Welcome to Arb's documentation! =============================== .. only:: latex Introduction :::::::::::: Arb is a C library for arbitrary-precision floating-point ball arithmetic, developed by `Fredrik Johansson `_ (fredrik.johansson@gmail.com). It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many transcendental functions. All is done with automatic, rigorous error bounds. The git repository is https://github.com/fredrik-johansson/arb/ The documentation website is http://fredrikj.net/arb/ .. only:: html .. image:: _static/arbtext.png Arb is a C library for arbitrary-precision floating-point ball arithmetic, developed by `Fredrik Johansson `_ (fredrik.johansson@gmail.com). It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many transcendental functions. All is done with automatic, rigorous error bounds. The git repository is https://github.com/fredrik-johansson/arb/ The documentation website is http://fredrikj.net/arb/ A `PDF version `_ of this documentation is available. General information :::::::::::::::::::: .. toctree:: :maxdepth: 2 overview.rst setup.rst issues.rst history.rst examples.rst Floating-point numbers :::::::::::::::::::::::::::::::::::: The radius and midpoint of a ball are represented using two specialized floating-point types. .. toctree:: :maxdepth: 2 mag.rst arf.rst Real and complex numbers :::::::::::::::::::::::::::::::::::: Real numbers (*arb_t*) are represented as midpoint-radius intervals, also known as balls. Complex numbers (*acb_t*) are represented in rectangular form, with balls for the real and imaginary parts. .. toctree:: :maxdepth: 2 arb.rst acb.rst Polynomials and power series :::::::::::::::::::::::::::::::::::: 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. .. toctree:: :maxdepth: 2 arb_poly.rst acb_poly.rst Matrices :::::::::::::::::::::::::::::::::::: These modules implement dense matrices with real and complex coefficients. Rudimentary linear algebra is supported. .. toctree:: :maxdepth: 2 arb_mat.rst acb_mat.rst Higher mathematical functions :::::::::::::::::::::::::::::::::::: These modules implement mathematical functions with complexity that goes beyond the basics covered directly in the *arb* and *acb* modules. .. toctree:: :maxdepth: 2 acb_hypgeom.rst acb_modular.rst acb_dirichlet.rst bernoulli.rst hypgeom.rst partitions.rst Calculus :::::::::::::::::::::::::::::::::::: 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. .. toctree:: :maxdepth: 2 arb_calc.rst acb_calc.rst Extra utility modules :::::::::::::::::::::::::::::::::::: Mainly for internal use. .. toctree:: :maxdepth: 1 fmpz_extras.rst Legacy modules (Arb 1.x types) :::::::::::::::::::::::::::::::::::: These modules are deprecated. They are mainly kept for testing the newer (and faster) implementations introduced in Arb 2.x. .. toctree:: :maxdepth: 1 fmpr.rst Supplementary algorithm notes :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: Here, we give extra proofs, error bounds, and formulas that would be too lengthy to reproduce in the documentation for each module. .. toctree:: :maxdepth: 1 constants.rst gamma.rst polylogarithms.rst hypergeometric.rst agm.rst Credits and references :::::::::::::::::::::::: .. toctree:: :maxdepth: 2 credits.rst