isInCoisotropic(Ideal,CoincidentRootLocus) -- test membership in a coisotropic hypersurface

• Function: isInCoisotropic

• Usage:

  isInCoisotropic(I,X)

• Inputs:
  • I, an ideal, generated by $r+1$ linearly independent binary forms of the same degree $n$, which corresponds to a point $p_I\in Grass(r,\mathbb{P}(Sym^n(K^2)))=Grass(r,n)$
  • X, a coincident root locus, of dimension $d$ and codimension $n-d$
• Optional inputs:
  • Duality => ..., default value null,
  • SingularLocus => ..., default value null,
• Outputs:
  • a Boolean value, whether $p_I$ belongs to the $(r+d+1-n)$-th coisotropic hypersurface of $X$

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