numgensByCodim -- maximum number of generators of localizations of a monomial ideal

• Usage:

  d = numgensByCodim(I,k)

  L = numgensByCodim(I)

• Inputs:
  • I, a monomial ideal,
  • k, an integer, an integer between 1 and the dimension of the ring
• Outputs:
  • d, an integer, the maximum number of generators of I localized at a prime P of codimension k.
  • L, a list, a list of the numbers of generators for each codimension from 1 to the dimension of the ring

i1 : R = QQ[x_0..x_4];

i2 : I = monomialIdeal{x_0^2,x_1*x_2,x_3*x_4^2}

                     2           2
o2 = monomialIdeal (x , x x , x x )
                     0   1 2   3 4

o2 : MonomialIdeal of R

i3 : numgensByCodim(I,2)

o3 = 1

i4 : numgensByCodim I

o4 = {1, 1, 3, 3, 3}

o4 : List