X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_operator.py;h=689b7ecec26c09a8423ca440ee6b00429d50073b;hb=HEAD;hp=75a08205ff949bf23a62b073b6c74196f5161823;hpb=b0cf7605e6811065dad67263596c7f5d1bd45b34;p=sage.d.git diff --git a/mjo/eja/eja_operator.py b/mjo/eja/eja_operator.py index 75a0820..689b7ec 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 FiniteDimensionalEJAOperator(Map): +class EJAOperator(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 FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator EXAMPLES: @@ -19,12 +19,12 @@ class FiniteDimensionalEJAOperator(Map): sage: J = HadamardEJA(3) sage: V = VectorSpace(J.base_ring(), 3) sage: M = matrix.identity(J.base_ring(), 3) - sage: FiniteDimensionalEJAOperator(V,J,M) + sage: EJAOperator(V,J,M) Traceback (most recent call last): ... TypeError: domain must be a finite-dimensional Euclidean Jordan algebra - sage: FiniteDimensionalEJAOperator(J,V,M) + sage: EJAOperator(J,V,M) Traceback (most recent call last): ... TypeError: codomain must be a finite-dimensional Euclidean @@ -33,14 +33,14 @@ class FiniteDimensionalEJAOperator(Map): """ def __init__(self, domain_eja, codomain_eja, mat): - from mjo.eja.eja_algebra import FiniteDimensionalEJA + from mjo.eja.eja_algebra import EJA # I guess we should check this, because otherwise you could # pass in pretty much anything algebraish. - if not isinstance(domain_eja, FiniteDimensionalEJA): + if not isinstance(domain_eja, EJA): raise TypeError('domain must be a finite-dimensional ' 'Euclidean Jordan algebra') - if not isinstance(codomain_eja, FiniteDimensionalEJA): + if not isinstance(codomain_eja, EJA): raise TypeError('codomain must be a finite-dimensional ' 'Euclidean Jordan algebra') @@ -76,7 +76,7 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator sage: from mjo.eja.eja_algebra import JordanSpinEJA EXAMPLES:: @@ -84,7 +84,7 @@ class FiniteDimensionalEJAOperator(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 = FiniteDimensionalEJAOperator(J,J,id) + sage: f = EJAOperator(J,J,id) sage: f(x) == x True @@ -98,7 +98,7 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator sage: from mjo.eja.eja_algebra import ( ....: JordanSpinEJA, ....: RealSymmetricEJA ) @@ -109,8 +109,8 @@ class FiniteDimensionalEJAOperator(Map): sage: J = RealSymmetricEJA(2) sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: f = FiniteDimensionalEJAOperator(J,J,id) - sage: g = FiniteDimensionalEJAOperator(J,J,id) + sage: f = EJAOperator(J,J,id) + sage: g = EJAOperator(J,J,id) sage: f + g Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -127,15 +127,15 @@ class FiniteDimensionalEJAOperator(Map): sage: id1 = identity_matrix(J1.base_ring(), 3) sage: J2 = JordanSpinEJA(3) sage: id2 = identity_matrix(J2.base_ring(), 3) - sage: f = FiniteDimensionalEJAOperator(J1,J1,id1) - sage: g = FiniteDimensionalEJAOperator(J2,J2,id2) + sage: f = EJAOperator(J1,J1,id1) + sage: g = EJAOperator(J2,J2,id2) sage: f + g Traceback (most recent call last): ... TypeError: unsupported operand parent(s) for +: ... """ - return FiniteDimensionalEJAOperator( + return EJAOperator( self.domain(), self.codomain(), self.matrix() + other.matrix()) @@ -148,7 +148,7 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator sage: from mjo.eja.eja_algebra import ( ....: JordanSpinEJA, ....: HadamardEJA, @@ -162,8 +162,8 @@ class FiniteDimensionalEJAOperator(Map): sage: mat1 = matrix(AA, [[1,2,3], ....: [4,5,6]]) sage: mat2 = matrix(AA, [[7,8]]) - sage: g = FiniteDimensionalEJAOperator(J1, J2, mat1) - sage: f = FiniteDimensionalEJAOperator(J2, J3, mat2) + sage: g = EJAOperator(J1, J2, mat1) + sage: f = EJAOperator(J2, J3, mat2) sage: f*g Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -174,7 +174,7 @@ class FiniteDimensionalEJAOperator(Map): Algebraic Real Field """ - return FiniteDimensionalEJAOperator( + return EJAOperator( other.domain(), self.codomain(), self.matrix()*other.matrix()) @@ -196,14 +196,14 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA EXAMPLES:: sage: J = RealSymmetricEJA(2) sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: f = FiniteDimensionalEJAOperator(J,J,id) + sage: f = EJAOperator(J,J,id) sage: ~f Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -214,7 +214,7 @@ class FiniteDimensionalEJAOperator(Map): Codomain: Euclidean Jordan algebra of dimension 3 over... """ - return FiniteDimensionalEJAOperator( + return EJAOperator( self.codomain(), self.domain(), ~self.matrix()) @@ -231,7 +231,7 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA EXAMPLES: @@ -239,8 +239,8 @@ class FiniteDimensionalEJAOperator(Map): We can scale an operator on a rational algebra by a rational number:: sage: J = RealSymmetricEJA(2) - sage: e0,e1,e2 = J.gens() - sage: x = 2*e0 + 4*e1 + 16*e2 + sage: b0,b1,b2 = J.gens() + sage: x = 2*b0 + 4*b1 + 16*b2 sage: x.operator() Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -261,7 +261,7 @@ class FiniteDimensionalEJAOperator(Map): """ try: if other in self.codomain().base_ring(): - return FiniteDimensionalEJAOperator( + return EJAOperator( self.domain(), self.codomain(), self.matrix()*other) @@ -272,8 +272,7 @@ class FiniteDimensionalEJAOperator(Map): # This should eventually delegate to _composition_ after performing # some sanity checks for us. - mor = super(FiniteDimensionalEJAOperator,self) - return mor.__mul__(other) + return super().__mul__(other) def _neg_(self): @@ -282,14 +281,14 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA EXAMPLES:: sage: J = RealSymmetricEJA(2) sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: f = FiniteDimensionalEJAOperator(J,J,id) + sage: f = EJAOperator(J,J,id) sage: -f Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -300,7 +299,7 @@ class FiniteDimensionalEJAOperator(Map): Codomain: Euclidean Jordan algebra of dimension 3 over... """ - return FiniteDimensionalEJAOperator( + return EJAOperator( self.domain(), self.codomain(), -self.matrix()) @@ -312,7 +311,7 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA TESTS: @@ -322,7 +321,7 @@ class FiniteDimensionalEJAOperator(Map): sage: J = RealSymmetricEJA(2) sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: f = FiniteDimensionalEJAOperator(J,J,id) + sage: f = EJAOperator(J,J,id) sage: f^0 + f^1 + f^2 Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -344,7 +343,7 @@ class FiniteDimensionalEJAOperator(Map): else: mat = self.matrix()**n - return FiniteDimensionalEJAOperator( + return EJAOperator( self.domain(), self.codomain(), mat) @@ -358,14 +357,14 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator sage: from mjo.eja.eja_algebra import JordanSpinEJA EXAMPLES:: sage: J = JordanSpinEJA(2) sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: FiniteDimensionalEJAOperator(J,J,id) + sage: EJAOperator(J,J,id) Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: [1 0] @@ -392,14 +391,14 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA EXAMPLES:: sage: J = RealSymmetricEJA(2) sage: id = identity_matrix(J.base_ring(),J.dimension()) - sage: f = FiniteDimensionalEJAOperator(J,J,id) + sage: f = EJAOperator(J,J,id) sage: f - (f*2) Linear operator between finite-dimensional Euclidean Jordan algebras represented by the matrix: @@ -443,7 +442,7 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator sage: from mjo.eja.eja_algebra import (random_eja, ....: JordanSpinEJA, ....: RealSymmetricEJA) @@ -456,13 +455,13 @@ class FiniteDimensionalEJAOperator(Map): sage: M = matrix(R, [ [0, 0], ....: [0, 0], ....: [0, 0] ]) - sage: L = FiniteDimensionalEJAOperator(J1,J2,M) + sage: L = EJAOperator(J1,J2,M) sage: L.is_zero() True sage: M = matrix(R, [ [0, 0], ....: [0, 1], ....: [0, 0] ]) - sage: L = FiniteDimensionalEJAOperator(J1,J2,M) + sage: L = EJAOperator(J1,J2,M) sage: L.is_zero() False @@ -471,7 +470,6 @@ class FiniteDimensionalEJAOperator(Map): The left-multiplication-by-zero operation on a given algebra is its zero map:: - sage: set_random_seed() sage: J = random_eja() sage: J.zero().operator().is_zero() True @@ -511,7 +509,6 @@ class FiniteDimensionalEJAOperator(Map): The identity operator is its own inverse:: - sage: set_random_seed() sage: J = random_eja() sage: idJ = J.one().operator() sage: idJ.inverse() == idJ @@ -519,7 +516,6 @@ class FiniteDimensionalEJAOperator(Map): The inverse of the inverse is the operator we started with:: - sage: set_random_seed() sage: x = random_eja().random_element() sage: L = x.operator() sage: not L.is_invertible() or (L.inverse().inverse() == L) @@ -562,14 +558,12 @@ class FiniteDimensionalEJAOperator(Map): The identity operator is always invertible:: - sage: set_random_seed() sage: J = random_eja() sage: J.one().operator().is_invertible() True The zero operator is never invertible in a nontrivial algebra:: - sage: set_random_seed() sage: J = random_eja() sage: not J.is_trivial() and J.zero().operator().is_invertible() False @@ -585,14 +579,14 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator 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 = FiniteDimensionalEJAOperator(J,J,mat) + sage: f = EJAOperator(J,J,mat) sage: f.matrix() [0 1 2] [3 4 5] @@ -609,7 +603,7 @@ class FiniteDimensionalEJAOperator(Map): SETUP:: - sage: from mjo.eja.eja_operator import FiniteDimensionalEJAOperator + sage: from mjo.eja.eja_operator import EJAOperator sage: from mjo.eja.eja_algebra import RealSymmetricEJA EXAMPLES:: @@ -674,7 +668,7 @@ class FiniteDimensionalEJAOperator(Map): # for the spectral theorem to work. us[i] = us[i]/us[i].norm() mat = us[i].column()*us[i].row() - Pi = FiniteDimensionalEJAOperator( + Pi = EJAOperator( self.domain(), self.codomain(), mat)