eliminateBetti -- elimination table for a Betti diagram

i1 : R = ZZ/8821[x,y,z,w]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x,y^2,z^4,w^8)

                2   4   8
o2 = ideal (x, y , z , w )

o2 : Ideal of R

i3 : B = betti res I

            0 1 2 3 4
o3 = total: 1 4 6 4 1
         0: 1 1 . . .
         1: . 1 1 . .
         2: . . . . .
         3: . 1 1 . .
         4: . . 1 1 .
         5: . . . . .
         6: . . . . .
         7: . 1 1 . .
         8: . . 1 1 .
         9: . . . . .
        10: . . 1 1 .
        11: . . . 1 1

o3 : BettiTally

i4 : eliminateBetti(B)

             0  1  2  3  4
o4 = total: 12 23 42 37 12
         0: 12  1  .  .  .
         1:  .  3  2  .  .
         2:  .  .  .  .  .
         3:  .  7  4  .  .
         4:  .  .  6  5  .
         5:  .  .  .  .  .
         6:  .  .  .  .  .
         7:  . 12  8  .  .
         8:  .  . 10  9  .
         9:  .  .  .  .  .
        10:  .  . 12 11  .
        11:  .  .  . 12 12

o4 : BettiEliminationTally