-- -*- M2-comint -*- {* hash: 1942988943 *}

i1 : degreesRing 3

o1 = ZZ[T , T , T ]
         0   1   2

o1 : PolynomialRing

i2 : describe oo

o2 = ZZ[T , T , T , Degrees => {3:{}}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 0, Inverses => true, Global => false]
         0   1   2                                      {Weights => {3:-1} }
                                                        {GroupLex => 3     }
                                                        {Position => Up    }

i3 : T_0

o3 = T
      0

o3 : IndexedVariable

i4 : use degreesRing 3

o4 = ZZ[T , T , T ]
         0   1   2

o4 : PolynomialRing

i5 : T_0

o5 = T
      0

o5 : ZZ[T , T , T ]
         0   1   2

i6 : W = degreesRing {1,2,5}

o6 = W

o6 : PolynomialRing

i7 : describe W

o7 = ZZ[T , T , T , Degrees => {1..2, 5}, MonomialOrder => {MonomialSize => 32     }, DegreeRank => 1, Inverses => true, Global => false]
         0   1   2                                         {Weights => {-1, -2, -5}}
                                                           {GroupLex => 3          }
                                                           {Position => Up         }

i8 : use W

o8 = W

o8 : PolynomialRing

i9 : (1+T_1+T_2^2)^3

                 2    3     2       2     2 2     4       4    6
o9 = 1 + 3T  + 3T  + T  + 3T  + 6T T  + 3T T  + 3T  + 3T T  + T
           1     1    1     2     1 2     1 2     2     1 2    2

o9 : W

i10 : degreesRing 3

o10 = ZZ[T , T , T ]
          0   1   2

o10 : PolynomialRing

i11 : describe oo

o11 = ZZ[T , T , T , Degrees => {3:{}}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 0, Inverses => true, Global => false]
          0   1   2                                      {Weights => {3:-1} }
                                                         {GroupLex => 3     }
                                                         {Position => Up    }

i12 : R = QQ[x,y,Degrees => {{1,-2},{2,-1}}];

i13 : heft R

o13 = {1, 0}

o13 : List

i14 : describe degreesRing R

o14 = ZZ[T , T , Degrees => {1, 0}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 1, Inverses => true, Global => false]
          0   1                                      {Weights => {-1..0}}
                                                     {GroupLex => 2     }
                                                     {Position => Up    }

i15 : S = QQ[x,y,Degrees => {-2,1}];

i16 : heft S

i17 : describe degreesRing S

o17 = ZZ[T, Degrees => {{}}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 0, Inverses => true, Global => false]
                                              {Weights => {-1}   }
                                              {GroupLex => 1     }
                                              {Position => Up    }

i18 :