# hilbertFunction(ZZ,DualSpace)

## Synopsis

• Function: hilbertFunction
• Usage:
k = hilbertFunction(d,S)
T = hilbertFunction(S)
K = hilbertFunction(D,S)
• Inputs:
• d, an integer, an integer, or a List of arguments
• S, an instance of the type DualSpace, a dual space
• Outputs:
• T, , of dimensions for each degree
• k, an integer, dimensions
• K, a list, of dimensions

## Description

counts the dimension of the dual space in each degree. A single degree can be specified, or a list of degrees. If no degree is specified, then a Tally is returned pairing each degree with its dimension.

 i1 : R = CC[x,y]; i2 : I = (ideal {x,y})^4; o2 : Ideal of R i3 : D = zeroDimensionalDual(origin R, I) o3 = | 1 y x .5y2 xy .5x2 .166667y3 .5xy2 .5x2y .166667x3 | o3 : DualSpace i4 : hilbertFunction D o4 = Tally{0 => 1} 1 => 2 2 => 3 3 => 4 o4 : Tally