hilbertPolynomial(CoherentSheaf) -- compute the Hilbert polynomial of the coherent sheaf

Synopsis

Usage:
hilbertPolynomial S
Function: hilbertPolynomial
Inputs:
- S, a coherent sheaf
Outputs:
- a projective Hilbert polynomial, unless the option Projective is false
Optional inputs:
- Projective => ..., -- choose how to display the Hilbert polynomial

Description

We compute the Hilbert polynomial of a coherent sheaf.

i1 : R = ZZ/101[x_0..x_2];

i2 : V = Proj R;

i3 : S = sheaf(image matrix {{x_0^3+x_1^3+x_2^3}})

o3 = image | x_0^3+x_1^3+x_2^3 |

                                         1
o3 : coherent sheaf on V, subsheaf of OO
                                        V

i4 : h = hilbertPolynomial S

o4 = 3*P  - 3*P  + P
        0      1    2

o4 : ProjectiveHilbertPolynomial

i5 : hilbertPolynomial(S, Projective=>false)

     1  2   3
o5 = -*i  - -*i + 1
     2      2

o5 : QQ [i]