ProjectiveHilbertPolynomial -- the class of all Hilbert polynomials

ProjectiveHilbertPolynomial -- the class of all Hilbert polynomials

The type ProjectiveHilbertPolynomial is a member of the class Type. Each object of class ProjectiveHilbertPolynomial is called a projective Hilbert polynomial. Each projective Hilbert polynomial is also a member of class HashTable.

More general types (whose methods may also apply) :

HashTable -- the class of all hash tables

For convenience, these polynomials are expressed in terms of the Hilbert polynomials of projective space.

The functions degree and dim are designed so they correspond the degree and dimension of the algebraic variety that may have been used to produce the Hilbert polynomial.

i1 : Z = Proj(QQ[x_0..x_12]/(x_0^3+x_12^3))



o1 = Z



o1 : ProjectiveVariety

i2 : hilbertPolynomial Z



o2 = P  - 3*P   + 3*P

      9      10      11



o2 : ProjectiveHilbertPolynomial

Functions and methods returning a a projective Hilbert polynomial :

- ProjectiveHilbertPolynomial

diff ProjectiveHilbertPolynomial -- differentiate

diff(ProjectiveHilbertPolynomial,ZZ) -- differentiate

hilbertPolynomial -- compute Hilbert polynomial

hilbertPolynomial Module

hilbertPolynomial ProjectiveVariety

hilbertPolynomial Ring

ProjectiveHilbertPolynomial + ProjectiveHilbertPolynomial

ProjectiveHilbertPolynomial - ProjectiveHilbertPolynomial

projectiveHilbertPolynomial ZZ

projectiveHilbertPolynomial(ZZ,ZZ)

ZZ * ProjectiveHilbertPolynomial

Methods for using a projective Hilbert polynomial :

degree ProjectiveHilbertPolynomial

dim ProjectiveHilbertPolynomial

euler ProjectiveHilbertPolynomial

expression ProjectiveHilbertPolynomial

hilbertSeries ProjectiveHilbertPolynomial

net ProjectiveHilbertPolynomial

ProjectiveHilbertPolynomial == ProjectiveHilbertPolynomial

ProjectiveHilbertPolynomial ZZ -- value of polynomial