Singular Manual: lpUfGraph

| #### 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

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