hilbertPolynomial -- compute the Hilbert polynomial

Synopsis

Optional inputs:
- Projective => ..., default value true, choose how to display the Hilbert polynomial

Description

In a singly graded ambient ring, the Hilbert function eventually is a polynomial called the Hilbert polynomial. By default this polynomial is written in terms of the Hilbert polynomials of projective spaces because it is a good form for extracting geometric information from the polynomial. The Hilbert polynomial of P^i is z |--> binomial(z + i, i).

Ways to use hilbertPolynomial :

hilbertPolynomial(ZZ,BettiTally) -- see BettiTally -- the class of all Betti tallies
hilbertPolynomial(CoherentSheaf) -- compute the Hilbert polynomial of the coherent sheaf
hilbertPolynomial(Ideal) -- compute the Hilbert polynomial of the quotient of the ambient ring by the ideal
hilbertPolynomial(Module) -- compute the Hilbert polynomial of the module
hilbertPolynomial(ProjectiveVariety) -- compute the Hilbert polynomial of the projective variety
hilbertPolynomial(Ring) -- compute the Hilbert polynomial of the ring

For the programmer

The object hilbertPolynomial is a method function with options.

hilbertPolynomial -- compute the Hilbert polynomial

Synopsis

Description

See also

Ways to use hilbertPolynomial :

For the programmer