criticalBettiNumberWithoutArtinanReduction -- computes the critical Betti number

i1 : (k,g,n)=(4,8,1000);

i2 : I=idealOfNodalCurve(k,g,n);

               ZZ
o2 : Ideal of ----[t , t , t , t , t , t , t , t ]
              1009  0   1   2   3   4   5   6   7

i3 : time criticalBettiNumberWithoutArtinanReduction(I)
     -- used 1.68421 seconds

o3 = 4

i4 : time criticalBettiNumberWithoutArtinanReduction(k,g,n)
     -- used 2.47962 seconds

o4 = 4

i5 : betti res I

            0  1  2  3  4  5 6
o5 = total: 1 15 39 50 39 15 1
         0: 1  .  .  .  .  . .
         1: . 15 35 25  4  . .
         2: .  .  4 25 35 15 .
         3: .  .  .  .  .  . 1

o5 : BettiTally