# filter -- computes the elements above given elements in a poset

## Synopsis

• Usage:
F = filter(P, L)
• Inputs:
• P, an instance of the type Poset,
• L, a list, elements of the poset
• Outputs:
• F, a list, containing all elements greater than or equal to at least one of the given elements

## Description

The filter of a given set of elements of a poset is all the elements in the poset which are greater than or equal to at least one of the elements in the given set.

 i1 : P = booleanLattice 3; i2 : filter(P, {"001", "100"}) o2 = {001, 011, 101, 111, 100, 110} o2 : List

• orderIdeal -- computes the elements below given elements in a poset
• principalFilter -- computes the elements above a given element in a poset
• principalOrderIdeal -- computes the elements below a given element in a poset

## Ways to use filter :

• "filter(Poset,List)"

## For the programmer

The object filter is .