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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
symbolic mathematics
(Or "symbolic math") The use of
computers to manipulate mathematical equations and expressions
in symbolic form, as opposed to manipulating the numerical
quantities represented by those symbols. Such a system might
be used for symbolic integration or differentiation,
substitution of one expression into another, simplification of
an expression, change of subject etc.
One of the best known symbolic mathematics software packages
is Mathematica. Others include ALAM, ALGY, AMP,
Ashmedai, AXIOM*, CAMAL, CAYLEY, CCalc, CLAM,
CoCoA(?), ESP, FLAP, FORM, FORMAL, Formula ALGOL,
GAP, JACAL, LiE, Macaulay, MACSYMA, Magic Paper,
MAO, Maple, Mathcad, MATHLAB, MuMath, Nother,
ORTHOCARTAN, Pari, REDUCE, SAC-1, SAC2, SAINT,
Schoonschip, Scratchpad I, SHEEP, STENSOR, SYMBAL,
SymbMath, Symbolic Mathematical Laboratory, TRIGMAN,
UBASIC.
Usenet newsgropup: sci.math.symbolic.
(1995-04-12)