Divine simplicity is the doctrine that God has no parts/composition. It implies that God is equivalent to his attributes and his attributes are equivalent to each other. So God is love and God is Justice and God's love is the same thing as God's Justice.
How does the doctrine of the Trinity mesh with this? There seems to be some distinction within God: three unique hypostases.
Perhaps the relations between the hypostases of the Trinity do not constitute "parts" or "composition" but are instead just "distinctions". If so that's a really "semantic" technical answer and I don't get it, some elaboration would be appreciated.
Perhaps it has something to do with the doctrine of interpenetration, aka circumincession aka perichoresis aka co-inherence. This being the doctrine that "the father fully contains the son and the spirit, the son fully contains the father and the spirit, and the spirit fully contains the father and the son." In this way, if you take any single member of the trinity, you get the entire trinity; it is impossible to separate one hypostasis from the others because whenever you take one hypostasis it always comes with the other two as well. In this way the trinity is inseparable and indivisible, just as the divine simplicity doctrine implies. Nevertheless it still looks sketchy because as mentioned, there is distinction between the hypostases.
How is divine simplicity reconciled with the doctrine of the Trinity?