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The study of algorithms useful for computer algebra systems is known as computer algebra.
The runtime of numerical programs implemented in computer algebra systems is normally longer than that of equivalent programs implemented in systems such as MATLAB, GNU octave[?] or directly in C, because the computer algebra languages are interpreted and the bignum system may cause overhead.
Computer algebra systems began to appear in the early 1970's, and evolved out of research into artificial intelligence (the fields are now regarded as largely separate). The first popular systems were Reduce[?], Derive[?] and Macsyma[?] which are still commercially available; a copyleft version of Macsyma called GNU Maxima is actively being maintained. The current market leaders are Maple and Mathematica; both are commonly used by research mathematicians. MuPAD[?] is a commercial system which provides a free version (with slightly restricted user interface) for noncommercial research and educational usage. Some computer algebra systems focus on a specific area of application; these are typically developed in academia and free. Examples include:
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