pickGorensteinIdeal -- select a codimension 3 Gorenstein ideal

Synopsis

• Usage:

  (J,M)=pickGorensteinIdeal(S,hV)

  (J,M)=pickGorensteinIdeal(S,d1,d2)

• Inputs:

  • S, a ring, Polynomial ring in which the output ideal will be chosen
  • hV, a list, an h-vector of a codimension 3 Gorenstein ideal, or
  • d1, a list
  • d2, a list, the List of degrees of the target and source of the Buchsbaum-Eisenbud skew-symmetric matrix
• Outputs:

  • J, an ideal, a Gorenstein ideal of codimension 3 with the given numerical invariant
  • M, a matrix, the Buchsbaum-Eisenbud skew symmetric presentation matrix of J

Description

i1 : S=ZZ/10009[x_0..x_2]

o1 = S

o1 : PolynomialRing

i2 : hV1=hVector 9; hV=hV1|reverse hV1

o3 = {1, 3, 5, 5, 3, 1}

o3 : List

i4 : (J,M)=pickGorensteinIdeal(S,hV);

i5 : betti res J

            0 1 2 3
o5 = total: 1 3 3 1
         0: 1 . . .
         1: . 1 . .
         2: . 2 . .
         3: . . 2 .
         4: . . 1 .
         5: . . . 1

o5 : BettiTally

i6 : hVector J

o6 = {1, 3, 5, 5, 3, 1}

o6 : List