Computer algebra system

A computer algebra system is software that transforms and evaluates mathematical expressions symbolically, representing quantities and operations exactly rather than only as numerical approximations.

Expression tree: A tree-shaped representation in which leaves hold values or symbols and internal nodes hold operations. Computer algebra systems represent formulas as trees that can be traversed and transformed.
Symbolic computation: Computation that manipulates symbols and mathematical structures rather than relying solely on numerical values. Computer algebra systems are a major form of symbolic computation.
Computer algebra system integration: The symbolic computation of antiderivatives or definite integrals by algorithms implemented in software. Integration is a major application, though general symbolic integration cannot always find an elementary form.
Numerical analysis: The study of algorithms that approximate mathematical quantities using finite computations. Numerical methods handle many problems that lack compact symbolic solutions or require approximate values.
Term rewriting: A method of computation that repeatedly replaces expressions using specified transformation rules. Symbolic simplification often applies rewrite rules to expressions until a chosen form is reached.
Rational number: A number expressible as the ratio of two integers with a nonzero denominator. Exact rational arithmetic avoids rounding errors common when fractions are stored as floating-point numbers.
Computer algebra system differentiation: The algorithmic computation of derivatives from symbolic expressions using differentiation rules. Differentiation rules let systems produce exact derivatives for complicated formulas.
Computer algebra system Mathematica: A commercial technical computing system developed by Wolfram Research, combining symbolic, numerical, and visualization tools. Mathematica is a prominent general-purpose example of a computer algebra system.
Pattern matching: A process that identifies whether data has a specified structure and binds variables to matching parts. Transformation rules use patterns to recognize subexpressions such as powers or products.
Floating-point arithmetic: A finite-precision method for representing real numbers using a significand and a scaled exponent. It contrasts with the exact symbolic representations many computer algebra operations preserve.

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