Coverage for local/lib/python2.7/site-packages/sage/categories/gcd_domains.py : 18%

r""" 

Gcd domains 

""" 

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

# Copyright (C) 2008 Teresa Gomez-Diaz (CNRS) <Teresa.Gomez-Diaz@univ-mlv.fr> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

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

from sage.categories.category_singleton import Category_singleton 

from sage.categories.integral_domains import IntegralDomains 

class GcdDomains(Category_singleton): 

""" 

The category of gcd domains 

domains where gcd can be computed but where there is no guarantee of 

factorisation into irreducibles 

EXAMPLES:: 

sage: GcdDomains() 

Category of gcd domains 

sage: GcdDomains().super_categories() 

[Category of integral domains] 

TESTS:: 

sage: TestSuite(GcdDomains()).run() 

""" 

def super_categories(self): 

""" 

EXAMPLES:: 

sage: GcdDomains().super_categories() 

[Category of integral domains] 

""" 

return [IntegralDomains()] 

def additional_structure(self): 

""" 

Return ``None``. 

Indeed, the category of gcd domains defines no additional 

structure: a ring morphism between two gcd domains is a gcd 

domain morphism. 

.. SEEALSO:: :meth:`Category.additional_structure` 

EXAMPLES:: 

sage: GcdDomains().additional_structure() 

""" 

return None 

class ParentMethods: 

pass 

class ElementMethods: 

# gcd(x,y) 

# lcm(x,y) 

pass