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+div .toctree-wrapper { column-count: 2; } + +div .toctree-wrapper > ul { margin: 0; } + +ul .toctree-l1 { + margin: 0; + -webkit-column-break-inside: avoid; + page-break-inside: avoid; + break-inside: avoid-column; +} + +div.body { + min-width: 450px; + max-width: 100%; +} + diff --git a/doc/source/acb_dirichlet.rst b/doc/source/acb_dirichlet.rst index 62baa2fe..b01549d6 100644 --- a/doc/source/acb_dirichlet.rst +++ b/doc/source/acb_dirichlet.rst @@ -1,6 +1,6 @@ .. _acb-dirichlet: -**acb_dirichlet.h** -- Dirichlet L-functions, zeta functions, and related functions +**acb_dirichlet.h** -- Dirichlet L-functions, Riemann zeta and related functions =================================================================================== *Warning: the interfaces in this module are experimental and may change diff --git a/doc/source/acb_modular.rst b/doc/source/acb_modular.rst index 39fba35e..61b73148 100644 --- a/doc/source/acb_modular.rst +++ b/doc/source/acb_modular.rst @@ -440,7 +440,7 @@ To avoid confusion, we only write `q^k` when `k` is an integer. each respective output variable. The *notransform* version does not move `\tau` to the fundamental domain or reduce `z` during the computation. -The Dedekind eta function +Dedekind eta function ------------------------------------------------------------------------------- .. function:: void acb_modular_addseq_eta(slong * exponents, slong * aindex, slong * bindex, slong num) diff --git a/doc/source/conf.py b/doc/source/conf.py index a918a719..f127d72a 100644 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -104,12 +104,26 @@ pygments_style = 'sphinx' # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. html_theme = 'default' -#html_theme = 'pyramid' + +html_context = { + 'css_files': ['_static/default.css'], +} # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the # documentation. -html_theme_options = {'sidebarwidth' : 300} +html_theme_options = { + 'sidebarwidth' : 280, + 'collapsiblesidebar': True, + 'bodyfont': "'arial', sans-serif", + 'headfont': "'arial', sans-serif", + 'sidebarbtncolor': '#666', + 'sidebarbgcolor': '#444', + 'sidebarlinkcolor': '#ddd', + 'relbarbgcolor': '#333', + 'footerbgcolor': '#333', + 'headbgcolor': '#fff', +} # Add any paths that contain custom themes here, relative to this directory. #html_theme_path = [] @@ -123,7 +137,7 @@ html_theme_options = {'sidebarwidth' : 300} # The name of an image file (relative to this directory) to place at the top # of the sidebar. -html_logo = "_static/arbwhite.png" +#html_logo = "_static/arbwhite.png" # The name of an image file (within the static path) to use as favicon of the # docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 diff --git a/doc/source/index.rst b/doc/source/index.rst index fec2d67f..9864a0f7 100644 --- a/doc/source/index.rst +++ b/doc/source/index.rst @@ -1,4 +1,4 @@ -Arb - a C library for arbitrary-precision interval arithmetic +Arb - a C library for arbitrary-precision ball arithmetic ============================================================= .. only:: latex @@ -7,11 +7,14 @@ Arb - a C library for arbitrary-precision interval arithmetic :::::::::::: Welcome to Arb's documentation! - Arb is a C library for arbitrary-precision interval arithmetic, - using a midpoint-radius representation ("ball arithmetic"). - It supports real and complex numbers, polynomials, power series, - matrices, and evaluation of many transcendental functions. - All operations are done with automatic, rigorous error bounds. + 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 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 @@ -32,21 +35,25 @@ Arb - a C library for arbitrary-precision interval arithmetic This documentation is available in HTML format at http://arblib.org and in PDF format at http://arblib.org/arb.pdf. - The version of the documentation you are currently reading was updated + This edition of the documentation was updated |today| and describes Arb |version|. Documentation for :ref:`specific release versions ` is also available in PDF format. .. only:: html - .. image:: _static/arbtext.png + .. image:: _static/banner.jpg + :align: center Welcome to Arb's documentation! - Arb is a C library for arbitrary-precision interval arithmetic, - using a midpoint-radius representation ("ball arithmetic"). - It supports real and complex numbers, polynomials, power series, - matrices, and evaluation of many transcendental functions. - All operations are done with automatic, rigorous error bounds. + 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 @@ -67,7 +74,7 @@ Arb - a C library for arbitrary-precision interval arithmetic This documentation is available in HTML format at http://arblib.org and in PDF format at http://arblib.org/arb.pdf. - The version of the documentation you are currently reading was updated + This edition of the documentation was updated |today| and describes Arb |version|. Documentation for :ref:`specific release versions ` is also available in PDF format. @@ -82,13 +89,23 @@ General information setup.rst using.rst issues.rst + credits.rst + +Example programs +:::::::::::::::::::: + +.. toctree:: + :maxdepth: 2 + examples.rst Floating-point numbers :::::::::::::::::::::::::::::::::::: -The radius and midpoint of a ball are represented using two specialized -floating-point types. +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. .. toctree:: :maxdepth: 2 @@ -101,7 +118,7 @@ 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. +form, with *arb_t* balls for the real and imaginary parts. .. toctree:: :maxdepth: 2 @@ -121,6 +138,10 @@ on polynomials, without introducing a separate power series type. arb_poly.rst acb_poly.rst + +.. toctree:: + :maxdepth: 2 + arb_fmpz_poly.rst Transforms @@ -143,7 +164,7 @@ Rudimentary linear algebra is supported. arb_mat.rst acb_mat.rst -Higher mathematical functions +Special functions :::::::::::::::::::::::::::::::::::: These modules implement mathematical functions with complexity @@ -206,14 +227,9 @@ lengthy to reproduce in the documentation for each module. hypergeometric.rst agm.rst -History, credits and references +Version history ::::::::::::::::::::::::::::::::: -.. toctree:: - :maxdepth: 2 - - credits.rst - .. toctree:: :maxdepth: 1 diff --git a/doc/source/issues.rst b/doc/source/issues.rst index 82c28922..66126199 100644 --- a/doc/source/issues.rst +++ b/doc/source/issues.rst @@ -71,6 +71,8 @@ internal representation of numbers (using limb arrays). Arb uses the following FLINT types for exact (integral and rational) arbitrary-size values. For details, refer to the FLINT documentation. +.. type:: fmpz + .. type:: fmpz_t The FLINT multi-precision integer type uses an inline representation for small @@ -80,6 +82,10 @@ arbitrary-size values. For details, refer to the FLINT documentation. The *fmpz_t* type is functionally identical to the GMP *mpz_t* type, but faster for small values. + An :type:`fmpz_t` is defined as an array of length one of type + :type:`fmpz` (which is just an alias for :type:`slong`), + permitting an :type:`fmpz_t` to be passed by reference. + .. type:: fmpq_t FLINT multi-precision rational number. @@ -236,7 +242,7 @@ Use of hardware floating-point arithmetic Arb uses hardware floating-point arithmetic (the ``double`` type in C) in two different ways. -Firstly, ``double`` arithmetic as well as transcendental ``libm`` functions +First, ``double`` arithmetic as well as transcendental ``libm`` functions (such as ``exp``, ``log``) are used to select parameters heuristically in various algorithms. Such heuristic use of approximate arithmetic does not affect correctness: when any error bounds depend on the parameters, the error @@ -245,7 +251,7 @@ in the floating-point arithmetic on a particular machine could cause an algorithm to become inefficient due to inefficient parameters being selected. -Secondly, ``double`` arithmetic is used internally for some rigorous error bound +Second, ``double`` arithmetic is used internally for some rigorous error bound calculations. To guarantee correctness, we make the following assumptions. With the stated exceptions, these should hold on all commonly used platforms.