# divisorPoset(RingElement) -- generates the poset of divisors

## Synopsis

• Function: divisorPoset
• Usage:
P = divisorPoset m
• Inputs:
• m, , which is a polynomial
• Outputs:
• P, an instance of the type Poset,

## Description

The divisor poset of a polynomial $m$ is the poset of divisors with order induced by divisibility.

 i1 : R = QQ[x,y]; i2 : divisorPoset(x^2*y) o2 = Relation Matrix: | 1 1 1 1 1 1 | | 0 1 0 1 0 1 | | 0 0 1 1 1 1 | | 0 0 0 1 0 1 | | 0 0 0 0 1 1 | | 0 0 0 0 0 1 | o2 : Poset

The method works with non-monomial divisors as well.

 i3 : divisorPoset(x*y^2 - 2*x*y + x) o3 = Relation Matrix: | 1 1 1 1 1 1 | | 0 1 0 1 1 1 | | 0 0 1 0 1 1 | | 0 0 0 1 0 1 | | 0 0 0 0 1 1 | | 0 0 0 0 0 1 | o3 : Poset