hVector -- compute the h-vector

Synopsis

Usage:
h=hVector d
h=hVector I
L = hVector M
Inputs:
- d, an integer
- I, an ideal
- M, a module
Outputs:
- h, a list, the h-vector
- L, a list, L₀ = initial degree of M, L₁ = h-vector M

Description

In case of an integer input d, we compute the h-vector of a generic set of d points in P³. In the case of an ideal input I, we compute the h-vector of (ring I)/I. In the case of a module M, we return the list L= initial degree M, h-vector M.

i1 : S=ZZ/101[x_0..x_3]

o1 = S

o1 : PolynomialRing

i2 : (J,M)=pickGorensteinIdeal(S,{1,3,6,6,3,1});

i3 : hVector J

o3 = {1, 3, 6, 6, 3, 1}

o3 : List

i4 : hVector (S^{2}/J)

o4 = {-2, {1, 3, 6, 6, 3, 1}}

o4 : List

i5 : hVector 10

o5 = {1, 3, 6}

o5 : List

Ways to use `hVector` :

hVector(Ideal)
hVector(Module)
hVector(ZZ)

hVector -- compute the h-vector

Synopsis

Description

Ways to use hVector :

Ways to use `hVector` :