i1 : R = QQ[a..d]; |
i2 : I = monomialCurveIdeal(R, {1,3,4}); o2 : Ideal of R |
i3 : h = hilbertPolynomial I o3 = - 3*P + 4*P 0 1 o3 : ProjectiveHilbertPolynomial |
i4 : hilbertPolynomial (R/I) o4 = - 3*P + 4*P 0 1 o4 : ProjectiveHilbertPolynomial |
i5 : hilbertPolynomial(I, Projective=>false) o5 = 4i + 1 o5 : QQ[i] |
These Hilbert polynomials can serve as Hilbert functions too since the values of the Hilbert polynomial eventually are the same as the Hilbert function.
i6 : apply(10, k-> h(k)) o6 = {1, 5, 9, 13, 17, 21, 25, 29, 33, 37} o6 : List |
i7 : apply(10, k-> hilbertFunction(k,I)) o7 = {1, 4, 9, 13, 17, 21, 25, 29, 33, 37} o7 : List |