The twisted cubic in Macaulay2:

i1 : R = QQ[x,y,z,w]

o1 = R

o1 : PolynomialRing

i2 : I = monomialCurveIdeal(R, {1,2,3})

             2                    2
o2 = ideal (z  - y*w, y*z - x*w, y  - x*z)

o2 : Ideal of R