I have to solve the problem 4 of the section 2 in the text "Ideal, varieties and algorithms" made by D. Cox, J. Little and D. O'Shea. The problem is that I must sketch some affine varieties in $\mathbb{R}^{3}$ in the software SINGULAR. For example $V(x+2, y-1.5,z)$. I tried to solving the system $f_1=f_2=f_3=0$, and the result is the point $(-2,1.5,0)$. This point is the variety correspondent. I used this code:
LIB "surf.lib"; ring R= 0, (x,y,z), dp; ideal H=x+2; ideal L= y-3/2; ideal K = z; ideal Q=intersect(H,L,K); plot(Q); Close window to exit from
singularsurf.
This code sketch the three maps $f_{1},f_{2},f_{3}$, but I need sketch only the point, e.g., the intersection of this maps. Can someone help me to solve this?.