-- -*- M2-comint -*- hash: 2945129754935580284

i1 : kk = ZZ/101

o1 = kk

o1 : QuotientRing

i2 : S = kk[a,b,c]

o2 = S

o2 : PolynomialRing

i3 : f = matrix"a4,b4,c4"

o3 = | a4 b4 c4 |

             1      3
o3 : Matrix S  <-- S

i4 : R = S/ideal f

o4 = R

o4 : QuotientRing

i5 : p = map(R,S)

o5 = map (R, S, {a, b, c})

o5 : RingMap R <-- S

i6 : M = coker map(R^2, R^{3:-1}, {{a,b,c},{b,c,a}})

o6 = cokernel | a b c |
              | b c a |

                            2
o6 : R-module, quotient of R

i7 : betti (FF =freeResolution( M, LengthLimit =>6))

            0 1 2 3 4  5  6
o7 = total: 2 3 4 6 9 13 18
         0: 2 3 . . .  .  .
         1: . . 1 . .  .  .
         2: . . 3 3 .  .  .
         3: . . . 3 3  .  .
         4: . . . . 3  3  .
         5: . . . . 3  9  6
         6: . . . . .  .  3
         7: . . . . .  1  9

o7 : BettiTally

i8 : MS = prune pushForward(p, coker FF.dd_6);

i9 : T = exteriorTorModule(f,MS);

i10 : betti T

              0   1
o10 = total: 84 252
          0: 13  39
          1: 33  99
          2: 29  87
          3:  9  27

o10 : BettiTally

i11 : betti freeResolution (PT = prune T, LengthLimit => 4)

              0  1  2   3   4
o11 = total: 31 55 87 127 175
          0: 13 24 39  58  81
          1: 18 31 48  69  94

o11 : BettiTally

i12 : ann PT

o12 = ideal(e e e )
             0 1 2

o12 : Ideal of kk[e ..e ]
                   0   2

i13 : PT0 = image (inducedMap(PT,cover PT)* ((cover PT)_{0..12}));

i14 : PT1 = image (inducedMap(PT,cover PT)* ((cover PT)_{13..30}));

i15 : betti freeResolution(prune PT0, LengthLimit => 4)

              0  1  2  3  4
o15 = total: 13 24 39 58 81
          0: 13 24 39 58 81

o15 : BettiTally

i16 : betti freeResolution(prune PT1, LengthLimit => 4)

              0  1  2  3  4
o16 = total: 18 28 39 51 64
          1: 18 28 39 51 64

o16 : BettiTally

i17 : betti freeResolution(prune PT, LengthLimit => 4)

              0  1  2   3   4
o17 = total: 31 55 87 127 175
          0: 13 24 39  58  81
          1: 18 31 48  69  94

o17 : BettiTally

i18 : 
