isStablePrime -- test whether a prime ideal is a stable prime of a ideal $I$

• Usage:

  isStablePrime(I,p)

• Inputs:
  • I, an ideal, a monomial ideal of polynomial ring $S = \mathbb{K}[x_1,\ldots,x_n]$, $\mathbb{K}$ a field
  • p, an ideal, a prime monomial ideal of $S$
• Outputs:
  • b, a Boolean value, whether $\mathfrak{p}$ is a stable prime 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 : p = ideal(x_1,x_2)

o3 = ideal (x , x )
             1   2

o3 : Ideal of S

i4 : isStablePrime(I,p)

o4 = true

i5 : S = QQ[a..e];

i6 : I = ideal(a*d,a*e,b*d,c*d,c*e);

o6 : Ideal of S

i7 : p = ideal(a,c);

o7 : Ideal of S

i8 : isStablePrime(I,p)

o8 = false