X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_subalgebra.py;fp=mjo%2Feja%2Feja_subalgebra.py;h=3eee24866216ca84aa8acf2484e07d01d6cad019;hb=4c8f9aac69d1cb4097b60b10e5b198b6372ec55e;hp=e7308ea34b9a36aef09a84069a1289e072487ec7;hpb=795ac83cd78143e36d47fa267fe6ddf1ca8da111;p=sage.d.git diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py index e7308ea..3eee248 100644 --- a/mjo/eja/eja_subalgebra.py +++ b/mjo/eja/eja_subalgebra.py @@ -1,9 +1,9 @@ from sage.matrix.constructor import matrix -from mjo.eja.eja_algebra import FiniteDimensionalEuclideanJordanAlgebra -from mjo.eja.eja_element import FiniteDimensionalEuclideanJordanAlgebraElement +from mjo.eja.eja_algebra import FiniteDimensionalEJA +from mjo.eja.eja_element import FiniteDimensionalEJAElement -class FiniteDimensionalEuclideanJordanSubalgebraElement(FiniteDimensionalEuclideanJordanAlgebraElement): +class FiniteDimensionalEJASubalgebraElement(FiniteDimensionalEJAElement): """ SETUP:: @@ -83,23 +83,12 @@ class FiniteDimensionalEuclideanJordanSubalgebraElement(FiniteDimensionalEuclide True """ - # As with the _element_constructor_() method on the - # algebra... even in a subspace of a subspace, the basis - # elements belong to the ambient space. As a result, only one - # level of coordinate_vector() is needed, regardless of how - # deeply we're nested. - W = self.parent().vector_space() - V = self.parent().superalgebra().vector_space() + return self._superalgebra(self.to_matrix()) - # Multiply on the left because basis_matrix() is row-wise. - ambient_coords = self.to_vector()*W.basis_matrix() - V_coords = V.coordinate_vector(ambient_coords) - return self.parent().superalgebra().from_vector(V_coords) - -class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJordanAlgebra): +class FiniteDimensionalEJASubalgebra(FiniteDimensionalEJA): """ A subalgebra of an EJA with a given basis. @@ -108,7 +97,7 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda sage: from mjo.eja.eja_algebra import (ComplexHermitianEJA, ....: JordanSpinEJA, ....: RealSymmetricEJA) - sage: from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra + sage: from mjo.eja.eja_subalgebra import FiniteDimensionalEJASubalgebra EXAMPLES: @@ -120,11 +109,11 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda ....: [0,0] ]) sage: E22 = matrix(AA, [ [0,0], ....: [0,1] ]) - sage: K1 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E11),)) + sage: K1 = FiniteDimensionalEJASubalgebra(J, (J(E11),)) sage: K1.one().to_matrix() [1 0] [0 0] - sage: K2 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E22),)) + sage: K2 = FiniteDimensionalEJASubalgebra(J, (J(E22),)) sage: K2.one().to_matrix() [0 0] [0 1] @@ -151,12 +140,10 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda 1 """ - def __init__(self, superalgebra, basis, category=None, check_axioms=True): + def __init__(self, superalgebra, basis, **kwargs): self._superalgebra = superalgebra V = self._superalgebra.vector_space() field = self._superalgebra.base_ring() - if category is None: - category = self._superalgebra.category() # A half-assed attempt to ensure that we don't collide with # the superalgebra's prefix (ignoring the fact that there @@ -170,52 +157,20 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda except ValueError: prefix = prefixen[0] - # If our superalgebra is a subalgebra of something else, then - # these vectors won't have the right coordinates for - # V.span_of_basis() unless we use V.from_vector() on them. - W = V.span_of_basis( (V.from_vector(b.to_vector()) for b in basis), - check=check_axioms) - - n = len(basis) - if check_axioms: - # The tables are square if we're verifying that they - # are commutative. - mult_table = [[W.zero() for j in range(n)] for i in range(n)] - ip_table = [ [ self._superalgebra.inner_product(basis[i],basis[j]) - for j in range(n) ] - for i in range(n) ] - else: - mult_table = [[W.zero() for j in range(i+1)] for i in range(n)] - ip_table = [ [ self._superalgebra.inner_product(basis[i],basis[j]) - for j in range(i+1) ] - for i in range(n) ] - - for i in range(n): - for j in range(i+1): - product = basis[i]*basis[j] - # product.to_vector() might live in a vector subspace - # if our parent algebra is already a subalgebra. We - # use V.from_vector() to make it "the right size" in - # that case. - product_vector = V.from_vector(product.to_vector()) - mult_table[i][j] = W.coordinate_vector(product_vector) - if check_axioms: - mult_table[j][i] = mult_table[i][j] - + # The superalgebra constructor expects these to be in original matrix + # form, not algebra-element form. matrix_basis = tuple( b.to_matrix() for b in basis ) + def jordan_product(x,y): + return (self._superalgebra(x)*self._superalgebra(y)).to_matrix() + def inner_product(x,y): + return self._superalgebra(x).inner_product(self._superalgebra(y)) - self._vector_space = W - - fdeja = super(FiniteDimensionalEuclideanJordanSubalgebra, self) - fdeja.__init__(field, - mult_table, - ip_table, - prefix=prefix, - category=category, - matrix_basis=matrix_basis, - check_field=False, - check_axioms=check_axioms) + super().__init__(matrix_basis, + jordan_product, + inner_product, + prefix=prefix, + **kwargs) @@ -228,7 +183,7 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda SETUP:: sage: from mjo.eja.eja_algebra import RealSymmetricEJA - sage: from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra + sage: from mjo.eja.eja_subalgebra import FiniteDimensionalEJASubalgebra EXAMPLES:: @@ -238,7 +193,7 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda ....: [1,0,0] ]) sage: x = J(X) sage: basis = ( x, x^2 ) # x^2 is the identity matrix - sage: K = FiniteDimensionalEuclideanJordanSubalgebra(J, basis) + sage: K = FiniteDimensionalEJASubalgebra(J, basis, orthonormalize=False) sage: K(J.one()) f1 sage: K(J.one() + x) @@ -247,23 +202,10 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda :: """ - if elt not in self.superalgebra(): - raise ValueError("not an element of this subalgebra") - - # The extra hackery is because foo.to_vector() might not live - # in foo.parent().vector_space()! Subspaces of subspaces still - # have user bases in the ambient space, though, so only one - # level of coordinate_vector() is needed. In other words, if V - # is itself a subspace, the basis elements for W will be of - # the same length as the basis elements for V -- namely - # whatever the dimension of the ambient (parent of V?) space is. - V = self.superalgebra().vector_space() - W = self.vector_space() - - # Multiply on the left because basis_matrix() is row-wise. - ambient_coords = elt.to_vector()*V.basis_matrix() - W_coords = W.coordinate_vector(ambient_coords) - return self.from_vector(W_coords) + if elt in self.superalgebra(): + return super()._element_constructor_(elt.to_matrix()) + else: + return super()._element_constructor_(elt) @@ -286,38 +228,4 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda return self._superalgebra - def vector_space(self): - """ - SETUP:: - - sage: from mjo.eja.eja_algebra import RealSymmetricEJA - sage: from mjo.eja.eja_subalgebra import FiniteDimensionalEuclideanJordanSubalgebra - - EXAMPLES:: - - sage: J = RealSymmetricEJA(3) - sage: E11 = matrix(ZZ, [ [1,0,0], - ....: [0,0,0], - ....: [0,0,0] ]) - sage: E22 = matrix(ZZ, [ [0,0,0], - ....: [0,1,0], - ....: [0,0,0] ]) - sage: b1 = J(E11) - sage: b2 = J(E22) - sage: basis = (b1, b2) - sage: K = FiniteDimensionalEuclideanJordanSubalgebra(J,basis) - sage: K.vector_space() - Vector space of degree 6 and dimension 2 over... - User basis matrix: - [1 0 0 0 0 0] - [0 0 1 0 0 0] - sage: b1.to_vector() - (1, 0, 0, 0, 0, 0) - sage: b2.to_vector() - (0, 0, 1, 0, 0, 0) - - """ - return self._vector_space - - - Element = FiniteDimensionalEuclideanJordanSubalgebraElement + Element = FiniteDimensionalEJASubalgebraElement