dual(CoincidentRootLocus) -- the projectively dual to a coincident root locus

i1 : X = coincidentRootLocus {5,3,2,2,1,1}

o1 = CRL(5,3,2,2,1,1)

o1 : Coincident root locus

i2 : dual X

o2 = CRL(11,1,1,1) * CRL(13,1) * CRL(14) * CRL(14) (dual of CRL(5,3,2,2,1,1))

o2 : Join of 4 coincident root loci

i3 : Y = dual coincidentRootLocus {4,2}

o3 = CRL(4,1,1) * CRL(6) (dual of CRL(4,2))

o3 : Join of 2 coincident root loci

i4 : ring Y

o4 = QQ[t ..t ]
         0   6

o4 : PolynomialRing

i5 : coefficientRing Y

o5 = QQ

o5 : Ring

i6 : dim Y

o6 = 5

i7 : codim Y

o7 = 1

i8 : degree Y

o8 = 18

i9 : dual Y

o9 = CRL(4,2)

o9 : Coincident root locus

i10 : G = random Y

            6        5           4 2         3 3           2 4             5
o10 = 10290t  + 3087t t  + 15435t t  + 68600t t  - 1186290t t  + 2658852t t 
            0        0 1         0 1         0 1           0 1           0 1
      -----------------------------------------------------------------------
                6
      - 1744982t
                1

o10 : QQ[t ..t ]
          0   1

i11 : member(G,Y)

o11 = true

i12 : ideal Y;

o12 : Ideal of QQ[t ..t ]
                   0   6

i13 : describe Y

o13 = Dual of the coincident root locus associated with the partition {4, 2} defined over QQ
      which coincides with the join of the coincident root loci associated with the partitions: ({4, 1, 1},{6})
      ambient: P^6 = Proj(QQ[t_0..t_6])
      dim    = 5
      codim  = 1
      degree = 18
      The defining polynomial has 3140 terms of degree 18