# openInterval -- computes the subposet contained strictly between two points

## Synopsis

• Usage:
I = openInterval(P, a, b)
• Inputs:
• P, an instance of the type Poset,
• a, , an element of the poset
• b, , an element of the poset
• Outputs:
• I, an instance of the type Poset, the open interval in $P$ between $a$ and $b$

## Description

The open interval between $a$ and $b$ is the subposet of $P$ induced by the elements $z$ such that $p < z < q$. If $a$ and $b$ are incomparable, then an error is thrown.

 i1 : P = booleanLattice 3; i2 : openInterval(P, "001", "111") o2 = Relation Matrix: | 1 0 | | 0 1 | o2 : Poset