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

Synopsis

• 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