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windows default iconMpmath for Windows Publisher's description

Mpmath is a pure-Python library for multiprecision floating-point arithmetic.

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. Almost any calculation can be performed just as well at 10-digit or 1000-digit precision, and in many cases mpmath implements asymptotically fast algorithms that scale well for extremely high precision work. Mpmath internally uses Python's builtin long integers by default, but automatically switches to GMP/MPIR for much faster high-precision arithmetic if gmpy is installed or if mpmath is imported from within Sage.

Mpmath is free (BSD license) and easy to install or include in other software due to being written entirely in Python with no additional required dependencies. It runs on Python 2.5 or higher, including Python 3.x. It can be used as a library, interactively via the Python interpreter, or via SymPy which uses it for numerical evaluation of symbolic expressions. Mpmath is also a standard component of Sage which uses it for special function evaluation.



Real and complex numbers with arbitrary precision
Unlimited exponent sizes / magnitudes
Support for infinities and not-a-numbers
Directed rounding
Real and complex interval arithmetic
Matrices with arbitrary-precision real, complex or interval elements

Special functions:

Elementary functions (sqrt, exp, log, trigonometric, hyperbolic, inverse trig and hyperbolic)
Standard mathematical constants: pi, e, the golden ratio, Euler's constant (gamma)
Less standard constants: Catalan's, Apery's, Khinchin's and Glaisher's constants
Lambert W function (all branches)
Error function (erf), imaginary and complementary error functions; inverse error function; normal distribution functions
Gamma functions (complete and incomplete), factorials, double factorials and binomial coefficients, log gamma function; complete and incomplete beta functions
Fibonacci numbers
Barnes G-function, super- and hyperfactorials
Polygamma functions
Riemann zeta function, Hurwitz zeta function, Riemann-Siegel and related functions; evaluation with the Riemann-Siegel expansion; Riemann zeta zeros
Bernoulli numbers (fast numerical and exact computation of large Bernoulli numbers), Bernoulli polynomials, Euler numbers and polynomials
Polylogarithms, Clausen functions
Stieltjes constants
Bessel functions; Hankel, Struve, Kelvin, Whittaker, Airy, Coulomb functions; Bessel function zeros; parabolic cylinder functions
Exponential and trigonometric integrals
Arithmetic-geometric mean
Complete and incomplete elliptic integrals (Legendre and Carlsen forms)
Jacobi elliptic functions and Jacobi theta functions
Jacobi, Legendre and Chebyshev and other orthogonal polynomials; associated Legendre functions; spherical harmonics
Generalized hypergeometric functions; the Meijer G-function; Borel regularized hypergeometric series; bilateral series; 2D hypergeometric series (Appell, Horn, KampГ© de FГ©riet functions)
q-factorials and q-hypergeometric series

Calculus and other general high-level mathematics:

Numerical integration (regular, double/triple integrals, oscillatory)
Numerical differentiation and differintegration (arbitrary orders); partial derivatives
Limits and summation of infinite series (with convergence acceleration)
Multidimensional series
Root-finding (1D and multidimensional; secant method, bisection, modified Newton's method, and other algorithms)
Polynomial evaluation and polynomial root-finding
Chebyshev approximation
ODE solvers
Fourier and Taylor series
Integer relation detection (constant recognition)
Linear algebra functions (linear system solving, LU factorization, matrix inverse, matrix norms, matrix exponentials/logarithms/square roots)

What's New in This Release:

В· Python 3 is now supported
В· Dropped Python 2.4 compatibility
В· Fixed Python 2.5 compatibility in matrix slicing code
В· Implemented Python 3.2-compatible hashing, making mpmath numbers
В· hash compatible with extremely large integers and with fractions
В· in Python versions >= 3.2 (contributed by Case Vanhorsen)

Special functions:
В· Implemented the von Mangoldt function (mangoldt())
В· Implemented the "secondary zeta function" (secondzeta()) (contributed
В· by Juan Arias de Reyna).
В· Implemented zeta zero counting (nzeros()) and the Backlund S function
В· backlunds()) (contributed by Juan Arias de Reyna)
В· Implemented derivatives of order 1-4 for siegelz() and siegeltheta()
В· contributed by Juan Arias de Reyna)
В· Improved Euler-Maclaurin summation for zeta() to give more accurate
В· results in the right half-plane when the reflection formula
В· cannot be used
В· Implemented the Lerch transcendent (lerchphi())
В· Fixed polygamma function to return a complex NaN at complex
В· infinity or NaN, instead of raising an u...

System Requirements:

В· Python
Program Release Status: New Release
Program Install Support: Install and Uninstall

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