# generic(CoincidentRootLocus) -- get the generic element

## Synopsis

• Function: generic
• Usage:
generic X
• Inputs:
• Optional inputs:
• Reduce => ..., default value false, reduce the number of variables
• Variable => ..., default value null, specify a name for a variable
• Outputs:
• , the generic binary form which belongs to X

## Description

 i1 : X = coincidentRootLocus {3,1,1} o1 = CRL(3,1,1) o1 : Coincident root locus i2 : F = generic X 3 5 3 3 2 4 3 o2 = t0 t1 t2 x + (t0 t1 t2 + t0 t1 t2 + 3t0 t0 t1 t2 )x x + (t0 t1 t2 + 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 ------------------------------------------------------------------------ 2 2 2 3 2 2 3t0 t0 t1 t2 + 3t0 t0 t1 t2 + 3t0 t0 t1 t2 )x x + (3t0 t0 t1 t2 + 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 ------------------------------------------------------------------------ 2 2 3 2 3 2 3t0 t0 t1 t2 + 3t0 t0 t1 t2 + t0 t1 t2 )x x + (3t0 t0 t1 t2 + 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 ------------------------------------------------------------------------ 3 3 4 3 5 t0 t1 t2 + t0 t1 t2 )x x + t0 t1 t2 x 1 0 1 1 1 0 0 1 1 1 1 1 o2 : QQ[t0 ..t0 , t1 ..t1 , t2 ..t2 ][x ..x ] 0 1 0 1 0 1 0 1 i3 : member(F,X) o3 = true i4 : factor F 3 o4 = (t2 x + t2 x )(t1 x + t1 x )(t0 x + t0 x ) 0 0 1 1 0 0 1 1 0 0 1 1 o4 : Expression of class Product i5 : G = generic(X,Reduce=>true) 5 5 4 4 4 4 3 2 3 3 o5 = t x + (3t t + t t + t t )x x + (3t t + 3t t t + 3t t t + 0 0 0 1 0 2 0 3 0 1 0 1 0 1 2 0 1 3 ------------------------------------------------------------------------ 3 3 2 2 3 2 2 2 2 2 2 3 3 t t t )x x + (t t + 3t t t + 3t t t + 3t t t t )x x + (t t t + 0 2 3 0 1 0 1 0 1 2 0 1 3 0 1 2 3 0 1 0 1 2 ------------------------------------------------------------------------ 3 2 4 3 5 t t t + 3t t t t )x x + t t t x 0 1 3 0 1 2 3 0 1 1 2 3 1 o5 : QQ[t ..t ][x ..x ] 0 3 0 1 i6 : member(G,X) o6 = true i7 : factor G 3 o7 = (t x + t x )(t x + t x )(t x + t x ) 0 0 3 1 0 0 2 1 0 0 1 1 o7 : Expression of class Product