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  2. Xcas - Wikipedia

    en.wikipedia.org/wiki/Xcas

    Xcas is written in C++. [3] Giac can be used directly inside software written in C++. Xcas has compatibility modes with many popular algebra systems like WolframAlpha, [4] Mathematica, [5] Maple, [6] or MuPAD. Users can use Giac/Xcas to develop formal algorithms or use it in other software. Giac is used in SageMath [4] for calculus operations.

  3. PARI/GP - Wikipedia

    en.wikipedia.org/wiki/PARI/GP

    PARI is a C library, allowing for fast computations, and which can be called from a high-level language application (for instance, written in C, C++, Pascal, Fortran, Perl, or Python). gp is an easy-to-use interactive command line interface giving access to the PARI functions.

  4. Complete Fermi–Dirac integral - Wikipedia

    en.wikipedia.org/wiki/Complete_Fermi–Dirac...

    Fermi-Dirac integral calculator for iPhone/iPad; Notes on Fermi-Dirac Integrals; Section in NIST Digital Library of Mathematical Functions; npplus: Python package that provides (among others) Fermi-Dirac integrals and inverses for several common orders. Wolfram's MathWorld: Definition given by Wolfram's MathWorld.

  5. WolframAlpha - Wikipedia

    en.wikipedia.org/wiki/WolframAlpha

    It is offered as an online service that answers factual queries by computing answers from externally sourced data. [4] [5] WolframAlpha was released on May 18, 2009, and is based on Wolfram's earlier product Wolfram Mathematica, a technical computing platform. [1]

  6. Numerical integration - Wikipedia

    en.wikipedia.org/wiki/Numerical_integration

    The integrand is evaluated at a finite set of points called integration points and a weighted sum of these values is used to approximate the integral. The integration points and weights depend on the specific method used and the accuracy required from the approximation.

  7. Monte Carlo integration - Wikipedia

    en.wikipedia.org/wiki/Monte_Carlo_integration

    An illustration of Monte Carlo integration. In this example, the domain D is the inner circle and the domain E is the square. Because the square's area (4) can be easily calculated, the area of the circle (π*1.0 2) can be estimated by the ratio (0.8) of the points inside the circle (40) to the total number of points (50), yielding an approximation for the circle's area of 4*0.8 = 3.2 ≈ π.

  8. Polylogarithm - Wikipedia

    en.wikipedia.org/wiki/Polylogarithm

    In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Li s (z) of order s and argument z.Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function.

  9. Romberg's method - Wikipedia

    en.wikipedia.org/wiki/Romberg's_method

    In numerical analysis, Romberg's method [1] is used to estimate the definite integral by applying Richardson extrapolation [2] repeatedly on the trapezium rule or the rectangle rule (midpoint rule). The estimates generate a triangular array .