-- -*- M2-comint -*- {* hash: -1398602193 *}

i1 : R = ZZ/101[a..h]

o1 = R

o1 : PolynomialRing

i2 : p = genericMatrix(R,a,2,4)

o2 = | a c e g |
     | b d f h |

             2       4
o2 : Matrix R  <--- R

i3 : q = generators gb p

o3 = | g e c a 0     0     0     0     0     0     |
     | h f d b fg-eh dg-ch bg-ah de-cf be-af bc-ad |

             2       10
o3 : Matrix R  <--- R

i4 : C = resolution cokernel leadTerm q

      2      10      14      7      1
o4 = R  <-- R   <-- R   <-- R  <-- R  <-- 0
                                           
     0      1       2       3      4      5

o4 : ChainComplex

i5 : betti C

            0  1  2 3 4
o5 = total: 2 10 14 7 1
         0: 2  4  6 4 1
         1: .  6  8 3 .

o5 : BettiTally

i6 : R = QQ[a,b,c,Degrees=>{-1,-2,-3}];

i7 : heft R       

o7 = {-1}

o7 : List

i8 : betti res coker vars R

            0 1 2 3
o8 = total: 1 3 3 1
         0: 1 1 . .
         1: . 1 1 .
         2: . 1 1 .
         3: . . 1 1

o8 : BettiTally

i9 : betti(oo, Weights => {1})

            0 1 2 3
o9 = total: 1 3 3 1
        -9: . . . 1
        -8: . . . .
        -7: . . 1 .
        -6: . . 1 .
        -5: . . 1 .
        -4: . 1 . .
        -3: . 1 . .
        -2: . 1 . .
        -1: . . . .
         0: 1 . . .

o9 : BettiTally

i10 : R = QQ[a,b,c,d,Degrees=>{{1,0},{2,1},{0,1},{-2,1}}];

i11 : heft R       

o11 = {1, 3}

o11 : List

i12 : b = betti res coker vars R

             0 1 2 3 4
o12 = total: 1 4 6 4 1
          0: 1 2 1 . .
          1: . . . . .
          2: . 1 2 1 .
          3: . . . . .
          4: . 1 2 1 .
          5: . . . . .
          6: . . 1 2 1

o12 : BettiTally

i13 : betti(b, Weights => {1,0})

             0 1 2 3 4
o13 = total: 1 4 6 4 1
         -4: . . 1 1 .
         -3: . 1 1 1 1
         -2: . . 1 1 .
         -1: . 1 1 . .
          0: 1 1 1 1 .
          1: . 1 1 . .

o13 : BettiTally

i14 : betti(b, Weights => {0,1})

             0 1 2 3 4
o14 = total: 1 4 6 4 1
         -1: . 1 3 3 1
          0: 1 3 3 1 .

o14 : BettiTally

i15 :