constraintGraph -- constraint graph of a polynomial set

Synopsis

Usage:

constraintGraph I
Inputs:
- I, an ideal,
Outputs:
- a graph, constraint graph of the generators of I

Description

This method constructs the constraint graph associated to a polynomial set $F = \{f_1,\dots,f_m\}$. The vertices of this graph are the variables, and there is an edge connecting two variables iff there is a polynomial that uses both of them.

i1 : R = QQ[x_0..x_3];

i2 : I = ideal {x_0^2*x_1*x_2 +2*x_1 +1, x_1^2 +x_2, x_1 +x_2, x_2*x_3};

o2 : Ideal of R

i3 : constraintGraph I

o3 = Graph{x  => {x , x }    }
            0      1   2
           x  => {x , x }
            1      0   2
           x  => {x , x , x }
            2      0   1   3
           x  => {x }
            3      2

o3 : Graph

Ways to use constraintGraph :

constraintGraph(Ideal)
constraintGraph(Ring,List)

For the programmer

The object constraintGraph is a method function.