Singular

D.4.21.2 cornerMonomials

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.

LIB "pointid.lib";
ring R = 0,x(1..3),rp;
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