanSpinEJA(3) sage: id2 = identity_matrix(J2.base_ring(), 3) - sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J1,J1,id1) - sage: g = FiniteDimensionalEuclideanJordanAlgebraOperator(J2,J2,id2) + sage: f = FiniteDimensionalEJAOperator(J1,J1,id1) + sage: g = FiniteDimensionalEJAOperator(J2,J2,id2) sage: f + g Traceback (most recent call last): ... TypeError: unsupported operand parent(s) for +: ... """ - return FiniteDimensionalEuclideanJordanAlgebraOperator( + return FiniteDimensionalEJAOperator( self.domain(), self.codomain(), self.matrix() + other.matrix()) @@ -150,7 +148,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import ( ....: JordanSpinEJA, ....: HadamardEJA, @@ -164,12 +162,8 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): sage: mat1 = matrix(AA, [[1,2,3], ....: [4,5,6]]) sage: mat2 = matrix(AA, [[7,8]]) - sage: g = FiniteDimensionalEuclideanJordanAlgebraOperator(J1, - ....: J2, - ....: mat1) - sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J2, - ....: J3, - ....: mat2) + sage: g = FiniteDimensionalEJAOperator(J1, J2, mat1) + sage: f = FiniteDimensionalEJAOperator(J2, J3, mat2) sage: f*g Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -180,7 +174,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): Algebraic Real Field """ - return FiniteDimensionalEuclideanJordanAlgebraOperator( + return FiniteDimensionalEJAOperator( other.domain(), self.codomain(), self.matrix()*other.matrix()) @@ -202,14 +196,14 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA EXAMPLES:: sage: J = RealSymmetricEJA(2) sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id) + sage: f = FiniteDimensionalEJAOperator(J,J,id) sage: ~f Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -220,7 +214,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): Codomain: Euclidean Jordan algebra of dimension 3 over... """ - return FiniteDimensionalEuclideanJordanAlgebraOperator( + return FiniteDimensionalEJAOperator( self.codomain(), self.domain(), ~self.matrix()) @@ -237,7 +231,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA EXAMPLES: @@ -267,7 +261,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): """ try: if other in self.codomain().base_ring(): - return FiniteDimensionalEuclideanJordanAlgebraOperator( + return FiniteDimensionalEJAOperator( self.domain(), self.codomain(), self.matrix()*other) @@ -278,7 +272,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): # This should eventually delegate to _composition_ after performing # some sanity checks for us. - mor = super(FiniteDimensionalEuclideanJordanAlgebraOperator,self) + mor = super(FiniteDimensionalEJAOperator,self) return mor.__mul__(other) @@ -288,14 +282,14 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA EXAMPLES:: sage: J = RealSymmetricEJA(2) sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id) + sage: f = FiniteDimensionalEJAOperator(J,J,id) sage: -f Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -306,7 +300,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): Codomain: Euclidean Jordan algebra of dimension 3 over... """ - return FiniteDimensionalEuclideanJordanAlgebraOperator( + return FiniteDimensionalEJAOperator( self.domain(), self.codomain(), -self.matrix()) @@ -318,7 +312,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA TESTS: @@ -328,7 +322,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): sage: J = RealSymmetricEJA(2) sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id) + sage: f = FiniteDimensionalEJAOperator(J,J,id) sage: f^0 + f^1 + f^2 Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -350,7 +344,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): else: mat = self.matrix()**n - return FiniteDimensionalEuclideanJordanAlgebraOperator( + return FiniteDimensionalEJAOperator( self.domain(), self.codomain(), mat) @@ -364,14 +358,14 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import JordanSpinEJA EXAMPLES:: sage: J = JordanSpinEJA(2) sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id) + sage: FiniteDimensionalEJAOperator(J,J,id) Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: [1 0] @@ -398,14 +392,14 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA EXAMPLES:: sage: J = RealSymmetricEJA(2) sage: id = identity_matrix(J.base_ring(),J.dimension()) - sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id) + sage: f = FiniteDimensionalEJAOperator(J,J,id) sage: f - (f*2) Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -449,7 +443,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import (random_eja, ....: JordanSpinEJA, ....: RealSymmetricEJA) @@ -462,13 +456,13 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): sage: M = matrix(R, [ [0, 0], ....: [0, 0], ....: [0, 0] ]) - sage: L = FiniteDimensionalEuclideanJordanAlgebraOperator(J1,J2,M) + sage: L = FiniteDimensionalEJAOperator(J1,J2,M) sage: L.is_zero() True sage: M = matrix(R, [ [0, 0], ....: [0, 1], ....: [0, 0] ]) - sage: L = FiniteDimensionalEuclideanJordanAlgebraOperator(J1,J2,M) + sage: L = FiniteDimensionalEJAOperator(J1,J2,M) sage: L.is_zero() False @@ -591,14 +585,14 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA EXAMPLES:: sage: J = RealSymmetricEJA(2) sage: mat = matrix(J.base_ring(), J.dimension(), range(9)) - sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,mat) + sage: f = FiniteDimensionalEJAOperator(J,J,mat) sage: f.matrix() [0 1 2] [3 4 5] @@ -615,7 +609,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator + sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA EXAMPLES:: @@ -680,7 +674,7 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): # for the spectral theorem to work. us[i] = us[i]/us[i].norm() mat = us[i].column()*us[i].row() - Pi = FiniteDimensionalEuclideanJordanAlgebraOperator( + Pi = FiniteDimensionalEJAOperator( self.domain(), self.codomain(), mat)