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];
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i2 : S = coimage map(R, R, {a^4, a^3*b, a*b^3, b^4});
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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.