Singular Manual: cornerMonomials

| #### D.4.25.2 cornerMonomials Procedure from library `pointid.lib` (see pointid_lib). Usage: cornerMonomials(N); N ideal Assume: N is given by monomials satisfying the condition that if a monomial is in N then any of its factors is in N (N is then called an order ideal) Return: ideal, the corner-monomials of the order ideal N The corner-monomials are the leading monomials of an ideal I s.t. N is a basis of basering/I. Note: In our applications, I is the vanishing ideal of a finte set of points. Example:
    LIB "pointid.lib";
    ring R = 0,x(1..3),ip;
    poly n1 = 1;
    poly n2 = x(1);
    poly n3 = x(2);
    poly n4 = x(1)^2;
    poly n5 = x(3);
    poly n6 = x(1)^3;
    poly n7 = x(2)*x(3);
    poly n8 = x(3)^2;
    poly n9 = x(1)*x(2);
    ideal N = n1,n2,n3,n4,n5,n6,n7,n8,n9;
    cornerMonomials(N);
    ==> _[1]=x(1)^4
    ==> _[2]=x(1)^2*x(2)
    ==> _[3]=x(2)^2
    ==> _[4]=x(1)*x(3)
    ==> _[5]=x(2)*x(3)^2
    ==> _[6]=x(3)^3

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