I'm trying to understand how to compute the Hilbert-Samuel polynomial of a specific example. Could someone help me with an elaborate computation so that I get it...
For example, what is the HS-polynomial of $\mathbb Z[x,y,z]_{(2,x,y-1,z-2)}$ (i.e. the localization of the ring $\mathbb Z[x,y,z]$ at the maximal ideal $(2,x,y-1,z-2)$)?
Thank you all in advance and happy new year to all!!!