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Packages » Posets :: divisorPoset(RingElement)

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divisorPoset(RingElement) -- generates the poset of divisors

Synopsis

Function: divisorPoset
Usage:

P = divisorPoset m
Inputs:
- m, a ring element, 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

See also

divisorPoset -- generates the poset of divisors
divisorPoset(ZZ) -- generates the poset of divisors
divisorPoset(RingElement,RingElement) -- generates the poset of divisors with a lower and upper bound
divisorPoset(List,List,PolynomialRing) -- generates the poset of divisors

Ways to use this method:

divisorPoset(RingElement) -- generates the poset of divisors