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

• Usage:

  lexIdeal (hp ,S)

  lexIdeal (hp, n)

  lexIdeal (d, S)

  lexIdeal (d, n)

• Inputs:
  • hp, a projective Hilbert polynomial, or
  • hp, a ring element, a Hilbert polynomial;
  • d, an integer, a positive integer corresponding to a constant Hilbert polynomial;
  • S, a polynomial ring, with numgens S > 1;
  • n, an integer, number of variables of the polynomial ring.
• Optional inputs:
  • CoefficientRing => ..., default value QQ, Option to set the ring of coefficients
  • OrderVariables => ..., default value Down, Option to set the order of indexed variables
• Outputs:
  • an ideal,

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