Coverage for local/lib/python2.7/site-packages/sage/categories/lattice_posets.py : 8%

r""" 

Lattice posets 

""" 

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

# 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.misc.abstract_method import abstract_method 

from sage.misc.lazy_import import LazyImport 

from sage.categories.category import Category 

from sage.categories.posets import Posets 

class LatticePosets(Category): 

r""" 

The category of lattices, i.e. partially ordered sets in which any 

two elements have a unique supremum (the elements' least upper 

bound; called their *join*) and a unique infimum (greatest lower bound; 

called their *meet*). 

EXAMPLES:: 

sage: LatticePosets() 

Category of lattice posets 

sage: LatticePosets().super_categories() 

[Category of posets] 

sage: LatticePosets().example() 

NotImplemented 

.. SEEALSO:: :class:`~sage.categories.posets.Posets`, :class:`FiniteLatticePosets`, :func:`LatticePoset` 

TESTS:: 

sage: C = LatticePosets() 

sage: TestSuite(C).run() 

""" 

@cached_method 

def super_categories(self): 

r""" 

Returns a list of the (immediate) super categories of 

``self``, as per :meth:`Category.super_categories`. 

EXAMPLES:: 

sage: LatticePosets().super_categories() 

[Category of posets] 

""" 

return [Posets()] 

Finite = LazyImport('sage.categories.finite_lattice_posets', 'FiniteLatticePosets') 

class ParentMethods: 

@abstract_method 

def meet(self, x, y): 

""" 

Returns the meet of `x` and `y` in this lattice 

INPUT: 

- ``x``, ``y`` -- elements of ``self`` 

EXAMPLES:: 

sage: D = LatticePoset((divisors(30), attrcall("divides"))) 

sage: D.meet( D(6), D(15) ) 

3 

""" 

@abstract_method 

def join(self, x, y): 

""" 

Returns the join of `x` and `y` in this lattice 

INPUT: 

- ``x``, ``y`` -- elements of ``self`` 

EXAMPLES:: 

sage: D = LatticePoset((divisors(60), attrcall("divides"))) 

sage: D.join( D(6), D(10) ) 

30 

"""