Mpmath Python library for arbitrary-precision floating-point arithmetic
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math library python library math library arithmetic arithmetic development

Mpmath Description

Python library for arbitrary-precision floating-point arithmetic Mpmath is a free and open source pure-Python library for arbitrary-precision floating-point arithmetic. Mpmath implements a large set of mathematical functions and provides utilities for arbitrary-precision numerical differentiation, integration, root-finding, interval arithmetic, and other tasks. Mpmath supports unlimited exponent sizes, has full support for complex numbers, and is faster than Python's standard decimal library.Mpmath is easy to install or include in other software due to being written entirely in Python with no additional dependencies. Here are some key features of "Mpmath": Arithmetic: · Real and complex numbers with arbitrary precision · Unlimited exponent sizes / magnitudes · Support for infinities and not-a-numbers · Directed rounding · Rudimentary interval arithmetic 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) · Gamma functions (complete and incomplete), factorials and binomial coefficients · Riemann zeta function and Bernoulli numbers · Bessel function of the first kind · Arithmetic-geometric mean · Complete elliptic integrals · Jacobi, Legendre and Chebyshev functions · Generic hypergeometric functions High-level features: · Integration · Differentiation · Limits and summation of infinite series (with convergence acceleration) · Root-finding · Polynomial evaluation and root-finding · Chebyshev approximation · Basic ODE solvers · Integer relation detection (constant recognition) Requirements: · Python What's New in This Release: New special functions: · The generalized exponential integral E_n (expint(), e1() for E_1) · The generalized incomplete beta function (betainc()) · Whittaker functions (whitm(), whitw()) · Struve functions (struveh(), struvel()) · Kelvin functions (ber(), bei(), ker(), kei()) · Cyclotomic polynomials (cyclotomic()) · The Meijer G-function (meijerg()) · Clausen functions (clsin(), clcos()) · The Appell F1 hypergeometric function of two variables (appellf1()) · The Hurwitz zeta function, with nth order derivatives (hurwitz()) · Dirichlet L-series (dirichlet()) · Coulomb wave functions (coulombf(), coulombg(), coulombc()) · Associated Legendre functions of 1st and 2nd kind (legenp(), legenq()) · Hermite polynomials (hermite()) · Gegenbauer polynomials (gegenbauer()) · Associated Laguerre polynomials (laguerre()) · Hypergeometric functions hyp1f2(), hyp2f2(), hyp2f3(), hyp2f0(), hyperu() Evaluation of hypergeometric functions: · Added the function hypercomb() for evaluating expressions containing · hypergeometric series, with automatic handling of limits · The available hypergeometric series (of orders up to and including 2F3) · implement asymptotic expansions with respect to the last argument z, allowing · fast and accurate evaluation anywhere in the complex plane. A massive number · of functions, including Bessel functions, error functions, etc., have been · updated to take advantage of this to support fast and accurate evaluation · anywhere in the complex plane. · Fixed hyp2f1 to handle z close to and on the unit circle (supporting · evaluation anywhere in the complex plane) · hyper() handles the 0F0 and 1F0 cases exactly · hyper() eventually raises NoConvergence instead of getting stuck in · an infinite loop if given a divergent or extremely slowly convergent series Other improvements and bug fixes to special functions: · gammainc is much faster for large arguments and avoids catastrophic · cancellation · Implemented specialized code for ei(x), e1(x), expint(n,x) and gammainc(n,x) · for small integers n, making evaluation much faster · Extended the domain of polylog · Fixed accuracy for asin(x) near x = 1 · Fast evaluation of Bernoulli polynomials for large z · Fixed Jacobi polynomials to handle some poles · Some Bessel functions support computing nth order derivatives · A set of "torture tests" for special functions is available as · tests/torture.py Other: · Implemented the differint() function for fractional differentiaton / iterated · integration · Added functions fadd, fsub, fneg, fmul, fdiv for high-level arithmetic with · controllable precision and rounding · Added the function mag() for quick order-of-magnitude estimates of numbers · Implemented powm1() for accurate calculation of x^y-1 · Improved speed and accuracy for raising a pure imaginary number to · an integer power · nthroot() renamed to root(); root() optionally computes any of · the non-principal roots of a number · Implemented unitroots() for generating all (primitive) roots of unity · Added the mp.pretty option for nicer repr output

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