criticalKoszulDegrees -- compute all d with $\sum_{p+q=d} (-1)^q dim K_{p,q}(S/I)==0$ for an artinian ideal I

i1 : setRandomSeed("ok")

o1 = 11318

i2 : R=ZZ/101[x_0..x_4];

i3 : I = ideal random(R^1,R^{7:-2});

o3 : Ideal of R

i4 : assert(dim I==0)

i5 : H=apply(3,i->hilbertFunction(i,I))

o5 = {1, 5, 8}

o5 : List

i6 : expectedSyzygies(5,H)

            0 1  2  3  4 5
o6 = total: 1 7 35 56 35 8
         0: 1 .  .  .  . .
         1: . 7  .  .  . .
         2: . . 35 56 35 8

o6 : BettiTally

i7 : cp=criticalKoszulDegrees(I)

o7 = {3}

o7 : List