--Poly. Ring R=QQ[x,y,z] --Paraboloid I=ideal(z-x^2-y^2) --Linear space/variety dim 1 in k^3 LinSpace=ideal(random(1,R),random(1,R)) degree I dim I --How many points are there after we slice with two planes? degree(I+LinSpace) --has dimension zero, so we do have points dim(I+LinSpace) -- --Saddle K=ideal(x^2-y^2*z^2+z^3) degree K --How many points are there after we slice with two planes? degree(K+LinSpace)