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Posets :: divisorPoset

divisorPoset -- generates the poset of divisors

Synopsis

Usage:

P = divisorPoset n
Inputs:
- n, an integer, which is not zero
Outputs:
- P, an instance of the type Poset,

Description

The divisor poset of an integer is the poset of positive divisors of an integer $n$ with order induced by divisibility.

i1 : divisorPoset 12

o1 = 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 |

o1 : Poset

i2 : divisorPoset 30

o2 = Relation Matrix: | 1 1 1 1 1 1 1 1 |
                      | 0 1 0 0 1 1 0 1 |
                      | 0 0 1 0 1 0 1 1 |
                      | 0 0 0 1 0 1 1 1 |
                      | 0 0 0 0 1 0 0 1 |
                      | 0 0 0 0 0 1 0 1 |
                      | 0 0 0 0 0 0 1 1 |
                      | 0 0 0 0 0 0 0 1 |

o2 : Poset

See also

divisorPoset(RingElement) -- 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 `divisorPoset` :

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

For the programmer

The object divisorPoset is a method function.