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Macaulay2Doc :: hilbertPolynomial(..., Projective => ...)

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

Synopsis

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

See also