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

## Synopsis

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

## Description

calculates the expected betti table from a given hilbert Numerator.

 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

## For the programmer

The object expectedBetti is .