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The SymPy library is split into a core with many optional modules. Currently, the core of SymPy has around 260,000 lines of code [8] (it also includes a comprehensive set of self-tests: over 100,000 lines in 350 files as of version 0.7.5), and its capabilities include: [4] [5] [9] [10] [11]
PARI/GP is a computer algebra system that facilitates number-theory computation. Besides support of factoring, algebraic number theory, and analysis of elliptic curves, it works with mathematical objects like matrices, polynomials, power series, algebraic numbers, and transcendental functions. [3]
Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math. Intel IPP is a multi-threaded software library of functions for multimedia and data processing applications. OpenBLAS is an open source implementation of the BLAS API with many hand-crafted optimizations for specific processor types ...
gnuplot is a command-line and GUI program that can generate two- and three-dimensional plots of functions, data, and data fits.The program runs on all major computers and operating systems (Linux, Unix, Microsoft Windows, macOS, FreeDOS, and many others). [3]
C/C++ based numerical computing and graphical plotting [1] DADiSP: DSP Development 1984 1987 6.7 B02 17 January 2017: $1995 (commercial), $129 (academic), Free (student) Proprietary: Numeric computations for science and engineering featuring a spreadsheet like interface. Dyalog APL: Dyalog Ltd. 1981 1983 18.0 10 June 2020
Matplotlib (portmanteau of MATLAB, plot, and library [3]) is a plotting library for the Python programming language and its numerical mathematics extension NumPy.It provides an object-oriented API for embedding plots into applications using general-purpose GUI toolkits like Tkinter, wxPython, Qt, or GTK.
The digamma function (), visualized using domain coloring Plots of the digamma and the next three polygamma functions along the real line (they are real-valued on the real line) In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: [1] [2] [3]
Repeated application of the recurrence relation for the lower incomplete gamma function leads to the power series expansion: [2] (,) = = (+) (+) = = (+ +). Given the rapid growth in absolute value of Γ(z + k) when k → ∞, and the fact that the reciprocal of Γ(z) is an entire function, the coefficients in the rightmost sum are well-defined, and locally the sum converges uniformly for all ...