 For example in both Maple and Magma these functions are named "HilbertSeries" and "HilbertPolynomial".In algebraic geometry, graded rings generated by elements of degree 1 produce projective schemes by Proj construction while finitely generated graded modules correspond to coherent sheaves.If formula_88 is a coherent sheaf over a projective scheme "X", we define the Hilbert polynomial of formula_88 as a function formula_90, where "χ" is the Euler characteristic of coherent sheaf, and formula_91 a Serre twist.