CoCoA:AffHilbert

AffHilbert

the affine Hilbert function

Description

The first form of this function computes the affine Hilbert function for R.

The second form computes the N-th value of the affine Hilbert function. The

weights of the indeterminates of R must all be 1. For repeated evaluations of the Hilbert function, use <ttref>EvalHilbertFn</ttref> instead of Hilbert(R,N) in order to speed up execution.

This function is the same as <ttref>AffHilbertFn</ttref>.

The coefficient ring must be a field.

Example

  Use R ::= Q[x,y,z];
  AffHilbert(R/Ideal(z^4-1, xz^4-y-3));
H(0) = 1
H(1) = 3
H(t) = 4t - 2   for t >= 2
-------------------------------

Syntax

AffHilbert(R:RING or TAGGED(<quotes>Quotient</quotes>)):TAGGED(<quotes><tt>$hp.Hilbert</tt></quotes>)
AffHilbert(R:RING or TAGGED(<quotes>Quotient</quotes>),N:INT):INT

AffHilbertSeries

EvalHilbertFn

   <type>groebner</type>
   <type>groebner-basic</type>
   <type>hilbert</type>
   <type>quotient</type>
   <type>ring</type>