# Compute the Hilbert-Samuel function

let $f\in R=k[x,y,z]_{(x,y,z)}$ be a homogeneous form of degree $d$, monic in $x$. Show that $(y,z)$, $(y^{2}, z^{2})$,and $(y,z)^{2}$ are all parameter ideals for $M=R/(f)$. Compute the corresponding Hilbert-Samuel functions.

I do not know why $(y^{3},z^{3})$ are not the ideals.I do the Hilbert-Samuel functions of $(y,z)$, but do not sure whether I am right, maybe somebody can do one of them as an example,thank you.

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