The singular locus of a coincident root locus is the union of certain subloci, as described in the paper by J. Chipalkatti - On equations defining coincident root loci - J. Algebra 267, 246-271, 2003; see also the paper by S. Kurmann - Some remarks on equations defining coincident root loci - J. Algebra 352, 223-231, 2012.
i1 : X = coincidentRootLocus {3,2,2,1,1,1,1} o1 = CRL(3,2,2,1,1,1,1) o1 : CoincidentRootLocus |
i2 : singularLocus X o2 = {CRL(4,4,3), CRL(3,3,2,2,1), CRL(3,2,2,2,1,1), CRL(5,2,1,1,1,1), ------------------------------------------------------------------------ CRL(4,2,2,1,1,1), CRL(3,3,2,1,1,1)} o2 : List |