-- -*- M2-comint -*- hash: 1838957643603978051

i1 : kk=ZZ/101

o1 = kk

o1 : QuotientRing

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

o2 = S

o2 : PolynomialRing

i3 : M = truncate(3,S^1)

o3 = image | d3 cd2 bd2 ad2 c2d bcd acd b2d abd a2d c3 bc2 ac2 b2c abc a2c b3 ab2 a2b a3 |

                             1
o3 : S-module, submodule of S

i4 : betti matrix S2(0,M)

            0  1
o4 = total: 1 20
         0: 1  .
         1: .  .
         2: . 20

o4 : BettiTally

i5 : betti matrix S2(1,M)

            0  1
o5 = total: 1 20
         0: 1  .
         1: .  .
         2: . 20

o5 : BettiTally

i6 : M = S^1/intersect(ideal"a,b,c", ideal"b,c,d",ideal"c,d,a",ideal"d,a,b")

o6 = cokernel | cd bd ad bc ac ab |

                            1
o6 : S-module, quotient of S

i7 : prune source S2(0,M)

o7 = cokernel | cd bd ad bc ac ab |

                            1
o7 : S-module, quotient of S

i8 : prune target S2(0,M)

o8 = cokernel {-1} | d c b 0 0 0 0 0 0 0 0 0 |
              {-1} | 0 0 0 d c a 0 0 0 0 0 0 |
              {-1} | 0 0 0 0 0 0 d b a 0 0 0 |
              {-1} | 0 0 0 0 0 0 0 0 0 c b a |

                            4
o8 : S-module, quotient of S

i9 : S = ZZ/101[x_0..x_2];

i10 : ff = apply(3, i->x_i^2);

i11 : R = S/ideal ff;

i12 : M = cokernel matrix {{x_0, x_1*x_2}};

i13 : b = 5;

i14 : Mb = prune syzygyModule(-b,M);

i15 : E = prune evenExtModule Mb;

i16 : S2map = S2(0,E);

o16 : Matrix

i17 : SE = prune target S2map;

i18 : extra = prune coker S2map;

i19 : KE = prune ker S2map;

i20 : betti freeResolution(Mb, LengthLimit => 10)

              0  1 2 3 4 5 6 7 8  9 10
o20 = total: 20 14 9 5 2 1 2 4 7 11 16
         -6: 20 14 9 5 2 . . . .  .  .
         -5:  .  . . . . 1 1 1 1  1  1
         -4:  .  . . . . . 1 3 6 10 15

o20 : BettiTally

i21 : apply (5, i-> hilbertFunction(i, KE))

o21 = {20, 9, 2, 0, 0}

o21 : List

i22 : apply (5, i-> hilbertFunction(i, E))

o22 = {20, 9, 2, 2, 7}

o22 : List

i23 : apply (5, i-> hilbertFunction(i, SE))

o23 = {1, 1, 1, 2, 7}

o23 : List

i24 : apply (5, i-> hilbertFunction(i, extra))

o24 = {1, 1, 1, 0, 0}

o24 : List

i25 : 
