Lattice posets#
- class sage.categories.lattice_posets.LatticePosets(s=None)#
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
See also
- 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 ofself
EXAMPLES:
sage: D = LatticePoset((divisors(60), attrcall("divides"))) # optional - sage.combinat sage: D.join( D(6), D(10) ) # optional - sage.combinat 30
- meet(x, y)#
Returns the meet of \(x\) and \(y\) in this lattice
INPUT:
x
,y
– elements ofself
EXAMPLES:
sage: D = LatticePoset((divisors(30), attrcall("divides"))) # optional - sage.combinat sage: D.meet( D(6), D(15) ) # optional - sage.combinat 3
- super_categories()#
Returns a list of the (immediate) super categories of
self
, as perCategory.super_categories()
.EXAMPLES:
sage: LatticePosets().super_categories() [Category of posets]