# principalOrderIdeal -- computes the elements below a given element in a poset

## Synopsis

• Usage:
I = principalOrderIdeal(P, a)
• Inputs:
• P, an instance of the type Poset,
• a, , an element of the poset
• Outputs:
• I, a list, containing all elements less than or equal to the given elements

## Description

The order ideal of a element of a poset is all the elements in the poset which are less than or equal to the given element.

 i1 : P = booleanLattice 3; i2 : principalOrderIdeal(P, "101") o2 = {000, 001, 100, 101} o2 : List