randomInCoisotropic(CoincidentRootLocus,ZZ) -- get a random element

Synopsis

Function: randomInCoisotropic
Usage:

randomInCoisotropic(X,i)
Inputs:
- X, a coincident root locus, of dimension $d$ and codimension $n-d$
- i, an integer
Outputs:
- an ideal, generated by $n-d+i$ linearly independent binary forms of the same degree $n$, which corresponds to a random point of the $i$-th coisotropic hypersurface $CH_i(X)\subset Grass(n-d-1+i,\mathbb{P}(Sym^n(K^2)))$

Description

i1 : X = coincidentRootLocus({2,2,1},ZZ/101)

o1 = CRL(2,2,1;ZZ/101)

o1 : Coincident root locus

i2 : I = randomInCoisotropic(X,1)

             3 2      2 3        4      5   4        2 3       4      5   5  
o2 = ideal (t t  + 42t t  + 32t t  - 32t , t t  + 14t t  + 4t t  - 44t , t  -
             0 1      0 1      0 1      1   0 1      0 1     0 1      1   0  
     ------------------------------------------------------------------------
        2 3        4      5
     40t t  - 18t t  - 36t )
        0 1      0 1      1

               ZZ
o2 : Ideal of ---[t ..t ]
              101  0   1

i3 : isInCoisotropic(I,X)

o3 = true

Ways to use this method: