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# coincidentRootLocus -- makes a coincident root locus

## Synopsis

• Usage:
coincidentRootLocus(l,K)
coincidentRootLocus l
• Inputs:
• l, , a partition of a number $n$, i.e., a list of $d$ positive integers $l_1,\ldots,l_d$ satisfying ${\sum}_{i} l_i = n$
• K, a ring, the coefficient ring (optional with default value QQ)
• Optional inputs:
• Variable => ..., default value "t", specify a name for a variable
• Outputs:
• , the coincident root locus associated with the partition $l$ over $K$, i.e., the subvariety of the projective $n$-space $\mathbb{P}(Sym^n(K^2))$ of all binary forms whose linear factors are distributed according to $l$

## Description

 i1 : X = coincidentRootLocus {6,4,3,3,2} o1 = CRL(6,4,3,3,2) o1 : Coincident root locus i2 : describe X o2 = Coincident root locus associated with the partition {6, 4, 3, 3, 2} defined over QQ ambient: P^18 = Proj(QQ[t_0..t_18]) dim = 5 codim = 13 degree = 25920 The singular locus is the union of the coincident root loci associated with the partitions: ({6, 6, 4, 2},{10, 3, 3, 2},{9, 4, 3, 2},{7, 6, 3, 2},{8, 4, 3, 3},{6, 6, 3, 3},{6, 5, 4, 3}) i3 : describe dual X o3 = Dual of the coincident root locus associated with the partition {6, 4, 3, 3, 2} defined over QQ which coincides with the join of the coincident root loci associated with the partitions: ({14, 1, 1, 1, 1},{16, 1, 1},{17, 1},{17, 1},{18}) ambient: P^18 = Proj(QQ[t_0..t_18]) dim = 17 codim = 1 degree = 21600

## Ways to use coincidentRootLocus :

• coincidentRootLocus(List)
• coincidentRootLocus(VisibleList,Ring)

## For the programmer

The object coincidentRootLocus is .