kk = ZZ/101
ringP3 = kk[a..d]
ringP1 = kk[s,t]

cubicMap = map(ringP1, ringP3, {s^3, s^2*t, s*t^2, t^3})
idealCubic = kernel cubicMap

idealCubic2 = monomialCurveIdeal(ringP3, {1,2,3})

M = matrix{{a,b,c},{b,c,d}}
idealCubic3 = minors(2, M)