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r""" Commutative algebra ideals """ from __future__ import absolute_import #***************************************************************************** # Copyright (C) 2005 David Kohel <kohel@maths.usyd.edu> # William Stein <wstein@math.ucsd.edu> # 2008-2009 Nicolas M. Thiery <nthiery at users.sf.net> # # Distributed under the terms of the GNU General Public License (GPL) # http://www.gnu.org/licenses/ #******************************************************************************
from .category_types import Category_ideal, Category_in_ambient from .algebra_ideals import AlgebraIdeals
class CommutativeAlgebraIdeals(Category_ideal): """ The category of ideals in a fixed commutative algebra `A`.
EXAMPLES::
sage: C = CommutativeAlgebraIdeals(QQ['x']) sage: C Category of commutative algebra ideals in Univariate Polynomial Ring in x over Rational Field """ def __init__(self, A): """ EXAMPLES::
sage: CommutativeAlgebraIdeals(ZZ['x']) Category of commutative algebra ideals in Univariate Polynomial Ring in x over Integer Ring
sage: CommutativeAlgebraIdeals(ZZ) Traceback (most recent call last): ... TypeError: A (=Integer Ring) must be a commutative algebra
sage: CommutativeAlgebraIdeals(IntegerModRing(4)) Traceback (most recent call last): ... TypeError: A (=Ring of integers modulo 4) must be a commutative algebra
sage: CommutativeAlgebraIdeals(Partitions(4)) Traceback (most recent call last): ... TypeError: A (=Partitions of the integer 4) must be a commutative algebra
TESTS::
sage: TestSuite(CommutativeAlgebraIdeals(QQ['x'])).run() """ # TODO: replace by ``A in CommutativeAlgebras(*)`` once a # suitable mantra has been implemented for this.
def algebra(self): """ EXAMPLES::
sage: CommutativeAlgebraIdeals(QQ['x']).algebra() Univariate Polynomial Ring in x over Rational Field """
def super_categories(self): """ EXAMPLES::
sage: CommutativeAlgebraIdeals(QQ['x']).super_categories() [Category of algebra ideals in Univariate Polynomial Ring in x over Rational Field] """ |