expectedBetti -- compute the expected betti table from the Hilbert numerator

• Usage:

  B=expectedBetti q

• Inputs:
  • q, a ring element, a polynomial in ZZ[t]
• Outputs:
  • B, a Betti tally, a Betti table that has Hilbert numerator q, assuming that each sign change in the coefficients of q corresponds to a step

i1 : T=ZZ[t]

o1 = T

o1 : PolynomialRing

i2 : q=1-3*t^2+2*t^3

       3     2
o2 = 2t  - 3t  + 1

o2 : T

i3 : expectedBetti q

            0 1 2
o3 = total: 1 3 2
         0: 1 . .
         1: . 3 2

o3 : BettiTally

i4 : q=1-5*t^2+5*t^3-t^5

        5     3     2
o4 = - t  + 5t  - 5t  + 1

o4 : T

i5 : expectedBetti q

            0 1 2 3
o5 = total: 1 5 5 1
         0: 1 . . .
         1: . 5 5 .
         2: . . . 1

o5 : BettiTally