monomialGraph -- Returns a monomial graph

Synopsis

Usage:

G = monomialGraph(I,n)
Inputs:
- I, a monomial ideal, This monomial ideal be part of forming a quotient ring with respect to the ambient ring the ideal is in
- n, an integer, This integer determines the degree of monomials that will be considered
Outputs:
- G, an instance of the type Graph, The monomial graph

Description

The monomial graph with respect to a monomial ideal and an integer n is a graph with a vertex set of the monomials of the expression of the sum of the generators of the ambient ring for I to the power n. The edge set is formed by the rule that there is an edge between two of the vertices (which we are reminded are monomials) if and only if the degree of the least common multiple of the two vertices is n+1.

i1 : R = QQ[x,y];

i2 : I = monomialIdeal (x^3, y^2*x);

o2 : MonomialIdeal of R

i3 : monomialGraph (I, 3)

            2
o3 = Graph{x y => {}}
            3
           y  => {}

o3 : Graph

Ways to use `monomialGraph` :

"monomialGraph(MonomialIdeal,ZZ)"

For the programmer

The object monomialGraph is a method function.

monomialGraph -- Returns a monomial graph

Synopsis

Description

See also

Ways to use monomialGraph :

For the programmer

Ways to use `monomialGraph` :