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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. 

from sage.algebras.algebra import is_Algebra 

from sage.rings.ring import CommutativeRing 

if not (is_Algebra(A) and isinstance(A, CommutativeRing)): 

raise TypeError("A (=%s) must be a commutative algebra"%A) 

Category_in_ambient.__init__(self, A) 

 

def algebra(self): 

""" 

EXAMPLES:: 

 

sage: CommutativeAlgebraIdeals(QQ['x']).algebra() 

Univariate Polynomial Ring in x over Rational Field 

""" 

return self.ambient() 

 

def super_categories(self): 

""" 

EXAMPLES:: 

 

sage: CommutativeAlgebraIdeals(QQ['x']).super_categories() 

[Category of algebra ideals in Univariate Polynomial Ring in x over Rational Field] 

""" 

R = self.algebra() 

return [AlgebraIdeals(R)]