Coverage for local/lib/python2.7/site-packages/sage/categories/commutative_ring_ideals.py : 42%

r""" 

Commutative ring 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 

from sage.categories.commutative_rings import CommutativeRings 

from .ring_ideals import RingIdeals 

class CommutativeRingIdeals(Category_ideal): 

""" 

The category of ideals in a fixed commutative ring. 

EXAMPLES:: 

sage: C = CommutativeRingIdeals(IntegerRing()) 

sage: C 

Category of commutative ring ideals in Integer Ring 

""" 

def __init__(self, R): 

""" 

EXAMPLES:: 

sage: CommutativeRingIdeals(ZZ) 

Category of commutative ring ideals in Integer Ring 

sage: CommutativeRingIdeals(IntegerModRing(4)) 

Category of commutative ring ideals in Ring of integers modulo 4 

TESTS:: 

sage: CommutativeRingIdeals(Partitions(4)) 

Traceback (most recent call last): 

... 

TypeError: R (=Partitions of the integer 4) must be a commutative ring 

sage: TestSuite(CommutativeRingIdeals(ZZ)).run() 

""" 

if R not in CommutativeRings(): 

raise TypeError("R (=%s) must be a commutative ring"%R) 

Category_ideal.__init__(self, R) 

def super_categories(self): 

""" 

EXAMPLES:: 

sage: CommutativeRingIdeals(ZZ).super_categories() 

[Category of ring ideals in Integer Ring] 

""" 

R = self.ring() 

return [RingIdeals(R)]