hilbertFunction(List,Ring) -- compute the Hilbert function of a ring

Synopsis

Usage:
hilbertFunction(d,R)
Function: hilbertFunction
Inputs:
- d, a list, which is a multidegree, or if R is singly graded, then one may write just ZZ
- R, a ring
Outputs:
- an integer, the value of the Hilbert function of the ring

Description

i1 : R = QQ[x,y,z, Degrees=>{3:{1,1}}];

i2 : hilbertFunction({3,3}, R)

o2 = 10

i3 : basis({3,3},R)

o3 = | x3 x2y x2z xy2 xyz xz2 y3 y2z yz2 z3 |

             1       10
o3 : Matrix R  <--- R

In the case where the ring is singly graded, then instead of having the input be a list of length 1 containing the degree, it is sufficient to write an integer.

i4 : R = QQ[x,y,z];

i5 : hilbertFunction(3, R)

o5 = 10

i6 : basis(3,R)

o6 = | x3 x2y x2z xy2 xyz xz2 y3 y2z yz2 z3 |

             1       10
o6 : Matrix R  <--- R