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Arbitrary precision integer, floating point, and complex numeric arithmetic
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.
Numerical linear algebra: linear systems,
eigenvalues and eigenvectors, SVD,
Numerical approximation: interpolating splines, B-splines, least squares,
Pade, continued fractions, Chebyshev series, Remez algorithm,
Numerical calculus: numerical integration, numerical evaluation
of infinite sums and products, solution of ODE's, root finding, FFT.