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StronglyStableIdeals :: stronglyStableIdeals

stronglyStableIdeals -- Compute the saturated strongly stable ideals in the given ambient space with given Hilbert polynomial

Synopsis

Description

Returns the list of all the saturated strongly stable ideals defining subschemes of \mathbb{P}^{n} or Proj S with Hilbert polynomial hp or d.

i1 : QQ[t];
i2 : S = QQ[x,y,z,w];
i3 : stronglyStableIdeals(4*t, S)

                 5   4 2                     2   4    5                2 
o3 = {ideal (x, y , y z ), ideal (x*z, x*y, x , y z, y ), ideal (x*y, x ,
     ------------------------------------------------------------------------
        2   4                2   3
     x*z , y ), ideal (x*y, x , y )}

o3 : List
i4 : stronglyStableIdeals(4*t, 4)

                  5   4 2                       2   4     5               
o4 = {ideal (x , x , x x ), ideal (x x , x x , x , x x , x ), ideal (x x ,
              0   1   1 2           0 2   0 1   0   1 2   1           0 1 
     ------------------------------------------------------------------------
      2     2   4                 2   3
     x , x x , x ), ideal (x x , x , x )}
      0   0 2   1           0 1   0   1

o4 : List
i5 : hp = hilbertPolynomial(oo#0)

o5 = - 4*P  + 4*P
          0      1

o5 : ProjectiveHilbertPolynomial
i6 : stronglyStableIdeals(hp, S)

                 5   4 2                     2   4    5                2 
o6 = {ideal (x, y , y z ), ideal (x*z, x*y, x , y z, y ), ideal (x*y, x ,
     ------------------------------------------------------------------------
        2   4                2   3
     x*z , y ), ideal (x*y, x , y )}

o6 : List
i7 : stronglyStableIdeals(hp, 4)

                  5   4 2                       2   4     5               
o7 = {ideal (x , x , x x ), ideal (x x , x x , x , x x , x ), ideal (x x ,
              0   1   1 2           0 2   0 1   0   1 2   1           0 1 
     ------------------------------------------------------------------------
      2     2   4                 2   3
     x , x x , x ), ideal (x x , x , x )}
      0   0 2   1           0 1   0   1

o7 : List
i8 : stronglyStableIdeals(5, S)

                    5                   2   4              2   3     2  
o8 = {ideal (y, x, z ), ideal (x, y*z, y , z ), ideal (x, y , z , y*z ),
     ------------------------------------------------------------------------
                       2        2   3
     ideal (y*z, x*z, y , x*y, x , z )}

o8 : List
i9 : stronglyStableIdeals(5, 4)

                      5                     2   4               2   3     2  
o9 = {ideal (x , x , x ), ideal (x , x x , x , x ), ideal (x , x , x , x x ),
              1   0   2           0   1 2   1   2           0   1   2   1 2  
     ------------------------------------------------------------------------
                         2         2   3
     ideal (x x , x x , x , x x , x , x )}
             1 2   0 2   1   0 1   0   2

o9 : List

Ways to use stronglyStableIdeals :

For the programmer

The object stronglyStableIdeals is a method function with options.