A simple and efficient algorithm for an extension of the subtree isomorphism problem is presented that computes a certificate for each rooted subtree of a given forest, thereby partitioning the set of rooted subtrees into isomorphism equivalence classes. The partitioning can be used to find all occurrences of a pattern tree in a text tree, or even all occurrences of every subtree of a pattern in a text, and the algorithm handles multiple pattern trees and also multiple text trees. The method combines a bottom-up forest traversal algorithm with a simple numbering scheme for rooted trees. The algorithm runs in expected time linear in the number of nodes, and can be applied to rooted trees of unbounded degree, either unordered or ordered, labeled or unlabeled. The algorithm also solves the problem of finding all $k$-th largest common subtrees and all $k$-th most often repeated subtrees. A C++ implementation of the algorithm using LEDA is given in full detail.