SINGULAR example:

// consider a line and a plane: ring R=0,(x,y,z),dp; number a,b,c,d,e=1,1,1,1,1; ideal L=a*x+b*y,z; poly P=c*x+d*y+e*z; ideal I=L,P; std(I); // the zero set is a line a=0; L=a*x+b*y,z; I=L,P; std(I); // the zero set is finite (a point)

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