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r""" 

G-Sets 

""" 

from __future__ import absolute_import 

#***************************************************************************** 

# Copyright (C) 2008 David Kohel <kohel@maths.usyd.edu> and 

# William Stein <wstein@math.ucsd.edu> 

# 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 sage.categories.category import Category 

from .sets_cat import Sets 

 

############################################################# 

# GSets 

# $G$-Sets play an important role in permutation groups. 

############################################################# 

class GSets(Category): 

""" 

The category of $G$-sets, for a group $G$. 

 

EXAMPLES:: 

 

sage: S = SymmetricGroup(3) 

sage: GSets(S) 

Category of G-sets for Symmetric group of order 3! as a permutation group 

 

TODO: should this derive from Category_over_base? 

""" 

def __init__(self, G): 

""" 

TESTS:: 

 

sage: S8 = SymmetricGroup(8) 

sage: TestSuite(GSets(S8)).run() 

""" 

Category.__init__(self) 

self.__G = G 

 

def _repr_object_names(self): 

""" 

EXAMPLES:: 

 

sage: GSets(SymmetricGroup(8)) # indirect doctests 

Category of G-sets for Symmetric group of order 8! as a permutation group 

""" 

return "G-sets for %s"%self.__G 

 

#def construction(self): 

# return (self.__class__, self.__G) 

 

def super_categories(self): 

""" 

EXAMPLES:: 

 

sage: GSets(SymmetricGroup(8)).super_categories() 

[Category of sets] 

""" 

return [Sets()] 

 

@classmethod 

def an_instance(cls): 

""" 

Returns an instance of this class. 

 

EXAMPLES:: 

 

sage: GSets.an_instance() # indirect doctest 

Category of G-sets for Symmetric group of order 8! as a permutation group 

""" 

from sage.groups.perm_gps.permgroup_named import SymmetricGroup 

G = SymmetricGroup(8) 

return cls(G)