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7.10.3.7 lpUfGraph

Procedure from library fpaprops.lib (see fpaprops_lib).

Usage:
lpUfGraph(G); G a set of monomials in a letterplace ring.

Return:
intmat or list

Note:
lpUfGraph(G); returns intmat. lpUfGraph(G,1); returns list L with L[1] an intmat and L[2] an ideal. The intmat is the Ufnarovskij Graph and the ideal contains the vertices.

Purpose:
Constructs the Ufnarovskij graph induced by G
the adjacency matrix of the Ufnarovskij graph induced by G

Assume:
- basering is a Letterplace ring
- G are the leading monomials of a Groebner basis

Example:
 
LIB "fpaprops.lib";
ring r = 0,(x,y,z),dp;
def R = freeAlgebra(r, 5); // constructs a Letterplace ring
setring R; // sets basering to Letterplace ring
ideal I = x*y, x*z, z*y, z*z;
lpUfGraph(I);
==> 1,0,0,
==> 1,1,1,
==> 1,0,0 
lpUfGraph(I,1);
==> [1]:
==>    1,0,0,
==>    1,1,1,
==>    1,0,0 
==> [2]:
==>    _[1]=x
==>    _[2]=y
==>    _[3]=z