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Resultants :: isInCoisotropic

isInCoisotropic -- test membership in a coisotropic hypersurface

Synopsis

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

See also

Ways to use isInCoisotropic :

For the programmer

The object isInCoisotropic is a method function with options.