-- -*- M2-comint -*- hash: 18436555528719512610

i1 : A = ZZ[x,y];

i2 : degreesRing A

o2 = ZZ[T]

o2 : PolynomialRing

i3 : degreesMonoid A

o3 = monoid[T, Degrees => {1}, MonomialOrder => {MonomialSize => 32}, Inverses => true, Global => false]
                                                {Weights => {-1}   }
                                                {GroupLex => 1     }
                                                {Position => Up    }

o3 : GeneralOrderedMonoid

i4 : degrees oo

o4 = {{1}}

o4 : List

i5 : heft A

o5 = {1}

o5 : List

i6 : R = QQ[x,y, Degrees => {{1,-2}, {2,-1}}];

i7 : degreesRing R

o7 = ZZ[T ..T ]
         0   1

o7 : PolynomialRing

i8 : degreesMonoid R

o8 = monoid[T ..T , Degrees => {1, 0}, MonomialOrder => {MonomialSize => 32}, Inverses => true, Global => false]
             0   1                                      {Weights => {-1..0}}
                                                        {GroupLex => 2     }
                                                        {Position => Up    }

o8 : GeneralOrderedMonoid

i9 : degrees oo

o9 = {{1}, {0}}

o9 : List

i10 : heft R

o10 = {1, 0}

o10 : List

i11 : S = QQ[x,y, Degrees => {-2,1}];

i12 : degreesRing S

o12 = ZZ[T]

o12 : PolynomialRing

i13 : degreesMonoid S

o13 = monoid[T, Degrees => {{}}, MonomialOrder => {MonomialSize => 32}, Inverses => true, Global => false]
                                                  {Weights => {-1}   }
                                                  {GroupLex => 1     }
                                                  {Position => Up    }

o13 : GeneralOrderedMonoid

i14 : degrees oo

o14 = {{}}

o14 : List

i15 : heft S

i16 : R = QQ[x,y, Degrees => {{1,-2,0}, {2,-1,1}}];

i17 : use degreesRing R

o17 = ZZ[T ..T ]
          0   2

o17 : PolynomialRing

i18 : hilbertSeries module ideal vars R

         -2    2 -1      3 -3
      T T   + T T  T  - T T  T
       0 1     0 1  2    0 1  2
o18 = -------------------------
             2 -1           -2
       (1 - T T  T )(1 - T T  )
             0 1  2       0 1

o18 : Expression of class Divide

i19 : (1+T_1+T_2^2)^3 

       3     2 2     2       4       2          6     4     2
o19 = T  + 3T T  + 3T  + 3T T  + 6T T  + 3T  + T  + 3T  + 3T  + 1
       1     1 2     1     1 2     1 2     1    2     2     2

o19 : ZZ[T ..T ]
          0   2

i20 : 
