Singular

LIB "polybori.lib";
ring rs=0,(x,y,z),Dp;
poly ps=(x+1)*(y+1)*(z+1);
zdd fz=ps;
boolean_set(fz);
==> {{x,y,z}, {x,y}, {x,z}, {x}, {y,z}, {y}, {z}, {}}
poly g=x*y*z+1;
zdd gz=g;
boolean_set(gz);
==> {{x,y,z}, {}}
ring R=0,(x(1..4)),Dp;
def Rb=boolean_poly_ring(R);
poly h=(x(1)+1)*(x(2)+1)*(x(3)+1)*(x(4)+1);
zdd hz=h;
boolean_set(hz);
==> {{x(1),x(2),x(3),x(4)}, {x(1),x(2),x(3)}, {x(1),x(2),x(4)}, {x(1),x(2)}, \
   {x(1),x(3),x(4)}, {x(1),x(3)}, {x(1),x(4)}, {x(1)}, {x(2),x(3),x(4)}, {x(\
   2),x(3)}, {x(2),x(4)}, {x(2)}, {x(3),x(4)}, {x(3)}, {x(4)}, {}}