Relation between symbolic computation and symbolic dynamics

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From what I read about the fields symbolic computation and symbolic dynamics , I expect these two fields to be having vivid connections . I would like to know what are some of the prominent topics connecting symbolic dynamics and symbolic computation . So , to put a question , How are the fields of symbolic dynamics and symbolic computation linked ?

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As you can see by inspecting their respective Wikipedia entries, symbolic computation and symbolics dynamics are two independent fields. The only link between them is that you can do some computations relevant to symbolic dynamics using an appropriate computer algebra software. For instance, the open source software SageMaths offers some facilities to deal with discrete dynamical systems.