containmentProblem -- computes the smallest symbolic power contained in a power of an ideal.

Synopsis

Usage:

containmentProblem(I,n)
Inputs:
- I, an ideal,
- n, an integer,
Optional inputs:
- CIPrimes => ..., default value false, compute the symbolic power by taking the intersection of the powers of the primary components
- InSymbolic => ..., default value false, an optional parameter used in containmentProblem.
- UseMinimalPrimes => ..., default value false, an option to only use minimal primes to calculate symbolic powers
Outputs:
- an integer, the minimum value m such that the m-th symbolic power of I is contained in I^n

Given an ideal $I$ and an integer $n$, containementProblem returns the order of the smallest symbolic power of $I$ contained in $I^n$.

i1 : B = QQ[x,y,z];

i2 : f = map(QQ[t],B,{t^3,t^4,t^5})

                      3   4   5
o2 = map (QQ[t], B, {t , t , t })

o2 : RingMap QQ[t] <-- B

i3 : I = ker f;

o3 : Ideal of B

i4 : m = containmentProblem(I,2)

o4 = 3