>The main difference between Leibniz and computer algebra systems is that Leibniz is a scientific notation whereas computer algebra systems are tools for doing

>The main difference between Leibniz and computer algebra systems is that Leibniz is a scientific notation whereas computer algebra systems are tools for doing computations. A notation needs to be clear, a tool needs to be flexible and efficient. Different priorities lead to different design decisions. In a computer algebra system, you never see a definition of a term algebra or a list of rewrite rules. They are hidden from the user, and in the case of commercial software even heavily encoded to make them inaccessible. A computer algebra system is the equivalent of a single giant unpublished Leibniz context. In contrast, Leibniz encourages small, readable, and remixable contexts that can be examined and understood by scientists with reasonable effort. However, Leibniz lacks the huge database of simplification rules that make up the bulk of a computer algebra system.