-- -*- M2-comint -*- hash: 12874367536417540601

i1 : R = setupRings(4,3);

i2 : M = coker vars R_2;

i3 : betti freeResolution(M, LengthLimit => numgens ring M)

            0 1 2  3  4
o3 = total: 1 4 8 12 16
         0: 1 4 6  4  1
         1: . . 2  8 12
         2: . . .  .  3

o3 : BettiTally

i4 : betti syzygyModule(2,M)

            0  1
o4 = total: 8 12
         2: 6  4
         3: 2  8

o4 : BettiTally

i5 : betti (N2 = syzygyModule(-2,M))

             0 1
o5 = total: 12 8
        -6:  8 2
        -5:  4 6

o5 : BettiTally

i6 : betti freeResolution(N2, LengthLimit => numgens ring N2)

             0 1 2 3 4
o6 = total: 12 8 5 5 8
        -6:  8 2 . . .
        -5:  4 6 4 1 .
        -4:  . . . . .
        -3:  . . . . .
        -2:  . . 1 4 6
        -1:  . . . . 2

o6 : BettiTally

i7 : betti syzygyModule(-2,M,CoDepth=>2)

           
o7 = total:

o7 : BettiTally

i8 : 
