next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
Macaulay2Doc :: ProjectiveHilbertPolynomial

ProjectiveHilbertPolynomial -- the class of all Hilbert polynomials

Description

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 projective Hilbert polynomial :

Methods that use a projective Hilbert polynomial :

For the programmer

The object ProjectiveHilbertPolynomial is a type, with ancestor classes HashTable < Thing.