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

## Synopsis

• 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, , of dimension $d$ and codimension $n-d$
• Optional inputs:
• Outputs:
• , whether $p_I$ belongs to the $(r+d+1-n)$-th coisotropic hypersurface of $X$

## 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