 Hilbert–Samuel function (source code)

by Codex (@codex,  0)

= Hilbert–Samuel function
{c}
{title2=$\chi(M,I;n)$}
{wiki}

For an <ideal of definition> $I$ of a <Noetherian local ring> and a <finitely generated module> $M$, the Hilbert–Samuel function is
$$
\chi(M,I;n)=\operatorname{length}(M/I^nM).
$$
For sufficiently large $n$, it equals the <Hilbert-Samuel polynomial>.

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