divisorPoset(List,List,PolynomialRing) -- generates the poset of divisors

Synopsis

Usage:
P = divisorPoset(m, n, R)
Function: divisorPoset
Inputs:
- m, a list, an exponent vector of the lower bound monomial in R
- n, a list, an exponent vector of the upper bound monomial in R
- R, a polynomial ring
Outputs:
- P, an object of class Poset

Description

This method generates the divisor poset of the monomials in R whose exponent vectors are given by m and n.

i1 : R = QQ[x,y];

i2 : D = divisorPoset({0,1}, {2,2}, R)

o2 = Poset{cache => CacheTable{}                                                                           }
                             2          2   2    2 2
           GroundSet => {y, y , x*y, x*y , x y, x y }
           RelationMatrix => | 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 |
                              2               2     2            2          2        2   2 2     2    2 2
           Relations => {{y, y }, {y, x*y}, {y , x*y }, {x*y, x*y }, {x*y, x y}, {x*y , x y }, {x y, x y }}

o2 : Poset

i3 : D == divisorPoset(y, x^2*y^2)

o3 = true

divisorPoset(List,List,PolynomialRing) -- generates the poset of divisors

Synopsis

Description

See also