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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() """
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 """
#def construction(self): # return (self.__class__, self.__G)
def super_categories(self): """ EXAMPLES::
sage: GSets(SymmetricGroup(8)).super_categories() [Category of 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 """ |