From: Michael Orlitzky Date: Sun, 28 Jul 2019 04:36:43 +0000 (-0400) Subject: eja: rewrite the operator class again to eliminate VectorSpaceMorphisms. X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=9717e0fafb2995a3a4d28fd76aafb70473089991;p=sage.d.git eja: rewrite the operator class again to eliminate VectorSpaceMorphisms. Wherever possible, I'd like to eliminate row-vector APIs from sneaking into userland. There's no reason for us to subclass VectorSpaceMorphism, because left-multiplication by a scalar doesn't work anyway. So, just drop it, and keep our own matrix variable around instead. --- diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py index 31717ee..5f9d5ba 100644 --- a/mjo/eja/euclidean_jordan_algebra.py +++ b/mjo/eja/euclidean_jordan_algebra.py @@ -6,8 +6,7 @@ what can be supported in a general Jordan Algebra. """ from sage.categories.finite_dimensional_algebras_with_basis import FiniteDimensionalAlgebrasWithBasis -from sage.categories.morphism import SetMorphism -from sage.modules.vector_space_morphism import VectorSpaceMorphism +from sage.categories.map import Map from sage.structure.element import is_Matrix from sage.structure.category_object import normalize_names @@ -15,23 +14,36 @@ from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra import from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_element import FiniteDimensionalAlgebraElement -class FiniteDimensionalEuclideanJordanAlgebraOperator(VectorSpaceMorphism): +class FiniteDimensionalEuclideanJordanAlgebraOperator(Map): def __init__(self, domain_eja, codomain_eja, mat): - # We save these so that we can output them as part of our - # text representation. Overriding the domain/codomain methods - # doesn't work because the EJAs aren't (directly) vector spaces. - self._domain_eja = domain_eja - self._codomain_eja = codomain_eja - - # Otherwise, we just feed everything to the vector space morphism - # constructor. - V = domain_eja.vector_space() - W = codomain_eja.vector_space() - homspace = V.Hom(W) - VectorSpaceMorphism.__init__(self, homspace, mat) - - - def __call__(self, x): + if not ( + isinstance(domain_eja, FiniteDimensionalEuclideanJordanAlgebra) and + isinstance(codomain_eja, FiniteDimensionalEuclideanJordanAlgebra) ): + raise ValueError('(co)domains must be finite-dimensional Euclidean ' + 'Jordan algebras') + + F = domain_eja.base_ring() + if not (F == codomain_eja.base_ring()): + raise ValueError("domain and codomain must have the same base ring") + + # We need to supply something here to avoid getting the + # default Homset of the parent FiniteDimensionalAlgebra class, + # which messes up e.g. equality testing. + parent = Hom(domain_eja, codomain_eja, VectorSpaces(F)) + + # 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) + + # Keep a matrix around to do all of the real work. It would + # be nice if we could use a VectorSpaceMorphism instead, but + # those use row vectors that we don't want to accidentally + # expose to our users. + self._matrix = mat + + + def _call_(self, x): """ Allow this operator to be called only on elements of an EJA. @@ -45,42 +57,10 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(VectorSpaceMorphism): True """ - # Overriding the single-underscore _call_ didn't work? - if x not in self._domain_eja: - raise ValueError("argument does not live in the operator's domain") - return self._codomain_eja(self.matrix()*x.vector()) - - - def _repr_(self): - r""" - - A text representation of this linear operator on a Euclidean - Jordan Algebra. - - EXAMPLES:: - - sage: J = JordanSpinEJA(2) - sage: id = identity_matrix(J.base_ring(), J.dimension()) - sage: FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id) - Linear operator between finite-dimensional Euclidean Jordan - algebras represented by the matrix: - [1 0] - [0 1] - Domain: Euclidean Jordan algebra of degree 2 over Rational Field - Codomain: Euclidean Jordan algebra of degree 2 over Rational Field - - """ - msg = ("Linear operator between finite-dimensional Euclidean Jordan " - "algebras represented by the matrix:\n", - "{!r}\n", - "Domain: {}\n", - "Codomain: {}") - return ''.join(msg).format(self.matrix(), - self._domain_eja, - self._codomain_eja) + return self.codomain()(self.matrix()*x.vector()) - def __add__(self, other): + def _add_(self, other): """ Add the ``other`` EJA operator to this one. @@ -112,17 +92,56 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(VectorSpaceMorphism): sage: f + g Traceback (most recent call last): ... - ValueError: operator (co)domains must match + TypeError: unsupported operand parent(s) for +: ... """ - if not (self._domain_eja == other._domain_eja and - self._codomain_eja == other._codomain_eja): - raise ValueError("operator (co)domains must match") return FiniteDimensionalEuclideanJordanAlgebraOperator( - self._domain_eja, - self._codomain_eja, - VectorSpaceMorphism.__add__(self,other)) + self.domain(), + self.codomain(), + self.matrix() + other.matrix()) + + + def _composition_(self, other, homset): + """ + Compose two EJA operators to get another one (and NOT a formal + composite object) back. + + EXAMPLES:: + sage: J1 = JordanSpinEJA(3) + sage: J2 = RealCartesianProductEJA(2) + sage: J3 = RealSymmetricEJA(1) + sage: mat1 = matrix(QQ, [[1,2,3], + ....: [4,5,6]]) + sage: mat2 = matrix(QQ, [[7,8]]) + sage: g = FiniteDimensionalEuclideanJordanAlgebraOperator(J1, + ....: J2, + ....: mat1) + sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J2, + ....: J3, + ....: mat2) + sage: f*g + Linear operator between finite-dimensional Euclidean Jordan + algebras represented by the matrix: + [39 54 69] + Domain: Euclidean Jordan algebra of degree 3 over Rational Field + Codomain: Euclidean Jordan algebra of degree 1 over Rational Field + + """ + return FiniteDimensionalEuclideanJordanAlgebraOperator( + other.domain(), + self.codomain(), + self.matrix()*other.matrix()) + + + def __eq__(self, other): + if self.domain() != other.domain(): + return False + if self.codomain() != other.codomain(): + return False + if self.matrix() != other.matrix(): + return False + return True def __invert__(self): """ @@ -144,31 +163,58 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(VectorSpaceMorphism): """ return FiniteDimensionalEuclideanJordanAlgebraOperator( - self._codomain_eja, - self._domain_eja, - VectorSpaceMorphism.__invert__(self)) + self.codomain(), + self.domain(), + ~self.matrix()) + def __mul__(self, other): """ - Compose this EJA operator with the ``other`` one, or scale it by - an element of its base ring. + Compose two EJA operators, or scale myself by an element of the + ambient vector space. + + We need to override the real ``__mul__`` function to prevent the + coercion framework from throwing an error when it fails to convert + a base ring element into a morphism. + + EXAMPLES: + + 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: x.operator() + Linear operator between finite-dimensional Euclidean Jordan algebras + represented by the matrix: + [ 2 4 0] + [ 2 9 2] + [ 0 4 16] + Domain: Euclidean Jordan algebra of degree 3 over Rational Field + Codomain: Euclidean Jordan algebra of degree 3 over Rational Field + sage: x.operator()*(1/2) + Linear operator between finite-dimensional Euclidean Jordan algebras + represented by the matrix: + [ 1 2 0] + [ 1 9/2 1] + [ 0 2 8] + Domain: Euclidean Jordan algebra of degree 3 over Rational Field + Codomain: Euclidean Jordan algebra of degree 3 over Rational Field + """ - if other in self._codomain_eja.base_ring(): + if other in self.codomain().base_ring(): return FiniteDimensionalEuclideanJordanAlgebraOperator( - self._domain_eja, - self._codomain_eja, - self._matrix*other) - - if not (self._domain_eja == other._codomain_eja): - raise ValueError("operator (co)domains must be compatible") + self.domain(), + self.codomain(), + self.matrix()*other) - return FiniteDimensionalEuclideanJordanAlgebraOperator( - other._domain_eja, - self._codomain_eja, - VectorSpaceMorphism.__mul__(self,other)) + # This should eventually delegate to _composition_ after performing + # some sanity checks for us. + mor = super(FiniteDimensionalEuclideanJordanAlgebraOperator,self) + return mor.__mul__(other) - def __neg__(self): + def _neg_(self): """ Negate this EJA operator. @@ -188,9 +234,9 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(VectorSpaceMorphism): """ return FiniteDimensionalEuclideanJordanAlgebraOperator( - self._domain_eja, - self._codomain_eja, - VectorSpaceMorphism.__neg__(self)) + self.domain(), + self.codomain(), + -self.matrix()) def __pow__(self, n): @@ -224,20 +270,84 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(VectorSpaceMorphism): cols = self.domain().dimension() mat = matrix.identity(self.base_ring(), rows, cols) else: - mat = VectorSpaceMorphism.__pow__(self,n) + mat = self.matrix()**n return FiniteDimensionalEuclideanJordanAlgebraOperator( - self._domain_eja, - self._codomain_eja, + self.domain(), + self.codomain(), mat) - def __sub__(self, other): + + def _repr_(self): + r""" + + A text representation of this linear operator on a Euclidean + Jordan Algebra. + + EXAMPLES:: + + sage: J = JordanSpinEJA(2) + sage: id = identity_matrix(J.base_ring(), J.dimension()) + sage: FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id) + Linear operator between finite-dimensional Euclidean Jordan + algebras represented by the matrix: + [1 0] + [0 1] + Domain: Euclidean Jordan algebra of degree 2 over Rational Field + Codomain: Euclidean Jordan algebra of degree 2 over Rational Field + + """ + msg = ("Linear operator between finite-dimensional Euclidean Jordan " + "algebras represented by the matrix:\n", + "{!r}\n", + "Domain: {}\n", + "Codomain: {}") + return ''.join(msg).format(self.matrix(), + self.domain(), + self.codomain()) + + + def _sub_(self, other): """ Subtract ``other`` from this EJA operator. + + EXAMPLES:: + + sage: J = RealSymmetricEJA(2) + sage: id = identity_matrix(J.base_ring(),J.dimension()) + sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,id) + sage: f - (f*2) + Linear operator between finite-dimensional Euclidean Jordan + algebras represented by the matrix: + [-1 0 0] + [ 0 -1 0] + [ 0 0 -1] + Domain: Euclidean Jordan algebra of degree 3 over Rational Field + Codomain: Euclidean Jordan algebra of degree 3 over Rational Field + """ return (self + (-other)) + def matrix(self): + """ + Return the matrix representation of this operator with respect + to the default bases of its (co)domain. + + EXAMPLES:: + + sage: J = RealSymmetricEJA(2) + sage: mat = matrix(J.base_ring(), J.dimension(), range(9)) + sage: f = FiniteDimensionalEuclideanJordanAlgebraOperator(J,J,mat) + sage: f.matrix() + [0 1 2] + [3 4 5] + [6 7 8] + + """ + return self._matrix + + class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra): @staticmethod def __classcall_private__(cls,