Lattice posets#

class sage.categories.lattice_posets.LatticePosets#

Bases: Category

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

Finite#: alias of FiniteLatticePosets

class ParentMethods#

Bases: object

join(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")))             # needs sage.graphs sage.modules
sage: D.join( D(6), D(10) )                                             # needs sage.graphs sage.modules
30

meet(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")))             # needs sage.graphs sage.modules
sage: D.meet( D(6), D(15) )                                             # needs sage.graphs sage.modules
3

super_categories()#

Returns a list of the (immediate) super categories of self, as per Category.super_categories().

EXAMPLES:

sage: LatticePosets().super_categories()
[Category of posets]