# hilbertPolynomial(...,Projective=>...) -- choose how to display the Hilbert polynomial

## Synopsis

• Usage:
hilbertPolynomial(...,Projective => b
• Inputs:
• b, , either true or false

## Description

Projective => true is an option to hilbertPolynomial which specifies that the Hilbert polynomial produced should be expressed in terms of the Hilbert polynomials of projective spaces. This is the default.

Projective => false is an option to hilbertPolynomial which specifies that the Hilbert polynomial produced should be expressed as a polynomial in the variable i.

We compute the Hilbert polynomial of a coordinate ring of the rational quartic curve in P^3.

 i1 : R = ZZ/101[a..d]; i2 : S = coimage map(R, R, {a^4, a^3*b, a*b^3, b^4}); i3 : hilbertPolynomial S o3 = - 3*P + 4*P 0 1 o3 : ProjectiveHilbertPolynomial i4 : hilbertPolynomial(S, Projective=>false) o4 = 4i + 1 o4 : QQ[i]
When the option Projective is false, the variable i is a local variable. The command use ringwill make iinto a global variable.

## Further information

• Default value: true
• Function: hilbertPolynomial -- compute the Hilbert polynomial
• Option key: Projective -- whether to produce a projective Hilbert polynomial