# ideal(CoincidentRootLocus) -- the defining ideal of a coincident root locus

## Synopsis

• Function: ideal
• Usage:
ideal X
• Inputs:
• Outputs:
• an ideal, the defining homogeneous ideal of X

## Description

This is the same as image map X.

 i1 : X = coincidentRootLocus {3,2} o1 = CRL(3,2) o1 : Coincident root locus i2 : ideal X 4 2 2 2 2 3 3 2 o2 = ideal (25t - 50t t t + 16t t + 12t t t - 3t t , 50t t - 80t t t - 4 3 4 5 3 5 2 4 5 1 5 3 4 3 4 5 ------------------------------------------------------------------------ 2 2 2 3 3 2 10t t t + 48t t t - 7t t t - t t , 50t t - 80t t t t - 5t t t + 2 4 5 2 3 5 1 4 5 0 5 2 4 2 3 4 5 1 4 5 ------------------------------------------------------------------------ 2 2 2 2 3 2 2 36t t + 2t t t - 3t t t , 25t t - 40t t t t - t t t + 18t t t - 2 5 1 3 5 0 4 5 1 4 1 3 4 5 0 4 5 1 2 5 ------------------------------------------------------------------------ 2 3 2 2 2 2 2 3 2t t t , 5t t - 8t t t t + t t + 2t t t , 25t t - 40t t + 0 3 5 0 4 0 3 4 5 1 5 0 2 5 3 4 3 5 ------------------------------------------------------------------------ 2 2 2 2 2 2 2 10t t t t - 10t t t + 9t t + 8t t t - 2t t t , 50t t t - 80t t t + 2 3 4 5 1 4 5 2 5 1 3 5 0 4 5 2 3 4 2 3 5 ------------------------------------------------------------------------ 2 2 2 2 2 2 30t t t - 15t t t t - 8t t t + 24t t t - t t t , 25t t t - 40t t t 2 4 5 1 3 4 5 0 4 5 1 2 5 0 3 5 1 3 4 1 3 5 ------------------------------------------------------------------------ 2 2 2 2 2 2 + 15t t t t - 9t t t t + 8t t + t t t , 10t t t - 16t t t + 5t t t 1 2 4 5 0 3 4 5 1 5 0 2 5 0 3 4 0 3 5 1 4 5 ------------------------------------------------------------------------ 2 2 2 2 2 - 2t t t t + 3t t t , 25t t - 30t t t - 15t t t + 25t t t t - 0 2 4 5 0 1 5 2 4 2 3 5 1 3 5 1 2 4 5 ------------------------------------------------------------------------ 2 2 2 2 2 12t t t t + 4t t + 3t t t , 25t t t - 30t t t t - 18t t t + 0 3 4 5 1 5 0 2 5 1 2 4 1 2 3 5 0 3 5 ------------------------------------------------------------------------ 2 2 2 2 20t t t - t t t t + 4t t t , 10t t t + 10t t t - 28t t t t + 1 4 5 0 2 4 5 0 1 5 0 2 4 1 3 5 0 2 3 5 ------------------------------------------------------------------------ 2 2 2 2 2 2 2 7t t t t + t t , 25t t - 48t t t t + 22t t t t + t t , 5t t t + 0 1 4 5 0 5 1 4 0 2 3 5 0 1 4 5 0 5 0 1 4 ------------------------------------------------------------------------ 2 2 2 2 2 3 10t t t - 16t t t - 2t t t t + 3t t t , t t + 5t t - 8t t t t + 1 2 5 0 2 5 0 1 3 5 0 4 5 0 4 1 5 0 1 2 5 ------------------------------------------------------------------------ 2 2 2 3 2 2 2t t t , 50t t t - 75t t t - 90t t + 160t t t t + 3t t t - 60t t t 0 3 5 2 3 4 1 3 4 2 5 1 2 3 5 0 3 5 1 4 5 ------------------------------------------------------------------------ 2 2 2 + 16t t t t - 4t t t , 25t t t t - 45t t t - 45t t t + 101t t t t - 0 2 4 5 0 1 5 1 2 3 4 0 3 4 1 2 5 0 2 3 5 ------------------------------------------------------------------------ 2 2 2 2 2 34t t t t - 2t t , 25t t t - 30t t t t - 40t t t + 46t t t + 0 1 4 5 0 5 1 3 4 0 2 3 4 1 2 5 0 2 5 ------------------------------------------------------------------------ 2 2 2 3 7t t t t - 8t t t , 5t t t - 8t t t + 3t t t t - 8t t + 11t t t t 0 1 3 5 0 4 5 1 2 4 0 2 4 0 1 3 4 1 5 0 1 2 5 ------------------------------------------------------------------------ 2 3 2 2 2 2 2 - 3t t t , 25t t - 40t t t t + 18t t t - t t t - 2t t t , 100t t - 0 3 5 1 4 0 1 2 4 0 3 4 0 1 5 0 2 5 2 3 ------------------------------------------------------------------------ 3 3 2 2 150t t - 150t t + 465t t t + 465t t t - 1166t t t t + 414t t t t + 1 3 2 4 0 3 4 1 2 5 0 2 3 5 0 1 4 5 ------------------------------------------------------------------------ 2 2 2 3 2 2 22t t , 50t t t - 90t t - 75t t t + 160t t t t + 120t t t - 0 5 1 2 3 0 3 1 2 4 0 2 3 4 1 2 5 ------------------------------------------------------------------------ 2 2 2 2 2 2 189t t t - 8t t t t + 32t t t , 5t t - 6t t t - 3t t t + 5t t t t 0 2 5 0 1 3 5 0 4 5 1 3 0 2 3 0 2 4 0 1 3 4 ------------------------------------------------------------------------ 3 2 2 2 2 - 4t t + 4t t t t - t t t , 50t t t - 80t t t + 30t t t - 1 5 0 1 2 5 0 3 5 1 2 3 0 2 3 0 1 3 ------------------------------------------------------------------------ 2 2 2 3 2 2 15t t t t + 24t t t - 8t t t - t t t , 50t t - 80t t t t + 36t t - 0 1 2 4 0 3 4 0 1 5 0 2 5 1 3 0 1 2 3 0 3 ------------------------------------------------------------------------ 2 2 2 2 2 3 2 2 5t t t + 2t t t - 3t t t , 25t t - 40t t + 10t t t t + 9t t - 0 1 4 0 2 4 0 1 5 1 2 0 2 0 1 2 3 0 3 ------------------------------------------------------------------------ 2 2 2 3 2 2 2 10t t t + 8t t t - 2t t t , 50t t - 80t t t - 10t t t + 48t t t - 0 1 4 0 2 4 0 1 5 1 2 0 1 2 0 1 3 0 2 3 ------------------------------------------------------------------------ 2 3 4 2 2 2 2 3 7t t t - t t , 25t - 50t t t + 16t t + 12t t t - 3t t ) 0 1 4 0 5 1 0 1 2 0 2 0 1 3 0 4 o2 : Ideal of QQ[t ..t ] 0 5