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lexIdeal -- Compute the saturated lexicographic ideal in the given ambient space with given Hilbert polynomial

Synopsis

Description

Returns the saturated lexicographic ideal defining a subscheme of \mathbb{P}^{n} or Proj S with Hilbert polynomial hp or d.

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

                5   4 2
o3 = ideal (x, y , y z )

o3 : Ideal of S
i4 : lexIdeal(4*t, 5)

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

o4 : Ideal of QQ[x ..x ]
                  0   4
i5 : hp = hilbertPolynomial oo

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

o5 : ProjectiveHilbertPolynomial
i6 : lexIdeal(hp, S)

                5   4 2
o6 = ideal (x, y , y z )

o6 : Ideal of S
i7 : lexIdeal(hp, 3)

             5   4 2
o7 = ideal (x , x x )
             0   0 1

o7 : Ideal of QQ[x ..x ]
                  0   2
i8 : lexIdeal(5, S)

                   5
o8 = ideal (y, x, z )

o8 : Ideal of S
i9 : lexIdeal(5, 3)

                 5
o9 = ideal (x , x )
             0   1

o9 : Ideal of QQ[x ..x ]
                  0   2

Ways to use lexIdeal:

For the programmer

The object lexIdeal is a method function with options.