Lattice posets

class sage.categories.lattice_posets.LatticePosets(s=None)

Bases: sage.categories.category.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

TESTS:

sage: C = LatticePosets()
sage: TestSuite(C).run()
class ParentMethods
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")))
sage: D.join( D(6), D(10) )
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")))
sage: D.meet( D(6), D(15) )
3
LatticePosets.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]

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