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These documentation pages include resources by third parties. This copyright
file applies only to those resources. The following third party resources are
included, and carry their own copyright notices and license terms:
* Fira Sans (FiraSans-Regular.woff, FiraSans-Medium.woff):
Copyright (c) 2014, Mozilla Foundation https://mozilla.org/
with Reserved Font Name Fira Sans.
Copyright (c) 2014, Telefonica S.A.
Licensed under the SIL Open Font License, Version 1.1.
See FiraSans-LICENSE.txt.
* rustdoc.css, main.js, and playpen.js:
Copyright 2015 The Rust Developers.
Licensed under the Apache License, Version 2.0 (see LICENSE-APACHE.txt) or
the MIT license (LICENSE-MIT.txt) at your option.
* normalize.css:
Copyright (c) Nicolas Gallagher and Jonathan Neal.
Licensed under the MIT license (see LICENSE-MIT.txt).
* Source Code Pro (SourceCodePro-Regular.woff, SourceCodePro-Semibold.woff):
Copyright 2010, 2012 Adobe Systems Incorporated (http://www.adobe.com/),
with Reserved Font Name 'Source'. All Rights Reserved. Source is a trademark
of Adobe Systems Incorporated in the United States and/or other countries.
Licensed under the SIL Open Font License, Version 1.1.
See SourceCodePro-LICENSE.txt.
* Source Serif Pro (SourceSerifPro-Regular.ttf.woff,
SourceSerifPro-Bold.ttf.woff, SourceSerifPro-It.ttf.woff):
Copyright 2014 Adobe Systems Incorporated (http://www.adobe.com/), with
Reserved Font Name 'Source'. All Rights Reserved. Source is a trademark of
Adobe Systems Incorporated in the United States and/or other countries.
Licensed under the SIL Open Font License, Version 1.1.
See SourceSerifPro-LICENSE.txt.
This copyright file is intended to be distributed with rustdoc output.

@ -0,0 +1,94 @@
Digitized data copyright (c) 2012-2015, The Mozilla Foundation and Telefonica S.A.
with Reserved Font Name < Fira >,
This Font Software is licensed under the SIL Open Font License, Version 1.1.
This license is copied below, and is also available with a FAQ at:
http://scripts.sil.org/OFL
-----------------------------------------------------------
SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
-----------------------------------------------------------
PREAMBLE
The goals of the Open Font License (OFL) are to stimulate worldwide
development of collaborative font projects, to support the font creation
efforts of academic and linguistic communities, and to provide a free and
open framework in which fonts may be shared and improved in partnership
with others.
The OFL allows the licensed fonts to be used, studied, modified and
redistributed freely as long as they are not sold by themselves. The
fonts, including any derivative works, can be bundled, embedded,
redistributed and/or sold with any software provided that any reserved
names are not used by derivative works. The fonts and derivatives,
however, cannot be released under any other type of license. The
requirement for fonts to remain under this license does not apply
to any document created using the fonts or their derivatives.
DEFINITIONS
"Font Software" refers to the set of files released by the Copyright
Holder(s) under this license and clearly marked as such. This may
include source files, build scripts and documentation.
"Reserved Font Name" refers to any names specified as such after the
copyright statement(s).
"Original Version" refers to the collection of Font Software components as
distributed by the Copyright Holder(s).
"Modified Version" refers to any derivative made by adding to, deleting,
or substituting -- in part or in whole -- any of the components of the
Original Version, by changing formats or by porting the Font Software to a
new environment.
"Author" refers to any designer, engineer, programmer, technical
writer or other person who contributed to the Font Software.
PERMISSION & CONDITIONS
Permission is hereby granted, free of charge, to any person obtaining
a copy of the Font Software, to use, study, copy, merge, embed, modify,
redistribute, and sell modified and unmodified copies of the Font
Software, subject to the following conditions:
1) Neither the Font Software nor any of its individual components,
in Original or Modified Versions, may be sold by itself.
2) Original or Modified Versions of the Font Software may be bundled,
redistributed and/or sold with any software, provided that each copy
contains the above copyright notice and this license. These can be
included either as stand-alone text files, human-readable headers or
in the appropriate machine-readable metadata fields within text or
binary files as long as those fields can be easily viewed by the user.
3) No Modified Version of the Font Software may use the Reserved Font
Name(s) unless explicit written permission is granted by the corresponding
Copyright Holder. This restriction only applies to the primary font name as
presented to the users.
4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font
Software shall not be used to promote, endorse or advertise any
Modified Version, except to acknowledge the contribution(s) of the
Copyright Holder(s) and the Author(s) or with their explicit written
permission.
5) The Font Software, modified or unmodified, in part or in whole,
must be distributed entirely under this license, and must not be
distributed under any other license. The requirement for fonts to
remain under this license does not apply to any document created
using the Font Software.
TERMINATION
This license becomes null and void if any of the above conditions are
not met.
DISCLAIMER
THE FONT SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE
COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL
DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM
OTHER DEALINGS IN THE FONT SOFTWARE.

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Apache License
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@ -0,0 +1,23 @@
Permission is hereby granted, free of charge, to any
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publish, distribute, sublicense, and/or sell copies of
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OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.

@ -0,0 +1,93 @@
Copyright 2010, 2012 Adobe Systems Incorporated (http://www.adobe.com/), with Reserved Font Name 'Source'. All Rights Reserved. Source is a trademark of Adobe Systems Incorporated in the United States and/or other countries.
This Font Software is licensed under the SIL Open Font License, Version 1.1.
This license is copied below, and is also available with a FAQ at: http://scripts.sil.org/OFL
-----------------------------------------------------------
SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
-----------------------------------------------------------
PREAMBLE
The goals of the Open Font License (OFL) are to stimulate worldwide
development of collaborative font projects, to support the font creation
efforts of academic and linguistic communities, and to provide a free and
open framework in which fonts may be shared and improved in partnership
with others.
The OFL allows the licensed fonts to be used, studied, modified and
redistributed freely as long as they are not sold by themselves. The
fonts, including any derivative works, can be bundled, embedded,
redistributed and/or sold with any software provided that any reserved
names are not used by derivative works. The fonts and derivatives,
however, cannot be released under any other type of license. The
requirement for fonts to remain under this license does not apply
to any document created using the fonts or their derivatives.
DEFINITIONS
"Font Software" refers to the set of files released by the Copyright
Holder(s) under this license and clearly marked as such. This may
include source files, build scripts and documentation.
"Reserved Font Name" refers to any names specified as such after the
copyright statement(s).
"Original Version" refers to the collection of Font Software components as
distributed by the Copyright Holder(s).
"Modified Version" refers to any derivative made by adding to, deleting,
or substituting -- in part or in whole -- any of the components of the
Original Version, by changing formats or by porting the Font Software to a
new environment.
"Author" refers to any designer, engineer, programmer, technical
writer or other person who contributed to the Font Software.
PERMISSION & CONDITIONS
Permission is hereby granted, free of charge, to any person obtaining
a copy of the Font Software, to use, study, copy, merge, embed, modify,
redistribute, and sell modified and unmodified copies of the Font
Software, subject to the following conditions:
1) Neither the Font Software nor any of its individual components,
in Original or Modified Versions, may be sold by itself.
2) Original or Modified Versions of the Font Software may be bundled,
redistributed and/or sold with any software, provided that each copy
contains the above copyright notice and this license. These can be
included either as stand-alone text files, human-readable headers or
in the appropriate machine-readable metadata fields within text or
binary files as long as those fields can be easily viewed by the user.
3) No Modified Version of the Font Software may use the Reserved Font
Name(s) unless explicit written permission is granted by the corresponding
Copyright Holder. This restriction only applies to the primary font name as
presented to the users.
4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font
Software shall not be used to promote, endorse or advertise any
Modified Version, except to acknowledge the contribution(s) of the
Copyright Holder(s) and the Author(s) or with their explicit written
permission.
5) The Font Software, modified or unmodified, in part or in whole,
must be distributed entirely under this license, and must not be
distributed under any other license. The requirement for fonts to
remain under this license does not apply to any document created
using the Font Software.
TERMINATION
This license becomes null and void if any of the above conditions are
not met.
DISCLAIMER
THE FONT SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE
COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL
DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM
OTHER DEALINGS IN THE FONT SOFTWARE.

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Copyright 2014-2018 Adobe (http://www.adobe.com/), with Reserved Font Name 'Source'. All Rights Reserved. Source is a trademark of Adobe in the United States and/or other countries.
This Font Software is licensed under the SIL Open Font License, Version 1.1.
This license is copied below, and is also available with a FAQ at: http://scripts.sil.org/OFL
-----------------------------------------------------------
SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
-----------------------------------------------------------
PREAMBLE
The goals of the Open Font License (OFL) are to stimulate worldwide
development of collaborative font projects, to support the font creation
efforts of academic and linguistic communities, and to provide a free and
open framework in which fonts may be shared and improved in partnership
with others.
The OFL allows the licensed fonts to be used, studied, modified and
redistributed freely as long as they are not sold by themselves. The
fonts, including any derivative works, can be bundled, embedded,
redistributed and/or sold with any software provided that any reserved
names are not used by derivative works. The fonts and derivatives,
however, cannot be released under any other type of license. The
requirement for fonts to remain under this license does not apply
to any document created using the fonts or their derivatives.
DEFINITIONS
"Font Software" refers to the set of files released by the Copyright
Holder(s) under this license and clearly marked as such. This may
include source files, build scripts and documentation.
"Reserved Font Name" refers to any names specified as such after the
copyright statement(s).
"Original Version" refers to the collection of Font Software components as
distributed by the Copyright Holder(s).
"Modified Version" refers to any derivative made by adding to, deleting,
or substituting -- in part or in whole -- any of the components of the
Original Version, by changing formats or by porting the Font Software to a
new environment.
"Author" refers to any designer, engineer, programmer, technical
writer or other person who contributed to the Font Software.
PERMISSION & CONDITIONS
Permission is hereby granted, free of charge, to any person obtaining
a copy of the Font Software, to use, study, copy, merge, embed, modify,
redistribute, and sell modified and unmodified copies of the Font
Software, subject to the following conditions:
1) Neither the Font Software nor any of its individual components,
in Original or Modified Versions, may be sold by itself.
2) Original or Modified Versions of the Font Software may be bundled,
redistributed and/or sold with any software, provided that each copy
contains the above copyright notice and this license. These can be
included either as stand-alone text files, human-readable headers or
in the appropriate machine-readable metadata fields within text or
binary files as long as those fields can be easily viewed by the user.
3) No Modified Version of the Font Software may use the Reserved Font
Name(s) unless explicit written permission is granted by the corresponding
Copyright Holder. This restriction only applies to the primary font name as
presented to the users.
4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font
Software shall not be used to promote, endorse or advertise any
Modified Version, except to acknowledge the contribution(s) of the
Copyright Holder(s) and the Author(s) or with their explicit written
permission.
5) The Font Software, modified or unmodified, in part or in whole,
must be distributed entirely under this license, and must not be
distributed under any other license. The requirement for fonts to
remain under this license does not apply to any document created
using the Font Software.
TERMINATION
This license becomes null and void if any of the above conditions are
not met.
DISCLAIMER
THE FONT SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE
COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL
DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM
OTHER DEALINGS IN THE FONT SOFTWARE.

@ -0,0 +1,93 @@
Copyright 2014 Adobe Systems Incorporated (http://www.adobe.com/), with Reserved Font Name 'Source'. All Rights Reserved. Source is a trademark of Adobe Systems Incorporated in the United States and/or other countries.
This Font Software is licensed under the SIL Open Font License, Version 1.1.
This license is copied below, and is also available with a FAQ at: http://scripts.sil.org/OFL
-----------------------------------------------------------
SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
-----------------------------------------------------------
PREAMBLE
The goals of the Open Font License (OFL) are to stimulate worldwide
development of collaborative font projects, to support the font creation
efforts of academic and linguistic communities, and to provide a free and
open framework in which fonts may be shared and improved in partnership
with others.
The OFL allows the licensed fonts to be used, studied, modified and
redistributed freely as long as they are not sold by themselves. The
fonts, including any derivative works, can be bundled, embedded,
redistributed and/or sold with any software provided that any reserved
names are not used by derivative works. The fonts and derivatives,
however, cannot be released under any other type of license. The
requirement for fonts to remain under this license does not apply
to any document created using the fonts or their derivatives.
DEFINITIONS
"Font Software" refers to the set of files released by the Copyright
Holder(s) under this license and clearly marked as such. This may
include source files, build scripts and documentation.
"Reserved Font Name" refers to any names specified as such after the
copyright statement(s).
"Original Version" refers to the collection of Font Software components as
distributed by the Copyright Holder(s).
"Modified Version" refers to any derivative made by adding to, deleting,
or substituting -- in part or in whole -- any of the components of the
Original Version, by changing formats or by porting the Font Software to a
new environment.
"Author" refers to any designer, engineer, programmer, technical
writer or other person who contributed to the Font Software.
PERMISSION & CONDITIONS
Permission is hereby granted, free of charge, to any person obtaining
a copy of the Font Software, to use, study, copy, merge, embed, modify,
redistribute, and sell modified and unmodified copies of the Font
Software, subject to the following conditions:
1) Neither the Font Software nor any of its individual components,
in Original or Modified Versions, may be sold by itself.
2) Original or Modified Versions of the Font Software may be bundled,
redistributed and/or sold with any software, provided that each copy
contains the above copyright notice and this license. These can be
included either as stand-alone text files, human-readable headers or
in the appropriate machine-readable metadata fields within text or
binary files as long as those fields can be easily viewed by the user.
3) No Modified Version of the Font Software may use the Reserved Font
Name(s) unless explicit written permission is granted by the corresponding
Copyright Holder. This restriction only applies to the primary font name as
presented to the users.
4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font
Software shall not be used to promote, endorse or advertise any
Modified Version, except to acknowledge the contribution(s) of the
Copyright Holder(s) and the Author(s) or with their explicit written
permission.
5) The Font Software, modified or unmodified, in part or in whole,
must be distributed entirely under this license, and must not be
distributed under any other license. The requirement for fonts to
remain under this license does not apply to any document created
using the Font Software.
TERMINATION
This license becomes null and void if any of the above conditions are
not met.
DISCLAIMER
THE FONT SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE
COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL
DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM
OTHER DEALINGS IN THE FONT SOFTWARE.

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="List of all items in this crate"><meta name="keywords" content="rust, rustlang, rust-lang"><title>List of all items in this crate</title><link rel="stylesheet" type="text/css" href="../normalize.css"><link rel="stylesheet" type="text/css" href="../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../dark.css"><link rel="stylesheet" type="text/css" href="../light.css" id="themeStyle"><script src="../storage.js"></script><noscript><link rel="stylesheet" href="../noscript.css"></noscript><link rel="shortcut icon" href="../favicon.ico"><style type="text/css">#crate-search{background-image:url("../down-arrow.svg");}</style></head><body class="rustdoc mod"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../adler32/index.html'><div class='logo-container'><img src='../rust-logo.png' alt='logo'></div></a></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../settings.html"><img src="../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span>
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<span class='in-band'>List of all items</span></h1><h3 id='Structs'>Structs</h3><ul class='structs docblock'><li><a href='struct.RollingAdler32.html'>RollingAdler32</a></li></ul><h3 id='Functions'>Functions</h3><ul class='functions docblock'><li><a href='fn.adler32.html'>adler32</a></li></ul></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../";window.currentCrate = "adler32";</script><script src="../aliases.js"></script><script src="../main.js"></script><script defer src="../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `adler32` fn in crate `adler32`."><meta name="keywords" content="rust, rustlang, rust-lang, adler32"><title>adler32::adler32 - Rust</title><link rel="stylesheet" type="text/css" href="../normalize.css"><link rel="stylesheet" type="text/css" href="../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../dark.css"><link rel="stylesheet" type="text/css" href="../light.css" id="themeStyle"><script src="../storage.js"></script><noscript><link rel="stylesheet" href="../noscript.css"></noscript><link rel="shortcut icon" href="../favicon.ico"><style type="text/css">#crate-search{background-image:url("../down-arrow.svg");}</style></head><body class="rustdoc fn"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../adler32/index.html'><div class='logo-container'><img src='../rust-logo.png' alt='logo'></div></a><div class="sidebar-elems"><p class='location'><a href='index.html'>adler32</a></p><script>window.sidebarCurrent = {name: 'adler32', ty: 'fn', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../settings.html"><img src="../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../src/adler32/lib.rs.html#188-197' title='goto source code'>[src]</a></span><span class='in-band'>Function <a href='index.html'>adler32</a>::<wbr><a class="fn" href=''>adler32</a></span></h1><pre class='rust fn'>pub fn adler32&lt;R:&nbsp;<a class="trait" href="https://doc.rust-lang.org/nightly/std/io/trait.Read.html" title="trait std::io::Read">Read</a>&gt;(reader: R) -&gt; <a class="type" href="https://doc.rust-lang.org/nightly/std/io/error/type.Result.html" title="type std::io::error::Result">Result</a>&lt;<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>&gt;</pre><div class='docblock'><p>Consume a Read object and returns the Adler32 hash.</p>
</div></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../";window.currentCrate = "adler32";</script><script src="../aliases.js"></script><script src="../main.js"></script><script defer src="../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `adler32` crate."><meta name="keywords" content="rust, rustlang, rust-lang, adler32"><title>adler32 - Rust</title><link rel="stylesheet" type="text/css" href="../normalize.css"><link rel="stylesheet" type="text/css" href="../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../dark.css"><link rel="stylesheet" type="text/css" href="../light.css" id="themeStyle"><script src="../storage.js"></script><noscript><link rel="stylesheet" href="../noscript.css"></noscript><link rel="shortcut icon" href="../favicon.ico"><style type="text/css">#crate-search{background-image:url("../down-arrow.svg");}</style></head><body class="rustdoc mod"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../adler32/index.html'><div class='logo-container'><img src='../rust-logo.png' alt='logo'></div></a><p class='location'>Crate adler32</p><div class="sidebar-elems"><a id='all-types' href='all.html'><p>See all adler32's items</p></a><div class="block items"><ul><li><a href="#structs">Structs</a></li><li><a href="#functions">Functions</a></li></ul></div><p class='location'></p><script>window.sidebarCurrent = {name: 'adler32', ty: 'mod', relpath: '../'};</script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../settings.html"><img src="../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../src/adler32/lib.rs.html#1-301' title='goto source code'>[src]</a></span><span class='in-band'>Crate <a class="mod" href=''>adler32</a></span></h1><div class='docblock'><p>A minimal implementation of Adler32 for Rust.</p>
<p>This provides the simple method adler32(), that exhausts a Read and
computes the Adler32 hash, as well as the RollingAdler32 struct, that can
build a hash byte-by-byte, allowing to 'forget' past bytes in a rolling
fashion.</p>
<p>The adler32 code has been translated (as accurately as I could manage) from
the zlib implementation.</p>
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<table><tr class='module-item'><td><a class="struct" href="struct.RollingAdler32.html" title='adler32::RollingAdler32 struct'>RollingAdler32</a></td><td class='docblock-short'><p>A rolling version of the Adler32 hash, which can 'forget' past bytes.</p>
</td></tr></table><h2 id='functions' class='section-header'><a href="#functions">Functions</a></h2>
<table><tr class='module-item'><td><a class="fn" href="fn.adler32.html" title='adler32::adler32 fn'>adler32</a></td><td class='docblock-short'><p>Consume a Read object and returns the Adler32 hash.</p>
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initSidebarItems({"fn":[["adler32","Consume a Read object and returns the Adler32 hash."]],"struct":[["RollingAdler32","A rolling version of the Adler32 hash, which can 'forget' past bytes."]]});

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `RollingAdler32` struct in crate `adler32`."><meta name="keywords" content="rust, rustlang, rust-lang, RollingAdler32"><title>adler32::RollingAdler32 - Rust</title><link rel="stylesheet" type="text/css" href="../normalize.css"><link rel="stylesheet" type="text/css" href="../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../dark.css"><link rel="stylesheet" type="text/css" href="../light.css" id="themeStyle"><script src="../storage.js"></script><noscript><link rel="stylesheet" href="../noscript.css"></noscript><link rel="shortcut icon" href="../favicon.ico"><style type="text/css">#crate-search{background-image:url("../down-arrow.svg");}</style></head><body class="rustdoc struct"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../adler32/index.html'><div class='logo-container'><img src='../rust-logo.png' alt='logo'></div></a><p class='location'>Struct RollingAdler32</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#methods">Methods</a><div class="sidebar-links"><a href="#method.from_buffer">from_buffer</a><a href="#method.from_value">from_value</a><a href="#method.hash">hash</a><a href="#method.new">new</a><a href="#method.remove">remove</a><a href="#method.update">update</a><a href="#method.update_buffer">update_buffer</a></div><a class="sidebar-title" href="#synthetic-implementations">Auto Trait Implementations</a><div class="sidebar-links"><a href="#impl-RefUnwindSafe">RefUnwindSafe</a><a href="#impl-Send">Send</a><a href="#impl-Sync">Sync</a><a href="#impl-Unpin">Unpin</a><a href="#impl-UnwindSafe">UnwindSafe</a></div><a class="sidebar-title" href="#blanket-implementations">Blanket Implementations</a><div class="sidebar-links"><a href="#impl-Any">Any</a><a href="#impl-Borrow%3CT%3E">Borrow&lt;T&gt;</a><a href="#impl-BorrowMut%3CT%3E">BorrowMut&lt;T&gt;</a><a href="#impl-From%3CT%3E">From&lt;T&gt;</a><a href="#impl-Into%3CU%3E">Into&lt;U&gt;</a><a href="#impl-TryFrom%3CU%3E">TryFrom&lt;U&gt;</a><a href="#impl-TryInto%3CU%3E">TryInto&lt;U&gt;</a></div></div><p class='location'><a href='index.html'>adler32</a></p><script>window.sidebarCurrent = {name: 'RollingAdler32', ty: 'struct', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../settings.html"><img src="../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../src/adler32/lib.rs.html#87-90' title='goto source code'>[src]</a></span><span class='in-band'>Struct <a href='index.html'>adler32</a>::<wbr><a class="struct" href=''>RollingAdler32</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust struct'>pub struct RollingAdler32 { /* fields omitted */ }</pre></div><div class='docblock'><p>A rolling version of the Adler32 hash, which can 'forget' past bytes.</p>
<p>Calling remove() will update the hash to the value it would have if that
past byte had never been fed to the algorithm. This allows you to get the
hash of a rolling window very efficiently.</p>
</div><h2 id='methods' class='small-section-header'>Methods<a href='#methods' class='anchor'></a></h2><h3 id='impl' class='impl'><code class='in-band'>impl <a class="struct" href="../adler32/struct.RollingAdler32.html" title="struct adler32::RollingAdler32">RollingAdler32</a></code><a href='#impl' class='anchor'></a><a class='srclink' href='../src/adler32/lib.rs.html#92-185' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.new' class="method"><code id='new.v'>pub fn <a href='#method.new' class='fnname'>new</a>() -&gt; <a class="struct" href="../adler32/struct.RollingAdler32.html" title="struct adler32::RollingAdler32">RollingAdler32</a></code><a class='srclink' href='../src/adler32/lib.rs.html#94-96' title='goto source code'>[src]</a></h4><div class='docblock'><p>Creates an empty Adler32 context (with hash 1).</p>
</div><h4 id='method.from_value' class="method"><code id='from_value.v'>pub fn <a href='#method.from_value' class='fnname'>from_value</a>(adler32: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>) -&gt; <a class="struct" href="../adler32/struct.RollingAdler32.html" title="struct adler32::RollingAdler32">RollingAdler32</a></code><a class='srclink' href='../src/adler32/lib.rs.html#99-103' title='goto source code'>[src]</a></h4><div class='docblock'><p>Creates an Adler32 context with the given initial value.</p>
</div><h4 id='method.from_buffer' class="method"><code id='from_buffer.v'>pub fn <a href='#method.from_buffer' class='fnname'>from_buffer</a>(buffer: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">&amp;[</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">]</a>) -&gt; <a class="struct" href="../adler32/struct.RollingAdler32.html" title="struct adler32::RollingAdler32">RollingAdler32</a></code><a class='srclink' href='../src/adler32/lib.rs.html#106-110' title='goto source code'>[src]</a></h4><div class='docblock'><p>Convenience function initializing a context from the hash of a buffer.</p>
</div><h4 id='method.hash' class="method"><code id='hash.v'>pub fn <a href='#method.hash' class='fnname'>hash</a>(&amp;self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a></code><a class='srclink' href='../src/adler32/lib.rs.html#113-115' title='goto source code'>[src]</a></h4><div class='docblock'><p>Returns the current hash.</p>
</div><h4 id='method.remove' class="method"><code id='remove.v'>pub fn <a href='#method.remove' class='fnname'>remove</a>(&amp;mut self, size: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.usize.html">usize</a>, byte: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>)</code><a class='srclink' href='../src/adler32/lib.rs.html#118-124' title='goto source code'>[src]</a></h4><div class='docblock'><p>Removes the given <code>byte</code> that was fed to the algorithm <code>size</code> bytes ago.</p>
</div><h4 id='method.update' class="method"><code id='update.v'>pub fn <a href='#method.update' class='fnname'>update</a>(&amp;mut self, byte: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a>)</code><a class='srclink' href='../src/adler32/lib.rs.html#127-131' title='goto source code'>[src]</a></h4><div class='docblock'><p>Feeds a new <code>byte</code> to the algorithm to update the hash.</p>
</div><h4 id='method.update_buffer' class="method"><code id='update_buffer.v'>pub fn <a href='#method.update_buffer' class='fnname'>update_buffer</a>(&amp;mut self, buffer: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">&amp;[</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.slice.html">]</a>)</code><a class='srclink' href='../src/adler32/lib.rs.html#134-184' title='goto source code'>[src]</a></h4><div class='docblock'><p>Feeds a vector of bytes to the algorithm to update the hash.</p>
</div></div><h2 id='synthetic-implementations' class='small-section-header'>Auto Trait Implementations<a href='#synthetic-implementations' class='anchor'></a></h2><div id='synthetic-implementations-list'><h3 id='impl-Send' class='impl'><code class='in-band'>impl <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Send.html" title="trait core::marker::Send">Send</a> for <a class="struct" href="../adler32/struct.RollingAdler32.html" title="struct adler32::RollingAdler32">RollingAdler32</a></code><a href='#impl-Send' class='anchor'></a></h3><div class='impl-items'></div><h3 id='impl-Unpin' class='impl'><code class='in-band'>impl <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Unpin.html" title="trait core::marker::Unpin">Unpin</a> for <a class="struct" href="../adler32/struct.RollingAdler32.html" title="struct adler32::RollingAdler32">RollingAdler32</a></code><a href='#impl-Unpin' class='anchor'></a></h3><div class='impl-items'></div><h3 id='impl-Sync' class='impl'><code class='in-band'>impl <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sync.html" title="trait core::marker::Sync">Sync</a> for <a class="struct" href="../adler32/struct.RollingAdler32.html" title="struct adler32::RollingAdler32">RollingAdler32</a></code><a href='#impl-Sync' class='anchor'></a></h3><div class='impl-items'></div><h3 id='impl-UnwindSafe' class='impl'><code class='in-band'>impl <a class="trait" href="https://doc.rust-lang.org/nightly/std/panic/trait.UnwindSafe.html" title="trait std::panic::UnwindSafe">UnwindSafe</a> for <a class="struct" href="../adler32/struct.RollingAdler32.html" title="struct adler32::RollingAdler32">RollingAdler32</a></code><a href='#impl-UnwindSafe' class='anchor'></a></h3><div class='impl-items'></div><h3 id='impl-RefUnwindSafe' class='impl'><code class='in-band'>impl <a class="trait" href="https://doc.rust-lang.org/nightly/std/panic/trait.RefUnwindSafe.html" title="trait std::panic::RefUnwindSafe">RefUnwindSafe</a> for <a class="struct" href="../adler32/struct.RollingAdler32.html" title="struct adler32::RollingAdler32">RollingAdler32</a></code><a href='#impl-RefUnwindSafe' class='anchor'></a></h3><div class='impl-items'></div></div><h2 id='blanket-implementations' class='small-section-header'>Blanket Implementations<a href='#blanket-implementations' class='anchor'></a></h2><div id='blanket-implementations-list'><h3 id='impl-Into%3CU%3E' class='impl'><code class='in-band'>impl&lt;T, U&gt; <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.Into.html" title="trait core::convert::Into">Into</a>&lt;U&gt; for T <span class="where fmt-newline">where<br>&nbsp;&nbsp;&nbsp;&nbsp;U: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.From.html" title="trait core::convert::From">From</a>&lt;T&gt;,&nbsp;</span></code><a href='#impl-Into%3CU%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#544-549' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.into' class="method hidden"><code id='into.v'>fn <a href='https://doc.rust-lang.org/nightly/core/convert/trait.Into.html#tymethod.into' class='fnname'>into</a>(self) -&gt; U</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#546-548' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the conversion.</p>
</div></div><h3 id='impl-From%3CT%3E' class='impl'><code class='in-band'>impl&lt;T&gt; <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.From.html" title="trait core::convert::From">From</a>&lt;T&gt; for T</code><a href='#impl-From%3CT%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#553-555' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.from' class="method hidden"><code id='from.v'>fn <a href='https://doc.rust-lang.org/nightly/core/convert/trait.From.html#tymethod.from' class='fnname'>from</a>(t: T) -&gt; T</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#554' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the conversion.</p>
</div></div><h3 id='impl-TryFrom%3CU%3E' class='impl'><code class='in-band'>impl&lt;T, U&gt; <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a>&lt;U&gt; for T <span class="where fmt-newline">where<br>&nbsp;&nbsp;&nbsp;&nbsp;U: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.Into.html" title="trait core::convert::Into">Into</a>&lt;T&gt;,&nbsp;</span></code><a href='#impl-TryFrom%3CU%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#572-578' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Error' class="type"><code id='Error.t'>type <a href='https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error' class="type">Error</a> = <a class="enum" href="https://doc.rust-lang.org/nightly/core/convert/enum.Infallible.html" title="enum core::convert::Infallible">Infallible</a></code></h4><div class='docblock'><p>The type returned in the event of a conversion error.</p>
</div><h4 id='method.try_from' class="method hidden"><code id='try_from.v'>fn <a href='https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#tymethod.try_from' class='fnname'>try_from</a>(value: U) -&gt; <a class="enum" href="https://doc.rust-lang.org/nightly/core/result/enum.Result.html" title="enum core::result::Result">Result</a>&lt;T, &lt;T as <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a>&lt;U&gt;&gt;::<a class="type" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error" title="type core::convert::TryFrom::Error">Error</a>&gt;</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#575-577' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the conversion.</p>
</div></div><h3 id='impl-TryInto%3CU%3E' class='impl'><code class='in-band'>impl&lt;T, U&gt; <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryInto.html" title="trait core::convert::TryInto">TryInto</a>&lt;U&gt; for T <span class="where fmt-newline">where<br>&nbsp;&nbsp;&nbsp;&nbsp;U: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a>&lt;T&gt;,&nbsp;</span></code><a href='#impl-TryInto%3CU%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#560-567' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Error-1' class="type"><code id='Error.t-1'>type <a href='https://doc.rust-lang.org/nightly/core/convert/trait.TryInto.html#associatedtype.Error' class="type">Error</a> = &lt;U as <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a>&lt;T&gt;&gt;::<a class="type" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error" title="type core::convert::TryFrom::Error">Error</a></code></h4><div class='docblock'><p>The type returned in the event of a conversion error.</p>
</div><h4 id='method.try_into' class="method hidden"><code id='try_into.v'>fn <a href='https://doc.rust-lang.org/nightly/core/convert/trait.TryInto.html#tymethod.try_into' class='fnname'>try_into</a>(self) -&gt; <a class="enum" href="https://doc.rust-lang.org/nightly/core/result/enum.Result.html" title="enum core::result::Result">Result</a>&lt;U, &lt;U as <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a>&lt;T&gt;&gt;::<a class="type" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error" title="type core::convert::TryFrom::Error">Error</a>&gt;</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#564-566' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the conversion.</p>
</div></div><h3 id='impl-BorrowMut%3CT%3E' class='impl'><code class='in-band'>impl&lt;T&gt; <a class="trait" href="https://doc.rust-lang.org/nightly/core/borrow/trait.BorrowMut.html" title="trait core::borrow::BorrowMut">BorrowMut</a>&lt;T&gt; for T <span class="where fmt-newline">where<br>&nbsp;&nbsp;&nbsp;&nbsp;T: ?<a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a>,&nbsp;</span></code><a href='#impl-BorrowMut%3CT%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#218-220' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.borrow_mut' class="method hidden"><code id='borrow_mut.v'>fn <a href='https://doc.rust-lang.org/nightly/core/borrow/trait.BorrowMut.html#tymethod.borrow_mut' class='fnname'>borrow_mut</a>(&amp;mut self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&amp;mut </a>T</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#219' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Mutably borrows from an owned value. <a href="https://doc.rust-lang.org/nightly/core/borrow/trait.BorrowMut.html#tymethod.borrow_mut">Read more</a></p>
</div></div><h3 id='impl-Borrow%3CT%3E' class='impl'><code class='in-band'>impl&lt;T&gt; <a class="trait" href="https://doc.rust-lang.org/nightly/core/borrow/trait.Borrow.html" title="trait core::borrow::Borrow">Borrow</a>&lt;T&gt; for T <span class="where fmt-newline">where<br>&nbsp;&nbsp;&nbsp;&nbsp;T: ?<a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a>,&nbsp;</span></code><a href='#impl-Borrow%3CT%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#213-215' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.borrow' class="method hidden"><code id='borrow.v'>fn <a href='https://doc.rust-lang.org/nightly/core/borrow/trait.Borrow.html#tymethod.borrow' class='fnname'>borrow</a>(&amp;self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&amp;</a>T</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#214' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Immutably borrows from an owned value. <a href="https://doc.rust-lang.org/nightly/core/borrow/trait.Borrow.html#tymethod.borrow">Read more</a></p>
</div></div><h3 id='impl-Any' class='impl'><code class='in-band'>impl&lt;T&gt; <a class="trait" href="https://doc.rust-lang.org/nightly/core/any/trait.Any.html" title="trait core::any::Any">Any</a> for T <span class="where fmt-newline">where<br>&nbsp;&nbsp;&nbsp;&nbsp;T: 'static + ?<a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a>,&nbsp;</span></code><a href='#impl-Any' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/any.rs.html#100-102' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.type_id' class="method hidden"><code id='type_id.v'>fn <a href='https://doc.rust-lang.org/nightly/core/any/trait.Any.html#tymethod.type_id' class='fnname'>type_id</a>(&amp;self) -&gt; <a class="struct" href="https://doc.rust-lang.org/nightly/core/any/struct.TypeId.html" title="struct core::any::TypeId">TypeId</a></code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/any.rs.html#101' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Gets the <code>TypeId</code> of <code>self</code>. <a href="https://doc.rust-lang.org/nightly/core/any/trait.Any.html#tymethod.type_id">Read more</a></p>
</div></div></div></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../";window.currentCrate = "adler32";</script><script src="../aliases.js"></script><script src="../main.js"></script><script defer src="../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `general` mod in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, general"><title>alga::general - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc mod"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Module general</p><div class="sidebar-elems"><div class="block items"><ul><li><a href="#structs">Structs</a></li><li><a href="#traits">Traits</a></li></ul></div><p class='location'><a href='../index.html'>alga</a></p><script>window.sidebarCurrent = {name: 'general', ty: 'mod', relpath: '../'};</script><script defer src="../sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/mod.rs.html#15-200' title='goto source code'>[src]</a></span><span class='in-band'>Module <a href='../index.html'>alga</a>::<wbr><a class="mod" href=''>general</a></span></h1><div class='docblock'><p>Fundamental algebraic structures.</p>
<p>For most applications requiring an abstraction over the reals, <code>RealField</code>
should be sufficient.</p>
<h2 id="algebraic-properties" class="section-header"><a href="#algebraic-properties">Algebraic properties</a></h2>
<p>The goal of algebraic structures is to allow elements of sets to be combined together using one
or several operators. The number and properties of those operators characterize the algebraic
structure. Abstract operators are usually noted <code></code>, <code>+</code>, or <code>×</code>. The last two are preferred
when their behavior conform with the usual meaning of addition and multiplication of reals.
Let <code>Self</code> be a set. Here is a list of the most common properties those operator may fulfill:</p>
<pre><code class="language-notrust">(Closure) a, b ∈ Self ⇒ a ∘ b ∈ Self,
(Divisibility) ∀ a, b ∈ Self, ∃! r, l ∈ Self such that l ∘ a = b and a ∘ r = b
(Invertibility) ∃ e ∈ Self, ∀ a ∈ Self, ∃ r, l ∈ Self such that l ∘ a = a ∘ r = e
If the right and left inverse are equal they are usually noted r = l = a⁻¹.
(Associativity) ∀ a, b, c ∈ Self, (a ∘ b) ∘ c = a ∘ (b ∘ c)
(Neutral Elt.) ∃ e ∈ Self, ∀ a ∈ Self, e ∘ a = a ∘ e = a
(Commutativity) ∀ a, b ∈ Self, a ∘ b = b ∘ a
</code></pre>
<h2 id="identity-elements" class="section-header"><a href="#identity-elements">Identity elements</a></h2>
<p>Two traits are provided that allow the definition of the additive and
multiplicative identity elements:</p>
<ul>
<li><code>IdentityAdditive</code></li>
<li><code>IdentityMultiplicative</code></li>
</ul>
<h2 id="abstractgroup-like-structures" class="section-header"><a href="#abstractgroup-like-structures">AbstractGroup-like structures</a></h2>
<p>These structures are provided for both the addition and multiplication.</p>
<p>These can be derived automatically by <code>alga_traits</code> attribute from <code>alga_derive</code> crate.</p>
<pre><code class="language-notrust"> AbstractMagma
|
_______/ \______
/ \
divisibility associativity
| |
V V
AbstractQuasigroup AbstractSemigroup
| |
identity identity
| |
V V
AbstractLoop AbstractMonoid
| |
associativity invertibility
\______ _______/
\ /
|
V
AbstractGroup
|
commutativity
|
V
AbstractGroupAbelian
</code></pre>
<p>The following traits are provided:</p>
<ul>
<li>(<code>Abstract</code>|<code>Additive</code>|<code>Multiplicative</code>)<code>Magma</code></li>
<li>(<code>Abstract</code>|<code>Additive</code>|<code>Multiplicative</code>)<code>Quasigroup</code></li>
<li>(<code>Abstract</code>|<code>Additive</code>|<code>Multiplicative</code>)<code>Loop</code></li>
<li>(<code>Abstract</code>|<code>Additive</code>|<code>Multiplicative</code>)<code>Semigroup</code></li>
<li>(<code>Abstract</code>|<code>Additive</code>|<code>Multiplicative</code>)<code>Monoid</code></li>
<li>(<code>Abstract</code>|<code>Additive</code>|<code>Multiplicative</code>)<code>Group</code></li>
<li>(<code>Abstract</code>|<code>Additive</code>|<code>Multiplicative</code>)<code>GroupAbelian</code></li>
</ul>
<h2 id="ring-like-structures" class="section-header"><a href="#ring-like-structures">Ring-like structures</a></h2>
<p>These can be derived automatically by <code>alga_traits</code> attribute from <code>alga_derive</code> crate.</p>
<pre><code class="language-notrust"> GroupAbelian Monoid
\________ ________/
\ /
|
V
Ring
|
commutativity_of_mul
|
V
RingCommutative GroupAbelian
\_______ ___________/
\ /
|
V
Field
</code></pre>
<p>The following traits are provided:</p>
<ul>
<li><code>Ring</code></li>
<li><code>RingCommutative</code></li>
<li><code>Field</code></li>
</ul>
<h2 id="module-like-structures" class="section-header"><a href="#module-like-structures">Module-like structures</a></h2>
<pre><code class="language-notrust"> GroupAbelian RingCommutative
\______ _____/
\ /
| |
V V
Module&lt;Scalar&gt; Field
\______ _____/
\ /
| |
V V
VectorSpace&lt;Scalar&gt;
</code></pre>
<p>The following traits are provided:</p>
<ul>
<li><code>Module</code></li>
<li><code>VectorSpace</code></li>
</ul>
<h1 id="quickcheck-properties" class="section-header"><a href="#quickcheck-properties">Quickcheck properties</a></h1>
<p>Functions are provided to test that algebraic properties like
associativity and commutativity hold for a given set of arguments.</p>
<p>These tests can be automatically derived by <code>alga_quickcheck</code> attribute from <code>alga_derive</code> crate.</p>
<p>For example:</p>
<div class='information'><div class='tooltip ignore'><span class='tooltiptext'>This example is not tested</span></div></div><div class="example-wrap"><pre class="rust rust-example-rendered ignore">
<span class="kw">use</span> <span class="ident">algebra</span>::<span class="ident">general</span>::<span class="ident">SemigroupMultiplicative</span>;
<span class="macro">quickcheck</span><span class="macro">!</span> {
<span class="kw">fn</span> <span class="ident">prop_mul_is_associative</span>(<span class="ident">args</span>: (<span class="ident">i32</span>, <span class="ident">i32</span>, <span class="ident">i32</span>)) <span class="op">-</span><span class="op">&gt;</span> <span class="ident">bool</span> {
<span class="ident">SemigroupMultiplicative</span>::<span class="ident">prop_mul_is_associative</span>(<span class="ident">args</span>)
}
}</pre></div>
</div><h2 id='structs' class='section-header'><a href="#structs">Structs</a></h2>
<table><tr class='module-item'><td><a class="struct" href="struct.Additive.html" title='alga::general::Additive struct'>Additive</a></td><td class='docblock-short'><p>The addition operator, commonly symbolized by <code>+</code>.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Id.html" title='alga::general::Id struct'>Id</a></td><td class='docblock-short'><p>The universal identity element wrt. a given operator, usually noted <code>Id</code> with a
context-dependent subscript.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Multiplicative.html" title='alga::general::Multiplicative struct'>Multiplicative</a></td><td class='docblock-short'><p>The multiplication operator, commonly symbolized by <code>×</code>.</p>
</td></tr></table><h2 id='traits' class='section-header'><a href="#traits">Traits</a></h2>
<table><tr class='module-item'><td><a class="trait" href="trait.AbstractField.html" title='alga::general::AbstractField trait'>AbstractField</a></td><td class='docblock-short'><p>A field is a commutative ring, and an Abelian group under both operators.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AbstractGroup.html" title='alga::general::AbstractGroup trait'>AbstractGroup</a></td><td class='docblock-short'><p>A group is a loop and a monoid at the same time.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AbstractGroupAbelian.html" title='alga::general::AbstractGroupAbelian trait'>AbstractGroupAbelian</a></td><td class='docblock-short'><p>An Abelian group is a <strong>commutative</strong> group.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AbstractLoop.html" title='alga::general::AbstractLoop trait'>AbstractLoop</a></td><td class='docblock-short'><p>A loop is a quasigroup with an unique <strong>identity element</strong>, e.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AbstractMagma.html" title='alga::general::AbstractMagma trait'>AbstractMagma</a></td><td class='docblock-short'><p>A magma is an algebraic structure which consists of a set equipped with a binary operation, ∘,
which must be closed.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AbstractModule.html" title='alga::general::AbstractModule trait'>AbstractModule</a></td><td class='docblock-short'><p>A module combines two sets: one with an Abelian group structure and another with a
commutative ring structure.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AbstractMonoid.html" title='alga::general::AbstractMonoid trait'>AbstractMonoid</a></td><td class='docblock-short'><p>A monoid is a semigroup equipped with an identity element, e.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AbstractQuasigroup.html" title='alga::general::AbstractQuasigroup trait'>AbstractQuasigroup</a></td><td class='docblock-short'><p>A quasigroup is a magma which that has the <strong>divisibility property</strong> (or Latin square property).
<em>A set with a closed binary operation with the divisibility property.</em></p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AbstractRing.html" title='alga::general::AbstractRing trait'>AbstractRing</a></td><td class='docblock-short'><p>A <strong>ring</strong> is the combination of an Abelian group and a multiplicative monoid structure.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AbstractRingCommutative.html" title='alga::general::AbstractRingCommutative trait'>AbstractRingCommutative</a></td><td class='docblock-short'><p>A ring with a commutative multiplication.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AbstractSemigroup.html" title='alga::general::AbstractSemigroup trait'>AbstractSemigroup</a></td><td class='docblock-short'><p>A semigroup is a quasigroup that is <strong>associative</strong>.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AdditiveGroup.html" title='alga::general::AdditiveGroup trait'>AdditiveGroup</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AdditiveGroupAbelian.html" title='alga::general::AdditiveGroupAbelian trait'>AdditiveGroupAbelian</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AdditiveLoop.html" title='alga::general::AdditiveLoop trait'>AdditiveLoop</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AdditiveMagma.html" title='alga::general::AdditiveMagma trait'>AdditiveMagma</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AdditiveMonoid.html" title='alga::general::AdditiveMonoid trait'>AdditiveMonoid</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AdditiveQuasigroup.html" title='alga::general::AdditiveQuasigroup trait'>AdditiveQuasigroup</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.AdditiveSemigroup.html" title='alga::general::AdditiveSemigroup trait'>AdditiveSemigroup</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.ClosedAdd.html" title='alga::general::ClosedAdd trait'>ClosedAdd</a></td><td class='docblock-short'><p>[Alias] Trait alias for <code>Add</code> and <code>AddAssign</code> with result of type <code>Self</code>.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.ClosedDiv.html" title='alga::general::ClosedDiv trait'>ClosedDiv</a></td><td class='docblock-short'><p>[Alias] Trait alias for <code>Div</code> and <code>DivAssign</code> with result of type <code>Self</code>.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.ClosedMul.html" title='alga::general::ClosedMul trait'>ClosedMul</a></td><td class='docblock-short'><p>[Alias] Trait alias for <code>Mul</code> and <code>MulAssign</code> with result of type <code>Self</code>.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.ClosedNeg.html" title='alga::general::ClosedNeg trait'>ClosedNeg</a></td><td class='docblock-short'><p>[Alias] Trait alias for <code>Neg</code> with result of type <code>Self</code>.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.ClosedSub.html" title='alga::general::ClosedSub trait'>ClosedSub</a></td><td class='docblock-short'><p>[Alias] Trait alias for <code>Sub</code> and <code>SubAssign</code> with result of type <code>Self</code>.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.ComplexField.html" title='alga::general::ComplexField trait'>ComplexField</a></td><td class='docblock-short'><p>Trait shared by all complex fields and its subfields (like real numbers).</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Field.html" title='alga::general::Field trait'>Field</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Identity.html" title='alga::general::Identity trait'>Identity</a></td><td class='docblock-short'><p>A type that is equipped with identity.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.JoinSemilattice.html" title='alga::general::JoinSemilattice trait'>JoinSemilattice</a></td><td class='docblock-short'><p>A set where every two elements have a supremum (i.e. smallest upper bound).</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Lattice.html" title='alga::general::Lattice trait'>Lattice</a></td><td class='docblock-short'><p>Partially orderable sets where every two elements have a supremum and infimum.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.MeetSemilattice.html" title='alga::general::MeetSemilattice trait'>MeetSemilattice</a></td><td class='docblock-short'><p>A set where every two elements have an infimum (i.e. greatest lower bound).</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Module.html" title='alga::general::Module trait'>Module</a></td><td class='docblock-short'><p>A module which overloads the <code>*</code> and <code>+</code> operators.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.MultiplicativeGroup.html" title='alga::general::MultiplicativeGroup trait'>MultiplicativeGroup</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.MultiplicativeGroupAbelian.html" title='alga::general::MultiplicativeGroupAbelian trait'>MultiplicativeGroupAbelian</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.MultiplicativeLoop.html" title='alga::general::MultiplicativeLoop trait'>MultiplicativeLoop</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.MultiplicativeMagma.html" title='alga::general::MultiplicativeMagma trait'>MultiplicativeMagma</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.MultiplicativeMonoid.html" title='alga::general::MultiplicativeMonoid trait'>MultiplicativeMonoid</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.MultiplicativeQuasigroup.html" title='alga::general::MultiplicativeQuasigroup trait'>MultiplicativeQuasigroup</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.MultiplicativeSemigroup.html" title='alga::general::MultiplicativeSemigroup trait'>MultiplicativeSemigroup</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Operator.html" title='alga::general::Operator trait'>Operator</a></td><td class='docblock-short'><p>Trait implemented by types representing abstract operators.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Real.html" title='alga::general::Real trait'>Real</a></td><td class='docblock-short'><span class="stab deprecated">Deprecated</span><p>The field of reals. This has been renamed to <code>RealField</code>.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.RealField.html" title='alga::general::RealField trait'>RealField</a></td><td class='docblock-short'><p>Trait shared by all reals.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Ring.html" title='alga::general::Ring trait'>Ring</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.RingCommutative.html" title='alga::general::RingCommutative trait'>RingCommutative</a></td><td class='docblock-short'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.SubsetOf.html" title='alga::general::SubsetOf trait'>SubsetOf</a></td><td class='docblock-short'><p>Nested sets and conversions between them (using an injective mapping). Useful to work with
substructures. In generic code, it is preferable to use <code>SupersetOf</code> as trait bound whenever
possible instead of <code>SubsetOf</code> (because SupersetOf is automatically implemented whenever
<code>SubsetOf</code> is).</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.SupersetOf.html" title='alga::general::SupersetOf trait'>SupersetOf</a></td><td class='docblock-short'><p>Nested sets and conversions between them. Useful to work with substructures. It is preferable
to implement the <code>SupersetOf</code> trait instead of <code>SubsetOf</code> whenever possible (because
<code>SupersetOf</code> is automatically implemented whenever <code>SubsetOf</code> is.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.TwoSidedInverse.html" title='alga::general::TwoSidedInverse trait'>TwoSidedInverse</a></td><td class='docblock-short'><p>Trait used to define the two_sided_inverse element relative to the given operator.</p>
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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `AbstractField` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, AbstractField"><title>alga::general::AbstractField - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait AbstractField</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#foreign-impls">Implementations on Foreign Types</a><div class="sidebar-links"><a href="#impl-AbstractField%3CAdditive%2C%20Multiplicative%3E-for-Complex%3CN%3E">Complex&lt;N&gt;</a><a href="#impl-AbstractField%3CAdditive%2C%20Multiplicative%3E-for-f32">f32</a><a href="#impl-AbstractField%3CAdditive%2C%20Multiplicative%3E-for-f64">f64</a></div><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'AbstractField', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/two_operators.rs.html#213-216' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>AbstractField</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait AbstractField&lt;A:&nbsp;<a class="trait" href="../../alga/general/trait.Operator.html" title="trait alga::general::Operator">Operator</a>&nbsp;=&nbsp;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>, M:&nbsp;<a class="trait" href="../../alga/general/trait.Operator.html" title="trait alga::general::Operator">Operator</a>&nbsp;=&nbsp;<a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt;: <a class="trait" href="../../alga/general/trait.AbstractRingCommutative.html" title="trait alga::general::AbstractRingCommutative">AbstractRingCommutative</a>&lt;A, M&gt; + <a class="trait" href="../../alga/general/trait.AbstractGroupAbelian.html" title="trait alga::general::AbstractGroupAbelian">AbstractGroupAbelian</a>&lt;M&gt; { }</pre></div><div class='docblock'><p>A field is a commutative ring, and an Abelian group under both operators.</p>
<p><em>A <strong>field</strong> is a set with two binary operations, an addition and a multiplication, which are both closed, commutative, associative
possess the divisibility property and an identity element, noted 0 and 1 respectively. Furthermore the multiplication is distributive
over the addition.</em></p>
</div>
<h2 id='foreign-impls' class='small-section-header'>Implementations on Foreign Types<a href='#foreign-impls' class='anchor'></a></h2><h3 id='impl-AbstractField%3CAdditive%2C%20Multiplicative%3E-for-f32' class='impl'><code class='in-band'>impl <a class="trait" href="../../alga/general/trait.AbstractField.html" title="trait alga::general::AbstractField">AbstractField</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>, <a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.f32.html">f32</a></code><a href='#impl-AbstractField%3CAdditive%2C%20Multiplicative%3E-for-f32' class='anchor'></a><a class='srclink' href='../../src/alga/macros.rs.html#102' title='goto source code'>[src]</a></h3><div class='impl-items'></div><h3 id='impl-AbstractField%3CAdditive%2C%20Multiplicative%3E-for-f64' class='impl'><code class='in-band'>impl <a class="trait" href="../../alga/general/trait.AbstractField.html" title="trait alga::general::AbstractField">AbstractField</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>, <a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.f64.html">f64</a></code><a href='#impl-AbstractField%3CAdditive%2C%20Multiplicative%3E-for-f64' class='anchor'></a><a class='srclink' href='../../src/alga/macros.rs.html#95' title='goto source code'>[src]</a></h3><div class='impl-items'></div><h3 id='impl-AbstractField%3CAdditive%2C%20Multiplicative%3E-for-Complex%3CN%3E' class='impl'><code class='in-band'>impl&lt;N:&nbsp;<a class="trait" href="../../num_traits/trait.Num.html" title="trait num_traits::Num">Num</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html" title="trait core::clone::Clone">Clone</a> + <a class="trait" href="../../alga/general/trait.ClosedNeg.html" title="trait alga::general::ClosedNeg">ClosedNeg</a> + <a class="trait" href="../../alga/general/trait.AbstractField.html" title="trait alga::general::AbstractField">AbstractField</a>&gt; <a class="trait" href="../../alga/general/trait.AbstractField.html" title="trait alga::general::AbstractField">AbstractField</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>, <a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; for <a class="struct" href="../../num_complex/struct.Complex.html" title="struct num_complex::Complex">Complex</a>&lt;N&gt;</code><a href='#impl-AbstractField%3CAdditive%2C%20Multiplicative%3E-for-Complex%3CN%3E' class='anchor'></a><a class='srclink' href='../../src/alga/general/two_operators.rs.html#289' title='goto source code'>[src]</a></h3><div class='impl-items'></div><span class='loading-content'>Loading content...</span>
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</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `AbstractModule` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, AbstractModule"><title>alga::general::AbstractModule - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait AbstractModule</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#associated-types">Associated Types</a><div class="sidebar-links"><a href="#associatedtype.AbstractRing">AbstractRing</a></div><a class="sidebar-title" href="#required-methods">Required Methods</a><div class="sidebar-links"><a href="#tymethod.multiply_by">multiply_by</a></div><a class="sidebar-title" href="#foreign-impls">Implementations on Foreign Types</a><div class="sidebar-links"><a href="#impl-AbstractModule%3CAdditive%2C%20Additive%2C%20Multiplicative%3E-for-Complex%3CN%3E">Complex&lt;N&gt;</a></div><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'AbstractModule', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/module.rs.html#22-33' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>AbstractModule</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait AbstractModule&lt;OpGroup:&nbsp;<a class="trait" href="../../alga/general/trait.Operator.html" title="trait alga::general::Operator">Operator</a>&nbsp;=&nbsp;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>, OpAdd:&nbsp;<a class="trait" href="../../alga/general/trait.Operator.html" title="trait alga::general::Operator">Operator</a>&nbsp;=&nbsp;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>, OpMul:&nbsp;<a class="trait" href="../../alga/general/trait.Operator.html" title="trait alga::general::Operator">Operator</a>&nbsp;=&nbsp;<a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt;: <a class="trait" href="../../alga/general/trait.AbstractGroupAbelian.html" title="trait alga::general::AbstractGroupAbelian">AbstractGroupAbelian</a>&lt;OpGroup&gt; {
type <a href='#associatedtype.AbstractRing' class="type">AbstractRing</a>: <a class="trait" href="../../alga/general/trait.AbstractRingCommutative.html" title="trait alga::general::AbstractRingCommutative">AbstractRingCommutative</a>&lt;OpAdd, OpMul&gt;;
fn <a href='#tymethod.multiply_by' class='fnname'>multiply_by</a>(&amp;self, r: Self::<a class="type" href="../../alga/general/trait.AbstractModule.html#associatedtype.AbstractRing" title="type alga::general::AbstractModule::AbstractRing">AbstractRing</a>) -&gt; Self;
}</pre></div><div class='docblock'><p>A module combines two sets: one with an Abelian group structure and another with a
commutative ring structure.</p>
<p><code>OpGroup</code> denotes the Abelian group operator (usually the addition). In addition, and external
multiplicative law noted <code></code> is defined. Let <code>S</code> be the ring with multiplicative operator
<code>OpMul</code> noted <code>×</code>, multiplicative identity element noted <code>1</code>, and additive operator <code>OpAdd</code>.
Then:</p>
<pre><code class="language-notrust">∀ a, b ∈ S
∀ x, y ∈ Self
a ∘ (x + y) = (a ∘ x) + (a ∘ y)
(a + b) ∘ x = (a ∘ x) + (b ∘ x)
(a × b) ∘ x = a ∘ (b ∘ x)
1 ∘ x = x
</code></pre>
</div>
<h2 id='associated-types' class='small-section-header'>Associated Types<a href='#associated-types' class='anchor'></a></h2><div class='methods'><h3 id='associatedtype.AbstractRing' class='method'><code id='AbstractRing.t'>type <a href='#associatedtype.AbstractRing' class="type">AbstractRing</a>: <a class="trait" href="../../alga/general/trait.AbstractRingCommutative.html" title="trait alga::general::AbstractRingCommutative">AbstractRingCommutative</a>&lt;OpAdd, OpMul&gt;</code></h3><div class='docblock'><p>The underlying scalar field.</p>
</div></div><span class='loading-content'>Loading content...</span>
<h2 id='required-methods' class='small-section-header'>Required methods<a href='#required-methods' class='anchor'></a></h2><div class='methods'><h3 id='tymethod.multiply_by' class='method'><code id='multiply_by.v'>fn <a href='#tymethod.multiply_by' class='fnname'>multiply_by</a>(&amp;self, r: Self::<a class="type" href="../../alga/general/trait.AbstractModule.html#associatedtype.AbstractRing" title="type alga::general::AbstractModule::AbstractRing">AbstractRing</a>) -&gt; Self</code></h3><div class='docblock'><p>Multiplies an element of the ring with an element of the module.</p>
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<h2 id='foreign-impls' class='small-section-header'>Implementations on Foreign Types<a href='#foreign-impls' class='anchor'></a></h2><h3 id='impl-AbstractModule%3CAdditive%2C%20Additive%2C%20Multiplicative%3E-for-Complex%3CN%3E' class='impl'><code class='in-band'>impl&lt;N:&nbsp;<a class="trait" href="../../alga/general/trait.AbstractRingCommutative.html" title="trait alga::general::AbstractRingCommutative">AbstractRingCommutative</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>, <a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../num_traits/trait.Num.html" title="trait num_traits::Num">Num</a> + <a class="trait" href="../../alga/general/trait.ClosedNeg.html" title="trait alga::general::ClosedNeg">ClosedNeg</a>&gt; <a class="trait" href="../../alga/general/trait.AbstractModule.html" title="trait alga::general::AbstractModule">AbstractModule</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>, <a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>, <a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; for <a class="struct" href="../../num_complex/struct.Complex.html" title="struct num_complex::Complex">Complex</a>&lt;N&gt;</code><a href='#impl-AbstractModule%3CAdditive%2C%20Additive%2C%20Multiplicative%3E-for-Complex%3CN%3E' class='anchor'></a><a class='srclink' href='../../src/alga/general/module.rs.html#35-45' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.AbstractRing-1' class="type"><code id='AbstractRing.t-1'>type <a href='#associatedtype.AbstractRing' class="type">AbstractRing</a> = N</code></h4><h4 id='method.multiply_by' class="method hidden"><code id='multiply_by.v-1'>fn <a href='#method.multiply_by' class='fnname'>multiply_by</a>(&amp;self, r: N) -&gt; Self</code><a class='srclink' href='../../src/alga/general/module.rs.html#42-44' title='goto source code'>[src]</a></h4></div><span class='loading-content'>Loading content...</span>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `AdditiveGroup` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, AdditiveGroup"><title>alga::general::AdditiveGroup - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait AdditiveGroup</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'AdditiveGroup', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/specialized.rs.html#13' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>AdditiveGroup</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait AdditiveGroup: <a class="trait" href="../../alga/general/trait.AbstractGroup.html" title="trait alga::general::AbstractGroup">AbstractGroup</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveLoop.html" title="trait alga::general::AdditiveLoop">AdditiveLoop</a> + <a class="trait" href="../../alga/general/trait.AdditiveMonoid.html" title="trait alga::general::AdditiveMonoid">AdditiveMonoid</a> { }</pre></div><div class='docblock'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-AdditiveGroup' class='impl'><code class='in-band'>impl&lt;T:&nbsp;<a class="trait" href="../../alga/general/trait.AbstractGroup.html" title="trait alga::general::AbstractGroup">AbstractGroup</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveLoop.html" title="trait alga::general::AdditiveLoop">AdditiveLoop</a> + <a class="trait" href="../../alga/general/trait.AdditiveMonoid.html" title="trait alga::general::AdditiveMonoid">AdditiveMonoid</a>&gt; AdditiveGroup for T</code><a href='#impl-AdditiveGroup' class='anchor'></a><a class='srclink' href='../../src/alga/general/specialized.rs.html#14' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `AdditiveGroupAbelian` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, AdditiveGroupAbelian"><title>alga::general::AdditiveGroupAbelian - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait AdditiveGroupAbelian</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'AdditiveGroupAbelian', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/specialized.rs.html#13' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>AdditiveGroupAbelian</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait AdditiveGroupAbelian: <a class="trait" href="../../alga/general/trait.AbstractGroupAbelian.html" title="trait alga::general::AbstractGroupAbelian">AbstractGroupAbelian</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveGroup.html" title="trait alga::general::AdditiveGroup">AdditiveGroup</a> { }</pre></div><div class='docblock'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-AdditiveGroupAbelian' class='impl'><code class='in-band'>impl&lt;T:&nbsp;<a class="trait" href="../../alga/general/trait.AbstractGroupAbelian.html" title="trait alga::general::AbstractGroupAbelian">AbstractGroupAbelian</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveGroup.html" title="trait alga::general::AdditiveGroup">AdditiveGroup</a>&gt; AdditiveGroupAbelian for T</code><a href='#impl-AdditiveGroupAbelian' class='anchor'></a><a class='srclink' href='../../src/alga/general/specialized.rs.html#14' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `AdditiveLoop` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, AdditiveLoop"><title>alga::general::AdditiveLoop - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait AdditiveLoop</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'AdditiveLoop', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/specialized.rs.html#13' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>AdditiveLoop</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait AdditiveLoop: <a class="trait" href="../../alga/general/trait.AbstractLoop.html" title="trait alga::general::AbstractLoop">AbstractLoop</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveQuasigroup.html" title="trait alga::general::AdditiveQuasigroup">AdditiveQuasigroup</a> + <a class="trait" href="../../alga/general/trait.ClosedNeg.html" title="trait alga::general::ClosedNeg">ClosedNeg</a> + <a class="trait" href="../../num_traits/identities/trait.Zero.html" title="trait num_traits::identities::Zero">Zero</a> { }</pre></div><div class='docblock'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-AdditiveLoop' class='impl'><code class='in-band'>impl&lt;T:&nbsp;<a class="trait" href="../../alga/general/trait.AbstractLoop.html" title="trait alga::general::AbstractLoop">AbstractLoop</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveQuasigroup.html" title="trait alga::general::AdditiveQuasigroup">AdditiveQuasigroup</a> + <a class="trait" href="../../alga/general/trait.ClosedNeg.html" title="trait alga::general::ClosedNeg">ClosedNeg</a> + <a class="trait" href="../../num_traits/identities/trait.Zero.html" title="trait num_traits::identities::Zero">Zero</a>&gt; AdditiveLoop for T</code><a href='#impl-AdditiveLoop' class='anchor'></a><a class='srclink' href='../../src/alga/general/specialized.rs.html#14' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
src="../../implementors/alga/general/trait.AdditiveLoop.js">
</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `AdditiveMagma` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, AdditiveMagma"><title>alga::general::AdditiveMagma - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait AdditiveMagma</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'AdditiveMagma', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/specialized.rs.html#13' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>AdditiveMagma</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait AdditiveMagma: <a class="trait" href="../../alga/general/trait.AbstractMagma.html" title="trait alga::general::AbstractMagma">AbstractMagma</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; { }</pre></div><div class='docblock'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-AdditiveMagma' class='impl'><code class='in-band'>impl&lt;T:&nbsp;<a class="trait" href="../../alga/general/trait.AbstractMagma.html" title="trait alga::general::AbstractMagma">AbstractMagma</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt;&gt; AdditiveMagma for T</code><a href='#impl-AdditiveMagma' class='anchor'></a><a class='srclink' href='../../src/alga/general/specialized.rs.html#14' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
src="../../implementors/alga/general/trait.AdditiveMagma.js">
</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `AdditiveMonoid` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, AdditiveMonoid"><title>alga::general::AdditiveMonoid - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait AdditiveMonoid</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'AdditiveMonoid', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/specialized.rs.html#13' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>AdditiveMonoid</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait AdditiveMonoid: <a class="trait" href="../../alga/general/trait.AbstractMonoid.html" title="trait alga::general::AbstractMonoid">AbstractMonoid</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveSemigroup.html" title="trait alga::general::AdditiveSemigroup">AdditiveSemigroup</a> + <a class="trait" href="../../num_traits/identities/trait.Zero.html" title="trait num_traits::identities::Zero">Zero</a> { }</pre></div><div class='docblock'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-AdditiveMonoid' class='impl'><code class='in-band'>impl&lt;T:&nbsp;<a class="trait" href="../../alga/general/trait.AbstractMonoid.html" title="trait alga::general::AbstractMonoid">AbstractMonoid</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveSemigroup.html" title="trait alga::general::AdditiveSemigroup">AdditiveSemigroup</a> + <a class="trait" href="../../num_traits/identities/trait.Zero.html" title="trait num_traits::identities::Zero">Zero</a>&gt; AdditiveMonoid for T</code><a href='#impl-AdditiveMonoid' class='anchor'></a><a class='srclink' href='../../src/alga/general/specialized.rs.html#14' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
src="../../implementors/alga/general/trait.AdditiveMonoid.js">
</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

@ -0,0 +1,5 @@
<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `AdditiveQuasigroup` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, AdditiveQuasigroup"><title>alga::general::AdditiveQuasigroup - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait AdditiveQuasigroup</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'AdditiveQuasigroup', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/specialized.rs.html#13' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>AdditiveQuasigroup</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait AdditiveQuasigroup: <a class="trait" href="../../alga/general/trait.AbstractQuasigroup.html" title="trait alga::general::AbstractQuasigroup">AbstractQuasigroup</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveMagma.html" title="trait alga::general::AdditiveMagma">AdditiveMagma</a> + <a class="trait" href="../../alga/general/trait.ClosedSub.html" title="trait alga::general::ClosedSub">ClosedSub</a> { }</pre></div><div class='docblock'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-AdditiveQuasigroup' class='impl'><code class='in-band'>impl&lt;T:&nbsp;<a class="trait" href="../../alga/general/trait.AbstractQuasigroup.html" title="trait alga::general::AbstractQuasigroup">AbstractQuasigroup</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveMagma.html" title="trait alga::general::AdditiveMagma">AdditiveMagma</a> + <a class="trait" href="../../alga/general/trait.ClosedSub.html" title="trait alga::general::ClosedSub">ClosedSub</a>&gt; AdditiveQuasigroup for T</code><a href='#impl-AdditiveQuasigroup' class='anchor'></a><a class='srclink' href='../../src/alga/general/specialized.rs.html#14' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `AdditiveSemigroup` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, AdditiveSemigroup"><title>alga::general::AdditiveSemigroup - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait AdditiveSemigroup</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'AdditiveSemigroup', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/specialized.rs.html#13' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>AdditiveSemigroup</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait AdditiveSemigroup: <a class="trait" href="../../alga/general/trait.AbstractSemigroup.html" title="trait alga::general::AbstractSemigroup">AbstractSemigroup</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveMagma.html" title="trait alga::general::AdditiveMagma">AdditiveMagma</a> + <a class="trait" href="../../alga/general/trait.ClosedAdd.html" title="trait alga::general::ClosedAdd">ClosedAdd</a> { }</pre></div><div class='docblock'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
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<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-AdditiveSemigroup' class='impl'><code class='in-band'>impl&lt;T:&nbsp;<a class="trait" href="../../alga/general/trait.AbstractSemigroup.html" title="trait alga::general::AbstractSemigroup">AbstractSemigroup</a>&lt;<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveMagma.html" title="trait alga::general::AdditiveMagma">AdditiveMagma</a> + <a class="trait" href="../../alga/general/trait.ClosedAdd.html" title="trait alga::general::ClosedAdd">ClosedAdd</a>&gt; AdditiveSemigroup for T</code><a href='#impl-AdditiveSemigroup' class='anchor'></a><a class='srclink' href='../../src/alga/general/specialized.rs.html#14' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `ClosedAdd` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, ClosedAdd"><title>alga::general::ClosedAdd - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait ClosedAdd</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'ClosedAdd', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/operator.rs.html#126' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>ClosedAdd</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait ClosedAdd&lt;Right&nbsp;=&nbsp;Self&gt;: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Add.html" title="trait core::ops::arith::Add">Add</a>&lt;Right, Output = Self&gt; + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.AddAssign.html" title="trait core::ops::arith::AddAssign">AddAssign</a>&lt;Right&gt; { }</pre></div><div class='docblock'><p>[Alias] Trait alias for <code>Add</code> and <code>AddAssign</code> with result of type <code>Self</code>.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-ClosedAdd%3CRight%3E' class='impl'><code class='in-band'>impl&lt;T, Right&gt; ClosedAdd&lt;Right&gt; for T <span class="where fmt-newline">where<br>&nbsp;&nbsp;&nbsp;&nbsp;T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Add.html" title="trait core::ops::arith::Add">Add</a>&lt;Right, Output = T&gt; + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.AddAssign.html" title="trait core::ops::arith::AddAssign">AddAssign</a>&lt;Right&gt;,&nbsp;</span></code><a href='#impl-ClosedAdd%3CRight%3E' class='anchor'></a><a class='srclink' href='../../src/alga/general/operator.rs.html#140' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
src="../../implementors/alga/general/trait.ClosedAdd.js">
</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `ClosedDiv` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, ClosedDiv"><title>alga::general::ClosedDiv - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait ClosedDiv</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'ClosedDiv', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/operator.rs.html#135' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>ClosedDiv</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait ClosedDiv&lt;Right&nbsp;=&nbsp;Self&gt;: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Div.html" title="trait core::ops::arith::Div">Div</a>&lt;Right, Output = Self&gt; + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.DivAssign.html" title="trait core::ops::arith::DivAssign">DivAssign</a>&lt;Right&gt; { }</pre></div><div class='docblock'><p>[Alias] Trait alias for <code>Div</code> and <code>DivAssign</code> with result of type <code>Self</code>.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-ClosedDiv%3CRight%3E' class='impl'><code class='in-band'>impl&lt;T, Right&gt; ClosedDiv&lt;Right&gt; for T <span class="where fmt-newline">where<br>&nbsp;&nbsp;&nbsp;&nbsp;T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Div.html" title="trait core::ops::arith::Div">Div</a>&lt;Right, Output = T&gt; + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.DivAssign.html" title="trait core::ops::arith::DivAssign">DivAssign</a>&lt;Right&gt;,&nbsp;</span></code><a href='#impl-ClosedDiv%3CRight%3E' class='anchor'></a><a class='srclink' href='../../src/alga/general/operator.rs.html#143' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `ClosedMul` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, ClosedMul"><title>alga::general::ClosedMul - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait ClosedMul</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'ClosedMul', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/operator.rs.html#132' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>ClosedMul</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait ClosedMul&lt;Right&nbsp;=&nbsp;Self&gt;: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html" title="trait core::ops::arith::Mul">Mul</a>&lt;Right, Output = Self&gt; + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.MulAssign.html" title="trait core::ops::arith::MulAssign">MulAssign</a>&lt;Right&gt; { }</pre></div><div class='docblock'><p>[Alias] Trait alias for <code>Mul</code> and <code>MulAssign</code> with result of type <code>Self</code>.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-ClosedMul%3CRight%3E' class='impl'><code class='in-band'>impl&lt;T, Right&gt; ClosedMul&lt;Right&gt; for T <span class="where fmt-newline">where<br>&nbsp;&nbsp;&nbsp;&nbsp;T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html" title="trait core::ops::arith::Mul">Mul</a>&lt;Right, Output = T&gt; + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.MulAssign.html" title="trait core::ops::arith::MulAssign">MulAssign</a>&lt;Right&gt;,&nbsp;</span></code><a href='#impl-ClosedMul%3CRight%3E' class='anchor'></a><a class='srclink' href='../../src/alga/general/operator.rs.html#142' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
src="../../implementors/alga/general/trait.ClosedMul.js">
</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `ClosedNeg` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, ClosedNeg"><title>alga::general::ClosedNeg - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait ClosedNeg</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'ClosedNeg', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/operator.rs.html#138' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>ClosedNeg</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait ClosedNeg: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Neg.html" title="trait core::ops::arith::Neg">Neg</a>&lt;Output = Self&gt; { }</pre></div><div class='docblock'><p>[Alias] Trait alias for <code>Neg</code> with result of type <code>Self</code>.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-ClosedNeg' class='impl'><code class='in-band'>impl&lt;T&gt; ClosedNeg for T <span class="where fmt-newline">where<br>&nbsp;&nbsp;&nbsp;&nbsp;T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Neg.html" title="trait core::ops::arith::Neg">Neg</a>&lt;Output = T&gt;,&nbsp;</span></code><a href='#impl-ClosedNeg' class='anchor'></a><a class='srclink' href='../../src/alga/general/operator.rs.html#144' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `ClosedSub` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, ClosedSub"><title>alga::general::ClosedSub - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait ClosedSub</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'ClosedSub', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/operator.rs.html#129' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>ClosedSub</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait ClosedSub&lt;Right&nbsp;=&nbsp;Self&gt;: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Sub.html" title="trait core::ops::arith::Sub">Sub</a>&lt;Right, Output = Self&gt; + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.SubAssign.html" title="trait core::ops::arith::SubAssign">SubAssign</a>&lt;Right&gt; { }</pre></div><div class='docblock'><p>[Alias] Trait alias for <code>Sub</code> and <code>SubAssign</code> with result of type <code>Self</code>.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-ClosedSub%3CRight%3E' class='impl'><code class='in-band'>impl&lt;T, Right&gt; ClosedSub&lt;Right&gt; for T <span class="where fmt-newline">where<br>&nbsp;&nbsp;&nbsp;&nbsp;T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Sub.html" title="trait core::ops::arith::Sub">Sub</a>&lt;Right, Output = T&gt; + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.SubAssign.html" title="trait core::ops::arith::SubAssign">SubAssign</a>&lt;Right&gt;,&nbsp;</span></code><a href='#impl-ClosedSub%3CRight%3E' class='anchor'></a><a class='srclink' href='../../src/alga/general/operator.rs.html#141' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `Field` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, Field"><title>alga::general::Field - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait Field</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'Field', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/specialized.rs.html#19' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>Field</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait Field: <a class="trait" href="../../alga/general/trait.AbstractField.html" title="trait alga::general::AbstractField">AbstractField</a> + <a class="trait" href="../../alga/general/trait.RingCommutative.html" title="trait alga::general::RingCommutative">RingCommutative</a> + <a class="trait" href="../../alga/general/trait.MultiplicativeGroupAbelian.html" title="trait alga::general::MultiplicativeGroupAbelian">MultiplicativeGroupAbelian</a> { }</pre></div><div class='docblock'><p>[Alias] Algebraic structure specialized for one kind of operation.</p>
</div>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-Field' class='impl'><code class='in-band'>impl&lt;T:&nbsp;<a class="trait" href="../../alga/general/trait.AbstractField.html" title="trait alga::general::AbstractField">AbstractField</a> + <a class="trait" href="../../alga/general/trait.RingCommutative.html" title="trait alga::general::RingCommutative">RingCommutative</a> + <a class="trait" href="../../alga/general/trait.MultiplicativeGroupAbelian.html" title="trait alga::general::MultiplicativeGroupAbelian">MultiplicativeGroupAbelian</a>&gt; Field for T</code><a href='#impl-Field' class='anchor'></a><a class='srclink' href='../../src/alga/general/specialized.rs.html#20' title='goto source code'>[src]</a></h3><div class='impl-items'></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `Module` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, Module"><title>alga::general::Module - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait Module</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#associated-types">Associated Types</a><div class="sidebar-links"><a href="#associatedtype.Ring">Ring</a></div><a class="sidebar-title" href="#foreign-impls">Implementations on Foreign Types</a><div class="sidebar-links"><a href="#impl-Module-for-Complex%3CN%3E">Complex&lt;N&gt;</a></div><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a></p><script>window.sidebarCurrent = {name: 'Module', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press S to search, ? for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../../src/alga/general/specialized.rs.html#45-52' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>general</a>::<wbr><a class="trait" href=''>Module</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait Module: <a class="trait" href="../../alga/general/trait.AbstractModule.html" title="trait alga::general::AbstractModule">AbstractModule</a>&lt;AbstractRing = Self::<a class="type" href="../../alga/general/trait.Module.html#associatedtype.Ring" title="type alga::general::Module::Ring">Ring</a>&gt; + <a class="trait" href="../../alga/general/trait.AdditiveGroupAbelian.html" title="trait alga::general::AdditiveGroupAbelian">AdditiveGroupAbelian</a> + <a class="trait" href="../../alga/general/trait.ClosedMul.html" title="trait alga::general::ClosedMul">ClosedMul</a>&lt;Self::<a class="type" href="../../alga/general/trait.Module.html#associatedtype.Ring" title="type alga::general::Module::Ring">Ring</a>&gt; {
type <a href='#associatedtype.Ring' class="type">Ring</a>: <a class="trait" href="../../alga/general/trait.RingCommutative.html" title="trait alga::general::RingCommutative">RingCommutative</a>;
}</pre></div><div class='docblock'><p>A module which overloads the <code>*</code> and <code>+</code> operators.</p>
</div>
<h2 id='associated-types' class='small-section-header'>Associated Types<a href='#associated-types' class='anchor'></a></h2><div class='methods'><h3 id='associatedtype.Ring' class='method'><code id='Ring.t'>type <a href='#associatedtype.Ring' class="type">Ring</a>: <a class="trait" href="../../alga/general/trait.RingCommutative.html" title="trait alga::general::RingCommutative">RingCommutative</a></code></h3><div class='docblock'><p>The underlying scalar field.</p>
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<h2 id='foreign-impls' class='small-section-header'>Implementations on Foreign Types<a href='#foreign-impls' class='anchor'></a></h2><h3 id='impl-Module-for-Complex%3CN%3E' class='impl'><code class='in-band'>impl&lt;N:&nbsp;<a class="trait" href="../../alga/general/trait.RingCommutative.html" title="trait alga::general::RingCommutative">RingCommutative</a> + <a class="trait" href="../../num_traits/trait.NumAssign.html" title="trait num_traits::NumAssign">NumAssign</a>&gt; <a class="trait" href="../../alga/general/trait.Module.html" title="trait alga::general::Module">Module</a> for <a class="struct" href="../../num_complex/struct.Complex.html" title="struct num_complex::Complex">Complex</a>&lt;N&gt;</code><a href='#impl-Module-for-Complex%3CN%3E' class='anchor'></a><a class='srclink' href='../../src/alga/general/specialized.rs.html#55-57' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Ring-1' class="type"><code id='Ring.t-1'>type <a href='#associatedtype.Ring' class="type">Ring</a> = N</code></h4></div><span class='loading-content'>Loading content...</span>
<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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</script></section><section id="search" class="content hidden"></section><section class="footer"></section><aside id="help" class="hidden"><div><h1 class="hidden">Help</h1><div class="shortcuts"><h2>Keyboard Shortcuts</h2><dl><dt><kbd>?</kbd></dt><dd>Show this help dialog</dd><dt><kbd>S</kbd></dt><dd>Focus the search field</dd><dt><kbd></kbd></dt><dd>Move up in search results</dd><dt><kbd></kbd></dt><dd>Move down in search results</dd><dt><kbd></kbd></dt><dd>Switch tab</dd><dt><kbd>&#9166;</kbd></dt><dd>Go to active search result</dd><dt><kbd>+</kbd></dt><dd>Expand all sections</dd><dt><kbd>-</kbd></dt><dd>Collapse all sections</dd></dl></div><div class="infos"><h2>Search Tricks</h2><p>Prefix searches with a type followed by a colon (e.g., <code>fn:</code>) to restrict the search to a given type.</p><p>Accepted types are: <code>fn</code>, <code>mod</code>, <code>struct</code>, <code>enum</code>, <code>trait</code>, <code>type</code>, <code>macro</code>, and <code>const</code>.</p><p>Search functions by type signature (e.g., <code>vec -> usize</code> or <code>* -> vec</code>)</p><p>Search multiple things at once by splitting your query with comma (e.g., <code>str,u8</code> or <code>String,struct:Vec,test</code>)</p></div></div></aside><script>window.rootPath = "../../";window.currentCrate = "alga";</script><script src="../../aliases.js"></script><script src="../../main.js"></script><script defer src="../../search-index.js"></script></body></html>

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