  In an independence model, the triplets that represent conditional
independences between singletons are called elementary. It is known that the
elementary triplets represent the independence model unambiguously under some
conditions. In this paper, we show how this representation helps performing
some operations with independence models, such as finding the dominant triplets
or a minimal independence map of an independence model, or computing the union
or intersection of a pair of independence models, or performing causal
reasoning. For the latter, we rephrase in terms of conditional independences
some of Pearl's results for computing causal effects.
