Welcome to Arb's documentation!
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.. only:: latex
Introduction
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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.
Arb is free software distributed under the
GNU Lesser General Public License (LGPL), version 2.1 or later
(see :ref:`license` for details).
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.
Arb is free software distributed under the
GNU Lesser General Public License (LGPL), version 2.1 or later
(see :ref:`license` for details).
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 (:ref:`older versions `).
General information
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.. toctree::
:maxdepth: 2
overview.rst
setup.rst
using.rst
issues.rst
examples.rst
Floating-point numbers
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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
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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
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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
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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
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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
arb_hypgeom.rst
acb_modular.rst
acb_dirichlet.rst
bernoulli.rst
hypgeom.rst
partitions.rst
Calculus
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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
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Mainly for internal use.
.. toctree::
:maxdepth: 1
fmpz_extras.rst
bool_mat.rst
fmpr.rst
Supplementary algorithm notes
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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
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.. toctree::
:maxdepth: 2
credits.rst
.. toctree::
:maxdepth: 1
history.rst