A software package (the successor to CAYLEY) designed to solve
computationally hard problems in algebra, number theory,
geometry, and combinatorics, and to provide a mathematically
rigorous environment for computing with algebraic,
number-theoretic, combinatoric, and geometric objects.
System for the manipulation of symbolic and numerical expressions.
Includes a collection of special functions.
Utilizes exact fractions, arbitrary precision integers, and arbitrary
precision floating point numbers.
MPFR is a C library for multiple-precision floating-point computations
with correct rounding. The main goal of MPFR is to provide a library
for multiple-precision floating-point computation which is both
efficient and has well-defined semantics. MPFR includes most of the
elementary functions. It also implements the gamma function, and more
special functions are planned in the future.
Mpmath is a pure-Python library for multiprecision floating-point arithmetic.
It provides an extensive set of transcendental functions, unlimited exponent sizes, complex numbers,
interval arithmetic, numerical integration and differentiation, root-finding, linear algebra,
and much more.
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►WebGL is supported in the current versions of most common web browsers.
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►1, some advanced features of X3DOM are currently not fully supported (see x3dom.org).
…If you have trouble viewing the WebGL visualizations in your web browser, see x3dom.org or caniuse.com/webgl for information on WebGL browser support.
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►After installing the viewer you must select Customize DLMF on the DLMF Menu bar and choose either VRML or X3D under “Visualization Format.
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►Please see caniuse.com/webgl or x3dom.org for information on WebGL browser support.
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►In this regard, he has been exploring mathematical knowledge management and the digital expression of mostly unambiguous context-free full semantic information for mathematical formulae.
The “Freely Distributable LIBM” package provides implementations of standard
elementary functions plus a few higher functions, e.g. gamma.
Double precision, maximum accuracy 20S.
Developed by Sun Microsystems.
L. W. Fullerton (1977)Portable Special Function Routines.
In Portability of Numerical Software (Oak Brook, Illinois, 1976), W. R. Cowell (Ed.),
Lecture Notes in Computer Science, Vol. 57, pp. 452–483.
Y. V. Fyodorov (2005)Introduction to the Random Matrix Theory: Gaussian Unitary Ensemble and Beyond.
In Recent Perspectives in Random Matrix Theory and Number Theory,
London Math. Soc. Lecture Note Ser., Vol. 322, pp. 31–78.
C. Kormanyos (2011)Algorithm 910: a portable C++ multiple-precision system for special-function calculations.
ACM Trans. Math. Software37 (4), pp. Art. 45, 27.
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Notes:
This system provides a uniform interface in C++, named e_float,
to perform arithmetic operations and to calculate mathematical functions
that are implemented in several different MP packages. It is a free, open-source,
multiple precision package that allows the computation of many special functions.
It supports calculations with 30….300 decimal digits and is
interoperable with Microsoft’s CLR, Python and Mathematica.
F. H. L. Essler, H. Frahm, A. R. Its, and V. E. Korepin (1996)Painlevé transcendent describes quantum correlation function of the antiferromagnet away from the free-fermion point.
J. Phys. A29 (17), pp. 5619–5626.
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►►►Figure 18.21.1: Askey scheme.
The number of free real parameters is zero for Hermite polynomials.
It increases by one for each row ascended in the scheme, culminating with four free real parameters for the Wilson and Racah polynomials.
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Computer algebra system designed for computations in number theory.
Many transcendental functions are also included.
PARI is also available as a C library to allow for faster computations.
Originally developed by Henri Cohen and co-workers at the Université Bordeaux I.
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