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Arbitrary precision integer, floating point, and complex numeric arithmetic
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Numerical evaluation of the elementary functions and a large library of special
functions including the error function, the Gamma and related functions,
the exponential integral, the Riemann zeta function, Bessel and related
functions, Hypergeometric functions, statistical distributions etc.
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Numerical linear algebra: linear systems,
eigenvalues and eigenvectors, SVD,
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Numerical approximation: interpolating splines, B-splines, least squares,
Pade, continued fractions, Chebyshev series, Remez algorithm,
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Numerical calculus: numerical integration, numerical evaluation
of infinite sums and products, solution of ODE's, root finding, FFT.