Coverage for local/lib/python2.7/site-packages/sage/categories/permutation_groups.py : 13%

r""" 

Permutation groups 

""" 

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

# Copyright (C) 2011 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.misc.cachefunc import cached_method 

from sage.categories.category import Category 

from sage.categories.groups import Groups 

from sage.misc.lazy_import import LazyImport 

class PermutationGroups(Category): 

r""" 

The category of permutation groups. 

A *permutation group* is a group whose elements are concretely 

represented by permutations of some set. In other words, the group 

comes endowed with a distinguished action on some set. 

This distinguished action should be preserved by permutation group 

morphisms. For details, see 

:Wikipedia:`Permutation_group#Permutation_isomorphic_groups`. 

.. TODO:: shall we accept only permutations with finite support or not? 

EXAMPLES:: 

sage: PermutationGroups() 

Category of permutation groups 

sage: PermutationGroups().super_categories() 

[Category of groups] 

The category of permutation groups defines additional structure 

that should be preserved by morphisms, namely the distinguished 

action:: 

sage: PermutationGroups().additional_structure() 

Category of permutation groups 

TESTS:: 

sage: C = PermutationGroups() 

sage: TestSuite(C).run() 

""" 

@cached_method 

def super_categories(self): 

""" 

Return a list of the immediate super categories of ``self``. 

EXAMPLES:: 

sage: PermutationGroups().super_categories() 

[Category of groups] 

""" 

return [Groups()] 

Finite = LazyImport('sage.categories.finite_permutation_groups', 'FinitePermutationGroups')