ProjectiveHilbertPolynomial -- the class of all Hilbert polynomials

Description

For convenience, these polynomials are expressed in terms of the Hilbert polynomials of projective space.

The functions degree and dim are designed so they correspond the degree and dimension of the algebraic variety that may have been used to produce the Hilbert polynomial.

 i1 : Z = Proj(QQ[x_0..x_12]/(x_0^3+x_12^3)) o1 = Z o1 : ProjectiveVariety i2 : hilbertPolynomial Z o2 = P - 3*P + 3*P 9 10 11 o2 : ProjectiveHilbertPolynomial

Functions and methods returning a projective Hilbert polynomial :

• "ProjectiveHilbertPolynomial * ZZ" -- see * -- a binary operator, usually used for multiplication
• "ZZ * ProjectiveHilbertPolynomial" -- see * -- a binary operator, usually used for multiplication
• "ProjectiveHilbertPolynomial + ProjectiveHilbertPolynomial" -- see + -- a unary or binary operator, usually used for addition
• "ProjectiveHilbertPolynomial + ZZ" -- see + -- a unary or binary operator, usually used for addition
• "ZZ + ProjectiveHilbertPolynomial" -- see + -- a unary or binary operator, usually used for addition
• "- ProjectiveHilbertPolynomial" -- see - -- a unary or binary operator, usually used for negation or subtraction
• "ProjectiveHilbertPolynomial - ProjectiveHilbertPolynomial" -- see - -- a unary or binary operator, usually used for negation or subtraction
• "ProjectiveHilbertPolynomial - ZZ" -- see - -- a unary or binary operator, usually used for negation or subtraction
• "ZZ - ProjectiveHilbertPolynomial" -- see - -- a unary or binary operator, usually used for negation or subtraction
• diff(ProjectiveHilbertPolynomial)
• diff(ProjectiveHilbertPolynomial,ZZ)
• hilbertPolynomial -- compute the Hilbert polynomial
• hilbertPolynomial(ProjectiveVariety) -- compute the Hilbert polynomial of the projective variety
• projectiveHilbertPolynomial -- Hilbert polynomial of projective space

For the programmer

The object ProjectiveHilbertPolynomial is a type, with ancestor classes HashTable < Thing.