The coincident root locus associated with a partition $\lambda=(\lambda_1,\ldots,\lambda_d)$ of a number $n$ is the closed subvariety of the projective space $\mathbb{P}^n = \mathbb{P}(Sym^n(K^2))$ given by binary forms that factor as ${L_1}^{\lambda_1}\cdots{L_d}^{\lambda_d}$ for some linear forms $L_1,\ldots,L_d$ over $\bar{K}$. For instance, if $\lambda=(2,1,\ldots,1)$, then we have the classical discriminant hypersurface; in the opposite case, if $\lambda=(n)$ we have the rational normal curve of degree $n$.
The object CoincidentRootLocus is a type, with ancestor classes MutableHashTable < HashTable < Thing.