randomEdgeIdeal -- Creates an edge ideal from a random graph with n vertices and t edges.

Usage:

(I,G) = randomEdgeIdeal(n,t)
Inputs:
- n, an integer, number of vertices
- t, an integer, number of edges
Outputs:
- I, an ideal, a random edge ideal
- G, a graph, the graph underlying I

Description

The edge ideal of a graph is the quadratic monomial ideal generated by x_v*x_w for all edges (v,w) in the graph. This method returns the edge ideal I of a random graph G which has n vertices and t edges.

i1 : randomEdgeIdeal(7, 4)

o1 = (Graph{"edges" => {{x , x }, {x , x }, {x , x }, {x , x }}},
                          3   4     1   4     6   7     3   5    
            "ring" => QQ[x ..x ]
                          1   7
            "vertices" => {x , x , x , x , x , x , x }
                            1   2   3   4   5   6   7
     ------------------------------------------------------------------------
     monomialIdeal (x x , x x , x x , x x ))
                     1 4   3 4   3 5   6 7

o1 : Sequence

Ways to use randomEdgeIdeal:

randomEdgeIdeal(ZZ,ZZ)

For the programmer

The object randomEdgeIdeal is a method function.

The source of this document is in RandomIdeals.m2:1393:0.

randomEdgeIdeal -- Creates an edge ideal from a random graph with n vertices and t edges.

Description

See also

Ways to use randomEdgeIdeal:

For the programmer