Symbolic computations

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Symbolic computations use symbols rather than rational or irrational numbers stated in a given numerical base, and are thus not subject to errors due to loss of machine precision. For example, $\scriptstyle \phi +1\,=\,{\frac {3+{\sqrt {5}}}{2}}\,$ is a symbolic computation, whereas 1.61803398875 + 1 = 2.61803398875 is a numerical computation.

The symbols in symbolic computations may represent not only numbers, but functions, operators, etc. For example you can do symbolic integration, e.g. in Mathematica you can evaluate the indefinite integral

Integrate[1/(x^3 + 1), x]

See also

• Numeric computations