next | previous | forward | backward | up | index | toc

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

## Synopsis

• Usage:
containmentProblem(I,n)
• Inputs:
• 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

## Description

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