-- -*- M2-comint -*- {* hash: -904316237 *}

i1 : R = ZZ/101[a..d];

i2 : S = coimage map(R, R, {a^4, a^3*b, a*b^3, b^4});

i3 : presentation S

o3 = | bc-ad c3-bd2 ac2-b2d b3-a2c |

             1       4
o3 : Matrix R  <--- R

i4 : h =  hilbertPolynomial S

o4 = - 3*P  + 4*P
          0      1

o4 : ProjectiveHilbertPolynomial

i5 : hilbertPolynomial(S, Projective=>false)

o5 = 4i + 1

o5 : QQ[i]

i6 : apply(5, k-> h(k))

o6 = {1, 5, 9, 13, 17}

o6 : List

i7 : apply(5, k-> hilbertFunction(k,S))

o7 = {1, 4, 9, 13, 17}

o7 : List

i8 :