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

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