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<!DOCTYPE html><htmllang="en"><head><metacharset="utf-8"><metaname="viewport"content="width=device-width, initial-scale=1.0"><metaname="generator"content="rustdoc"><metaname="description"content="API documentation for the Rust `AbstractGroup` trait in crate `alga`."><metaname="keywords"content="rust, rustlang, rust-lang, AbstractGroup"><title>alga::general::AbstractGroup - Rust</title><linkrel="stylesheet"type="text/css"href="../../normalize.css"><linkrel="stylesheet"type="text/css"href="../../rustdoc.css"id="mainThemeStyle"><linkrel="stylesheet"type="text/css"href="../../dark.css"><linkrel="stylesheet"type="text/css"href="../../light.css"id="themeStyle"><scriptsrc="../../storage.js"></script><noscript><linkrel="stylesheet"href="../../noscript.css"></noscript><linkrel="shortcut icon"href="../../favicon.ico"><styletype="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><bodyclass="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><navclass="sidebar"><divclass="sidebar-menu">☰</div><ahref='../../alga/index.html'><divclass='logo-container'><imgsrc='../../rust-logo.png'alt='logo'></div></a><pclass='location'>Trait AbstractGroup</p><divclass="sidebar-elems"><divclass="block items"><aclass="sidebar-title"href="#foreign-impls">Implementations on Foreign Types</a><divclass="sidebar-links"><ahref="#impl-AbstractGroup%3CAdditive%3E-for-Complex%3CN%3E">Complex<N></a><ahref="#impl-AbstractGroup%3CAdditive%3E-for-f32">f32</a><ahref="#impl-AbstractGroup%3CAdditive%3E-for-f64">f64</a><ahref="#impl-AbstractGroup%3CAdditive%3E-for-i16">i16</a><ahref="#impl-AbstractGroup%3CAdditive%3E-for-i32">i32</a><ahref="#impl-AbstractGroup%3CAdditive%3E-for-i64">i64</a><ahref="#impl-AbstractGroup%3CAdditive%3E-for-i8">i8</a><ahref="#impl-AbstractGroup%3CAdditive%3E-for-isize">isize</a><ahref="#impl-AbstractGroup%3CMultiplicative%3E-for-Complex%3CN%3E">Complex<N></a><ahref="#impl-AbstractGroup%3CMultiplicative%3E-for-f32">f32</a><ahref="#impl-AbstractGroup%3CMultiplicative%3E-for-f64">f64</a></div><aclass="sidebar-title"href="#implementors">Implementors</a></div><pclass='location'><ahref='../index.html'>alga</a>::<wbr><ahref='index.html'>general</a></p><script>window.sidebarCurrent={name:'AbstractGroup',ty:'trait',relpath:''};</script><scriptdefersrc="sidebar-items.js"></script></div></nav><divclass="theme-picker"><buttonid="theme-picker"aria-label="Pick another theme!"><imgsrc="../../brush.svg"width="18"alt="Pick another theme!"></button><divid="theme-choices"></div></div><scriptsrc="../../theme.js"></script><navclass="sub"><formclass="search-form js-only"><divclass="search-container"><div><selectid="crate-search"><optionvalue="All crates">All crates</option></select><inputclass="search-input"name="search"autocomplete="off"spellcheck="false"placeholder="Click or press ‘S’ to search, ‘?’ for more options…"type="search"></div><aid="settings-menu"href="../../settings.html"><imgsrc="../../wheel.svg"width="18"alt="Change settings"></a></div></form></nav><sectionid="main"class="content"><h1class='fqn'><spanclass='out-of-band'><spanid='render-detail'><aid="toggle-all-docs"href="javascript:void(0)"title="collapse all docs">[<spanclass='inner'>−</span>]</a></span><aclass='srclink'href='../../src/alga/general/one_operator.rs.html#297'title='goto source code'>[src]</a></span><spanclass='in-band'>Trait <ahref='../index.html'>alga</a>::<wbr><ahref='index.html'>general</a>::<wbr><aclass="trait"href=''>AbstractGroup</a></span></h1><divclass="docblock type-decl hidden-by-usual-hider"><preclass='rust trait'>pub trait AbstractGroup<O: <aclass="trait"href="../../alga/general/trait.Operator.html"title="trait alga::general::Operator">Operator</a>>: <aclass="trait"href="../../alga/general/trait.AbstractLoop.html"title="trait alga::general::AbstractLoop">AbstractLoop</a><O> + <aclass="trait"href="../../alga/general/trait.AbstractMonoid.html"title="trait alga::general::AbstractMonoid">AbstractMonoid</a><O> { }</pre></div><divclass='docblock'><p>A group is a loop and a monoid at the same time.</p>
<p><em>A groups is a set with a closed associative binary operation with the divisibility property and an identity element.</em></p>
</div>
<h2id='foreign-impls'class='small-section-header'>Implementations on Foreign Types<ahref='#foreign-impls'class='anchor'></a></h2><h3id='impl-AbstractGroup%3CMultiplicative%3E-for-Complex%3CN%3E'class='impl'><codeclass='in-band'>impl<N><aclass="trait"href="../../alga/general/trait.AbstractGroup.html"title="trait alga::general::AbstractGroup">AbstractGroup</a><<aclass="struct"href="../../alga/general/struct.Multiplicative.html"title="struct alga::general::Multiplicative">Multiplicative</a>> for <aclass="struct"href="../../num_complex/struct.Complex.html"title="struct num_complex::Complex">Complex</a><N><spanclass="where fmt-newline">where<br> N: <aclass="trait"href="../../num_traits/trait.Num.html"title="trait num_traits::Num">Num</a> + <aclass="trait"href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html"title="trait core::clone::Clone">Clone</a> + <aclass="trait"href="../../alga/general/trait.ClosedNeg.html"title="trait alga::general::ClosedNeg">ClosedNeg</a>, </span></code><ahref='#impl-AbstractGroup%3CMultiplicative%3E-for-Complex%3CN%3E'class='anchor'></a><aclass='srclink'href='../../src/alga/macros.rs.html#42-44'title='goto source code'>[src]</a></h3><divclass='impl-items'></div><h3id='impl-AbstractGroup%3CAdditive%3E-for-Complex%3CN%3E'class='impl'><codeclass='in-band'>impl<N><aclass="trait"href="../../alga/general/trait.AbstractGroup.html"title="trait alga::general::AbstractGroup">AbstractGroup</a><<aclass="struct"href="../../alga/general/struct.Additive.html"title="struct alga::general::Additive">Additive</a>> for <aclass="struct"href="../../num_complex/struct.Complex.html"title="struct num_complex::Complex">Complex</a><N><spanclass="where fmt-newline">where<br> N: <aclass="trait"href="../../alga/general/trait.AbstractGroupAbelian.html"title="trait alga::general::AbstractGroupAbelian">AbstractGroupAbelian</a><<aclass="struct"href="../../alga/general/struct.Additive.html"title="struct alga::general::Additive">Additive</a>>, </span></code><ahref='#impl-AbstractGroup%3CAdditive%3E-for-Complex%3CN%3E'class='anchor'></a><aclass='srclink'href='../../src/alga/macros.rs.html#42-44'title='goto source code'>[src]</a></h3><divclass='impl-items'></div><h3id='impl-AbstractGroup%3CAdditive%3E-for-i8'class='impl'><codeclass='in-band'>impl <aclass="trait"href="../../alga/general/trait.AbstractGroup.html"title="trait alga::general::AbstractGroup">AbstractGroup</a><<aclass="struct"href="../../alga/general/struct.Additive.html"title="struct alga::general::Additive">Additive</a>> for <aclass="primitive"href="https://doc.rust-lang.org/nightly/std/primitive.i8.html">i8</a></code><ahref='#impl-AbstractGroup%3CAdditive%3E-for-i8'class='anchor'></a><aclass='srclink'href='../../src/alga/macros.rs.html#102'title='goto source code'>[src]</a></h3><divclass='impl-items'></div><h3id='impl-AbstractGroup%3CAdditive%3E-for-i16'class='impl'><codeclass='in-band'>impl <aclass="trait"href="../../alga/general/trait.AbstractGroup.html"title="trait alga::general::AbstractGroup">AbstractGroup</a><<aclass="struct"href="../../alga/general/struct.Additive.html"title="struct alga::general::Additive">Additive</a>> for <aclass="primitive"href="https://doc.rust-lang.org/nightly/std/primitive.i16.html">i16</a></code><ahref='#impl-AbstractGroup%3CAdditive%3E-for-i16'class='anchor'></a><aclass='srclink'href='../../src/alga/macros.rs.html#102'title='goto source code'>[src]</a></h3><divclass='impl-items'></div><h3id='impl-AbstractGroup%3CAdditive%3E-for-i32'class='impl'><codeclass='in-band'>impl <aclass="trait"href="../../alga/general/trait.AbstractGroup.html"title="trait alga::general::AbstractGroup">AbstractGroup</a><<aclass="struct"href="../../alga/general/struct.Additive.html"title="struct alga::general::Additive">Additive</a>> for <aclass="primitive"href="https://doc.rust-lang.org/nightly/std/primitive.i32.html">i32</a></code><ahref='#impl-AbstractGroup%3CAdditive%3E-for-i32'class='anchor'></a><aclass='srclink'href='../../src/alga/macros.rs.html#102'title='goto source code'>[src]</a></h3><divclass='impl-items'></div><h3id='impl-AbstractGroup%3CAdditive%3E-for-i64'class='impl'><codeclass='in-band'>impl <aclass="trait"href="../../alga/general/trait.AbstractGroup.html"title="trait alga::general::AbstractGroup">AbstractGroup</a><<aclass="struct"href="../../alga/general/struct.Additive.html"title="struct alga::general::Additive">Additive</a>> for <aclass="primitive"href="https://doc.rust-lang.org/nightly/std/primitive.i64.html">i64</a></code><ahref='#impl-AbstractGroup%3CAdditive%3E-for-i64'class='anchor'></a><aclass='srclink'href='../../src/alga/macros.rs.html#102'title='goto source code'>[src]</a></h3><divclass='impl-items'></div><h3id='impl-AbstractGroup%3CAdditive%3E-for-isize'class='impl'><codeclass='in-band'>impl <aclass="trait"href="../../alga/general/trait.AbstractGroup.html"title="trait alga::general::AbstractGroup">AbstractGroup</a><<aclass="struct"href="../../alga/general/struct.Additive.html"title="struct alga::general::Additive">Additive</a>> for <aclass="primitive"href="https://doc.rust-lang.org/nightly/std/primitive.isize.html">isize</a></code><ahref='#impl-AbstractGroup%3CAdditive%3E-for-isize'class='anchor'></a><aclass='srclink'href='../../src/alga/macros.rs.html#95'title='goto source code'>[src]</a></h3><divclass='impl-items'></div><h3id='impl-AbstractGroup%3CAdditive%3E-for-f32'class='impl'><codeclass='in-band'>impl <aclass="trait"href="../../alga/general/trait.AbstractGroup.html"title="trait alga::general::AbstractGroup">AbstractGroup</a><<aclass="struct"href="../../alga/general/struct.Additive.html"title="struct alga::general::Additive">Additive</a>> for <aclass="primitive"href="https://doc.rust-lang.org/nightly/std/primitive.f32.html">f32</a></code><ahref='#impl-AbstractGroup%3CAdditive%3E-for-f32'class='anchor'></a><aclass='srclink'href='../../src/alga/macros.rs.html#102'title='goto source code'>[src]</a></h3><divclass='impl-items'></div><h3id='impl-AbstractGroup%3CAdditive%3E-for-f64'class='impl'><codeclass='in-band'>impl <aclass="trait"href="../../alga/general/trait.AbstractGroup.html"title="trait alga::general::AbstractGroup">AbstractGroup</a><<aclass="struct"href="../../alga/general/struct.Additive.html"title="struct alga::general::Additive">Additive</a>> for <aclass="primitive"href="https://doc.rust-lang.org/nightly/std/primitive.f64.html">f64</a></code><ahref='#impl-AbstractGroup%3CAdditive%3E-for-f64'class='anchor'></a><aclass='srclink'href='../../src/alga/macros.rs.html#95'title='goto source code'>[src]</a></h3><divclass='impl-items'></div><h3id='impl-AbstractGroup%3CMultiplicative%3E-for-f32'class='impl'><codeclass='in-band'>impl <aclass="trait"href="../../alga/general/trait.AbstractGroup.html"title="trait alga::general::AbstractGroup">AbstractGroup</a><<aclass="struct"href="../../alga/general/struct.Multiplicative.html"title="struct alga::general::Multiplicative">Multiplicative</a>> for <aclass="primitive"href="https://doc.rust-lang.org/nightly/std/primitive.f32.html">f32</a></code><ahref='#impl-AbstractGroup%3CMultiplicative%3E-for-f32'class='anchor'></a><aclass='srclink'href='../../src/alga/macros.rs.html#102'title='goto source code'>[src]</a></h3><divclass='impl-items'></div><h3id='impl-AbstractGroup%3CMultiplicative%3E-for-f64'class='impl'><codeclass='in-band'>impl <aclass="trait"href="../../alga/general/trait.AbstractGroup.html"title="trait alga::general::AbstractGroup">AbstractGroup</a><<aclass="struct"href="../../alga/general/struct.Multiplicative.html"title="struct alga::general::Multiplicative">Multiplicative</a>> for <aclass="primitive"href="https://doc.rust-lang.org/nightly/std/primitive.f64.html">f64</a></code><ahref='#impl-AbstractGroup%3CMultiplicative%3E-for-f64'class='anchor'></a><aclass='srclink'href='../../src/alga/macros.rs.html#95'title='goto source code'>[src]</a></h3><divclass='impl-items'></div><spanclass='loading-content'>Loading content...</span>
<h2id='implementors'class='small-section-header'>Implementors<ahref='#implementors'class='anchor'></a></h2><divclass='item-list'id='implementors-list'><h3id='impl-AbstractGroup%3CO%3E'class='impl'><codeclass='in-band'>impl<O: <aclass="trait"href="../../alga/general/trait.Operator.html"title="trait alga::general::Operator">Operator</a>> AbstractGroup<O> for <aclass="struct"href="../../alga/general/struct.Id.html"title="struct alga::general::Id">Id</a><O></code><ahref='#impl-AbstractGroup%3CO%3E'class='anchor'></a><aclass='srclink'href='../../src/alga/general/identity.rs.html#227'title='goto source code'>[src]</a></h3><divclass='impl-items'></div></div><spanclass='loading-content'>Loading content...</span><scripttype="text/javascript">window.inlined_types=newSet([]);</script><scripttype="text/javascript"async
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