mirror of
https://github.com/vale981/arb
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181 lines
4.1 KiB
ReStructuredText
181 lines
4.1 KiB
ReStructuredText
Welcome to Arb's documentation!
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===============================
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.. only:: latex
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Introduction
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::::::::::::
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Arb is a C library for arbitrary-precision floating-point ball arithmetic,
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developed by `Fredrik Johansson <http://fredrikj.net/>`_
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(fredrik.johansson@gmail.com).
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It supports real and complex numbers, polynomials, power series, matrices,
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and evaluation of many transcendental functions.
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All is done with automatic, rigorous error bounds.
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Arb is free software distributed under the
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GNU Lesser General Public License (LGPL), version 2.1 or later
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(see :ref:`license` for details).
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The git repository is https://github.com/fredrik-johansson/arb/
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The documentation website is http://fredrikj.net/arb/
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.. only:: html
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.. image:: _static/arbtext.png
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Arb is a C library for arbitrary-precision floating-point ball arithmetic,
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developed by `Fredrik Johansson <http://fredrikj.net/>`_
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(fredrik.johansson@gmail.com).
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It supports real and complex numbers, polynomials, power series, matrices,
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and evaluation of many transcendental functions.
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All is done with automatic, rigorous error bounds.
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Arb is free software distributed under the
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GNU Lesser General Public License (LGPL), version 2.1 or later
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(see :ref:`license` for details).
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The git repository is https://github.com/fredrik-johansson/arb/
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The documentation website is http://fredrikj.net/arb/
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A `PDF version <http://fredrikj.net/arb/arb.pdf>`_ of this documentation
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is available (:ref:`older versions <history>`).
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General information
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.. toctree::
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:maxdepth: 2
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overview.rst
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setup.rst
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using.rst
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issues.rst
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examples.rst
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Floating-point numbers
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The radius and midpoint of a ball are represented using two specialized
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floating-point types.
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.. toctree::
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:maxdepth: 2
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mag.rst
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arf.rst
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Real and complex numbers
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::::::::::::::::::::::::::::::::::::
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Real numbers (*arb_t*) are represented as midpoint-radius intervals,
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also known as balls. Complex numbers (*acb_t*) are represented in rectangular
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form, with balls for the real and imaginary parts.
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.. toctree::
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:maxdepth: 2
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arb.rst
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acb.rst
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Polynomials and power series
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::::::::::::::::::::::::::::::::::::
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These modules implement dense univariate polynomials with real and complex
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coefficients. Truncated power series are supported via methods acting
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on polynomials, without introducing a separate power series type.
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.. toctree::
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:maxdepth: 2
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arb_poly.rst
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acb_poly.rst
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Matrices
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These modules implement dense matrices with real and complex coefficients.
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Rudimentary linear algebra is supported.
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.. toctree::
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:maxdepth: 2
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arb_mat.rst
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acb_mat.rst
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Higher mathematical functions
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These modules implement mathematical functions with complexity
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that goes beyond the basics covered directly in the *arb* and *acb*
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modules.
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.. toctree::
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:maxdepth: 2
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acb_hypgeom.rst
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arb_hypgeom.rst
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acb_modular.rst
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dirichlet.rst
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acb_dirichlet.rst
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bernoulli.rst
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hypgeom.rst
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partitions.rst
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Calculus
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Using ball arithmetic, it is possible to do rigorous root-finding and
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integration (among other operations)
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with generic functions. This code should be considered experimental.
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.. toctree::
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:maxdepth: 2
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arb_calc.rst
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acb_calc.rst
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Extra utility modules
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Mainly for internal use.
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.. toctree::
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:maxdepth: 1
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fmpz_extras.rst
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bool_mat.rst
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dlog.rst
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fmpr.rst
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Supplementary algorithm notes
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::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
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Here, we give extra proofs, error bounds, and formulas that would be too
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lengthy to reproduce in the documentation for each module.
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.. toctree::
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:maxdepth: 1
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formulas.rst
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constants.rst
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gamma.rst
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polylogarithms.rst
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hypergeometric.rst
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agm.rst
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History, credits and references
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:::::::::::::::::::::::::::::::::
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.. toctree::
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:maxdepth: 2
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credits.rst
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.. toctree::
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:maxdepth: 1
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history.rst
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