# postulationNumber -- computes the largest degree at which the hilbert function of the graded module M is not equal to the hilbertPolynomial

## Synopsis

• Usage:
v = postulationNumber(M)
• Inputs:
• Outputs:
• v, an integer, largest degree at which the hilbert function of the graded module M is not equal to the hilbertPolynomial

## Description

This function computes the postulation number of M which is defined as the largest degree at which the hilbert function of the graded module M is not equal to the hilbertPolynomial

 i1 : V = {{0,0},{1,0},{1,1},{0,1}}; i2 : F = {{0,1,2},{0,2,3}}; i3 : E = {{0,1},{0,2},{0,3},{1,2},{2,3}}; i4 : M = splineModule(V,F,E,2) o4 = image | 1 t_0^3-3t_0^2t_1+3t_0t_1^2-t_1^3 | | 1 0 | 2 o4 : QQ[t ..t ]-module, submodule of (QQ[t ..t ]) 0 2 0 2 i5 : postulationNumber(M) o5 = 0

## Ways to use postulationNumber :

• "postulationNumber(Module)"

## For the programmer

The object postulationNumber is .