koszulDepth -- Computes the depths of the Koszul homology

Synopsis

• Usage:

  L = koszulDepth I

  d = koszulDepth(k,I)

• Inputs:
  • I, an ideal,
  • k, an integer, the homological index to compute
• Outputs:
  • L, a list, a list of the depths of Kozul homology
  • d, an integer, the depth of the k-th Koszul homology

Description

i1 : R = QQ[x_1..x_6];

i2 : I = ideal{x_1*x_2,x_1*x_3,x_2*x_4*x_5,x_1*x_6,x_4*x_6,x_5*x_6};

o2 : Ideal of R

i3 : koszulDepth I

o3 = {3, 0, 2}

o3 : List

i4 : koszulDepth(2,I)

o4 = 2

See also

• isStronglyCM -- Checks if the given ideal is Strongly Cohen Macaulay
• hasSlidingDepth -- Checks if an ideal has the sliding depth property