stableMax -- compute the set of stable primes of a monomial ideal that are maximal with respect to the inclusion.

• Usage:

  stableMax I

• Inputs:
  • I, an ideal, a monomial ideal of polynomial ring $S = \mathbb{K}[x_1,\ldots,x_n]$, $\mathbb{K}$ a field
• Outputs:
  • l, a list, all maximal stable primes of $I$

i1 : S = QQ[x_1..x_3];

i2 : I = ideal(x_1*x_2,x_1*x_3,x_2*x_3)

o2 = ideal (x x , x x , x x )
             1 2   1 3   2 3

o2 : Ideal of S

i3 : stableMax I

o3 = {ideal (x , x , x )}
              1   2   3

o3 : List

i4 : S = QQ[a..e];

i5 : I = ideal(a*d,a*e,b*d,c*d,c*e);

o5 : Ideal of S

i6 : stableMax I

o6 = {ideal (c, b, a), ideal (d, c, a), ideal (e, d)}

o6 : List