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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">☰</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<N></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'>−</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<OpGroup: <a class="trait" href="../../alga/general/trait.Operator.html" title="trait alga::general::Operator">Operator</a> = <a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>, OpAdd: <a class="trait" href="../../alga/general/trait.Operator.html" title="trait alga::general::Operator">Operator</a> = <a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a>, OpMul: <a class="trait" href="../.
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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><OpAdd, OpMul>;
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fn <a href='#tymethod.multiply_by' class='fnname'>multiply_by</a>(&self, r: Self::<a class="type" href="../../alga/general/trait.AbstractModule.html#associatedtype.AbstractRing" title="type alga::general::AbstractModule::AbstractRing">AbstractRing</a>) -> Self;
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}</pre></div><div class='docblock'><p>A module combines two sets: one with an Abelian group structure and another with a
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commutative ring structure.</p>
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<p><code>OpGroup</code> denotes the Abelian group operator (usually the addition). In addition, and external
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multiplicative law noted <code>∘</code> is defined. Let <code>S</code> be the ring with multiplicative operator
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<code>OpMul</code> noted <code>×</code>, multiplicative identity element noted <code>1</code>, and additive operator <code>OpAdd</code>.
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Then:</p>
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<pre><code class="language-notrust">∀ a, b ∈ S
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∀ x, y ∈ Self
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a ∘ (x + y) = (a ∘ x) + (a ∘ y)
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(a + b) ∘ x = (a ∘ x) + (b ∘ x)
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(a × b) ∘ x = a ∘ (b ∘ x)
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1 ∘ x = x
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</code></pre>
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</div>
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<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><OpAdd, OpMul></code></h3><div class='docblock'><p>The underlying scalar field.</p>
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</div></div><span class='loading-content'>Loading content...</span>
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<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>(&self, r: Self::<a class="type" href="../../alga/general/trait.AbstractModule.html#associatedtype.AbstractRing" title="type alga::general::AbstractModule::AbstractRing">AbstractRing</a>) -> Self</code></h3><div class='docblock'><p>Multiplies an element of the ring with an element of the module.</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-AbstractModule%3CAdditive%2C%20Additive%2C%20Multiplicative%3E-for-Complex%3CN%3E' class='impl'><code class='in-band'>impl<N: <a class="trait" href="../../alga/general/trait.AbstractRingCommutative.html" title="trait alga::general::AbstractRingCommutative">AbstractRingCommutative</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>> + <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>> <a class="trait" href="../../alga/general/trait.AbstractModule.html" title="trait alga::general::AbstractModule">AbstractModule</a><<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>> for <a class="struct" href="../../num_complex/struct.Complex.html" title="struct num_complex::Complex">Complex</a><N></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>(&self, r: N) -> 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>
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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'></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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