Lattice posets¶
- class sage.categories.lattice_posets.LatticePosets[source]¶
- 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 - >>> from sage.all import * >>> LatticePosets() Category of lattice posets >>> LatticePosets().super_categories() [Category of posets] >>> LatticePosets().example() NotImplemented - See also - Finite[source]¶
- alias of - FiniteLatticePosets
 - class ParentMethods[source]¶
- Bases: - object- join(x, y)[source]¶
- Return 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 - >>> from sage.all import * >>> D = LatticePoset((divisors(Integer(60)), attrcall("divides"))) # needs sage.graphs sage.modules >>> D.join( D(Integer(6)), D(Integer(10)) ) # needs sage.graphs sage.modules 30 
 - meet(x, y)[source]¶
- Return 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 - >>> from sage.all import * >>> D = LatticePoset((divisors(Integer(30)), attrcall("divides"))) # needs sage.graphs sage.modules >>> D.meet( D(Integer(6)), D(Integer(15)) ) # needs sage.graphs sage.modules 3 
 
 - super_categories()[source]¶
- Return a list of the (immediate) super categories of - self, as per- Category.super_categories().- EXAMPLES: - sage: LatticePosets().super_categories() [Category of posets] - >>> from sage.all import * >>> LatticePosets().super_categories() [Category of posets]