CoCoA:HilbertPoly

HilbertPoly

the Hilbert polynomial

Description

This function returns the Hilbert polynomial for R as a polynomial in

the standard CoCoA ring Qt (= Q[t]).

The weights of the indeterminates of R must all be 1, and the

coefficient ring must be a field.

If the input is not homogeneous, the Hilbert polynomial of the

corresponding leading term (initial) ideal or module is calculated.

For the Hilbert *function*, see <ttref>Hilbert</ttref>.

Example

  Use R ::= Q[w,x,y,z];
  I := Ideal(z^2-xy,xz^2+w^3);
  Hilbert(R/I);
H(0) = 1
H(1) = 4
H(t) = 6t-3   for t >= 2
-------------------------------
  F := HilbertPoly(R/I);
  F;  -- a polynomial in the ring Qt
Qt :: 6t-3
-------------------------------
  Subst(F,Qt::t,3);
Qt :: 15
-------------------------------

Syntax

Hilbert(R:RING or TAGGED(<quotes>Quotient</quotes>)):POLY in the ring Qt.

EvalHilbertFn

Hilbert

HVector

HilbertSeries

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