isHilbertPolynomial -- Determine whether a numerical polynomial can be a Hilbert polynomial

Synopsis

Usage:

isHilbertPolynomial p
Inputs:
- p, a projective Hilbert polynomial, or
- p, a ring element, a numerical univariate polynomial.
Outputs:
- a Boolean value,

Returns true if the input polynomial is an admissible Hilbert polynomial, false otherwise.

i1 : QQ[t];

i2 : isHilbertPolynomial(3*t+4)

o2 = true

i3 : isHilbertPolynomial((2/3)*t-1)

o3 = false

i4 : isHilbertPolynomial(2*projectiveHilbertPolynomial(2))

o4 = true

i5 : isHilbertPolynomial(2*projectiveHilbertPolynomial(2,-1))

o5 = false