The dimension of a coincident root locus $X$ associated with a partition $\lambda=(\lambda_1,\ldots,\lambda_d)$ is $d$, the number of parts of $\lambda$.
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The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/CoincidentRootLoci/documentation.m2:30:0.