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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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<!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>
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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>(&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>
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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>
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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-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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<!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>
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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-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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<!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>
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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-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
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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>

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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 `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
src="../../implementors/alga/general/trait.AdditiveQuasigroup.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 `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>
</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-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
src="../../implementors/alga/general/trait.AdditiveSemigroup.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 `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
src="../../implementors/alga/general/trait.ClosedDiv.js">
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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
src="../../implementors/alga/general/trait.ClosedSub.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 `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
src="../../implementors/alga/general/trait.Field.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 `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>
</div></div><span class='loading-content'>Loading content...</span>
<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
src="../../implementors/alga/general/trait.Module.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 `MultiplicativeGroup` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, MultiplicativeGroup"><title>alga::general::MultiplicativeGroup - 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 MultiplicativeGroup</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: 'MultiplicativeGroup', 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=''>MultiplicativeGroup</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait MultiplicativeGroup: <a class="trait" href="../../alga/general/trait.AbstractGroup.html" title="trait alga::general::AbstractGroup">AbstractGroup</a>&lt;<a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeLoop.html" title="trait alga::general::MultiplicativeLoop">MultiplicativeLoop</a> + <a class="trait" href="../../alga/general/trait.MultiplicativeMonoid.html" title="trait alga::general::MultiplicativeMonoid">MultiplicativeMonoid</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-MultiplicativeGroup' 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.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeLoop.html" title="trait alga::general::MultiplicativeLoop">MultiplicativeLoop</a> + <a class="trait" href="../../alga/general/trait.MultiplicativeMonoid.html" title="trait alga::general::MultiplicativeMonoid">MultiplicativeMonoid</a>&gt; MultiplicativeGroup for T</code><a href='#impl-MultiplicativeGroup' 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.MultiplicativeGroup.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 `MultiplicativeGroupAbelian` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, MultiplicativeGroupAbelian"><title>alga::general::MultiplicativeGroupAbelian - 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 MultiplicativeGroupAbelian</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: 'MultiplicativeGroupAbelian', 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=''>MultiplicativeGroupAbelian</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait MultiplicativeGroupAbelian: <a class="trait" href="../../alga/general/trait.AbstractGroupAbelian.html" title="trait alga::general::AbstractGroupAbelian">AbstractGroupAbelian</a>&lt;<a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeGroup.html" title="trait alga::general::MultiplicativeGroup">MultiplicativeGroup</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-MultiplicativeGroupAbelian' 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.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeGroup.html" title="trait alga::general::MultiplicativeGroup">MultiplicativeGroup</a>&gt; MultiplicativeGroupAbelian for T</code><a href='#impl-MultiplicativeGroupAbelian' 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 `MultiplicativeLoop` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, MultiplicativeLoop"><title>alga::general::MultiplicativeLoop - 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 MultiplicativeLoop</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: 'MultiplicativeLoop', 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=''>MultiplicativeLoop</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait MultiplicativeLoop: <a class="trait" href="../../alga/general/trait.AbstractLoop.html" title="trait alga::general::AbstractLoop">AbstractLoop</a>&lt;<a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeQuasigroup.html" title="trait alga::general::MultiplicativeQuasigroup">MultiplicativeQuasigroup</a> + <a class="trait" href="../../num_traits/identities/trait.One.html" title="trait num_traits::identities::One">One</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-MultiplicativeLoop' 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.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeQuasigroup.html" title="trait alga::general::MultiplicativeQuasigroup">MultiplicativeQuasigroup</a> + <a class="trait" href="../../num_traits/identities/trait.One.html" title="trait num_traits::identities::One">One</a>&gt; MultiplicativeLoop for T</code><a href='#impl-MultiplicativeLoop' 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.MultiplicativeLoop.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 `MultiplicativeMagma` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, MultiplicativeMagma"><title>alga::general::MultiplicativeMagma - 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 MultiplicativeMagma</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: 'MultiplicativeMagma', 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=''>MultiplicativeMagma</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait MultiplicativeMagma: <a class="trait" href="../../alga/general/trait.AbstractMagma.html" title="trait alga::general::AbstractMagma">AbstractMagma</a>&lt;<a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</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-MultiplicativeMagma' 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.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt;&gt; MultiplicativeMagma for T</code><a href='#impl-MultiplicativeMagma' 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 `MultiplicativeMonoid` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, MultiplicativeMonoid"><title>alga::general::MultiplicativeMonoid - 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 MultiplicativeMonoid</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: 'MultiplicativeMonoid', 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=''>MultiplicativeMonoid</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait MultiplicativeMonoid: <a class="trait" href="../../alga/general/trait.AbstractMonoid.html" title="trait alga::general::AbstractMonoid">AbstractMonoid</a>&lt;<a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeSemigroup.html" title="trait alga::general::MultiplicativeSemigroup">MultiplicativeSemigroup</a> + <a class="trait" href="../../num_traits/identities/trait.One.html" title="trait num_traits::identities::One">One</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-MultiplicativeMonoid' 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.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeSemigroup.html" title="trait alga::general::MultiplicativeSemigroup">MultiplicativeSemigroup</a> + <a class="trait" href="../../num_traits/identities/trait.One.html" title="trait num_traits::identities::One">One</a>&gt; MultiplicativeMonoid for T</code><a href='#impl-MultiplicativeMonoid' 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.MultiplicativeMonoid.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 `MultiplicativeQuasigroup` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, MultiplicativeQuasigroup"><title>alga::general::MultiplicativeQuasigroup - 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 MultiplicativeQuasigroup</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: 'MultiplicativeQuasigroup', 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=''>MultiplicativeQuasigroup</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait MultiplicativeQuasigroup: <a class="trait" href="../../alga/general/trait.AbstractQuasigroup.html" title="trait alga::general::AbstractQuasigroup">AbstractQuasigroup</a>&lt;<a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeMagma.html" title="trait alga::general::MultiplicativeMagma">MultiplicativeMagma</a> + <a class="trait" href="../../alga/general/trait.ClosedDiv.html" title="trait alga::general::ClosedDiv">ClosedDiv</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-MultiplicativeQuasigroup' 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.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeMagma.html" title="trait alga::general::MultiplicativeMagma">MultiplicativeMagma</a> + <a class="trait" href="../../alga/general/trait.ClosedDiv.html" title="trait alga::general::ClosedDiv">ClosedDiv</a>&gt; MultiplicativeQuasigroup for T</code><a href='#impl-MultiplicativeQuasigroup' 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 `MultiplicativeSemigroup` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, MultiplicativeSemigroup"><title>alga::general::MultiplicativeSemigroup - 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 MultiplicativeSemigroup</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: 'MultiplicativeSemigroup', 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=''>MultiplicativeSemigroup</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait MultiplicativeSemigroup: <a class="trait" href="../../alga/general/trait.AbstractSemigroup.html" title="trait alga::general::AbstractSemigroup">AbstractSemigroup</a>&lt;<a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeMagma.html" title="trait alga::general::MultiplicativeMagma">MultiplicativeMagma</a> + <a class="trait" href="../../alga/general/trait.ClosedMul.html" title="trait alga::general::ClosedMul">ClosedMul</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-MultiplicativeSemigroup' 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.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a>&gt; + <a class="trait" href="../../alga/general/trait.MultiplicativeMagma.html" title="trait alga::general::MultiplicativeMagma">MultiplicativeMagma</a> + <a class="trait" href="../../alga/general/trait.ClosedMul.html" title="trait alga::general::ClosedMul">ClosedMul</a>&gt; MultiplicativeSemigroup for T</code><a href='#impl-MultiplicativeSemigroup' 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.MultiplicativeSemigroup.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 `Operator` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, Operator"><title>alga::general::Operator - 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 Operator</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#required-methods">Required Methods</a><div class="sidebar-links"><a href="#tymethod.operator_token">operator_token</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: 'Operator', 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#10-13' 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=''>Operator</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait Operator: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Copy.html" title="trait core::marker::Copy">Copy</a> {
fn <a href='#tymethod.operator_token' class='fnname'>operator_token</a>() -&gt; Self;
}</pre></div><div class='docblock'><p>Trait implemented by types representing abstract operators.</p>
</div>
<h2 id='required-methods' class='small-section-header'>Required methods<a href='#required-methods' class='anchor'></a></h2><div class='methods'><h3 id='tymethod.operator_token' class='method'><code id='operator_token.v'>fn <a href='#tymethod.operator_token' class='fnname'>operator_token</a>() -&gt; Self</code></h3><div class='docblock'><p>Returns the structure that identifies the operator.</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-Operator' class='impl'><code class='in-band'>impl Operator for <a class="struct" href="../../alga/general/struct.Additive.html" title="struct alga::general::Additive">Additive</a></code><a href='#impl-Operator' class='anchor'></a><a class='srclink' href='../../src/alga/general/operator.rs.html#51-56' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.operator_token' class="method hidden"><code id='operator_token.v-1'>fn <a href='#method.operator_token' class='fnname'>operator_token</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/operator.rs.html#53-55' title='goto source code'>[src]</a></h4></div><h3 id='impl-Operator-1' class='impl'><code class='in-band'>impl Operator for <a class="struct" href="../../alga/general/struct.Multiplicative.html" title="struct alga::general::Multiplicative">Multiplicative</a></code><a href='#impl-Operator-1' class='anchor'></a><a class='srclink' href='../../src/alga/general/operator.rs.html#58-63' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.operator_token-1' class="method hidden"><code id='operator_token.v-2'>fn <a href='#method.operator_token-1' class='fnname'>operator_token</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/operator.rs.html#60-62' title='goto source code'>[src]</a></h4></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 `Real` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, Real"><title>alga::general::Real - 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 Real</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: 'Real', 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/mod.rs.html#198' 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=''>Real</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait Real: <a class="trait" href="../../alga/general/trait.RealField.html" title="trait alga::general::RealField">RealField</a> { }</pre></div><div class='stability'><div class='stab deprecated'>Deprecated: <p>This has been renamed <code>RealField</code>.</p>
</div></div><div class='docblock'><p>The field of reals. This has been renamed to <code>RealField</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-Real' class='impl'><code class='in-band'>impl&lt;T:&nbsp;<a class="trait" href="../../alga/general/trait.RealField.html" title="trait alga::general::RealField">RealField</a>&gt; Real for T</code><a href='#impl-Real' class='anchor'></a><a class='srclink' href='../../src/alga/general/mod.rs.html#200' 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 `RealField` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, RealField"><title>alga::general::RealField - 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 RealField</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#required-methods">Required Methods</a><div class="sidebar-links"><a href="#tymethod.atan2">atan2</a><a href="#tymethod.e">e</a><a href="#tymethod.frac_1_pi">frac_1_pi</a><a href="#tymethod.frac_2_pi">frac_2_pi</a><a href="#tymethod.frac_2_sqrt_pi">frac_2_sqrt_pi</a><a href="#tymethod.frac_pi_2">frac_pi_2</a><a href="#tymethod.frac_pi_3">frac_pi_3</a><a href="#tymethod.frac_pi_4">frac_pi_4</a><a href="#tymethod.frac_pi_6">frac_pi_6</a><a href="#tymethod.frac_pi_8">frac_pi_8</a><a href="#tymethod.is_sign_negative">is_sign_negative</a><a href="#tymethod.is_sign_positive">is_sign_positive</a><a href="#tymethod.ln_10">ln_10</a><a href="#tymethod.ln_2">ln_2</a><a href="#tymethod.log10_e">log10_e</a><a href="#tymethod.log2_e">log2_e</a><a href="#tymethod.max">max</a><a href="#tymethod.min">min</a><a href="#tymethod.pi">pi</a><a href="#tymethod.two_pi">two_pi</a></div><a class="sidebar-title" href="#foreign-impls">Implementations on Foreign Types</a><div class="sidebar-links"><a href="#impl-RealField-for-f32">f32</a><a href="#impl-RealField-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: 'RealField', 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/real.rs.html#26-58' 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=''>RealField</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait RealField: <a class="trait" href="../../alga/general/trait.ComplexField.html" title="trait alga::general::ComplexField">ComplexField</a>&lt;RealField = Self&gt; + <a class="trait" href="../../approx/relative_eq/trait.RelativeEq.html" title="trait approx::relative_eq::RelativeEq">RelativeEq</a>&lt;Epsilon = Self&gt; + <a class="trait" href="../../approx/ulps_eq/trait.UlpsEq.html" title="trait approx::ulps_eq::UlpsEq">UlpsEq</a>&lt;Epsilon = Self&gt; + <a class="trait" href="../../alga/general/trait.Lattice.html" title="trait alga::general::Lattice">Lattice</a> + <a class="trait" href="../../num_traits/sign/trait.Signed.html" title="trait num_traits::sign::Signed">Signed</a> + <a class="trait" href="../../num_traits/bounds/trait.Bounded.html" title="trait num_traits::bounds::Bounded">Bounded</a> {
fn <a href='#tymethod.is_sign_positive' class='fnname'>is_sign_positive</a>(self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a>;
<div class='item-spacer'></div> fn <a href='#tymethod.is_sign_negative' class='fnname'>is_sign_negative</a>(self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a>;
<div class='item-spacer'></div> fn <a href='#tymethod.max' class='fnname'>max</a>(self, other: Self) -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.min' class='fnname'>min</a>(self, other: Self) -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.atan2' class='fnname'>atan2</a>(self, other: Self) -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.pi' class='fnname'>pi</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.two_pi' class='fnname'>two_pi</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.frac_pi_2' class='fnname'>frac_pi_2</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.frac_pi_3' class='fnname'>frac_pi_3</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.frac_pi_4' class='fnname'>frac_pi_4</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.frac_pi_6' class='fnname'>frac_pi_6</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.frac_pi_8' class='fnname'>frac_pi_8</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.frac_1_pi' class='fnname'>frac_1_pi</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.frac_2_pi' class='fnname'>frac_2_pi</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.frac_2_sqrt_pi' class='fnname'>frac_2_sqrt_pi</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.e' class='fnname'>e</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.log2_e' class='fnname'>log2_e</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.log10_e' class='fnname'>log10_e</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.ln_2' class='fnname'>ln_2</a>() -&gt; Self;
<div class='item-spacer'></div> fn <a href='#tymethod.ln_10' class='fnname'>ln_10</a>() -&gt; Self;
}</pre></div><div class='docblock'><p>Trait shared by all reals.</p>
<p>Reals are equipped with functions that are commonly used on reals. The results of those
functions only have to be approximately equal to the actual theoretical values.</p>
</div>
<h2 id='required-methods' class='small-section-header'>Required methods<a href='#required-methods' class='anchor'></a></h2><div class='methods'><h3 id='tymethod.is_sign_positive' class='method'><code id='is_sign_positive.v'>fn <a href='#tymethod.is_sign_positive' class='fnname'>is_sign_positive</a>(self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code></h3><h3 id='tymethod.is_sign_negative' class='method'><code id='is_sign_negative.v'>fn <a href='#tymethod.is_sign_negative' class='fnname'>is_sign_negative</a>(self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code></h3><h3 id='tymethod.max' class='method'><code id='max.v'>fn <a href='#tymethod.max' class='fnname'>max</a>(self, other: Self) -&gt; Self</code></h3><h3 id='tymethod.min' class='method'><code id='min.v'>fn <a href='#tymethod.min' class='fnname'>min</a>(self, other: Self) -&gt; Self</code></h3><h3 id='tymethod.atan2' class='method'><code id='atan2.v'>fn <a href='#tymethod.atan2' class='fnname'>atan2</a>(self, other: Self) -&gt; Self</code></h3><h3 id='tymethod.pi' class='method'><code id='pi.v'>fn <a href='#tymethod.pi' class='fnname'>pi</a>() -&gt; Self</code></h3><h3 id='tymethod.two_pi' class='method'><code id='two_pi.v'>fn <a href='#tymethod.two_pi' class='fnname'>two_pi</a>() -&gt; Self</code></h3><h3 id='tymethod.frac_pi_2' class='method'><code id='frac_pi_2.v'>fn <a href='#tymethod.frac_pi_2' class='fnname'>frac_pi_2</a>() -&gt; Self</code></h3><h3 id='tymethod.frac_pi_3' class='method'><code id='frac_pi_3.v'>fn <a href='#tymethod.frac_pi_3' class='fnname'>frac_pi_3</a>() -&gt; Self</code></h3><h3 id='tymethod.frac_pi_4' class='method'><code id='frac_pi_4.v'>fn <a href='#tymethod.frac_pi_4' class='fnname'>frac_pi_4</a>() -&gt; Self</code></h3><h3 id='tymethod.frac_pi_6' class='method'><code id='frac_pi_6.v'>fn <a href='#tymethod.frac_pi_6' class='fnname'>frac_pi_6</a>() -&gt; Self</code></h3><h3 id='tymethod.frac_pi_8' class='method'><code id='frac_pi_8.v'>fn <a href='#tymethod.frac_pi_8' class='fnname'>frac_pi_8</a>() -&gt; Self</code></h3><h3 id='tymethod.frac_1_pi' class='method'><code id='frac_1_pi.v'>fn <a href='#tymethod.frac_1_pi' class='fnname'>frac_1_pi</a>() -&gt; Self</code></h3><h3 id='tymethod.frac_2_pi' class='method'><code id='frac_2_pi.v'>fn <a href='#tymethod.frac_2_pi' class='fnname'>frac_2_pi</a>() -&gt; Self</code></h3><h3 id='tymethod.frac_2_sqrt_pi' class='method'><code id='frac_2_sqrt_pi.v'>fn <a href='#tymethod.frac_2_sqrt_pi' class='fnname'>frac_2_sqrt_pi</a>() -&gt; Self</code></h3><h3 id='tymethod.e' class='method'><code id='e.v'>fn <a href='#tymethod.e' class='fnname'>e</a>() -&gt; Self</code></h3><h3 id='tymethod.log2_e' class='method'><code id='log2_e.v'>fn <a href='#tymethod.log2_e' class='fnname'>log2_e</a>() -&gt; Self</code></h3><h3 id='tymethod.log10_e' class='method'><code id='log10_e.v'>fn <a href='#tymethod.log10_e' class='fnname'>log10_e</a>() -&gt; Self</code></h3><h3 id='tymethod.ln_2' class='method'><code id='ln_2.v'>fn <a href='#tymethod.ln_2' class='fnname'>ln_2</a>() -&gt; Self</code></h3><h3 id='tymethod.ln_10' class='method'><code id='ln_10.v'>fn <a href='#tymethod.ln_10' class='fnname'>ln_10</a>() -&gt; Self</code></h3></div><span class='loading-content'>Loading content...</span>
<h2 id='foreign-impls' class='small-section-header'>Implementations on Foreign Types<a href='#foreign-impls' class='anchor'></a></h2><h3 id='impl-RealField-for-f32' class='impl'><code class='in-band'>impl <a class="trait" href="../../alga/general/trait.RealField.html" title="trait alga::general::RealField">RealField</a> for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.f32.html">f32</a></code><a href='#impl-RealField-for-f32' class='anchor'></a><a class='srclink' href='../../src/alga/general/real.rs.html#62-178' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.is_sign_positive' class="method hidden"><code id='is_sign_positive.v-1'>fn <a href='#method.is_sign_positive' class='fnname'>is_sign_positive</a>(self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../../src/alga/general/real.rs.html#64-66' title='goto source code'>[src]</a></h4><h4 id='method.is_sign_negative' class="method hidden"><code id='is_sign_negative.v-1'>fn <a href='#method.is_sign_negative' class='fnname'>is_sign_negative</a>(self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../../src/alga/general/real.rs.html#69-71' title='goto source code'>[src]</a></h4><h4 id='method.max' class="method hidden"><code id='max.v-1'>fn <a href='#method.max' class='fnname'>max</a>(self, other: Self) -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#74-76' title='goto source code'>[src]</a></h4><h4 id='method.min' class="method hidden"><code id='min.v-1'>fn <a href='#method.min' class='fnname'>min</a>(self, other: Self) -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#79-81' title='goto source code'>[src]</a></h4><h4 id='method.atan2' class="method hidden"><code id='atan2.v-1'>fn <a href='#method.atan2' class='fnname'>atan2</a>(self, other: Self) -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#84-86' title='goto source code'>[src]</a></h4><h4 id='method.pi' class="method"><code id='pi.v-1'>fn <a href='#method.pi' class='fnname'>pi</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#90-92' title='goto source code'>[src]</a></h4><div class='docblock'><p>Archimedes' constant.</p>
</div><h4 id='method.two_pi' class="method"><code id='two_pi.v-1'>fn <a href='#method.two_pi' class='fnname'>two_pi</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#96-98' title='goto source code'>[src]</a></h4><div class='docblock'><p>2.0 * pi.</p>
</div><h4 id='method.frac_pi_2' class="method"><code id='frac_pi_2.v-1'>fn <a href='#method.frac_pi_2' class='fnname'>frac_pi_2</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#102-104' title='goto source code'>[src]</a></h4><div class='docblock'><p>pi / 2.0.</p>
</div><h4 id='method.frac_pi_3' class="method"><code id='frac_pi_3.v-1'>fn <a href='#method.frac_pi_3' class='fnname'>frac_pi_3</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#108-110' title='goto source code'>[src]</a></h4><div class='docblock'><p>pi / 3.0.</p>
</div><h4 id='method.frac_pi_4' class="method"><code id='frac_pi_4.v-1'>fn <a href='#method.frac_pi_4' class='fnname'>frac_pi_4</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#114-116' title='goto source code'>[src]</a></h4><div class='docblock'><p>pi / 4.0.</p>
</div><h4 id='method.frac_pi_6' class="method"><code id='frac_pi_6.v-1'>fn <a href='#method.frac_pi_6' class='fnname'>frac_pi_6</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#120-122' title='goto source code'>[src]</a></h4><div class='docblock'><p>pi / 6.0.</p>
</div><h4 id='method.frac_pi_8' class="method"><code id='frac_pi_8.v-1'>fn <a href='#method.frac_pi_8' class='fnname'>frac_pi_8</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#126-128' title='goto source code'>[src]</a></h4><div class='docblock'><p>pi / 8.0.</p>
</div><h4 id='method.frac_1_pi' class="method"><code id='frac_1_pi.v-1'>fn <a href='#method.frac_1_pi' class='fnname'>frac_1_pi</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#132-134' title='goto source code'>[src]</a></h4><div class='docblock'><p>1.0 / pi.</p>
</div><h4 id='method.frac_2_pi' class="method"><code id='frac_2_pi.v-1'>fn <a href='#method.frac_2_pi' class='fnname'>frac_2_pi</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#138-140' title='goto source code'>[src]</a></h4><div class='docblock'><p>2.0 / pi.</p>
</div><h4 id='method.frac_2_sqrt_pi' class="method"><code id='frac_2_sqrt_pi.v-1'>fn <a href='#method.frac_2_sqrt_pi' class='fnname'>frac_2_sqrt_pi</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#144-146' title='goto source code'>[src]</a></h4><div class='docblock'><p>2.0 / sqrt(pi).</p>
</div><h4 id='method.e' class="method"><code id='e.v-1'>fn <a href='#method.e' class='fnname'>e</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#151-153' title='goto source code'>[src]</a></h4><div class='docblock'><p>Euler's number.</p>
</div><h4 id='method.log2_e' class="method"><code id='log2_e.v-1'>fn <a href='#method.log2_e' class='fnname'>log2_e</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#157-159' title='goto source code'>[src]</a></h4><div class='docblock'><p>log2(e).</p>
</div><h4 id='method.log10_e' class="method"><code id='log10_e.v-1'>fn <a href='#method.log10_e' class='fnname'>log10_e</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#163-165' title='goto source code'>[src]</a></h4><div class='docblock'><p>log10(e).</p>
</div><h4 id='method.ln_2' class="method"><code id='ln_2.v-1'>fn <a href='#method.ln_2' class='fnname'>ln_2</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#169-171' title='goto source code'>[src]</a></h4><div class='docblock'><p>ln(2.0).</p>
</div><h4 id='method.ln_10' class="method"><code id='ln_10.v-1'>fn <a href='#method.ln_10' class='fnname'>ln_10</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#175-177' title='goto source code'>[src]</a></h4><div class='docblock'><p>ln(10.0).</p>
</div></div><h3 id='impl-RealField-for-f64' class='impl'><code class='in-band'>impl <a class="trait" href="../../alga/general/trait.RealField.html" title="trait alga::general::RealField">RealField</a> for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.f64.html">f64</a></code><a href='#impl-RealField-for-f64' class='anchor'></a><a class='srclink' href='../../src/alga/general/real.rs.html#62-178' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.is_sign_positive-1' class="method hidden"><code id='is_sign_positive.v-2'>fn <a href='#method.is_sign_positive' class='fnname'>is_sign_positive</a>(self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../../src/alga/general/real.rs.html#64-66' title='goto source code'>[src]</a></h4><h4 id='method.is_sign_negative-1' class="method hidden"><code id='is_sign_negative.v-2'>fn <a href='#method.is_sign_negative' class='fnname'>is_sign_negative</a>(self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../../src/alga/general/real.rs.html#69-71' title='goto source code'>[src]</a></h4><h4 id='method.max-1' class="method hidden"><code id='max.v-2'>fn <a href='#method.max' class='fnname'>max</a>(self, other: Self) -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#74-76' title='goto source code'>[src]</a></h4><h4 id='method.min-1' class="method hidden"><code id='min.v-2'>fn <a href='#method.min' class='fnname'>min</a>(self, other: Self) -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#79-81' title='goto source code'>[src]</a></h4><h4 id='method.atan2-1' class="method hidden"><code id='atan2.v-2'>fn <a href='#method.atan2' class='fnname'>atan2</a>(self, other: Self) -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#84-86' title='goto source code'>[src]</a></h4><h4 id='method.pi-1' class="method"><code id='pi.v-2'>fn <a href='#method.pi' class='fnname'>pi</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#90-92' title='goto source code'>[src]</a></h4><div class='docblock'><p>Archimedes' constant.</p>
</div><h4 id='method.two_pi-1' class="method"><code id='two_pi.v-2'>fn <a href='#method.two_pi' class='fnname'>two_pi</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#96-98' title='goto source code'>[src]</a></h4><div class='docblock'><p>2.0 * pi.</p>
</div><h4 id='method.frac_pi_2-1' class="method"><code id='frac_pi_2.v-2'>fn <a href='#method.frac_pi_2' class='fnname'>frac_pi_2</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#102-104' title='goto source code'>[src]</a></h4><div class='docblock'><p>pi / 2.0.</p>
</div><h4 id='method.frac_pi_3-1' class="method"><code id='frac_pi_3.v-2'>fn <a href='#method.frac_pi_3' class='fnname'>frac_pi_3</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#108-110' title='goto source code'>[src]</a></h4><div class='docblock'><p>pi / 3.0.</p>
</div><h4 id='method.frac_pi_4-1' class="method"><code id='frac_pi_4.v-2'>fn <a href='#method.frac_pi_4' class='fnname'>frac_pi_4</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#114-116' title='goto source code'>[src]</a></h4><div class='docblock'><p>pi / 4.0.</p>
</div><h4 id='method.frac_pi_6-1' class="method"><code id='frac_pi_6.v-2'>fn <a href='#method.frac_pi_6' class='fnname'>frac_pi_6</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#120-122' title='goto source code'>[src]</a></h4><div class='docblock'><p>pi / 6.0.</p>
</div><h4 id='method.frac_pi_8-1' class="method"><code id='frac_pi_8.v-2'>fn <a href='#method.frac_pi_8' class='fnname'>frac_pi_8</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#126-128' title='goto source code'>[src]</a></h4><div class='docblock'><p>pi / 8.0.</p>
</div><h4 id='method.frac_1_pi-1' class="method"><code id='frac_1_pi.v-2'>fn <a href='#method.frac_1_pi' class='fnname'>frac_1_pi</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#132-134' title='goto source code'>[src]</a></h4><div class='docblock'><p>1.0 / pi.</p>
</div><h4 id='method.frac_2_pi-1' class="method"><code id='frac_2_pi.v-2'>fn <a href='#method.frac_2_pi' class='fnname'>frac_2_pi</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#138-140' title='goto source code'>[src]</a></h4><div class='docblock'><p>2.0 / pi.</p>
</div><h4 id='method.frac_2_sqrt_pi-1' class="method"><code id='frac_2_sqrt_pi.v-2'>fn <a href='#method.frac_2_sqrt_pi' class='fnname'>frac_2_sqrt_pi</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#144-146' title='goto source code'>[src]</a></h4><div class='docblock'><p>2.0 / sqrt(pi).</p>
</div><h4 id='method.e-1' class="method"><code id='e.v-2'>fn <a href='#method.e' class='fnname'>e</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#151-153' title='goto source code'>[src]</a></h4><div class='docblock'><p>Euler's number.</p>
</div><h4 id='method.log2_e-1' class="method"><code id='log2_e.v-2'>fn <a href='#method.log2_e' class='fnname'>log2_e</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#157-159' title='goto source code'>[src]</a></h4><div class='docblock'><p>log2(e).</p>
</div><h4 id='method.log10_e-1' class="method"><code id='log10_e.v-2'>fn <a href='#method.log10_e' class='fnname'>log10_e</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#163-165' title='goto source code'>[src]</a></h4><div class='docblock'><p>log10(e).</p>
</div><h4 id='method.ln_2-1' class="method"><code id='ln_2.v-2'>fn <a href='#method.ln_2' class='fnname'>ln_2</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#169-171' title='goto source code'>[src]</a></h4><div class='docblock'><p>ln(2.0).</p>
</div><h4 id='method.ln_10-1' class="method"><code id='ln_10.v-2'>fn <a href='#method.ln_10' class='fnname'>ln_10</a>() -&gt; Self</code><a class='srclink' href='../../src/alga/general/real.rs.html#175-177' title='goto source code'>[src]</a></h4><div class='docblock'><p>ln(10.0).</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 `Ring` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, Ring"><title>alga::general::Ring - 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 Ring</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: 'Ring', 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=''>Ring</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait Ring: <a class="trait" href="../../alga/general/trait.AbstractRing.html" title="trait alga::general::AbstractRing">AbstractRing</a> + <a class="trait" href="../../alga/general/trait.AdditiveGroupAbelian.html" title="trait alga::general::AdditiveGroupAbelian">AdditiveGroupAbelian</a> + <a class="trait" href="../../alga/general/trait.MultiplicativeMonoid.html" title="trait alga::general::MultiplicativeMonoid">MultiplicativeMonoid</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-Ring' class='impl'><code class='in-band'>impl&lt;T:&nbsp;<a class="trait" href="../../alga/general/trait.AbstractRing.html" title="trait alga::general::AbstractRing">AbstractRing</a> + <a class="trait" href="../../alga/general/trait.AdditiveGroupAbelian.html" title="trait alga::general::AdditiveGroupAbelian">AdditiveGroupAbelian</a> + <a class="trait" href="../../alga/general/trait.MultiplicativeMonoid.html" title="trait alga::general::MultiplicativeMonoid">MultiplicativeMonoid</a>&gt; Ring for T</code><a href='#impl-Ring' 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 `RingCommutative` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, RingCommutative"><title>alga::general::RingCommutative - 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 RingCommutative</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: 'RingCommutative', 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=''>RingCommutative</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait RingCommutative: <a class="trait" href="../../alga/general/trait.AbstractRingCommutative.html" title="trait alga::general::AbstractRingCommutative">AbstractRingCommutative</a> + <a class="trait" href="../../alga/general/trait.Ring.html" title="trait alga::general::Ring">Ring</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-RingCommutative' class='impl'><code class='in-band'>impl&lt;T:&nbsp;<a class="trait" href="../../alga/general/trait.AbstractRingCommutative.html" title="trait alga::general::AbstractRingCommutative">AbstractRingCommutative</a> + <a class="trait" href="../../alga/general/trait.Ring.html" title="trait alga::general::Ring">Ring</a>&gt; RingCommutative for T</code><a href='#impl-RingCommutative' 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
src="../../implementors/alga/general/trait.RingCommutative.js">
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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 `SupersetOf` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, SupersetOf"><title>alga::general::SupersetOf - 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 SupersetOf</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#required-methods">Required Methods</a><div class="sidebar-links"><a href="#tymethod.from_subset">from_subset</a><a href="#tymethod.is_in_subset">is_in_subset</a><a href="#tymethod.to_subset_unchecked">to_subset_unchecked</a></div><a class="sidebar-title" href="#provided-methods">Provided Methods</a><div class="sidebar-links"><a href="#method.to_subset">to_subset</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: 'SupersetOf', 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/subset.rs.html#64-85' 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=''>SupersetOf</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait SupersetOf&lt;T&gt;: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a> {
fn <a href='#tymethod.is_in_subset' class='fnname'>is_in_subset</a>(&amp;self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a>;
<div class='item-spacer'></div> unsafe fn <a href='#tymethod.to_subset_unchecked' class='fnname'>to_subset_unchecked</a>(&amp;self) -&gt; T;
<div class='item-spacer'></div> fn <a href='#tymethod.from_subset' class='fnname'>from_subset</a>(element: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&amp;</a>T) -&gt; Self;
fn <a href='#method.to_subset' class='fnname'>to_subset</a>(&amp;self) -&gt; <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a>&lt;T&gt; { ... }
}</pre></div><div class='docblock'><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>
<p>The notion of &quot;nested sets&quot; is very broad and applies to what the types are <em>supposed to
represent</em>, independently from their actual implementation details and limitations. For
example:</p>
<ul>
<li>f32 and f64 are both supposed to represent reals and are thus considered equal (even if in
practice f64 has more elements).</li>
<li>u32 and i8 are respectively supposed to represent natural and relative numbers. Thus, i8 is
a superset of u32.</li>
<li>A quaternion and a 3x3 orthogonal matrix with unit determinant are both sets of rotations.
They can thus be considered equal.</li>
</ul>
<p>In other words, implementation details due to machine limitations are ignored (otherwise we
could not even, e.g., convert a u64 to an i64). If considering those limitations are
important, other crates allowing you to query the limitations of given types should be used.</p>
</div>
<h2 id='required-methods' class='small-section-header'>Required methods<a href='#required-methods' class='anchor'></a></h2><div class='methods'><h3 id='tymethod.is_in_subset' class='method'><code id='is_in_subset.v'>fn <a href='#tymethod.is_in_subset' class='fnname'>is_in_subset</a>(&amp;self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code></h3><div class='docblock'><p>Checks if <code>self</code> is actually part of its subset <code>T</code> (and can be converted to it).</p>
</div><h3 id='tymethod.to_subset_unchecked' class='method'><code id='to_subset_unchecked.v'>unsafe fn <a href='#tymethod.to_subset_unchecked' class='fnname'>to_subset_unchecked</a>(&amp;self) -&gt; T</code></h3><div class='docblock'><p>Use with care! Same as <code>self.to_subset</code> but without any property checks. Always succeeds.</p>
</div><h3 id='tymethod.from_subset' class='method'><code id='from_subset.v'>fn <a href='#tymethod.from_subset' class='fnname'>from_subset</a>(element: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&amp;</a>T) -&gt; Self</code></h3><div class='docblock'><p>The inclusion map: converts <code>self</code> to the equivalent element of its superset.</p>
</div></div><span class='loading-content'>Loading content...</span>
<h2 id='provided-methods' class='small-section-header'>Provided methods<a href='#provided-methods' class='anchor'></a></h2><div class='methods'><h3 id='method.to_subset' class='method'><code id='to_subset.v'>fn <a href='#method.to_subset' class='fnname'>to_subset</a>(&amp;self) -&gt; <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a>&lt;T&gt;</code></h3><div class='docblock'><p>The inverse inclusion map: attempts to construct <code>self</code> from the equivalent element of its
superset.</p>
<p>Must return <code>None</code> if <code>element</code> has no equivalent in <code>Self</code>.</p>
</div></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'><h3 id='impl-SupersetOf%3CSS%3E' class='impl'><code class='in-band'>impl&lt;SS:&nbsp;<a class="trait" href="../../alga/general/trait.SubsetOf.html" title="trait alga::general::SubsetOf">SubsetOf</a>&lt;SP&gt;, SP&gt; SupersetOf&lt;SS&gt; for SP</code><a href='#impl-SupersetOf%3CSS%3E' class='anchor'></a><a class='srclink' href='../../src/alga/general/subset.rs.html#87-107' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.to_subset-1' class="method hidden"><code id='to_subset.v-1'>fn <a href='#method.to_subset-1' class='fnname'>to_subset</a>(&amp;self) -&gt; <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a>&lt;SS&gt;</code><a class='srclink' href='../../src/alga/general/subset.rs.html#89-91' title='goto source code'>[src]</a></h4><h4 id='method.is_in_subset' class="method hidden"><code id='is_in_subset.v-1'>fn <a href='#method.is_in_subset' class='fnname'>is_in_subset</a>(&amp;self) -&gt; <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../../src/alga/general/subset.rs.html#94-96' title='goto source code'>[src]</a></h4><h4 id='method.to_subset_unchecked' class="method hidden"><code id='to_subset_unchecked.v-1'>unsafe fn <a href='#method.to_subset_unchecked' class='fnname'>to_subset_unchecked</a>(&amp;self) -&gt; SS</code><a class='srclink' href='../../src/alga/general/subset.rs.html#99-101' title='goto source code'>[src]</a></h4><h4 id='method.from_subset' class="method hidden"><code id='from_subset.v-1'>fn <a href='#method.from_subset' class='fnname'>from_subset</a>(element: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&amp;</a>SS) -&gt; Self</code><a class='srclink' href='../../src/alga/general/subset.rs.html#104-106' title='goto source code'>[src]</a></h4></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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