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5 years ago
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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 `AbstractMonoid` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, AbstractMonoid"><title>alga::general::AbstractMonoid - 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">☰</div><a href='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait AbstractMonoid</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#provided-methods">Provided Methods</a><div class="sidebar-links"><a href="#method.prop_operating_identity_element_is_noop">prop_operating_identity_element_is_noop</a><a href="#method.prop_operating_identity_element_is_noop_approx">prop_operating_identity_element_is_noop_approx</a></div><a class="sidebar-title" href="#foreign-impls">Implementations on Foreign Types</a><div class="sidebar-links"><a href="#impl-AbstractMonoid%3CAdditive%3E-for-Complex%3CN%3E">Complex<N></a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-f32">f32</a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-f64">f64</a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-i16">i16</a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-i32">i32</a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-i64">i64</a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-i8">i8</a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-isize">isize</a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-u16">u16</a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-u32">u32</a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-u64">u64</a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-u8">u8</a><a href="#impl-AbstractMonoid%3CAdditive%3E-for-usize">usize</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-Complex%3CN%3E">Complex<N></a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-f32">f32</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-f64">f64</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-i16">i16</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-i32">i32</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-i64">i64</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-i8">i8</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-isize">isize</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-u16">u16</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-u32">u32</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-u64">u64</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-u8">u8</a><a href="#impl-AbstractMonoid%3CMultiplicative%3E-for-usize">usize</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: 'AbstractMonoid', 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-
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fn <a href='#method.prop_operating_identity_element_is_noop_approx' class='fnname'>prop_operating_identity_element_is_noop_approx</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">,)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a><br> <span class="where">where<br> Self: <a class="trait" href="../../approx/relative_eq/trait.RelativeEq.html" title="trait approx::relative_eq::RelativeEq">RelativeEq</a></span>,
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{ ... }
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<div class='item-spacer'></div> fn <a href='#method.prop_operating_identity_element_is_noop' class='fnname'>prop_operating_identity_element_is_noop</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">,)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a><br> <span class="where">where<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.Eq.html" title="trait core::cmp::Eq">Eq</a></span>,
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{ ... }
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}</pre></div><div class='docblock'><p>A monoid is a semigroup equipped with an identity element, e.</p>
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<p><em>A set equipped with a closed associative binary operation with the divisibility property and
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an identity element.</em></p>
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<h1 id="identity-element" class="section-header"><a href="#identity-element">Identity element</a></h1>
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<pre><code class="language-notrust">∃ e ∈ Self, ∀ a ∈ Self, e ∘ a = a ∘ e = a
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</code></pre>
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</div>
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<h2 id='provided-methods' class='small-section-header'>Provided methods<a href='#provided-methods' class='anchor'></a></h2><div class='methods'><h3 id='method.prop_operating_identity_element_is_noop_approx' class='method'><code id='prop_operating_identity_element_is_noop_approx.v'>fn <a href='#method.prop_operating_identity_element_is_noop_approx' class='fnname'>prop_operating_identity_element_is_noop_approx</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">,)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="../../approx/relative_eq/trait.RelativeEq.html" title="trait approx::relative_eq::RelativeEq">RelativeEq</a>, </span></code></h3><div class='docblock'><p>Checks whether operating with the identity element is a no-op for the given
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argument. Approximate equality is used for verifications.</p>
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</div><h3 id='method.prop_operating_identity_element_is_noop' class='method'><code id='prop_operating_identity_element_is_noop.v'>fn <a href='#method.prop_operating_identity_element_is_noop' class='fnname'>prop_operating_identity_element_is_noop</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">,)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.Eq.html" title="trait core::cmp::Eq">Eq</a>, </span></code></h3><div class='docblock'><p>Checks whether operating with the identity element is a no-op for the given
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argument.</p>
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</div></div><span class='loading-content'>Loading content...</span>
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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-AbstractMonoid%3CAdditive%3E-for-u8' class='impl'><code class='in-band'>impl <a class="trait" href="../../alga/general/trait.AbstractMonoid.html" title="trait alga::general::AbstractMonoid">AbstractMonoid</a><<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>> for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a></code><a href='#impl-AbstractMonoid%3CAdditive%3E-for-u8' 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-AbstractMonoid%3CAdditive%3E-for-u16' class='impl'><code class='in-band'>impl <a class="trait" href="../../alga/general/trait.AbstractMonoid.html" title="trait alga::general::AbstractMonoid">AbstractMonoid</a><<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>> for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u16.html">u16</a></code><a href='#impl-AbstractMonoid%3CAdditive%3E-for-u16' 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-AbstractMonoid%3CAdditive%3E-for-u32' class='impl'><code class='in-band'>impl <a class="trait" href="../../alga/general/trait.AbstractMonoid.html" title="trait alga::general::AbstractMonoid">AbstractMonoid</a><<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>> for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a></code><a href='#impl-AbstractMonoid%3CAdditive%3E-for-u32' 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-AbstractMonoid%3CAdditive%3E-for-u64' class='impl'><code class='in-band'>impl <a class="trait" href="../../alga/general/trait.AbstractMonoid.html" title="trait alga::general::AbstractMonoid">AbstractMonoid</a><<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>> for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u64.html">u64</a></code><a href='#impl-AbstractMonoid%3CAdditive%3E-for-u64' 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-AbstractMonoid%3CAdditive%3E-for-usize' class='impl'><code class='in-band'>impl <a class="trait" href="../../alga/general/trait.AbstractMonoid.html" title="trait alga::general::AbstractMonoid">AbstractMonoid</a><<a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>> for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.usize.html">usize</a></code><a href='#impl-AbstractMonoid%3CAdditive%3E-for-usize' 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-AbstractMonoid%3CMultiplicative%3E-for-u8' class='impl'><code class='in-band'>impl <a class="trait" href="../../alga/general/trait.AbstractMonoid.html" title="trait alga::general::AbstractMonoid">AbstractMonoid</a><<a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>> for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u8.html">u8</a></code><a href='#impl-AbstractMonoid%3CMultiplicative%3E-for-u8' 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-Ab
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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-AbstractMonoid%3CO%3E' class='impl'><code class='in-band'>impl<O: <a class="trait" href="../../alga/general/trait.Operator.html" title="trait alga::general::Operator">Operator</a>> AbstractMonoid<O> for <a class="struct" href="../../alga/general/struct.Id.html" title="struct alga::general::Id">Id</a><O></code><a href='#impl-AbstractMonoid%3CO%3E' class='anchor'></a><a class='srclink' href='../../src/alga/general/identity.rs.html#225' 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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src="../../implementors/alga/general/trait.AbstractMonoid.js">
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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>⏎</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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