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free
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an open source numerical library - includes special functions, linear algebra, probability models, random numbers, interpolation, integral transforms.
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in addition to a purely managed implementation will also support native hardware optimization.
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constants & special functions
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complex type support
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real and complex, dense and sparse linear algebra (with LU, QR, eigenvalues, ... decompositions)
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non-uniform probability distributions, multivariate distributions, sample generation
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alternative uniform random number generators
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descriptive statistics, including order statistics
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various interpolation methods, including barycentric approaches and splines
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numerical function integration (quadrature) routines
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integral transforms, like fourier transform (FFT) with arbitrary lengths support, and hartley
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spectral-space aware sequence manipulation (signal processing)
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combinatorics, polynomials, quaternions, basic number theory.
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parallelized where appropriate, to leverage multi-core and multi-processor systems
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fully managed or (if available) using native libraries (Intel MKL, ACMS, CUDA, FFTW)
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provides a native facade for F# developers