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A computer algebra system (CAS) is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.
Types of expressions The expressions manipulated by the CAS typically include polynomials in multiple variables; standard functions of expressions (sine, exponential, etc.); various special functions (gamma, zeta, erf, Bessel, etc.); arbitrary functions of expressions; derivatives, integrals, sums, and products of expressions; truncated series with expressions as coefficients, matrices of expressions, and so on. (This is a recursive definition.) Symbolic manipulations The symbolic manipulations supported typically include (In the above, the word some indicates that the operation cannot always be performed.) Other features In addition, most CASs include numeric operations for: Many also include a high level programming language, allowing users to implement their own algorithms. The study of algorithms useful for computer algebra systems is known as computer algebra. The run-time 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, since they are programmed for full symbolic generality and thus cannot use machine numerical operations directly for most of their functions. History Computer algebra systems began to appear in the early 1970s, and evolved out of research into artificial intelligence, though the fields are now regarded as largely separate. Pioneering work was conducted by the Nobel Prize laureate Martin Veltman, who designed a program for symbolic mathematics, especially High Energy Physics, called Schoonship (Dutch for "clean ship") in 1963. The first popular systems were Reduce, Derive, and Macsyma which are still commercially available; a copyleft version of Macsyma called Maxima is actively being maintained. The current market leaders are Maple and Mathematica; both are commonly used by research mathematicians, scientists, and engineers. MuPAD and MathCad are other commercial systems. Some computer algebra systems focus on a specific area of application; these are typically developed in academia and free. In 1995, Texas instruments released the TI-92. This, along with its successors (including the Ti-89 series) feature a reasonably capable and relatively inexpensive handheld computer algebra system, featuring derivatives and integrals with respect to 1 variable, limits, and some differential equations. Mathematics used in computer algebra systems See also | ||||||||
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