coincidentRootLocus -- makes a coincident root locus

Synopsis

• Usage:

  coincidentRootLocus(l,K)

  coincidentRootLocus l

• Inputs:
  • l, a visible list, 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:
  • a coincident root locus, 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