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# hilbertPolynomial(EmbeddedProjectiveVariety) -- the Hilbert polynomial of the variety

- Function: hilbertPolynomial
- Usage:
    `hilbertPolynomial X`
- Inputs:
  - X, an embedded projective variety
- Optional inputs:
  - Projective => ..., default value true,
- Outputs:
  - a projective Hilbert polynomial, the Hilbert polynomial of X (calculated as hilbertPolynomial ideal X)

## Description

    i1 : X = PP_QQ^(2,3);

    o1 : ProjectiveVariety, surface in PP^9

    i2 : hilbertPolynomial X

    o2 = P  - 9*P  + 9*P
          0      1      2

    o2 : ProjectiveHilbertPolynomial

    i3 : hilbertPolynomial(X,Projective=>false)

         9 2   9
    o3 = -i  + -i + 1
         2     2

    o3 : QQ[i]

## See also

- hilbertPolynomial(Ideal) -- compute the Hilbert polynomial of the quotient of the ambient ring by the ideal

## Ways to use this method:

- hilbertPolynomial(EmbeddedProjectiveVariety) -- the Hilbert polynomial of the variety

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:2587:0.