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Macaulay2Doc :: hilbertPolynomial(CoherentSheaf)

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

Synopsis

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]