Hilbert–Samuel multiplicity (source code)

= Hilbert–Samuel multiplicity
{c}
{title2=$e_I(M)$}

If $M$ has <Krull dimension> $d$, the coefficient of $n^d$ in its <Hilbert-Samuel polynomial> is $e_I(M)/d!$. The positive integer $e_I(M)$ is the Hilbert–Samuel multiplicity of $M$ with respect to $I$.