A partition of a number $n$ is a hook if at most one part is not 1. The inputs of this method are required to be coincident root loci associated with hook partitions of $n$. In this case, the returned object is the dual of a certain coincident root locus; see the paper by H. Lee and B. Sturmfels - Duality of multiple root loci - J. Algebra 446, 499-526, 2016.
i1 : X = coincidentRootLocus {11,1,1,1,1}
o1 = CRL(11,1,1,1,1)
o1 : CoincidentRootLocus
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i2 : Y = coincidentRootLocus {13,1,1}
o2 = CRL(13,1,1)
o2 : CoincidentRootLocus
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i3 : X * Y o3 = CRL(11,1,1,1,1) * CRL(13,1,1) (dual of CRL(6,4,1,1,1,1,1)) o3 : JoinOfCoincidentRootLoci |
i4 : X * Y * Y o4 = CRL(11,1,1,1,1) * CRL(13,1,1) * CRL(13,1,1) (dual of CRL(6,4,4,1)) o4 : JoinOfCoincidentRootLoci |
More generally, if $I_1,I_2,\ldots$ is a sequence of homogeneous ideals (resp. parameterizations) of projective varieties $X_1,X_2,\ldots \subset \mathbb{P}^n$, then projectiveJoin(I_1,I_2,...) is the ideal of the projective join $X_1\,*\,X_2\,*\,\cdots \subset \mathbb{P}^n$.
i5 : I = ideal coincidentRootLocus {4}
2 2 2
o5 = ideal (t - t t , t t - t t , t t - t t , t - t t , t t - t t , t -
3 2 4 2 3 1 4 1 3 0 4 2 0 4 1 2 0 3 1
------------------------------------------------------------------------
t t )
0 2
o5 : Ideal of QQ[t , t , t , t , t ]
0 1 2 3 4
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i6 : projectiveJoin(I,I)
3 2 2
o6 = ideal(t - 2t t t + t t + t t - t t t )
2 1 2 3 0 3 1 4 0 2 4
o6 : Ideal of QQ[t , t , t , t , t ]
0 1 2 3 4
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