-- -*- M2-comint -*- {* hash: -642059967 *}

i1 : R = ZZ/101[x, Degrees => {2}];

i2 : I = ideal x^2

            2
o2 = ideal(x )

o2 : Ideal of R

i3 : s = hilbertSeries I

           4
      1 - T
o3 = --------
           2
     (1 - T )

o3 : Expression of class Divide

i4 : numerator s

          4
o4 = 1 - T

o4 : ZZ[T]

i5 : poincare I

          4
o5 = 1 - T

o5 : ZZ[T]

i6 : reduceHilbert s

          2
     1 + T
o6 = ------
        1

o6 : Expression of class Divide

i7 : R=ZZ/101[x, Degrees => {{1,1}}];

i8 : I = ideal x^2;

o8 : Ideal of R

i9 : s = hilbertSeries I

           2 2
      1 - T T
           0 1
o9 = ----------
     (1 - T T )
           0 1

o9 : Expression of class Divide

i10 : numerator s

           2 2
o10 = 1 - T T
           0 1

o10 : ZZ[T , T ]
          0   1

i11 : poincare I

           2 2
o11 = 1 - T T
           0 1

o11 : ZZ[T , T ]
          0   1

i12 : reduceHilbert s

      1 + T T
           0 1
o12 = --------
          1

o12 : Expression of class Divide

i13 :