蓝鲸加速器vpm-老王vp官网

_images/banner.jpg

Welcome to Arb’s documentation! Arb is a C library for rigorous real and complex arithmetic with arbitrary precision. Arb tracks numerical errors automatically using ball arithmetic, a form of interval arithmetic based on a midpoint-radius representation. On top of this, Arb provides a wide range of mathematical functionality, including polynomials, power series, matrices, integration, root-finding, and many transcendental functions. Arb is designed with efficiency as a primary goal, and is usually competitive with or faster than other arbitrary-precision packages. The code is thread-safe, portable, and extensively tested.

Arb is free software distributed under the GNU Lesser General Public License (LGPL), version 2.1 or later (see 在中国如何用谷歌).

The git repository is http://github.com/fredrik-johansson/arb/

Arb is developed by Fredrik Johansson (fredrik.johansson@gmail.com), with help from many contributors (see Credits and references). Questions and discussion about Arb are welcome on the flint-devel mailing list. There is also an issue tracker for bug reports and feature requests. Development progress is sometimes covered on Fredrik’s blog.

This documentation is available in HTML format at http://b5wejw.wcbzw.com and in PDF format at http://b5wejw.wcbzw.com/arb.pdf. This edition of the documentation was updated Jun 25, 2024 and describes Arb 2.18.1. Documentation for specific release versions is also available in PDF format.

蓝鲸加速器vpm-老王vp官网

  • Feature overview
  • 中国用谷歌商店加速软件
    • Package managers
    • 在中国如何用谷歌
    • Dependencies
    • Standalone installation
    • Running tests
    • 中国用谷歌商店加速软件
    • Running code
    • Computer algebra systems and wrappers
  • Using ball arithmetic
    • Ball semantics
    • Binary and decimal
    • Quality of enclosures
    • Predicates
    • A worked example: the sine function
    • 中国用谷歌商店加速软件
    • Polynomial time guarantee
  • Technical conventions and potential issues
    • Integer types
    • Integer overflow
    • Aliasing
    • Thread safety and caches
    • Use of hardware floating-point arithmetic
    • Interface changes
    • General note on correctness
  • Contributing to Arb
    • Code conventions
    • Test code
  • Credits and references
    • License
    • Authors
    • Funding
    • Software
    • Citing Arb
    • Bibliography

蓝鲸加速器vpm-老王vp官网

  • Example programs
    • pi.c
    • hilbert_matrix.c
    • keiper_li.c
    • logistic.c
    • real_roots.c
    • poly_roots.c
    • complex_plot.c
    • lvalue.c
    • lcentral.c
    • integrals.c

蓝鲸加速器vpm-老王vp官网

Arb uses two custom floating-point types in its implementation of ball arithmetic. The radius of a ball is represented using the type mag_t which is unsigned and has a fixed precision. The midpoint is represented using the type arf_t which has arbitrary precision.

  • mag.h – fixed-precision unsigned floating-point numbers for bounds
    • Types, macros and constants
    • Memory management
    • Special values
    • Assignment and conversions
    • Comparisons
    • Input and output
    • Random generation
    • Arithmetic
    • Fast, unsafe arithmetic
    • Powers and logarithms
    • Special functions
  • 在中国如何用谷歌 – arbitrary-precision floating-point numbers
    • Types, macros and constants
    • Memory management
    • 在中国如何用谷歌
    • Assignment, rounding and conversions
    • Comparisons and bounds
    • Magnitude functions
    • 中国用谷歌商店加速软件
    • Random number generation
    • Input and output
    • Addition and multiplication
    • 在中国如何用谷歌
    • Division
    • 中国用谷歌商店加速软件
    • Complex arithmetic
    • Low-level methods

蓝鲸加速器vpm-老王vp官网

Real numbers (arb_t) are represented as midpoint-radius intervals, also known as balls. Complex numbers (acb_t) are represented in rectangular form, with arb_t balls for the real and imaginary parts.

  • arb.h – real numbers
    • Types, macros and constants
    • Memory management
    • Assignment and rounding
    • Assignment of special values
    • 在中国如何用谷歌
    • Random number generation
    • Radius and interval operations
    • Comparisons
    • Arithmetic
    • Dot product
    • Powers and roots
    • Exponentials and logarithms
    • Trigonometric functions
    • Inverse trigonometric functions
    • Hyperbolic functions
    • Inverse hyperbolic functions
    • Constants
    • Lambert W function
    • Gamma function and factorials
    • Zeta function
    • Bernoulli numbers and polynomials
    • Polylogarithms
    • Other special functions
    • Internals for computing elementary functions
    • Vector functions
  • acb.h – complex numbers
    • Types, macros and constants
    • 中国用谷歌商店加速软件
    • Basic manipulation
    • Input and output
    • Random number generation
    • 在中国如何用谷歌
    • 在中国如何用谷歌
    • Arithmetic
    • 中国用谷歌商店加速软件
    • Mathematical constants
    • Powers and roots
    • Exponentials and logarithms
    • 中国用谷歌商店加速软件
    • Inverse trigonometric functions
    • Hyperbolic functions
    • Inverse hyperbolic functions
    • Lambert W function
    • Rising factorials
    • Gamma function
    • Zeta function
    • Polylogarithms
    • Arithmetic-geometric mean
    • Other special functions
    • Piecewise real functions
    • Vector functions

蓝鲸加速器vpm-老王vp官网

These modules implement dense univariate polynomials with real and complex coefficients. Truncated power series are supported via methods acting on polynomials, without introducing a separate power series type.

  • arb_poly.h – polynomials over the real numbers
    • Types, macros and constants
    • Memory management
    • Basic manipulation
    • Conversions
    • Input and output
    • Random generation
    • Comparisons
    • Bounds
    • Arithmetic
    • Composition
    • Evaluation
    • Product trees
    • Multipoint evaluation
    • Interpolation
    • Differentiation
    • 中国用谷歌商店加速软件
    • Powers and elementary functions
    • Lambert W function
    • Gamma function and factorials
    • Zeta function
    • Root-finding
    • Other special polynomials
  • acb_poly.h – polynomials over the complex numbers
    • 在中国如何用谷歌
    • Memory management
    • 谷歌空间有限速，快来谷歌商店吧 - bilibili:2021-8-24 · 教你怎么不用谷歌商店，快速玩谷歌游戏꒰⌗´͈ ᵕ ` ͈⌗꒱৩-Q君-1220播放 · 0弹幕 02:44 2个技巧去除应用广告、获取谷歌商店原生应用 ... 这个网站能直接下载谷歌商店软件，所有历史版本也能下载，99% 的人都不知道！搜罗君 5308播放 · 6弹幕 05:38 ...
    • Input and output
    • Random generation
    • Comparisons
    • Conversions
    • Bounds
    • Arithmetic
    • Composition
    • Evaluation
    • Product trees
    • 在中国如何用谷歌
    • Interpolation
    • Differentiation
    • 中国用谷歌商店加速软件
    • Elementary functions
    • Lambert W function
    • Gamma function
    • Power sums
    • Zeta function
    • Other special functions
    • Root-finding
  • arb_fmpz_poly.h – extra methods for integer polynomials
    • Evaluation
    • Utility methods
    • Polynomial roots
    • Special polynomials

蓝鲸加速器vpm-老王vp官网

  • acb_dft.h – Discrete Fourier transform
    • Main DFT functions
    • DFT on products
    • Convolution
    • 在中国如何用谷歌

蓝鲸加速器vpm-老王vp官网

These modules implement dense matrices with real and complex coefficients. Rudimentary linear algebra is supported.

  • 在中国如何用谷歌 – matrices over the real numbers
    • 中国用谷歌商店加速软件
    • Memory management
    • Conversions
    • Random generation
    • Input and output
    • Comparisons
    • Special matrices
    • Transpose
    • 中国用谷歌商店加速软件
    • 在中国如何用谷歌
    • 在中国如何用谷歌
    • Gaussian elimination and solving
    • Cholesky decomposition and solving
    • Characteristic polynomial and companion matrix
    • Special functions
    • Sparsity structure
    • Component and error operations
    • Eigenvalues and eigenvectors
  • acb_mat.h – matrices over the complex numbers
    • Types, macros and constants
    • Memory management
    • Conversions
    • Random generation
    • Input and output
    • Comparisons
    • 中国用谷歌商店加速软件
    • Transpose
    • 中国用谷歌商店加速软件
    • 在中国如何用谷歌
    • Scalar arithmetic
    • Gaussian elimination and solving
    • Characteristic polynomial and companion matrix
    • Special functions
    • Component and error operations
    • 中国用谷歌商店加速软件

蓝鲸加速器vpm-老王vp官网

These modules implement mathematical functions with complexity that goes beyond the basics covered directly in the arb and acb modules.

  • acb_hypgeom.h – hypergeometric functions of complex variables
    • Convergent series
    • Asymptotic series
    • Generalized hypergeometric function
    • Confluent hypergeometric functions
    • 外媒：谷歌浏览器造成大规模用户安全信息泄露 - Google ...:今天 · 北京时间6月18日下午消息，据外媒报道，AwakeSecurity的研究人员表示，他伔在谷歌的Chrome浏览器的扩展程序中发现了一个间谍软件，含有这个间谍软件 ...
    • 中国用谷歌商店加速软件
    • Modified Bessel functions
    • 在中国如何用谷歌
    • Coulomb wave functions
    • Incomplete gamma and beta functions
    • Exponential and trigonometric integrals
    • 在中国如何用谷歌
    • Orthogonal polynomials and functions
    • Dilogarithm
  • arb_hypgeom.h – hypergeometric functions of real variables
    • 谷歌商店下载不了-时间财富网 - 680.com:2021-5-16 · 众华为手机为例，其谷歌商店下载不了，是因为谷歌已经退出中国大陆市场，连接国内普通网络目前无法访问谷歌服务器。 音频内容： 大家好，我是时间财富网智能客服时间君，上述问题将由我为大家进行解答。 众华为手机为例，其谷歌商店下载不了，是因为谷歌已经退出中国大陆市场，连接国内 ...
    • Confluent hypergeometric functions
    • Gauss hypergeometric function
    • 软件商店下载安装_电脑软件商店安装-腾讯电脑管家:2021-2-28 · 腾讯电脑管家软件下载中心，提供腾讯视频、qq音乐等软甲下载。到腾讯电脑管家软件中心，有海量客户端软件可众进行下载，畅快速度，值得体验。下载安装腾讯电脑管家，为你带来不一样的体 …
    • Incomplete gamma and beta functions
    • 求助：华为matepad 谷歌安装怎么解决？？？ - 华为 ...:2021-6-3 · 新买的pad，试了好几种安装谷歌play的方法，每次到的步骤都不一样，有点击“登录”无反应，有强行选择无线网络进行不了下一步的，还有验证账号密码（备注：正确的）一直验证不通过的。有大神遇到这种问题或者有成熟 ... 求助：华为matepad 谷歌安装怎么解决？
    • Bessel functions
    • Airy functions
    • Coulomb wave functions
    • Orthogonal polynomials and functions
    • Dilogarithm
    • Hypergeometric sequences
  • acb_elliptic.h – elliptic integrals and functions of complex variables
    • Complete elliptic integrals
    • Legendre incomplete elliptic integrals
    • Carlson symmetric elliptic integrals
    • Weierstrass elliptic functions
  • acb_modular.h – modular forms of complex variables
    • 中国用谷歌商店加速软件
    • Modular transformations
    • Addition sequences
    • Jacobi theta functions
    • Dedekind eta function
    • Modular forms
    • Elliptic integrals and functions
    • Class polynomials
  • dirichlet.h – Dirichlet characters
    • Dirichlet characters
    • Multiplicative group modulo q
    • Character type
    • Character properties
    • Character evaluation
    • Character operations
  • acb_dirichlet.h – Dirichlet L-functions, Riemann zeta and related functions
    • Roots of unity
    • Truncated L-series and power sums
    • Riemann zeta function
    • Riemann-Siegel formula
    • Hurwitz zeta function
    • 安卓手机如何安装Google play store（谷歌商店-百度经验:2021-6-22 · 安卓手机如何安装Google play store（谷歌商店,因为谷歌在国内的退出，导致现在很多人没法安装Googlelaytore。今天我来教大家用一个超简单的方法安装谷歌商店。
    • 在中国如何用谷歌
    • Dirichlet character evaluation
    • Dirichlet character Gauss, Jacobi and theta sums
    • Discrete Fourier transforms
    • Dirichlet L-functions
    • Hardy Z-functions
    • Gram points
    • Riemann zeta function zeros
    • Riemann zeta function zeros (Platt’s method)
  • bernoulli.h – support for Bernoulli numbers
    • Generation of Bernoulli numbers
    • Caching
    • Bounding
  • hypgeom.h – support for hypergeometric series
    • Strategy for error bounding
    • Types, macros and constants
    • Memory management
    • Error bounding
    • Summation
  • partitions.h – computation of the partition function

蓝鲸加速器vpm-老王vp官网

Using ball arithmetic, it is possible to do rigorous root-finding and integration (among other operations) with generic functions. This code should be considered experimental.

  • arb_calc.h – calculus with real-valued functions
    • Types, macros and constants
    • Debugging
    • Subdivision-based root finding
    • Newton-based root finding
  • acb_calc.h – calculus with complex-valued functions
    • Types, macros and constants
    • Integration
    • Local integration algorithms
    • Integration (old)

Extra utility modules¶

中国用谷歌商店加速软件

  • fmpz_extras.h – extra methods for FLINT integers
  • bool_mat.h – matrices over booleans
  • dlog.h – discrete logarithms mod ulong primes
  • fmpr.h – Arb 1.x floating-point numbers (deprecated)

Supplementary algorithm notes¶

安卓手机打不开Google Play商店？一个APP就能帮你解决 ...:2021-11-15 · 好多人都会问GooglePlay商店为什么打不开？老是闪退怎么办？究其原因还是因为谷歌退出了大陆，才会导致谷歌相关应用程序在安卓手机中无法安装使用。那该怎么办呢？没关系，下面小编给大家推荐一个为国内用户提供GooglePlay商店的软件 ...

  • General formulas and bounds
  • Algorithms for mathematical constants
  • Algorithms for the gamma function
  • Algorithms for the Hurwitz zeta function
  • 中国用谷歌商店加速软件
  • Algorithms for hypergeometric functions
  • Algorithms for the arithmetic-geometric mean

中国用谷歌商店加速软件

  • History and changes