arb/doc/source/index.rst

Welcome to Arb's documentation!
===============================

.. only:: latex

    Introduction
    ::::::::::::

    Arb is a C library for arbitrary-precision floating-point ball arithmetic,
    developed by `Fredrik Johansson <http://fredrikj.net/>`_
    (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 <http://fredrikj.net/>`_
    (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 <http://fredrikj.net/arb/arb.pdf>`_ of this documentation
    is available (:ref:`older versions <history>`).

General information
::::::::::::::::::::

.. toctree::
   :maxdepth: 2

   overview.rst
   setup.rst
   using.rst
   issues.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
   bool_mat.rst
   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

   formulas.rst
   constants.rst
   gamma.rst
   polylogarithms.rst
   hypergeometric.rst
   agm.rst

History, credits and references
:::::::::::::::::::::::::::::::::

.. toctree::
   :maxdepth: 2

   credits.rst

.. toctree::
   :maxdepth: 1

   history.rst