Coverage for local/lib/python2.7/site-packages/sage/categories/r_trivial_semigroups.py : 100%

# -*- coding: utf-8 -*- 

r""" 

R-trivial semigroups 

""" 

from __future__ import absolute_import 

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

# Copyright (C) 2016 Nicolas M. Thiéry <nthiery at users.sf.net> 

# 

# This program is free software: you can redistribute it and/or modify 

# it under the terms of the GNU General Public License as published by 

# the Free Software Foundation, either version 2 of the License, or 

# (at your option) any later version. 

# http://www.gnu.org/licenses/ 

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

from sage.categories.category_with_axiom import CategoryWithAxiom 

from .semigroups import Semigroups 

class RTrivialSemigroups(CategoryWithAxiom): 

def extra_super_categories(self): 

r""" 

Implement the fact that a `R`-trivial semigroup is `H`-trivial. 

EXAMPLES:: 

sage: Semigroups().RTrivial().extra_super_categories() 

[Category of h trivial semigroups] 

""" 

return [Semigroups().HTrivial()] 

def Commutative_extra_super_categories(self): 

r""" 

Implement the fact that a commutative `R`-trivial semigroup is `J`-trivial. 

EXAMPLES:: 

sage: Semigroups().RTrivial().Commutative_extra_super_categories() 

[Category of j trivial semigroups] 

TESTS:: 

sage: Semigroups().RTrivial().Commutative() is Semigroups().JTrivial().Commutative() 

True 

""" 

return [self.JTrivial()]