Given an ideal $I$, we can determine if $I^{(m)} \subseteq I^n$. For example, here is an ideal that fails the containment $I^{(3)} \subseteq I^2$:
|
|
|
We can also determine the smallest symbolic power contained in a given power.
In our example, $I^{(4)}$ is the smallest symbolic power contained in $I^2$:
|
We can ask the same question backwards: what is the largest power of I that contains $I^{(4)}$?
|