# isInCoisotropic -- test membership in a coisotropic hypersurface

## Synopsis

• Usage:
isInCoisotropic(L,I)
• Inputs:
• L, an ideal, the ideal of a $k$-dimensional linear subspace $V(L)\subset\mathbb{P}^n$, which corresponds to a point $p_L\in\mathbb{G}(k,\mathbb{P}^n)$
• I, an ideal, the ideal of a $d$-dimensional projective variety $X=V(I)\subset\mathbb{P}^n$
• Optional inputs:
• Duality => ..., default value null, whether to use dual Plucker coordinates
• SingularLocus => ..., default value null, pass the singular locus of the variety
• Outputs:
• , whether $p_L$ belongs to the $s$-th associated subvariety $Z_s(X)\subset\mathbb{G}(k,\mathbb{P}^n)$ with $s = k+d+1-n$

## Description

This is equivalent to isSubset(ideal tangentialChowForm(I,s),plucker L), but it does not compute the tangential Chow form.

 i1 : use Grass(0,5,ZZ/33331,Variable=>x) ZZ o1 = -----[x ..x ] 33331 0 5 o1 : PolynomialRing i2 : I = minors(2,matrix {{x_0,x_1,x_3,x_4},{x_1,x_2,x_4,x_5}}) -- rational normal scroll surface 2 o2 = ideal (- x + x x , - x x + x x , - x x + x x , - x x + x x , - x x 1 0 2 1 3 0 4 2 3 1 4 1 4 0 5 2 4 ------------------------------------------------------------------------ 2 + x x , - x + x x ) 1 5 4 3 5 ZZ o2 : Ideal of -----[x ..x ] 33331 0 5 i3 : L = ideal(x_1-12385*x_2-16397*x_3-7761*x_4+827*x_5,x_0+2162*x_2-8686*x_3+2380*x_4+9482*x_5) -- linear 3-dimensional subspace o3 = ideal (x - 12385x - 16397x - 7761x + 827x , x + 2162x - 8686x + 1 2 3 4 5 0 2 3 ------------------------------------------------------------------------ 2380x + 9482x ) 4 5 ZZ o3 : Ideal of -----[x ..x ] 33331 0 5 i4 : time isInCoisotropic(L,I) -- whether L belongs to Z_1(V(I)) -- used 0.0365535 seconds o4 = true