hilbertSeries(ProjectiveVariety) -- compute the Hilbert series of a projective variety

Synopsis

Usage:
hilbertSeries V
Function: hilbertSeries
Inputs:
- V, a projective variety
Outputs:
- a divide expression, the Hilbert series
Optional inputs:
- Order => ..., -- display the truncated power series expansion

Description

We compute the Hilbert series of a projective variety, that is, the Hilbert series of the homogeneous coordinate ring of V. The saturation of the ideal may need to be computed.

i1 : V = Proj(QQ[x,y])

o1 = V

o1 : ProjectiveVariety

i2 : s = hilbertSeries V

         1
o2 = --------
            2
     (1 - T)

o2 : Expression of class Divide

i3 : numerator s

o3 = 1

o3 : ZZ [T, MonomialOrder => RevLex, Inverses => true]