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

Synopsis

Description

This method returns true if $\mathfrak{p}\in\text{Ass}^\infty(I)$, otherwise false.

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

See also

Ways to use isStablePrime :

For the programmer

The object isStablePrime is a method function.