We propose a novel approach for studying rooted trees by using functions thatwe will call descent functions. We provide a construction method for rootedtrees that allows to study their properties through the use of descentfunctions. Moreover, in this way, we are able to compose rooted trees with eachother. Such a new composition of rooted trees is a very powerful tool appliedin this paper in order to obtain important results as the creation of newrational and Pythagorean trees.
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