multiplicity I
multiplicity(I,f)
Given an ideal $I\subset{} R$, ``multiplicity I'' returns the degree of the normal cone of $I$. When $R/I$ has finite length this is the sum of the Samuel multiplicities of $I$ at the various localizations of $R$. When $I$ is generated by a complete intersection, this is the length of the ring $R/I$ but in general it is greater. For example,
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The normal cone is computed using the Rees algebra, thus may be slow.
The object multiplicity is a method function with options.