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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 `Id` struct in crate `nalgebra`."><meta name="keywords" content="rust, rustlang, rust-lang, Id"><title>nalgebra::Id - 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="http://nalgebra.org/img/favicon.ico"><style type="text/css">#crate-search{background-image:url("../down-arrow.svg");}</style></head><body class="rustdoc struct"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">☰</div><a href='../nalgebra/index.html'><div class='logo-container'><img src='../rust-logo.png' alt='logo'></div></a><p class='location'>Struct Id</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#methods">Methods</a><div class="sidebar-links"><a href="#method.new">new</a></div><a class="sidebar-title" href="#implementations">Trait Implementations</a><div class="sidebar-links"><a href="#impl-AbsDiffEq%3CId%3CO%3E%3E">AbsDiffEq<Id<O>></a><a href="#impl-AbstractGroup%3CO%3E">AbstractGroup<O></a><a href="#impl-AbstractGroupAbelian%3CO%3E">AbstractGroupAbelian<O></a><a href="#impl-AbstractLoop%3CO%3E">AbstractLoop<O></a><a href="#impl-AbstractMagma%3CO%3E">AbstractMagma<O></a><a href="#impl-AbstractMonoid%3CO%3E">AbstractMonoid<O></a><a href="#impl-AbstractQuasigroup%3CO%3E">AbstractQuasigroup<O></a><a href="#impl-AbstractSemigroup%3CO%3E">AbstractSemigroup<O></a><a href="#impl-Add%3CId%3CAdditive%3E%3E">Add<Id<Additive>></a><a href="#impl-AddAssign%3CId%3CAdditive%3E%3E">AddAssign<Id<Additive>></a><a href="#impl-AffineTransformation%3CE%3E">AffineTransformation<E></a><a href="#impl-Clone">Clone</a><a href="#impl-Copy">Copy</a><a href="#impl-Debug">Debug</a><a href="#impl-DirectIsometry%3CE%3E">DirectIsometry<E></a><a href="#impl-Display">Display</a><a href="#impl-Div%3CId%3CMultiplicative%3E%3E">Div<Id<Multiplicative>></a><a href="#impl-DivAssign%3CId%3CMultiplicative%3E%3E">DivAssign<Id<Multiplicative>></a><a href="#impl-Eq">Eq</a><a href="#impl-Identity%3CO%3E">Identity<O></a><a href="#impl-Isometry%3CE%3E">Isometry<E></a><a href="#impl-JoinSemilattice">JoinSemilattice</a><a href="#impl-Lattice">Lattice</a><a href="#impl-MeetSemilattice">MeetSemilattice</a><a href="#impl-Mul%3CId%3CMultiplicative%3E%3E">Mul<Id<Multiplicative>></a><a href="#impl-MulAssign%3CId%3CMultiplicative%3E%3E">MulAssign<Id<Multiplicative>></a><a href="#impl-One">One</a><a href="#impl-OrthogonalTransformation%3CE%3E">OrthogonalTransformation<E></a><a href="#impl-PartialEq%3CId%3CO%3E%3E">PartialEq<Id<O>></a><a href="#impl-PartialOrd%3CId%3CO%3E%3E">PartialOrd<Id<O>></a><a href="#impl-ProjectiveTransformation%3CE%3E">ProjectiveTransformation<E></a><a href="#impl-RelativeEq%3CId%3CO%3E%3E">RelativeEq<Id<O>></a><a href="#impl-Rotation%3CE%3E">Rotation<E></a><a href="#impl-Scaling%3CE%3E">Scaling<E></a><a href="#impl-Similarity%3CE%3E">Similarity<E></a><a href="#impl-SubsetOf%3CT%3E">SubsetOf<T></a><a href="#impl-Transformation%3CE%3E">Transformation<E></a><a href="#impl-Translation%3CE%3E">Translation<E></a><a href="#impl-TwoSidedInverse%3CO%3E">TwoSidedInverse<O></a><a href="#impl-UlpsEq%3CId%3CO%3E%3E">UlpsEq<Id<O>></a><a href="#impl-Zero">Zero</a></div><a class="sidebar-title" href="#synthetic-implementations">Auto Trait Implementations</a><div class="sidebar-links"><a href="#impl-RefUnwindSafe">RefUnwindSafe</a><a href="#impl-Send">Send</a><a href="#impl-Sync">Sync</a><a href="#impl-Unpin">Unpin</a><a href="#impl-UnwindSafe">UnwindSafe</a></div><a class="sidebar-title" href="#blanket-implementations">Blanket Implementations</a><div class="sidebar-links"><a href="#impl-AdditiveMagma">AdditiveMagma</a><a href="#impl-AdditiveMonoid">AdditiveMonoid</a><a href="#impl-AdditiveSemigroup">AdditiveSemigroup</a><a href="#impl-AffineTransformation%3CE%3E">AffineTransformation<E></a><a href="#impl-Any">Any</a><a href="#impl-Borrow%3CT%3E">Borrow<T></a><a href="#impl-BorrowMut%3CT%3E">BorrowMut<T></a><a href="#impl-ClosedAdd%3CRight%3E">ClosedAdd<Right></a><a href="#impl-ClosedDiv%3CRight%3E">ClosedDiv<Right></a><a href="#impl-ClosedMul%3CRight%3E">ClosedMul<Right></a><a href="#impl-From%3CT%3E">From<T></a><a href="#impl-Into%3CU%3E">Into<U></a><a href="#impl-MultiplicativeGroup">MultiplicativeGroup</a><a href="#impl-MultiplicativeGroupAbelian">MultiplicativeGroupAbelian</a><a href="#impl-MultiplicativeLoop">MultiplicativeLoop</a><a href="#impl-MultiplicativeMagma">MultiplicativeMagma</a><a href="#impl-MultiplicativeMonoid">MultiplicativeMonoid</a><a href="#impl-MultiplicativeQuasigroup">MultiplicativeQuasigroup</a><a href="#impl-MultiplicativeSemigroup">MultiplicativeSemigroup</a><a href="#impl-ProjectiveTransformation%3CE%3E">ProjectiveTransformation<E></a><a href="#impl-Same%3CT%3E">Same<T></a><a href="#impl-Scaling%3CE%3E">Scaling<E></a><a href="#impl-Similarity%3CE%3E">Similarity<E></a><a href="#impl-SupersetOf%3CSS%3E">SupersetOf<SS></a><a href="#impl-ToOwned">ToOwned</a><a href="#impl-ToString">ToString</a><a href="#impl-Transformation%3CE%3E">Transformation<E></a><a href="#impl-TryFrom%3CU%3E">TryFrom<U></a><a href="#impl-TryInto%3CU%3E">TryInto<U></a></div></div><p class='location'><a href='index.html'>nalgebra</a></p><script>window.sidebarCurrent = {name: 'Id', ty: 'struct', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><a id="settings-menu" href="../settings.html"><img src="../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>−</span>]</a></span><a class='srclink' href='../src/alga/general/identity.rs.html#69-71' title='goto source code'>[src]</a></span><span class='in-band'>Struct <a href='index.html'>nalgebra</a>::<wbr><a class="struct" href=''>Id</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust struct'><span class="docblock attributes top-attr">#[repr(C)]
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</span>pub struct Id<O = <a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span> { /* fields omitted */ }</pre></div><div class='docblock'><p>The universal identity element wrt. a given operator, usually noted <code>Id</code> with a
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context-dependent subscript.</p>
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<p>By default, it is the multiplicative identity element. It represents the degenerate set
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containing only the identity element of any group-like structure. It has no dimension known at
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compile-time. All its operations are no-ops.</p>
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</div><h2 id='methods' class='small-section-header'>Methods<a href='#methods' class='anchor'></a></h2><h3 id='impl' class='impl'><code class='in-band'>impl<O> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#73-79' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.new' class="method"><code id='new.v'>pub fn <a href='#method.new' class='fnname'>new</a>() -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O></code><a class='srclink' href='../src/alga/general/identity.rs.html#76-78' title='goto source code'>[src]</a></h4><div class='docblock'><p>Creates a new identity element.</p>
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</div></div><h2 id='implementations' class='small-section-header'>Trait Implementations<a href='#implementations' class='anchor'></a></h2><div id='implementations-list'><h3 id='impl-Transformation%3CE%3E' class='impl'><code class='in-band'>impl<E> <a class="trait" href="../alga/linear/transformation/trait.Transformation.html" title="trait alga::linear::transformation::Transformation">Transformation</a><E> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>, </span></code><a href='#impl-Transformation%3CE%3E' class='anchor'></a><a class='srclink' href='../src/alga/linear/id.rs.html#13-23' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.transform_point' class="method hidden"><code id='transform_point.v'>fn <a href='../alga/linear/transformation/trait.Transformation.html#tymethod.transform_point' class='fnname'>transform_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/id.rs.html#15-17' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this group's action on a point from the euclidean space.</p>
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</div><h4 id='method.transform_vector' class="method hidden"><code id='transform_vector.v'>fn <a href='../alga/linear/transformation/trait.Transformation.html#tymethod.transform_vector' class='fnname'>transform_vector</a>(<br> &self, <br> v: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/id.rs.html#20-22' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this group's action on a vector from the euclidean space. <a href="../alga/linear/transformation/trait.Transformation.html#tymethod.transform_vector">Read more</a></p>
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</div></div><h3 id='impl-Rotation%3CE%3E' class='impl'><code class='in-band'>impl<E> <a class="trait" href="../alga/linear/transformation/trait.Rotation.html" title="trait alga::linear::transformation::Rotation">Rotation</a><E> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>, </span></code><a href='#impl-Rotation%3CE%3E' class='anchor'></a><a class='srclink' href='../src/alga/linear/id.rs.html#102-125' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.powf' class="method hidden"><code id='powf.v'>fn <a href='../alga/linear/transformation/trait.Rotation.html#tymethod.powf' class='fnname'>powf</a>(&self, <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::vector::EuclideanSpace::RealField">RealField</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>></code><a class='srclink' href='../src/alga/linear/id.rs.html#104-106' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Raises this rotation to a power. If this is a simple rotation, the result must be equivalent to multiplying the rotation angle by <code>n</code>. <a href="../alga/linear/transformation/trait.Rotation.html#tymethod.powf">Read more</a></p>
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</div><h4 id='method.rotation_between' class="method hidden"><code id='rotation_between.v'>fn <a href='../alga/linear/transformation/trait.Rotation.html#tymethod.rotation_between' class='fnname'>rotation_between</a>(<br> a: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>, <br> b: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>></code><a class='srclink' href='../src/alga/linear/id.rs.html#109-115' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Computes a simple rotation that makes the angle between <code>a</code> and <code>b</code> equal to zero, i.e., <code>b.angle(a * delta_rotation(a, b)) = 0</code>. If <code>a</code> and <code>b</code> are collinear, the computed rotation may not be unique. Returns <code>None</code> if no such simple rotation exists in the subgroup represented by <code>Self</code>. <a href="../alga/linear/transformation/trait.Rotation.html#tymethod.rotation_between">Read more</a></p>
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</div><h4 id='method.scaled_rotation_between' class="method hidden"><code id='scaled_rotation_between.v'>fn <a href='../alga/linear/transformation/trait.Rotation.html#tymethod.scaled_rotation_between' class='fnname'>scaled_rotation_between</a>(<br> a: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>, <br> b: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>, <br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::vector::EuclideanSpace::RealField">RealField</a><br>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>></code><a class='srclink' href='../src/alga/linear/id.rs.html#118-124' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Computes the rotation between <code>a</code> and <code>b</code> and raises it to the power <code>n</code>. <a href="../alga/linear/transformation/trait.Rotation.html#tymethod.scaled_rotation_between">Read more</a></p>
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</div></div><h3 id='impl-AbstractMonoid%3CO%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/one_operator/trait.AbstractMonoid.html" title="trait alga::general::one_operator::AbstractMonoid">AbstractMonoid</a><O> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-AbstractMonoid%3CO%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#225' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.prop_operating_identity_element_is_noop_approx' class="method hidden"><code id='prop_operating_identity_element_is_noop_approx.v'>fn <a href='../alga/general/one_operator/trait.AbstractMonoid.html#method.prop_operating_identity_element_is_noop_approx' class='fnname'>prop_operating_identity_element_is_noop_approx</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">,)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="../approx/relative_eq/trait.RelativeEq.html" title="trait approx::relative_eq::RelativeEq">RelativeEq</a><Self>, </span></code><a class='srclink' href='../src/alga/general/one_operator.rs.html#242-249' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications. <a href="../alga/general/one_operator/trait.AbstractMonoid.html#method.prop_operating_identity_element_is_noop_approx">Read more</a></p>
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</div><h4 id='method.prop_operating_identity_element_is_noop' class="method hidden"><code id='prop_operating_identity_element_is_noop.v'>fn <a href='../alga/general/one_operator/trait.AbstractMonoid.html#method.prop_operating_identity_element_is_noop' class='fnname'>prop_operating_identity_element_is_noop</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">,)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.Eq.html" title="trait core::cmp::Eq">Eq</a>, </span></code><a class='srclink' href='../src/alga/general/one_operator.rs.html#253-259' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Checks whether operating with the identity element is a no-op for the given argument. <a href="../alga/general/one_operator/trait.AbstractMonoid.html#method.prop_operating_identity_element_is_noop">Read more</a></p>
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</div></div><h3 id='impl-Translation%3CE%3E' class='impl'><code class='in-band'>impl<E> <a class="trait" href="../alga/linear/transformation/trait.Translation.html" title="trait alga::linear::transformation::Translation">Translation</a><E> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>, </span></code><a href='#impl-Translation%3CE%3E' class='anchor'></a><a class='srclink' href='../src/alga/linear/id.rs.html#127-141' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.to_vector' class="method hidden"><code id='to_vector.v'>fn <a href='../alga/linear/transformation/trait.Translation.html#tymethod.to_vector' class='fnname'>to_vector</a>(&self) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/id.rs.html#129-131' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Converts this translation to a vector.</p>
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</div><h4 id='method.from_vector' class="method hidden"><code id='from_vector.v'>fn <a href='../alga/linear/transformation/trait.Translation.html#tymethod.from_vector' class='fnname'>from_vector</a>(<br> v: <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>></code><a class='srclink' href='../src/alga/linear/id.rs.html#134-140' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Attempts to convert a vector to this translation. Returns <code>None</code> if the translation represented by <code>v</code> is not part of the translation subgroup represented by <code>Self</code>. <a href="../alga/linear/transformation/trait.Translation.html#tymethod.from_vector">Read more</a></p>
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</div><h4 id='method.powf-1' class="method hidden"><code id='powf.v-1'>fn <a href='../alga/linear/transformation/trait.Translation.html#method.powf' class='fnname'>powf</a>(&self, n: <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::vector::EuclideanSpace::RealField">RealField</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#246-248' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Raises the translation to a power. The result must be equivalent to <code>self.to_superset() * n</code>. Returns <code>None</code> if the result is not representable by <code>Self</code>. <a href="../alga/linear/transformation/trait.Translation.html#method.powf">Read more</a></p>
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</div><h4 id='method.translation_between' class="method hidden"><code id='translation_between.v'>fn <a href='../alga/linear/transformation/trait.Translation.html#method.translation_between' class='fnname'>translation_between</a>(a: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E, b: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#252-254' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The translation needed to make <code>a</code> coincide with <code>b</code>, i.e., <code>b = a * translation_to(a, b)</code>.</p>
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</div></div><h3 id='impl-Display' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/core/fmt/trait.Display.html" title="trait core::fmt::Display">Display</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-Display' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#90-94' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.fmt' class="method hidden"><code id='fmt.v'>fn <a href='https://doc.rust-lang.org/nightly/core/fmt/trait.Display.html#tymethod.fmt' class='fnname'>fmt</a>(&self, f: &mut <a class="struct" href="https://doc.rust-lang.org/nightly/core/fmt/struct.Formatter.html" title="struct core::fmt::Formatter">Formatter</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/result/enum.Result.html" title="enum core::result::Result">Result</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.unit.html">()</a>, <a class="struct" href="https://doc.rust-lang.org/nightly/core/fmt/struct.Error.html" title="struct core::fmt::Error">Error</a>></code><a class='srclink' href='../src/alga/general/identity.rs.html#91-93' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Formats the value using the given formatter. <a href="https://doc.rust-lang.org/nightly/core/fmt/trait.Display.html#tymethod.fmt">Read more</a></p>
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</div></div><h3 id='impl-Scaling%3CE%3E' class='impl'><code class='in-band'>impl<E> <a class="trait" href="../alga/linear/transformation/trait.Scaling.html" title="trait alga::linear::transformation::Scaling">Scaling</a><E> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>, </span></code><a href='#impl-Scaling%3CE%3E' class='anchor'></a><a class='srclink' href='../src/alga/linear/id.rs.html#97' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.to_real' class="method hidden"><code id='to_real.v'>fn <a href='../alga/linear/transformation/trait.Scaling.html#method.to_real' class='fnname'>to_real</a>(&self) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::vector::EuclideanSpace::RealField">RealField</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#202-204' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Converts this scaling factor to a real. Same as <code>self.to_superset()</code>.</p>
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</div><h4 id='method.from_real' class="method hidden"><code id='from_real.v'>fn <a href='../alga/linear/transformation/trait.Scaling.html#method.from_real' class='fnname'>from_real</a>(r: <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::vector::EuclideanSpace::RealField">RealField</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#209-211' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Attempts to convert a real to an element of this scaling subgroup. Same as <code>Self::from_superset()</code>. Returns <code>None</code> if no such scaling is possible for this subgroup. <a href="../alga/linear/transformation/trait.Scaling.html#method.from_real">Read more</a></p>
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</div><h4 id='method.powf-2' class="method hidden"><code id='powf.v-2'>fn <a href='../alga/linear/transformation/trait.Scaling.html#method.powf' class='fnname'>powf</a>(&self, n: <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::vector::EuclideanSpace::RealField">RealField</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#216-218' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Raises the scaling to a power. The result must be equivalent to <code>self.to_superset().powf(n)</code>. Returns <code>None</code> if the result is not representable by <code>Self</code>. <a href="../alga/linear/transformation/trait.Scaling.html#method.powf">Read more</a></p>
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</div><h4 id='method.scale_between' class="method hidden"><code id='scale_between.v'>fn <a href='../alga/linear/transformation/trait.Scaling.html#method.scale_between' class='fnname'>scale_between</a>(<br> a: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>, <br> b: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#223-225' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The scaling required to make <code>a</code> have the same norm as <code>b</code>, i.e., <code>|b| = |a| * norm_ratio(a, b)</code>. <a href="../alga/linear/transformation/trait.Scaling.html#method.scale_between">Read more</a></p>
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</div></div><h3 id='impl-Isometry%3CE%3E' class='impl'><code class='in-band'>impl<E> <a class="trait" href="../alga/linear/transformation/trait.Isometry.html" title="trait alga::linear::transformation::Isometry">Isometry</a><E> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>, </span></code><a href='#impl-Isometry%3CE%3E' class='anchor'></a><a class='srclink' href='../src/alga/linear/id.rs.html#98' title='goto source code'>[src]</a></h3><div class='impl-items'></div><h3 id='impl-TwoSidedInverse%3CO%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/operator/trait.TwoSidedInverse.html" title="trait alga::general::operator::TwoSidedInverse">TwoSidedInverse</a><O> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-TwoSidedInverse%3CO%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#211-221' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.two_sided_inverse' class="method hidden"><code id='two_sided_inverse.v'>fn <a href='../alga/general/operator/trait.TwoSidedInverse.html#tymethod.two_sided_inverse' class='fnname'>two_sided_inverse</a>(&self) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O></code><a class='srclink' href='../src/alga/general/identity.rs.html#213-215' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns the two_sided_inverse of <code>self</code>, relative to the operator <code>O</code>. <a href="../alga/general/operator/trait.TwoSidedInverse.html#tymethod.two_sided_inverse">Read more</a></p>
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</div><h4 id='method.two_sided_inverse_mut' class="method hidden"><code id='two_sided_inverse_mut.v'>fn <a href='../alga/general/operator/trait.TwoSidedInverse.html#method.two_sided_inverse_mut' class='fnname'>two_sided_inverse_mut</a>(&mut self)</code><a class='srclink' href='../src/alga/general/identity.rs.html#218-220' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>In-place inversion of <code>self</code>, relative to the operator <code>O</code>. <a href="../alga/general/operator/trait.TwoSidedInverse.html#method.two_sided_inverse_mut">Read more</a></p>
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</div></div><h3 id='impl-Add%3CId%3CAdditive%3E%3E' class='impl'><code class='in-band'>impl <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Add.html" title="trait core::ops::arith::Add">Add</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>>> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>></code><a href='#impl-Add%3CId%3CAdditive%3E%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#190-196' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Output' class="type"><code id='Output.t'>type <a href='https://doc.rust-lang.org/nightly/core/ops/arith/trait.Add.html#associatedtype.Output' class="type">Output</a> = <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>></code></h4><div class='docblock'><p>The resulting type after applying the <code>+</code> operator.</p>
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</div><h4 id='method.add' class="method hidden"><code id='add.v'>fn <a href='https://doc.rust-lang.org/nightly/core/ops/arith/trait.Add.html#tymethod.add' class='fnname'>add</a>(self, <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>></code><a class='srclink' href='../src/alga/general/identity.rs.html#193-195' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the <code>+</code> operation.</p>
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</div></div><h3 id='impl-Zero' class='impl'><code class='in-band'>impl <a class="trait" href="../num_traits/identities/trait.Zero.html" title="trait num_traits::identities::Zero">Zero</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>></code><a href='#impl-Zero' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#237-247' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.zero' class="method hidden"><code id='zero.v'>fn <a href='../num_traits/identities/trait.Zero.html#tymethod.zero' class='fnname'>zero</a>() -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>></code><a class='srclink' href='../src/alga/general/identity.rs.html#239-241' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns the additive identity element of <code>Self</code>, <code>0</code>. # Purity <a href="../num_traits/identities/trait.Zero.html#tymethod.zero">Read more</a></p>
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</div><h4 id='method.is_zero' class="method hidden"><code id='is_zero.v'>fn <a href='../num_traits/identities/trait.Zero.html#tymethod.is_zero' class='fnname'>is_zero</a>(&self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../src/alga/general/identity.rs.html#244-246' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns <code>true</code> if <code>self</code> is equal to the additive identity.</p>
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</div><h4 id='method.set_zero' class="method hidden"><code id='set_zero.v'>fn <a href='../num_traits/identities/trait.Zero.html#method.set_zero' class='fnname'>set_zero</a>(&mut self)</code><a class='srclink' href='../src/num_traits/identities.rs.html#23-25' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Sets <code>self</code> to the additive identity element of <code>Self</code>, <code>0</code>.</p>
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</div></div><h3 id='impl-Debug' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html" title="trait core::fmt::Debug">Debug</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html" title="trait core::fmt::Debug">Debug</a>, </span></code><a href='#impl-Debug' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#68' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.fmt-1' class="method hidden"><code id='fmt.v-1'>fn <a href='https://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html#tymethod.fmt' class='fnname'>fmt</a>(&self, f: &mut <a class="struct" href="https://doc.rust-lang.org/nightly/core/fmt/struct.Formatter.html" title="struct core::fmt::Formatter">Formatter</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/result/enum.Result.html" title="enum core::result::Result">Result</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.unit.html">()</a>, <a class="struct" href="https://doc.rust-lang.org/nightly/core/fmt/struct.Error.html" title="struct core::fmt::Error">Error</a>></code><a class='srclink' href='../src/alga/general/identity.rs.html#68' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Formats the value using the given formatter. <a href="https://doc.rust-lang.org/nightly/core/fmt/trait.Debug.html#tymethod.fmt">Read more</a></p>
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</div></div><h3 id='impl-AbstractMagma%3CO%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/one_operator/trait.AbstractMagma.html" title="trait alga::general::one_operator::AbstractMagma">AbstractMagma</a><O> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-AbstractMagma%3CO%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#204-209' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.operate' class="method hidden"><code id='operate.v'>fn <a href='../alga/general/one_operator/trait.AbstractMagma.html#tymethod.operate' class='fnname'>operate</a>(&self, &<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O></code><a class='srclink' href='../src/alga/general/identity.rs.html#206-208' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs an operation.</p>
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</div><h4 id='method.op' class="method hidden"><code id='op.v'>fn <a href='../alga/general/one_operator/trait.AbstractMagma.html#method.op' class='fnname'>op</a>(&self, O, lhs: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self) -> Self</code><a class='srclink' href='../src/alga/general/one_operator.rs.html#25-27' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs specific operation.</p>
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</div></div><h3 id='impl-MeetSemilattice' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/lattice/trait.MeetSemilattice.html" title="trait alga::general::lattice::MeetSemilattice">MeetSemilattice</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-MeetSemilattice' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#271-276' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.meet' class="method hidden"><code id='meet.v'>fn <a href='../alga/general/lattice/trait.MeetSemilattice.html#tymethod.meet' class='fnname'>meet</a>(&self, &<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O></code><a class='srclink' href='../src/alga/general/identity.rs.html#273-275' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns the meet (aka. infimum) of two values.</p>
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</div></div><h3 id='impl-AddAssign%3CId%3CAdditive%3E%3E' class='impl'><code class='in-band'>impl <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.AddAssign.html" title="trait core::ops::arith::AddAssign">AddAssign</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>>> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>></code><a href='#impl-AddAssign%3CId%3CAdditive%3E%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#198-202' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.add_assign' class="method hidden"><code id='add_assign.v'>fn <a href='https://doc.rust-lang.org/nightly/core/ops/arith/trait.AddAssign.html#tymethod.add_assign' class='fnname'>add_assign</a>(&mut self, <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>>)</code><a class='srclink' href='../src/alga/general/identity.rs.html#199-201' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the <code>+=</code> operation.</p>
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</div></div><h3 id='impl-AffineTransformation%3CE%3E' class='impl'><code class='in-band'>impl<E> <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>, </span></code><a href='#impl-AffineTransformation%3CE%3E' class='anchor'></a><a class='srclink' href='../src/alga/linear/id.rs.html#37-76' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Rotation' class="type"><code id='Rotation.t'>type <a href='../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Rotation' class="type">Rotation</a> = <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code></h4><div class='docblock'><p>Type of the first rotation to be applied.</p>
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</div><h4 id='associatedtype.NonUniformScaling' class="type"><code id='NonUniformScaling.t'>type <a href='../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.NonUniformScaling' class="type">NonUniformScaling</a> = <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code></h4><div class='docblock'><p>Type of the non-uniform scaling to be applied.</p>
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</div><h4 id='associatedtype.Translation' class="type"><code id='Translation.t'>type <a href='../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Translation' class="type">Translation</a> = <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code></h4><div class='docblock'><p>The type of the pure translation part of this affine transformation.</p>
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</div><h4 id='method.decompose' class="method hidden"><code id='decompose.v'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.decompose' class='fnname'>decompose</a>(<br> &self<br>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a><a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>, <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>, <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>, <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a></code><a class='srclink' href='../src/alga/linear/id.rs.html#43-45' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation. <a href="../alga/linear/transformation/trait.AffineTransformation.html#tymethod.decompose">Read more</a></p>
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</div><h4 id='method.append_translation' class="method hidden"><code id='append_translation.v'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.append_translation' class='fnname'>append_translation</a>(<br> &self, <br> &<<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::transformation::AffineTransformation::Translation">Translation</a><br>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a class='srclink' href='../src/alga/linear/id.rs.html#48-50' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Appends a translation to this similarity.</p>
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</div><h4 id='method.prepend_translation' class="method hidden"><code id='prepend_translation.v'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.prepend_translation' class='fnname'>prepend_translation</a>(<br> &self, <br> &<<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::transformation::AffineTransformation::Translation">Translation</a><br>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a class='srclink' href='../src/alga/linear/id.rs.html#53-55' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Prepends a translation to this similarity.</p>
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</div><h4 id='method.append_rotation' class="method hidden"><code id='append_rotation.v'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.append_rotation' class='fnname'>append_rotation</a>(<br> &self, <br> &<<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::transformation::AffineTransformation::Rotation">Rotation</a><br>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a class='srclink' href='../src/alga/linear/id.rs.html#58-60' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Appends a rotation to this similarity.</p>
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</div><h4 id='method.prepend_rotation' class="method hidden"><code id='prepend_rotation.v'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.prepend_rotation' class='fnname'>prepend_rotation</a>(<br> &self, <br> &<<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::transformation::AffineTransformation::Rotation">Rotation</a><br>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a class='srclink' href='../src/alga/linear/id.rs.html#63-65' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Prepends a rotation to this similarity.</p>
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</div><h4 id='method.append_scaling' class="method hidden"><code id='append_scaling.v'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.append_scaling' class='fnname'>append_scaling</a>(<br> &self, <br> &<<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.NonUniformScaling" title="type alga::linear::transformation::AffineTransformation::NonUniformScaling">NonUniformScaling</a><br>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a class='srclink' href='../src/alga/linear/id.rs.html#68-70' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Appends a scaling factor to this similarity.</p>
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</div><h4 id='method.prepend_scaling' class="method hidden"><code id='prepend_scaling.v'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.prepend_scaling' class='fnname'>prepend_scaling</a>(<br> &self, <br> &<<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.NonUniformScaling" title="type alga::linear::transformation::AffineTransformation::NonUniformScaling">NonUniformScaling</a><br>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a class='srclink' href='../src/alga/linear/id.rs.html#73-75' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Prepends a scaling factor to this similarity.</p>
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</div><h4 id='method.append_rotation_wrt_point' class="method hidden"><code id='append_rotation_wrt_point.v'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#method.append_rotation_wrt_point' class='fnname'>append_rotation_wrt_point</a>(&self, r: &Self::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::transformation::AffineTransformation::Rotation">Rotation</a>, p: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#84-95' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Appends to this similarity a rotation centered at the point <code>p</code>, i.e., this point is left invariant. <a href="../alga/linear/transformation/trait.AffineTransformation.html#method.append_rotation_wrt_point">Read more</a></p>
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</div></div><h3 id='impl-SubsetOf%3CT%3E' class='impl'><code class='in-band'>impl<O, T> <a class="trait" href="../alga/general/subset/trait.SubsetOf.html" title="trait alga::general::subset::SubsetOf">SubsetOf</a><T> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>,<br> T: <a class="trait" href="../alga/general/identity/trait.Identity.html" title="trait alga::general::identity::Identity">Identity</a><O> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html" title="trait core::cmp::PartialEq">PartialEq</a><T>, </span></code><a href='#impl-SubsetOf%3CT%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#254-269' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.to_superset' class="method hidden"><code id='to_superset.v'>fn <a href='../alga/general/subset/trait.SubsetOf.html#tymethod.to_superset' class='fnname'>to_superset</a>(&self) -> T</code><a class='srclink' href='../src/alga/general/identity.rs.html#256-258' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The inclusion map: converts <code>self</code> to the equivalent element of its superset.</p>
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</div><h4 id='method.is_in_subset' class="method hidden"><code id='is_in_subset.v'>fn <a href='../alga/general/subset/trait.SubsetOf.html#tymethod.is_in_subset' class='fnname'>is_in_subset</a>(t: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>T) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../src/alga/general/identity.rs.html#261-263' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Checks if <code>element</code> is actually part of the subset <code>Self</code> (and can be converted to it).</p>
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</div><h4 id='method.from_superset_unchecked' class="method hidden"><code id='from_superset_unchecked.v'>unsafe fn <a href='../alga/general/subset/trait.SubsetOf.html#tymethod.from_superset_unchecked' class='fnname'>from_superset_unchecked</a>(<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>T) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O></code><a class='srclink' href='../src/alga/general/identity.rs.html#266-268' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Use with care! Same as <code>self.to_superset</code> but without any property checks. Always succeeds.</p>
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</div><h4 id='method.from_superset' class="method hidden"><code id='from_superset.v'>fn <a href='../alga/general/subset/trait.SubsetOf.html#method.from_superset' class='fnname'>from_superset</a>(element: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>T) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self></code><a class='srclink' href='../src/alga/general/subset.rs.html#32-38' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The inverse inclusion map: attempts to construct <code>self</code> from the equivalent element of its superset. <a href="../alga/general/subset/trait.SubsetOf.html#method.from_superset">Read more</a></p>
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</div></div><h3 id='impl-AbstractGroupAbelian%3CO%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/one_operator/trait.AbstractGroupAbelian.html" title="trait alga::general::one_operator::AbstractGroupAbelian">AbstractGroupAbelian</a><O> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-AbstractGroupAbelian%3CO%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#228' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.prop_is_commutative_approx' class="method hidden"><code id='prop_is_commutative_approx.v'>fn <a href='../alga/general/one_operator/trait.AbstractGroupAbelian.html#method.prop_is_commutative_approx' class='fnname'>prop_is_commutative_approx</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self, Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="../approx/relative_eq/trait.RelativeEq.html" title="trait approx::relative_eq::RelativeEq">RelativeEq</a><Self>, </span></code><a class='srclink' href='../src/alga/general/one_operator.rs.html#351-357' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns <code>true</code> if the operator is commutative for the given argument tuple. Approximate equality is used for verifications. <a href="../alga/general/one_operator/trait.AbstractGroupAbelian.html#method.prop_is_commutative_approx">Read more</a></p>
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</div><h4 id='method.prop_is_commutative' class="method hidden"><code id='prop_is_commutative.v'>fn <a href='../alga/general/one_operator/trait.AbstractGroupAbelian.html#method.prop_is_commutative' class='fnname'>prop_is_commutative</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self, Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.Eq.html" title="trait core::cmp::Eq">Eq</a>, </span></code><a class='srclink' href='../src/alga/general/one_operator.rs.html#360-366' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns <code>true</code> if the operator is commutative for the given argument tuple.</p>
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</div></div><h3 id='impl-AbsDiffEq%3CId%3CO%3E%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../approx/abs_diff_eq/trait.AbsDiffEq.html" title="trait approx::abs_diff_eq::AbsDiffEq">AbsDiffEq</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-AbsDiffEq%3CId%3CO%3E%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#119-131' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Epsilon' class="type"><code id='Epsilon.t'>type <a href='../approx/abs_diff_eq/trait.AbsDiffEq.html#associatedtype.Epsilon' class="type">Epsilon</a> = <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O></code></h4><div class='docblock'><p>Used for specifying relative comparisons.</p>
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</div><h4 id='method.default_epsilon' class="method hidden"><code id='default_epsilon.v'>fn <a href='../approx/abs_diff_eq/trait.AbsDiffEq.html#tymethod.default_epsilon' class='fnname'>default_epsilon</a>() -> <<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> as <a class="trait" href="../approx/abs_diff_eq/trait.AbsDiffEq.html" title="trait approx::abs_diff_eq::AbsDiffEq">AbsDiffEq</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>>>::<a class="type" href="../approx/abs_diff_eq/trait.AbsDiffEq.html#associatedtype.Epsilon" title="type approx::abs_diff_eq::AbsDiffEq::Epsilon">Epsilon</a></code><a class='srclink' href='../src/alga/general/identity.rs.html#123-125' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The default tolerance to use when testing values that are close together. <a href="../approx/abs_diff_eq/trait.AbsDiffEq.html#tymethod.default_epsilon">Read more</a></p>
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</div><h4 id='method.abs_diff_eq' class="method hidden"><code id='abs_diff_eq.v'>fn <a href='../approx/abs_diff_eq/trait.AbsDiffEq.html#tymethod.abs_diff_eq' class='fnname'>abs_diff_eq</a>(&self, &<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>, <<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> as <a class="trait" href="../approx/abs_diff_eq/trait.AbsDiffEq.html" title="trait approx::abs_diff_eq::AbsDiffEq">AbsDiffEq</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>>>::<a class="type" href="../approx/abs_diff_eq/trait.AbsDiffEq.html#associatedtype.Epsilon" title="type approx::abs_diff_eq::AbsDiffEq::Epsilon">Epsilon</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../src/alga/general/identity.rs.html#128-130' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>A test for equality that uses the absolute difference to compute the approximate equality of two numbers. <a href="../approx/abs_diff_eq/trait.AbsDiffEq.html#tymethod.abs_diff_eq">Read more</a></p>
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</div><h4 id='method.abs_diff_ne' class="method hidden"><code id='abs_diff_ne.v'>fn <a href='../approx/abs_diff_eq/trait.AbsDiffEq.html#method.abs_diff_ne' class='fnname'>abs_diff_ne</a>(&self, other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Rhs, epsilon: Self::<a class="type" href="../approx/abs_diff_eq/trait.AbsDiffEq.html#associatedtype.Epsilon" title="type approx::abs_diff_eq::AbsDiffEq::Epsilon">Epsilon</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../src/approx/abs_diff_eq.rs.html#26-28' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The inverse of <code>ApproxEq::abs_diff_eq</code>.</p>
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</div></div><h3 id='impl-RelativeEq%3CId%3CO%3E%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../approx/relative_eq/trait.RelativeEq.html" title="trait approx::relative_eq::RelativeEq">RelativeEq</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-RelativeEq%3CId%3CO%3E%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#133-143' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.default_max_relative' class="method hidden"><code id='default_max_relative.v'>fn <a href='../approx/relative_eq/trait.RelativeEq.html#tymethod.default_max_relative' class='fnname'>default_max_relative</a>() -> <<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> as <a class="trait" href="../approx/abs_diff_eq/trait.AbsDiffEq.html" title="trait approx::abs_diff_eq::AbsDiffEq">AbsDiffEq</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>>>::<a class="type" href="../approx/abs_diff_eq/trait.AbsDiffEq.html#associatedtype.Epsilon" title="type approx::abs_diff_eq::AbsDiffEq::Epsilon">Epsilon</a></code><a class='srclink' href='../src/alga/general/identity.rs.html#135-137' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The default relative tolerance for testing values that are far-apart. <a href="../approx/relative_eq/trait.RelativeEq.html#tymethod.default_max_relative">Read more</a></p>
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</div><h4 id='method.relative_eq' class="method hidden"><code id='relative_eq.v'>fn <a href='../approx/relative_eq/trait.RelativeEq.html#tymethod.relative_eq' class='fnname'>relative_eq</a>(<br> &self, <br> &<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>, <br> <<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> as <a class="trait" href="../approx/abs_diff_eq/trait.AbsDiffEq.html" title="trait approx::abs_diff_eq::AbsDiffEq">AbsDiffEq</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>>>::<a class="type" href="../approx/abs_diff_eq/trait.AbsDiffEq.html#associatedtype.Epsilon" title="type approx::abs_diff_eq::AbsDiffEq::Epsilon">Epsilon</a>, <br> <<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> as <a class="trait" href="../approx/abs_diff_eq/trait.AbsDiffEq.html" title="trait approx::abs_diff_eq::AbsDiffEq">AbsDiffEq</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>>>::<a class="type" href="../approx/abs_diff_eq/trait.AbsDiffEq.html#associatedtype.Epsilon" title="type approx::abs_diff_eq::AbsDiffEq::Epsilon">Epsilon</a><br>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../src/alga/general/identity.rs.html#140-142' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>A test for equality that uses a relative comparison if the values are far apart.</p>
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</div><h4 id='method.relative_ne' class="method hidden"><code id='relative_ne.v'>fn <a href='../approx/relative_eq/trait.RelativeEq.html#method.relative_ne' class='fnname'>relative_ne</a>(<br> &self, <br> other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Rhs, <br> epsilon: Self::<a class="type" href="../approx/abs_diff_eq/trait.AbsDiffEq.html#associatedtype.Epsilon" title="type approx::abs_diff_eq::AbsDiffEq::Epsilon">Epsilon</a>, <br> max_relative: Self::<a class="type" href="../approx/abs_diff_eq/trait.AbsDiffEq.html#associatedtype.Epsilon" title="type approx::abs_diff_eq::AbsDiffEq::Epsilon">Epsilon</a><br>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../src/approx/relative_eq.rs.html#29-36' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The inverse of <code>ApproxEq::relative_eq</code>.</p>
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</div></div><h3 id='impl-Clone' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html" title="trait core::clone::Clone">Clone</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-Clone' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#83-88' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.clone' class="method hidden"><code id='clone.v'>fn <a href='https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html#tymethod.clone' class='fnname'>clone</a>(&self) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O></code><a class='srclink' href='../src/alga/general/identity.rs.html#85-87' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns a copy of the value. <a href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html#tymethod.clone">Read more</a></p>
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</div><h4 id='method.clone_from' class="method hidden"><code id='clone_from.v'>fn <a href='https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html#method.clone_from' class='fnname'>clone_from</a>(&mut self, source: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self)</code><span class='since' title='Stable since Rust version 1.0.0'>1.0.0</span><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/clone.rs.html#131-133' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs copy-assignment from <code>source</code>. <a href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html#method.clone_from">Read more</a></p>
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</div></div><h3 id='impl-DirectIsometry%3CE%3E' class='impl'><code class='in-band'>impl<E> <a class="trait" href="../alga/linear/transformation/trait.DirectIsometry.html" title="trait alga::linear::transformation::DirectIsometry">DirectIsometry</a><E> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>, </span></code><a href='#impl-DirectIsometry%3CE%3E' class='anchor'></a><a class='srclink' href='../src/alga/linear/id.rs.html#99' title='goto source code'>[src]</a></h3><div class='impl-items'></div><h3 id='impl-Copy' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Copy.html" title="trait core::marker::Copy">Copy</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-Copy' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#81' title='goto source code'>[src]</a></h3><div class='impl-items'></div><h3 id='impl-Similarity%3CE%3E' class='impl'><code class='in-band'>impl<E> <a class="trait" href="../alga/linear/transformation/trait.Similarity.html" title="trait alga::linear::transformation::Similarity">Similarity</a><E> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>, </span></code><a href='#impl-Similarity%3CE%3E' class='anchor'></a><a class='srclink' href='../src/alga/linear/id.rs.html#78-95' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scaling' class="type"><code id='Scaling.t'>type <a href='../alga/linear/transformation/trait.Similarity.html#associatedtype.Scaling' class="type">Scaling</a> = <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code></h4><div class='docblock'><p>The type of the pure (uniform) scaling part of this similarity transformation.</p>
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</div><h4 id='method.translation' class="method hidden"><code id='translation.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#tymethod.translation' class='fnname'>translation</a>(<br> &self<br>) -> <<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::transformation::AffineTransformation::Translation">Translation</a></code><a class='srclink' href='../src/alga/linear/id.rs.html#82-84' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The pure translational component of this similarity transformation.</p>
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</div><h4 id='method.rotation' class="method hidden"><code id='rotation.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#tymethod.rotation' class='fnname'>rotation</a>(&self) -> <<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::transformation::AffineTransformation::Rotation">Rotation</a></code><a class='srclink' href='../src/alga/linear/id.rs.html#87-89' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The pure rotational component of this similarity transformation.</p>
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</div><h4 id='method.scaling' class="method hidden"><code id='scaling.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#tymethod.scaling' class='fnname'>scaling</a>(&self) -> <<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> as <a class="trait" href="../alga/linear/transformation/trait.Similarity.html" title="trait alga::linear::transformation::Similarity">Similarity</a><E>>::<a class="type" href="../alga/linear/transformation/trait.Similarity.html#associatedtype.Scaling" title="type alga::linear::transformation::Similarity::Scaling">Scaling</a></code><a class='srclink' href='../src/alga/linear/id.rs.html#92-94' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The pure scaling component of this similarity transformation.</p>
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</div><h4 id='method.translate_point' class="method hidden"><code id='translate_point.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.translate_point' class='fnname'>translate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#124-126' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation's pure translational part to a point.</p>
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</div><h4 id='method.rotate_point' class="method hidden"><code id='rotate_point.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.rotate_point' class='fnname'>rotate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#130-132' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation's pure rotational part to a point.</p>
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</div><h4 id='method.scale_point' class="method hidden"><code id='scale_point.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.scale_point' class='fnname'>scale_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#136-138' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation's pure scaling part to a point.</p>
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</div><h4 id='method.rotate_vector' class="method hidden"><code id='rotate_vector.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.rotate_vector' class='fnname'>rotate_vector</a>(<br> &self, <br> pt: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#142-144' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation's pure rotational part to a vector.</p>
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</div><h4 id='method.scale_vector' class="method hidden"><code id='scale_vector.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.scale_vector' class='fnname'>scale_vector</a>(<br> &self, <br> pt: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#148-150' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation's pure scaling part to a vector.</p>
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</div><h4 id='method.inverse_translate_point' class="method hidden"><code id='inverse_translate_point.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.inverse_translate_point' class='fnname'>inverse_translate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#157-159' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation inverse's pure translational part to a point.</p>
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</div><h4 id='method.inverse_rotate_point' class="method hidden"><code id='inverse_rotate_point.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.inverse_rotate_point' class='fnname'>inverse_rotate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#163-165' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation inverse's pure rotational part to a point.</p>
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</div><h4 id='method.inverse_scale_point' class="method hidden"><code id='inverse_scale_point.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.inverse_scale_point' class='fnname'>inverse_scale_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#169-171' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation inverse's pure scaling part to a point.</p>
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</div><h4 id='method.inverse_rotate_vector' class="method hidden"><code id='inverse_rotate_vector.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.inverse_rotate_vector' class='fnname'>inverse_rotate_vector</a>(<br> &self, <br> pt: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#175-177' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation inverse's pure rotational part to a vector.</p>
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</div><h4 id='method.inverse_scale_vector' class="method hidden"><code id='inverse_scale_vector.v'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.inverse_scale_vector' class='fnname'>inverse_scale_vector</a>(<br> &self, <br> pt: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#181-183' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation inverse's pure scaling part to a vector.</p>
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</div></div><h3 id='impl-One' class='impl'><code class='in-band'>impl <a class="trait" href="../num_traits/identities/trait.One.html" title="trait num_traits::identities::One">One</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a href='#impl-One' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#230-235' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.one' class="method hidden"><code id='one.v'>fn <a href='../num_traits/identities/trait.One.html#tymethod.one' class='fnname'>one</a>() -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a class='srclink' href='../src/alga/general/identity.rs.html#232-234' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns the multiplicative identity element of <code>Self</code>, <code>1</code>. <a href="../num_traits/identities/trait.One.html#tymethod.one">Read more</a></p>
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</div><h4 id='method.set_one' class="method hidden"><code id='set_one.v'>fn <a href='../num_traits/identities/trait.One.html#method.set_one' class='fnname'>set_one</a>(&mut self)</code><a class='srclink' href='../src/num_traits/identities.rs.html#103-105' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Sets <code>self</code> to the multiplicative identity element of <code>Self</code>, <code>1</code>.</p>
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</div><h4 id='method.is_one' class="method hidden"><code id='is_one.v'>fn <a href='../num_traits/identities/trait.One.html#method.is_one' class='fnname'>is_one</a>(&self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html" title="trait core::cmp::PartialEq">PartialEq</a><Self>, </span></code><a class='srclink' href='../src/num_traits/identities.rs.html#113-118' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns <code>true</code> if <code>self</code> is equal to the multiplicative identity. <a href="../num_traits/identities/trait.One.html#method.is_one">Read more</a></p>
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</div></div><h3 id='impl-Eq' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.Eq.html" title="trait core::cmp::Eq">Eq</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-Eq' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#103' title='goto source code'>[src]</a></h3><div class='impl-items'></div><h3 id='impl-AbstractLoop%3CO%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/one_operator/trait.AbstractLoop.html" title="trait alga::general::one_operator::AbstractLoop">AbstractLoop</a><O> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-AbstractLoop%3CO%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#226' title='goto source code'>[src]</a></h3><div class='impl-items'></div><h3 id='impl-Identity%3CO%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/identity/trait.Identity.html" title="trait alga::general::identity::Identity">Identity</a><O> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-Identity%3CO%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#112-117' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.identity' class="method hidden"><code id='identity.v'>fn <a href='../alga/general/identity/trait.Identity.html#tymethod.identity' class='fnname'>identity</a>() -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O></code><a class='srclink' href='../src/alga/general/identity.rs.html#114-116' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The identity element.</p>
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</div><h4 id='method.id' class="method hidden"><code id='id.v'>fn <a href='../alga/general/identity/trait.Identity.html#method.id' class='fnname'>id</a>(O) -> Self</code><a class='srclink' href='../src/alga/general/identity.rs.html#27-32' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Specific identity.</p>
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</div></div><h3 id='impl-JoinSemilattice' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/lattice/trait.JoinSemilattice.html" title="trait alga::general::lattice::JoinSemilattice">JoinSemilattice</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-JoinSemilattice' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#278-283' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.join' class="method hidden"><code id='join.v'>fn <a href='../alga/general/lattice/trait.JoinSemilattice.html#tymethod.join' class='fnname'>join</a>(&self, &<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O></code><a class='srclink' href='../src/alga/general/identity.rs.html#280-282' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns the join (aka. supremum) of two values.</p>
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</div></div><h3 id='impl-ProjectiveTransformation%3CE%3E' class='impl'><code class='in-band'>impl<E> <a class="trait" href="../alga/linear/transformation/trait.ProjectiveTransformation.html" title="trait alga::linear::transformation::ProjectiveTransformation">ProjectiveTransformation</a><E> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>, </span></code><a href='#impl-ProjectiveTransformation%3CE%3E' class='anchor'></a><a class='srclink' href='../src/alga/linear/id.rs.html#25-35' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.inverse_transform_point' class="method hidden"><code id='inverse_transform_point.v'>fn <a href='../alga/linear/transformation/trait.ProjectiveTransformation.html#tymethod.inverse_transform_point' class='fnname'>inverse_transform_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/id.rs.html#27-29' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this group's two_sided_inverse action on a point from the euclidean space.</p>
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</div><h4 id='method.inverse_transform_vector' class="method hidden"><code id='inverse_transform_vector.v'>fn <a href='../alga/linear/transformation/trait.ProjectiveTransformation.html#tymethod.inverse_transform_vector' class='fnname'>inverse_transform_vector</a>(<br> &self, <br> v: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/id.rs.html#32-34' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this group's two_sided_inverse action on a vector from the euclidean space. <a href="../alga/linear/transformation/trait.ProjectiveTransformation.html#tymethod.inverse_transform_vector">Read more</a></p>
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</div></div><h3 id='impl-PartialEq%3CId%3CO%3E%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html" title="trait core::cmp::PartialEq">PartialEq</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-PartialEq%3CId%3CO%3E%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#96-101' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.eq' class="method hidden"><code id='eq.v'>fn <a href='https://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html#tymethod.eq' class='fnname'>eq</a>(&self, &<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../src/alga/general/identity.rs.html#98-100' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>This method tests for <code>self</code> and <code>other</code> values to be equal, and is used by <code>==</code>. <a href="https://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html#tymethod.eq">Read more</a></p>
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</div><h4 id='method.ne' class="method hidden"><code id='ne.v'><span class="docblock attributes">#[must_use]
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</span>fn <a href='https://doc.rust-lang.org/nightly/core/cmp/trait.PartialEq.html#method.ne' class='fnname'>ne</a>(&self, other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Rhs) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><span class='since' title='Stable since Rust version 1.0.0'>1.0.0</span><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/cmp.rs.html#208' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>This method tests for <code>!=</code>.</p>
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</div></div><h3 id='impl-AbstractSemigroup%3CO%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/one_operator/trait.AbstractSemigroup.html" title="trait alga::general::one_operator::AbstractSemigroup">AbstractSemigroup</a><O> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-AbstractSemigroup%3CO%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#223' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.prop_is_associative_approx' class="method hidden"><code id='prop_is_associative_approx.v'>fn <a href='../alga/general/one_operator/trait.AbstractSemigroup.html#method.prop_is_associative_approx' class='fnname'>prop_is_associative_approx</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self, Self, Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="../approx/relative_eq/trait.RelativeEq.html" title="trait approx::relative_eq::RelativeEq">RelativeEq</a><Self>, </span></code><a class='srclink' href='../src/alga/general/one_operator.rs.html#128-134' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns <code>true</code> if associativity holds for the given arguments. Approximate equality is used for verifications. <a href="../alga/general/one_operator/trait.AbstractSemigroup.html#method.prop_is_associative_approx">Read more</a></p>
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</div><h4 id='method.prop_is_associative' class="method hidden"><code id='prop_is_associative.v'>fn <a href='../alga/general/one_operator/trait.AbstractSemigroup.html#method.prop_is_associative' class='fnname'>prop_is_associative</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self, Self, Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.Eq.html" title="trait core::cmp::Eq">Eq</a>, </span></code><a class='srclink' href='../src/alga/general/one_operator.rs.html#137-143' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns <code>true</code> if associativity holds for the given arguments.</p>
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</div></div><h3 id='impl-OrthogonalTransformation%3CE%3E' class='impl'><code class='in-band'>impl<E> <a class="trait" href="../alga/linear/transformation/trait.OrthogonalTransformation.html" title="trait alga::linear::transformation::OrthogonalTransformation">OrthogonalTransformation</a><E> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>, </span></code><a href='#impl-OrthogonalTransformation%3CE%3E' class='anchor'></a><a class='srclink' href='../src/alga/linear/id.rs.html#100' title='goto source code'>[src]</a></h3><div class='impl-items'></div><h3 id='impl-Mul%3CId%3CMultiplicative%3E%3E' class='impl'><code class='in-band'>impl <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html" title="trait core::ops::arith::Mul">Mul</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a href='#impl-Mul%3CId%3CMultiplicative%3E%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#162-168' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Output-1' class="type"><code id='Output.t-1'>type <a href='https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html#associatedtype.Output' class="type">Output</a> = <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code></h4><div class='docblock'><p>The resulting type after applying the <code>*</code> operator.</p>
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</div><h4 id='method.mul' class="method hidden"><code id='mul.v'>fn <a href='https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html#tymethod.mul' class='fnname'>mul</a>(self, <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a class='srclink' href='../src/alga/general/identity.rs.html#165-167' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the <code>*</code> operation.</p>
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</div></div><h3 id='impl-PartialOrd%3CId%3CO%3E%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html" title="trait core::cmp::PartialOrd">PartialOrd</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-PartialOrd%3CId%3CO%3E%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#105-110' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.partial_cmp' class="method hidden"><code id='partial_cmp.v'>fn <a href='https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html#tymethod.partial_cmp' class='fnname'>partial_cmp</a>(&self, &<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><<a class="enum" href="https://doc.rust-lang.org/nightly/core/cmp/enum.Ordering.html" title="enum core::cmp::Ordering">Ordering</a>></code><a class='srclink' href='../src/alga/general/identity.rs.html#107-109' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>This method returns an ordering between <code>self</code> and <code>other</code> values if one exists. <a href="https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html#tymethod.partial_cmp">Read more</a></p>
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</div><h4 id='method.lt' class="method hidden"><code id='lt.v'><span class="docblock attributes">#[must_use]
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</span>fn <a href='https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html#method.lt' class='fnname'>lt</a>(&self, other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Rhs) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><span class='since' title='Stable since Rust version 1.0.0'>1.0.0</span><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/cmp.rs.html#801-806' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>This method tests less than (for <code>self</code> and <code>other</code>) and is used by the <code><</code> operator. <a href="https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html#method.lt">Read more</a></p>
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</div><h4 id='method.le' class="method hidden"><code id='le.v'><span class="docblock attributes">#[must_use]
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</span>fn <a href='https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html#method.le' class='fnname'>le</a>(&self, other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Rhs) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><span class='since' title='Stable since Rust version 1.0.0'>1.0.0</span><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/cmp.rs.html#823-828' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>This method tests less than or equal to (for <code>self</code> and <code>other</code>) and is used by the <code><=</code> operator. <a href="https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html#method.le">Read more</a></p>
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</div><h4 id='method.gt' class="method hidden"><code id='gt.v'><span class="docblock attributes">#[must_use]
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</span>fn <a href='https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html#method.gt' class='fnname'>gt</a>(&self, other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Rhs) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><span class='since' title='Stable since Rust version 1.0.0'>1.0.0</span><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/cmp.rs.html#844-849' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>This method tests greater than (for <code>self</code> and <code>other</code>) and is used by the <code>></code> operator. <a href="https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html#method.gt">Read more</a></p>
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</div><h4 id='method.ge' class="method hidden"><code id='ge.v'><span class="docblock attributes">#[must_use]
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</span>fn <a href='https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html#method.ge' class='fnname'>ge</a>(&self, other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Rhs) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><span class='since' title='Stable since Rust version 1.0.0'>1.0.0</span><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/cmp.rs.html#866-871' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>This method tests greater than or equal to (for <code>self</code> and <code>other</code>) and is used by the <code>>=</code> operator. <a href="https://doc.rust-lang.org/nightly/core/cmp/trait.PartialOrd.html#method.ge">Read more</a></p>
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</div></div><h3 id='impl-DivAssign%3CId%3CMultiplicative%3E%3E' class='impl'><code class='in-band'>impl <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.DivAssign.html" title="trait core::ops::arith::DivAssign">DivAssign</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a href='#impl-DivAssign%3CId%3CMultiplicative%3E%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#184-188' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.div_assign' class="method hidden"><code id='div_assign.v'>fn <a href='https://doc.rust-lang.org/nightly/core/ops/arith/trait.DivAssign.html#tymethod.div_assign' class='fnname'>div_assign</a>(&mut self, <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>)</code><a class='srclink' href='../src/alga/general/identity.rs.html#185-187' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the <code>/=</code> operation.</p>
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</div></div><h3 id='impl-AbstractGroup%3CO%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/one_operator/trait.AbstractGroup.html" title="trait alga::general::one_operator::AbstractGroup">AbstractGroup</a><O> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-AbstractGroup%3CO%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#227' title='goto source code'>[src]</a></h3><div class='impl-items'></div><h3 id='impl-MulAssign%3CId%3CMultiplicative%3E%3E' class='impl'><code class='in-band'>impl <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.MulAssign.html" title="trait core::ops::arith::MulAssign">MulAssign</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a href='#impl-MulAssign%3CId%3CMultiplicative%3E%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#170-174' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.mul_assign' class="method hidden"><code id='mul_assign.v'>fn <a href='https://doc.rust-lang.org/nightly/core/ops/arith/trait.MulAssign.html#tymethod.mul_assign' class='fnname'>mul_assign</a>(&mut self, <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>)</code><a class='srclink' href='../src/alga/general/identity.rs.html#171-173' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the <code>*=</code> operation.</p>
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</div></div><h3 id='impl-Div%3CId%3CMultiplicative%3E%3E' class='impl'><code class='in-band'>impl <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Div.html" title="trait core::ops::arith::Div">Div</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a href='#impl-Div%3CId%3CMultiplicative%3E%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#176-182' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Output-2' class="type"><code id='Output.t-2'>type <a href='https://doc.rust-lang.org/nightly/core/ops/arith/trait.Div.html#associatedtype.Output' class="type">Output</a> = <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code></h4><div class='docblock'><p>The resulting type after applying the <code>/</code> operator.</p>
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</div><h4 id='method.div' class="method hidden"><code id='div.v'>fn <a href='https://doc.rust-lang.org/nightly/core/ops/arith/trait.Div.html#tymethod.div' class='fnname'>div</a>(self, <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>) -> <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code><a class='srclink' href='../src/alga/general/identity.rs.html#179-181' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the <code>/</code> operation.</p>
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</div></div><h3 id='impl-UlpsEq%3CId%3CO%3E%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../approx/ulps_eq/trait.UlpsEq.html" title="trait approx::ulps_eq::UlpsEq">UlpsEq</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-UlpsEq%3CId%3CO%3E%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#145-155' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.default_max_ulps' class="method hidden"><code id='default_max_ulps.v'>fn <a href='../approx/ulps_eq/trait.UlpsEq.html#tymethod.default_max_ulps' class='fnname'>default_max_ulps</a>() -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a></code><a class='srclink' href='../src/alga/general/identity.rs.html#147-149' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The default ULPs to tolerate when testing values that are far-apart. <a href="../approx/ulps_eq/trait.UlpsEq.html#tymethod.default_max_ulps">Read more</a></p>
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</div><h4 id='method.ulps_eq' class="method hidden"><code id='ulps_eq.v'>fn <a href='../approx/ulps_eq/trait.UlpsEq.html#tymethod.ulps_eq' class='fnname'>ulps_eq</a>(&self, &<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>, <<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> as <a class="trait" href="../approx/abs_diff_eq/trait.AbsDiffEq.html" title="trait approx::abs_diff_eq::AbsDiffEq">AbsDiffEq</a><<a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O>>>::<a class="type" href="../approx/abs_diff_eq/trait.AbsDiffEq.html#associatedtype.Epsilon" title="type approx::abs_diff_eq::AbsDiffEq::Epsilon">Epsilon</a>, <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../src/alga/general/identity.rs.html#152-154' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>A test for equality that uses units in the last place (ULP) if the values are far apart.</p>
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</div><h4 id='method.ulps_ne' class="method hidden"><code id='ulps_ne.v'>fn <a href='../approx/ulps_eq/trait.UlpsEq.html#method.ulps_ne' class='fnname'>ulps_ne</a>(&self, other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Rhs, epsilon: Self::<a class="type" href="../approx/abs_diff_eq/trait.AbsDiffEq.html#associatedtype.Epsilon" title="type approx::abs_diff_eq::AbsDiffEq::Epsilon">Epsilon</a>, max_ulps: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code><a class='srclink' href='../src/approx/ulps_eq.rs.html#24-26' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The inverse of <code>ApproxEq::ulps_eq</code>.</p>
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</div></div><h3 id='impl-AbstractQuasigroup%3CO%3E' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/one_operator/trait.AbstractQuasigroup.html" title="trait alga::general::one_operator::AbstractQuasigroup">AbstractQuasigroup</a><O> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-AbstractQuasigroup%3CO%3E' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#224' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.prop_inv_is_latin_square_approx' class="method hidden"><code id='prop_inv_is_latin_square_approx.v'>fn <a href='../alga/general/one_operator/trait.AbstractQuasigroup.html#method.prop_inv_is_latin_square_approx' class='fnname'>prop_inv_is_latin_square_approx</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self, Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="../approx/relative_eq/trait.RelativeEq.html" title="trait approx::relative_eq::RelativeEq">RelativeEq</a><Self>, </span></code><a class='srclink' href='../src/alga/general/one_operator.rs.html#57-66' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns <code>true</code> if latin squareness holds for the given arguments. Approximate equality is used for verifications. <a href="../alga/general/one_operator/trait.AbstractQuasigroup.html#method.prop_inv_is_latin_square_approx">Read more</a></p>
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</div><h4 id='method.prop_inv_is_latin_square' class="method hidden"><code id='prop_inv_is_latin_square.v'>fn <a href='../alga/general/one_operator/trait.AbstractQuasigroup.html#method.prop_inv_is_latin_square' class='fnname'>prop_inv_is_latin_square</a>(args: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self, Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/cmp/trait.Eq.html" title="trait core::cmp::Eq">Eq</a>, </span></code><a class='srclink' href='../src/alga/general/one_operator.rs.html#73-82' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns <code>true</code> if latin squareness holds for the given arguments. <a href="../alga/general/one_operator/trait.AbstractQuasigroup.html#method.prop_inv_is_latin_square">Read more</a></p>
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</div></div><h3 id='impl-Lattice' class='impl'><code class='in-band'>impl<O> <a class="trait" href="../alga/general/lattice/trait.Lattice.html" title="trait alga::general::lattice::Lattice">Lattice</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="../alga/general/operator/trait.Operator.html" title="trait alga::general::operator::Operator">Operator</a>, </span></code><a href='#impl-Lattice' class='anchor'></a><a class='srclink' href='../src/alga/general/identity.rs.html#285' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.meet_join' class="method hidden"><code id='meet_join.v'>fn <a href='../alga/general/lattice/trait.Lattice.html#method.meet_join' class='fnname'>meet_join</a>(&self, other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self, Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a></code><a class='srclink' href='../src/alga/general/lattice.rs.html#21-23' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Returns the infimum and the supremum simultaneously.</p>
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</div><h4 id='method.partial_min' class="method hidden"><code id='partial_min.v'>fn <a href='../alga/general/lattice/trait.Lattice.html#method.partial_min' class='fnname'>partial_min</a>(&'a self, other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self></code><a class='srclink' href='../src/alga/general/lattice.rs.html#27-36' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Return the minimum of <code>self</code> and <code>other</code> if they are comparable.</p>
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</div><h4 id='method.partial_max' class="method hidden"><code id='partial_max.v'>fn <a href='../alga/general/lattice/trait.Lattice.html#method.partial_max' class='fnname'>partial_max</a>(&'a self, other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self></code><a class='srclink' href='../src/alga/general/lattice.rs.html#40-49' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Return the maximum of <code>self</code> and <code>other</code> if they are comparable.</p>
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</div><h4 id='method.partial_sort2' class="method hidden"><code id='partial_sort2.v'>fn <a href='../alga/general/lattice/trait.Lattice.html#method.partial_sort2' class='fnname'>partial_sort2</a>(&'a self, other: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self, <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a>></code><a class='srclink' href='../src/alga/general/lattice.rs.html#53-62' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Sorts two values in increasing order using a partial ordering.</p>
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</div><h4 id='method.partial_clamp' class="method hidden"><code id='partial_clamp.v'>fn <a href='../alga/general/lattice/trait.Lattice.html#method.partial_clamp' class='fnname'>partial_clamp</a>(&'a self, min: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self, max: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><<a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&'a </a>Self></code><a class='srclink' href='../src/alga/general/lattice.rs.html#67-79' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Clamp <code>value</code> between <code>min</code> and <code>max</code>. Returns <code>None</code> if <code>value</code> is not comparable to <code>min</code> or <code>max</code>. <a href="../alga/general/lattice/trait.Lattice.html#method.partial_clamp">Read more</a></p>
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</div></div></div><h2 id='synthetic-implementations' class='small-section-header'>Auto Trait Implementations<a href='#synthetic-implementations' class='anchor'></a></h2><div id='synthetic-implementations-list'><h3 id='impl-Send' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Send.html" title="trait core::marker::Send">Send</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Send.html" title="trait core::marker::Send">Send</a>, </span></code><a href='#impl-Send' class='anchor'></a></h3><div class='impl-items'></div><h3 id='impl-Unpin' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Unpin.html" title="trait core::marker::Unpin">Unpin</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Unpin.html" title="trait core::marker::Unpin">Unpin</a>, </span></code><a href='#impl-Unpin' class='anchor'></a></h3><div class='impl-items'></div><h3 id='impl-Sync' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sync.html" title="trait core::marker::Sync">Sync</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sync.html" title="trait core::marker::Sync">Sync</a>, </span></code><a href='#impl-Sync' class='anchor'></a></h3><div class='impl-items'></div><h3 id='impl-UnwindSafe' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/std/panic/trait.UnwindSafe.html" title="trait std::panic::UnwindSafe">UnwindSafe</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="https://doc.rust-lang.org/nightly/std/panic/trait.UnwindSafe.html" title="trait std::panic::UnwindSafe">UnwindSafe</a>, </span></code><a href='#impl-UnwindSafe' class='anchor'></a></h3><div class='impl-items'></div><h3 id='impl-RefUnwindSafe' class='impl'><code class='in-band'>impl<O> <a class="trait" href="https://doc.rust-lang.org/nightly/std/panic/trait.RefUnwindSafe.html" title="trait std::panic::RefUnwindSafe">RefUnwindSafe</a> for <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><O> <span class="where fmt-newline">where<br> O: <a class="trait" href="https://doc.rust-lang.org/nightly/std/panic/trait.RefUnwindSafe.html" title="trait std::panic::RefUnwindSafe">RefUnwindSafe</a>, </span></code><a href='#impl-RefUnwindSafe' class='anchor'></a></h3><div class='impl-items'></div></div><h2 id='blanket-implementations' class='small-section-header'>Blanket Implementations<a href='#blanket-implementations' class='anchor'></a></h2><div id='blanket-implementations-list'><h3 id='impl-ToOwned' class='impl'><code class='in-band'>impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html" title="trait alloc::borrow::ToOwned">ToOwned</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html" title="trait core::clone::Clone">Clone</a>, </span></code><a href='#impl-ToOwned' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/alloc/borrow.rs.html#81-92' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Owned' class="type"><code id='Owned.t'>type <a href='https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html#associatedtype.Owned' class="type">Owned</a> = T</code></h4><div class='docblock'><p>The resulting type after obtaining ownership.</p>
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</div><h4 id='method.to_owned' class="method hidden"><code id='to_owned.v'>fn <a href='https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html#tymethod.to_owned' class='fnname'>to_owned</a>(&self) -> T</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/alloc/borrow.rs.html#85-87' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Creates owned data from borrowed data, usually by cloning. <a href="https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html#tymethod.to_owned">Read more</a></p>
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</div><h4 id='method.clone_into' class="method hidden"><code id='clone_into.v'>fn <a href='https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html#method.clone_into' class='fnname'>clone_into</a>(&self, target: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&mut </a>T)</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/alloc/borrow.rs.html#89-91' title='goto source code'>[src]</a></h4><div class='stability hidden'><div class='stab unstable'><details><summary><span class='emoji'>🔬</span> This is a nightly-only experimental API. (<code>toowned_clone_into</code>)</summary><p>recently added</p>
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</details></div></div><div class='docblock hidden'><p>Uses borrowed data to replace owned data, usually by cloning. <a href="https://doc.rust-lang.org/nightly/alloc/borrow/trait.ToOwned.html#method.clone_into">Read more</a></p>
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</div></div><h3 id='impl-Into%3CU%3E' class='impl'><code class='in-band'>impl<T, U> <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.Into.html" title="trait core::convert::Into">Into</a><U> for T <span class="where fmt-newline">where<br> U: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.From.html" title="trait core::convert::From">From</a><T>, </span></code><a href='#impl-Into%3CU%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#544-549' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.into' class="method hidden"><code id='into.v'>fn <a href='https://doc.rust-lang.org/nightly/core/convert/trait.Into.html#tymethod.into' class='fnname'>into</a>(self) -> U</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#546-548' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the conversion.</p>
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</div></div><h3 id='impl-From%3CT%3E' class='impl'><code class='in-band'>impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.From.html" title="trait core::convert::From">From</a><T> for T</code><a href='#impl-From%3CT%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#553-555' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.from' class="method hidden"><code id='from.v'>fn <a href='https://doc.rust-lang.org/nightly/core/convert/trait.From.html#tymethod.from' class='fnname'>from</a>(t: T) -> T</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#554' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the conversion.</p>
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</div></div><h3 id='impl-ToString' class='impl'><code class='in-band'>impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/alloc/string/trait.ToString.html" title="trait alloc::string::ToString">ToString</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="https://doc.rust-lang.org/nightly/core/fmt/trait.Display.html" title="trait core::fmt::Display">Display</a> + ?<a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a>, </span></code><a href='#impl-ToString' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/alloc/string.rs.html#2134-2144' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.to_string' class="method hidden"><code id='to_string.v'>default fn <a href='https://doc.rust-lang.org/nightly/alloc/string/trait.ToString.html#tymethod.to_string' class='fnname'>to_string</a>(&self) -> <a class="struct" href="https://doc.rust-lang.org/nightly/alloc/string/struct.String.html" title="struct alloc::string::String">String</a></code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/alloc/string.rs.html#2136-2143' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Converts the given value to a <code>String</code>. <a href="https://doc.rust-lang.org/nightly/alloc/string/trait.ToString.html#tymethod.to_string">Read more</a></p>
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</div></div><h3 id='impl-TryFrom%3CU%3E' class='impl'><code class='in-band'>impl<T, U> <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a><U> for T <span class="where fmt-newline">where<br> U: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.Into.html" title="trait core::convert::Into">Into</a><T>, </span></code><a href='#impl-TryFrom%3CU%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#572-578' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Error' class="type"><code id='Error.t'>type <a href='https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error' class="type">Error</a> = <a class="enum" href="https://doc.rust-lang.org/nightly/core/convert/enum.Infallible.html" title="enum core::convert::Infallible">Infallible</a></code></h4><div class='docblock'><p>The type returned in the event of a conversion error.</p>
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</div><h4 id='method.try_from' class="method hidden"><code id='try_from.v'>fn <a href='https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#tymethod.try_from' class='fnname'>try_from</a>(value: U) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/result/enum.Result.html" title="enum core::result::Result">Result</a><T, <T as <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a><U>>::<a class="type" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error" title="type core::convert::TryFrom::Error">Error</a>></code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#575-577' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the conversion.</p>
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</div></div><h3 id='impl-TryInto%3CU%3E' class='impl'><code class='in-band'>impl<T, U> <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryInto.html" title="trait core::convert::TryInto">TryInto</a><U> for T <span class="where fmt-newline">where<br> U: <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a><T>, </span></code><a href='#impl-TryInto%3CU%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#560-567' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Error-1' class="type"><code id='Error.t-1'>type <a href='https://doc.rust-lang.org/nightly/core/convert/trait.TryInto.html#associatedtype.Error' class="type">Error</a> = <U as <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a><T>>::<a class="type" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error" title="type core::convert::TryFrom::Error">Error</a></code></h4><div class='docblock'><p>The type returned in the event of a conversion error.</p>
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</div><h4 id='method.try_into' class="method hidden"><code id='try_into.v'>fn <a href='https://doc.rust-lang.org/nightly/core/convert/trait.TryInto.html#tymethod.try_into' class='fnname'>try_into</a>(self) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/result/enum.Result.html" title="enum core::result::Result">Result</a><U, <U as <a class="trait" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html" title="trait core::convert::TryFrom">TryFrom</a><T>>::<a class="type" href="https://doc.rust-lang.org/nightly/core/convert/trait.TryFrom.html#associatedtype.Error" title="type core::convert::TryFrom::Error">Error</a>></code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/convert.rs.html#564-566' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Performs the conversion.</p>
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</div></div><h3 id='impl-BorrowMut%3CT%3E' class='impl'><code class='in-band'>impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/borrow/trait.BorrowMut.html" title="trait core::borrow::BorrowMut">BorrowMut</a><T> for T <span class="where fmt-newline">where<br> T: ?<a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a>, </span></code><a href='#impl-BorrowMut%3CT%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#218-220' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.borrow_mut' class="method hidden"><code id='borrow_mut.v'>fn <a href='https://doc.rust-lang.org/nightly/core/borrow/trait.BorrowMut.html#tymethod.borrow_mut' class='fnname'>borrow_mut</a>(&mut self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&mut </a>T</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#219' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Mutably borrows from an owned value. <a href="https://doc.rust-lang.org/nightly/core/borrow/trait.BorrowMut.html#tymethod.borrow_mut">Read more</a></p>
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</div></div><h3 id='impl-Borrow%3CT%3E' class='impl'><code class='in-band'>impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/borrow/trait.Borrow.html" title="trait core::borrow::Borrow">Borrow</a><T> for T <span class="where fmt-newline">where<br> T: ?<a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a>, </span></code><a href='#impl-Borrow%3CT%3E' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#213-215' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.borrow' class="method hidden"><code id='borrow.v'>fn <a href='https://doc.rust-lang.org/nightly/core/borrow/trait.Borrow.html#tymethod.borrow' class='fnname'>borrow</a>(&self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>T</code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/borrow.rs.html#214' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Immutably borrows from an owned value. <a href="https://doc.rust-lang.org/nightly/core/borrow/trait.Borrow.html#tymethod.borrow">Read more</a></p>
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</div></div><h3 id='impl-Any' class='impl'><code class='in-band'>impl<T> <a class="trait" href="https://doc.rust-lang.org/nightly/core/any/trait.Any.html" title="trait core::any::Any">Any</a> for T <span class="where fmt-newline">where<br> T: 'static + ?<a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sized.html" title="trait core::marker::Sized">Sized</a>, </span></code><a href='#impl-Any' class='anchor'></a><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/any.rs.html#100-102' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.type_id' class="method hidden"><code id='type_id.v'>fn <a href='https://doc.rust-lang.org/nightly/core/any/trait.Any.html#tymethod.type_id' class='fnname'>type_id</a>(&self) -> <a class="struct" href="https://doc.rust-lang.org/nightly/core/any/struct.TypeId.html" title="struct core::any::TypeId">TypeId</a></code><a class='srclink' href='https://doc.rust-lang.org/nightly/src/core/any.rs.html#101' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Gets the <code>TypeId</code> of <code>self</code>. <a href="https://doc.rust-lang.org/nightly/core/any/trait.Any.html#tymethod.type_id">Read more</a></p>
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</div></div><h3 id='impl-Same%3CT%3E' class='impl'><code class='in-band'>impl<T> <a class="trait" href="../typenum/type_operators/trait.Same.html" title="trait typenum::type_operators::Same">Same</a><T> for T</code><a href='#impl-Same%3CT%3E' class='anchor'></a><a class='srclink' href='../src/typenum/type_operators.rs.html#32-34' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Output-3' class="type"><code id='Output.t-3'>type <a href='../typenum/type_operators/trait.Same.html#associatedtype.Output' class="type">Output</a> = T</code></h4><div class='docblock'><p>Should always be <code>Self</code></p>
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</div></div><h3 id='impl-SupersetOf%3CSS%3E' class='impl'><code class='in-band'>impl<SS, SP> <a class="trait" href="../alga/general/subset/trait.SupersetOf.html" title="trait alga::general::subset::SupersetOf">SupersetOf</a><SS> for SP <span class="where fmt-newline">where<br> SS: <a class="trait" href="../alga/general/subset/trait.SubsetOf.html" title="trait alga::general::subset::SubsetOf">SubsetOf</a><SP>, </span></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' class="method hidden"><code id='to_subset.v'>fn <a href='../alga/general/subset/trait.SupersetOf.html#method.to_subset' class='fnname'>to_subset</a>(&self) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><SS></code><a class='srclink' href='../src/alga/general/subset.rs.html#89-91' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The inverse inclusion map: attempts to construct <code>self</code> from the equivalent element of its superset. <a href="../alga/general/subset/trait.SupersetOf.html#method.to_subset">Read more</a></p>
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</div><h4 id='method.is_in_subset-1' class="method hidden"><code id='is_in_subset.v-1'>fn <a href='../alga/general/subset/trait.SupersetOf.html#tymethod.is_in_subset' class='fnname'>is_in_subset</a>(&self) -> <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><div class='docblock hidden'><p>Checks if <code>self</code> is actually part of its subset <code>T</code> (and can be converted to it).</p>
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</div><h4 id='method.to_subset_unchecked' class="method hidden"><code id='to_subset_unchecked.v'>unsafe fn <a href='../alga/general/subset/trait.SupersetOf.html#tymethod.to_subset_unchecked' class='fnname'>to_subset_unchecked</a>(&self) -> SS</code><a class='srclink' href='../src/alga/general/subset.rs.html#99-101' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Use with care! Same as <code>self.to_subset</code> but without any property checks. Always succeeds.</p>
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</div><h4 id='method.from_subset' class="method hidden"><code id='from_subset.v'>fn <a href='../alga/general/subset/trait.SupersetOf.html#tymethod.from_subset' class='fnname'>from_subset</a>(element: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>SS) -> SP</code><a class='srclink' href='../src/alga/general/subset.rs.html#104-106' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The inclusion map: converts <code>self</code> to the equivalent element of its superset.</p>
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</div></div><h3 id='impl-ClosedAdd%3CRight%3E' class='impl'><code class='in-band'>impl<T, Right> <a class="trait" href="../alga/general/operator/trait.ClosedAdd.html" title="trait alga::general::operator::ClosedAdd">ClosedAdd</a><Right> for T <span class="where fmt-newline">where<br> 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><Right, Output = T> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.AddAssign.html" title="trait core::ops::arith::AddAssign">AddAssign</a><Right>, </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><h3 id='impl-ClosedMul%3CRight%3E' class='impl'><code class='in-band'>impl<T, Right> <a class="trait" href="../alga/general/operator/trait.ClosedMul.html" title="trait alga::general::operator::ClosedMul">ClosedMul</a><Right> for T <span class="where fmt-newline">where<br> 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><Right, Output = T> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.MulAssign.html" title="trait core::ops::arith::MulAssign">MulAssign</a><Right>, </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><h3 id='impl-ClosedDiv%3CRight%3E' class='impl'><code class='in-band'>impl<T, Right> <a class="trait" href="../alga/general/operator/trait.ClosedDiv.html" title="trait alga::general::operator::ClosedDiv">ClosedDiv</a><Right> for T <span class="where fmt-newline">where<br> 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><Right, Output = T> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.DivAssign.html" title="trait core::ops::arith::DivAssign">DivAssign</a><Right>, </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><h3 id='impl-AdditiveMagma' class='impl'><code class='in-band'>impl<T> <a class="trait" href="../alga/general/specialized/trait.AdditiveMagma.html" title="trait alga::general::specialized::AdditiveMagma">AdditiveMagma</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="../alga/general/one_operator/trait.AbstractMagma.html" title="trait alga::general::one_operator::AbstractMagma">AbstractMagma</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>>, </span></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><h3 id='impl-AdditiveSemigroup' class='impl'><code class='in-band'>impl<T> <a class="trait" href="../alga/general/specialized/trait.AdditiveSemigroup.html" title="trait alga::general::specialized::AdditiveSemigroup">AdditiveSemigroup</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="../alga/general/one_operator/trait.AbstractSemigroup.html" title="trait alga::general::one_operator::AbstractSemigroup">AbstractSemigroup</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>> + <a class="trait" href="../alga/general/operator/trait.ClosedAdd.html" title="trait alga::general::operator::ClosedAdd">ClosedAdd</a><T> + <a class="trait" href="../alga/general/specialized/trait.AdditiveMagma.html" title="trait alga::general::specialized::AdditiveMagma">AdditiveMagma</a>, </span></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><h3 id='impl-AdditiveMonoid' class='impl'><code class='in-band'>impl<T> <a class="trait" href="../alga/general/specialized/trait.AdditiveMonoid.html" title="trait alga::general::specialized::AdditiveMonoid">AdditiveMonoid</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="../alga/general/one_operator/trait.AbstractMonoid.html" title="trait alga::general::one_operator::AbstractMonoid">AbstractMonoid</a><<a class="struct" href="../alga/general/operator/struct.Additive.html" title="struct alga::general::operator::Additive">Additive</a>> + <a class="trait" href="../alga/general/specialized/trait.AdditiveSemigroup.html" title="trait alga::general::specialized::AdditiveSemigroup">AdditiveSemigroup</a> + <a class="trait" href="../num_traits/identities/trait.Zero.html" title="trait num_traits::identities::Zero">Zero</a>, </span></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><h3 id='impl-MultiplicativeMagma' class='impl'><code class='in-band'>impl<T> <a class="trait" href="../alga/general/specialized/trait.MultiplicativeMagma.html" title="trait alga::general::specialized::MultiplicativeMagma">MultiplicativeMagma</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="../alga/general/one_operator/trait.AbstractMagma.html" title="trait alga::general::one_operator::AbstractMagma">AbstractMagma</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>, </span></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><h3 id='impl-MultiplicativeQuasigroup' class='impl'><code class='in-band'>impl<T> <a class="trait" href="../alga/general/specialized/trait.MultiplicativeQuasigroup.html" title="trait alga::general::specialized::MultiplicativeQuasigroup">MultiplicativeQuasigroup</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="../alga/general/one_operator/trait.AbstractQuasigroup.html" title="trait alga::general::one_operator::AbstractQuasigroup">AbstractQuasigroup</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> + <a class="trait" href="../alga/general/operator/trait.ClosedDiv.html" title="trait alga::general::operator::ClosedDiv">ClosedDiv</a><T> + <a class="trait" href="../alga/general/specialized/trait.MultiplicativeMagma.html" title="trait alga::general::specialized::MultiplicativeMagma">MultiplicativeMagma</a>, </span></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><h3 id='impl-MultiplicativeLoop' class='impl'><code class='in-band'>impl<T> <a class="trait" href="../alga/general/specialized/trait.MultiplicativeLoop.html" title="trait alga::general::specialized::MultiplicativeLoop">MultiplicativeLoop</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="../alga/general/one_operator/trait.AbstractLoop.html" title="trait alga::general::one_operator::AbstractLoop">AbstractLoop</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> + <a class="trait" href="../alga/general/specialized/trait.MultiplicativeQuasigroup.html" title="trait alga::general::specialized::MultiplicativeQuasigroup">MultiplicativeQuasigroup</a> + <a class="trait" href="../num_traits/identities/trait.One.html" title="trait num_traits::identities::One">One</a>, </span></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><h3 id='impl-MultiplicativeSemigroup' class='impl'><code class='in-band'>impl<T> <a class="trait" href="../alga/general/specialized/trait.MultiplicativeSemigroup.html" title="trait alga::general::specialized::MultiplicativeSemigroup">MultiplicativeSemigroup</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="../alga/general/one_operator/trait.AbstractSemigroup.html" title="trait alga::general::one_operator::AbstractSemigroup">AbstractSemigroup</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> + <a class="trait" href="../alga/general/operator/trait.ClosedMul.html" title="trait alga::general::operator::ClosedMul">ClosedMul</a><T> + <a class="trait" href="../alga/general/specialized/trait.MultiplicativeMagma.html" title="trait alga::general::specialized::MultiplicativeMagma">MultiplicativeMagma</a>, </span></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><h3 id='impl-MultiplicativeMonoid' class='impl'><code class='in-band'>impl<T> <a class="trait" href="../alga/general/specialized/trait.MultiplicativeMonoid.html" title="trait alga::general::specialized::MultiplicativeMonoid">MultiplicativeMonoid</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="../alga/general/one_operator/trait.AbstractMonoid.html" title="trait alga::general::one_operator::AbstractMonoid">AbstractMonoid</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> + <a class="trait" href="../alga/general/specialized/trait.MultiplicativeSemigroup.html" title="trait alga::general::specialized::MultiplicativeSemigroup">MultiplicativeSemigroup</a> + <a class="trait" href="../num_traits/identities/trait.One.html" title="trait num_traits::identities::One">One</a>, </span></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><h3 id='impl-MultiplicativeGroup' class='impl'><code class='in-band'>impl<T> <a class="trait" href="../alga/general/specialized/trait.MultiplicativeGroup.html" title="trait alga::general::specialized::MultiplicativeGroup">MultiplicativeGroup</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="../alga/general/one_operator/trait.AbstractGroup.html" title="trait alga::general::one_operator::AbstractGroup">AbstractGroup</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> + <a class="trait" href="../alga/general/specialized/trait.MultiplicativeLoop.html" title="trait alga::general::specialized::MultiplicativeLoop">MultiplicativeLoop</a> + <a class="trait" href="../alga/general/specialized/trait.MultiplicativeMonoid.html" title="trait alga::general::specialized::MultiplicativeMonoid">MultiplicativeMonoid</a>, </span></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><h3 id='impl-MultiplicativeGroupAbelian' class='impl'><code class='in-band'>impl<T> <a class="trait" href="../alga/general/specialized/trait.MultiplicativeGroupAbelian.html" title="trait alga::general::specialized::MultiplicativeGroupAbelian">MultiplicativeGroupAbelian</a> for T <span class="where fmt-newline">where<br> T: <a class="trait" href="../alga/general/one_operator/trait.AbstractGroupAbelian.html" title="trait alga::general::one_operator::AbstractGroupAbelian">AbstractGroupAbelian</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>> + <a class="trait" href="../alga/general/specialized/trait.MultiplicativeGroup.html" title="trait alga::general::specialized::MultiplicativeGroup">MultiplicativeGroup</a>, </span></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><h3 id='impl-ProjectiveTransformation%3CE%3E-1' class='impl'><code class='in-band'>impl<R, E> <a class="trait" href="../alga/linear/transformation/trait.ProjectiveTransformation.html" title="trait alga::linear::transformation::ProjectiveTransformation">ProjectiveTransformation</a><E> for R <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a><RealField = R>,<br> R: <a class="trait" href="../nalgebra/trait.RealField.html" title="trait nalgebra::RealField">RealField</a>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedMul.html" title="trait alga::general::operator::ClosedMul">ClosedMul</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedDiv.html" title="trait alga::general::operator::ClosedDiv">ClosedDiv</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedNeg.html" title="trait alga::general::operator::ClosedNeg">ClosedNeg</a>, </span></code><a href='#impl-ProjectiveTransformation%3CE%3E-1' class='anchor'></a><a class='srclink' href='../src/alga/linear/transformation.rs.html#309-326' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.inverse_transform_point-1' class="method hidden"><code id='inverse_transform_point.v-1'>fn <a href='../alga/linear/transformation/trait.ProjectiveTransformation.html#tymethod.inverse_transform_point' class='fnname'>inverse_transform_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#316-319' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this group's two_sided_inverse action on a point from the euclidean space.</p>
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</div><h4 id='method.inverse_transform_vector-1' class="method hidden"><code id='inverse_transform_vector.v-1'>fn <a href='../alga/linear/transformation/trait.ProjectiveTransformation.html#tymethod.inverse_transform_vector' class='fnname'>inverse_transform_vector</a>(<br> &self, <br> v: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#322-325' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this group's two_sided_inverse action on a vector from the euclidean space. <a href="../alga/linear/transformation/trait.ProjectiveTransformation.html#tymethod.inverse_transform_vector">Read more</a></p>
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</div></div><h3 id='impl-Transformation%3CE%3E-1' class='impl'><code class='in-band'>impl<R, E> <a class="trait" href="../alga/linear/transformation/trait.Transformation.html" title="trait alga::linear::transformation::Transformation">Transformation</a><E> for R <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a><RealField = R>,<br> R: <a class="trait" href="../nalgebra/trait.RealField.html" title="trait nalgebra::RealField">RealField</a>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedMul.html" title="trait alga::general::operator::ClosedMul">ClosedMul</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedDiv.html" title="trait alga::general::operator::ClosedDiv">ClosedDiv</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedNeg.html" title="trait alga::general::operator::ClosedNeg">ClosedNeg</a>, </span></code><a href='#impl-Transformation%3CE%3E-1' class='anchor'></a><a class='srclink' href='../src/alga/linear/transformation.rs.html#292-307' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.transform_point-1' class="method hidden"><code id='transform_point.v-1'>fn <a href='../alga/linear/transformation/trait.Transformation.html#tymethod.transform_point' class='fnname'>transform_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#299-301' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this group's action on a point from the euclidean space.</p>
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</div><h4 id='method.transform_vector-1' class="method hidden"><code id='transform_vector.v-1'>fn <a href='../alga/linear/transformation/trait.Transformation.html#tymethod.transform_vector' class='fnname'>transform_vector</a>(<br> &self, <br> v: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#304-306' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this group's action on a vector from the euclidean space. <a href="../alga/linear/transformation/trait.Transformation.html#tymethod.transform_vector">Read more</a></p>
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</div></div><h3 id='impl-Similarity%3CE%3E-1' class='impl'><code class='in-band'>impl<R, E> <a class="trait" href="../alga/linear/transformation/trait.Similarity.html" title="trait alga::linear::transformation::Similarity">Similarity</a><E> for R <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a><RealField = R>,<br> R: <a class="trait" href="../nalgebra/trait.RealField.html" title="trait nalgebra::RealField">RealField</a> + <a class="trait" href="../alga/general/subset/trait.SubsetOf.html" title="trait alga::general::subset::SubsetOf">SubsetOf</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedMul.html" title="trait alga::general::operator::ClosedMul">ClosedMul</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedDiv.html" title="trait alga::general::operator::ClosedDiv">ClosedDiv</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedNeg.html" title="trait alga::general::operator::ClosedNeg">ClosedNeg</a>, </span></code><a href='#impl-Similarity%3CE%3E-1' class='anchor'></a><a class='srclink' href='../src/alga/linear/transformation.rs.html#401-420' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scaling-1' class="type"><code id='Scaling.t-1'>type <a href='../alga/linear/transformation/trait.Similarity.html#associatedtype.Scaling' class="type">Scaling</a> = R</code></h4><div class='docblock'><p>The type of the pure (uniform) scaling part of this similarity transformation.</p>
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</div><h4 id='method.translation-1' class="method hidden"><code id='translation.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#tymethod.translation' class='fnname'>translation</a>(&self) -> <R as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::transformation::AffineTransformation::Translation">Translation</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#409-411' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The pure translational component of this similarity transformation.</p>
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</div><h4 id='method.rotation-1' class="method hidden"><code id='rotation.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#tymethod.rotation' class='fnname'>rotation</a>(&self) -> <R as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::transformation::AffineTransformation::Rotation">Rotation</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#413-415' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The pure rotational component of this similarity transformation.</p>
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</div><h4 id='method.scaling-1' class="method hidden"><code id='scaling.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#tymethod.scaling' class='fnname'>scaling</a>(&self) -> <R as <a class="trait" href="../alga/linear/transformation/trait.Similarity.html" title="trait alga::linear::transformation::Similarity">Similarity</a><E>>::<a class="type" href="../alga/linear/transformation/trait.Similarity.html#associatedtype.Scaling" title="type alga::linear::transformation::Similarity::Scaling">Scaling</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#417-419' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The pure scaling component of this similarity transformation.</p>
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</div><h4 id='method.translate_point-1' class="method hidden"><code id='translate_point.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.translate_point' class='fnname'>translate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#124-126' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation's pure translational part to a point.</p>
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</div><h4 id='method.rotate_point-1' class="method hidden"><code id='rotate_point.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.rotate_point' class='fnname'>rotate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#130-132' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation's pure rotational part to a point.</p>
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</div><h4 id='method.scale_point-1' class="method hidden"><code id='scale_point.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.scale_point' class='fnname'>scale_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#136-138' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation's pure scaling part to a point.</p>
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</div><h4 id='method.rotate_vector-1' class="method hidden"><code id='rotate_vector.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.rotate_vector' class='fnname'>rotate_vector</a>(<br> &self, <br> pt: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#142-144' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation's pure rotational part to a vector.</p>
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</div><h4 id='method.scale_vector-1' class="method hidden"><code id='scale_vector.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.scale_vector' class='fnname'>scale_vector</a>(<br> &self, <br> pt: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#148-150' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation's pure scaling part to a vector.</p>
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</div><h4 id='method.inverse_translate_point-1' class="method hidden"><code id='inverse_translate_point.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.inverse_translate_point' class='fnname'>inverse_translate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#157-159' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation inverse's pure translational part to a point.</p>
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</div><h4 id='method.inverse_rotate_point-1' class="method hidden"><code id='inverse_rotate_point.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.inverse_rotate_point' class='fnname'>inverse_rotate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#163-165' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation inverse's pure rotational part to a point.</p>
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</div><h4 id='method.inverse_scale_point-1' class="method hidden"><code id='inverse_scale_point.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.inverse_scale_point' class='fnname'>inverse_scale_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#169-171' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation inverse's pure scaling part to a point.</p>
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</div><h4 id='method.inverse_rotate_vector-1' class="method hidden"><code id='inverse_rotate_vector.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.inverse_rotate_vector' class='fnname'>inverse_rotate_vector</a>(<br> &self, <br> pt: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#175-177' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation inverse's pure rotational part to a vector.</p>
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</div><h4 id='method.inverse_scale_vector-1' class="method hidden"><code id='inverse_scale_vector.v-1'>fn <a href='../alga/linear/transformation/trait.Similarity.html#method.inverse_scale_vector' class='fnname'>inverse_scale_vector</a>(<br> &self, <br> pt: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#181-183' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Applies this transformation inverse's pure scaling part to a vector.</p>
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</div></div><h3 id='impl-AffineTransformation%3CE%3E-1' class='impl'><code class='in-band'>impl<R, E> <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E> for R <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a><RealField = R>,<br> R: <a class="trait" href="../nalgebra/trait.RealField.html" title="trait nalgebra::RealField">RealField</a>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedMul.html" title="trait alga::general::operator::ClosedMul">ClosedMul</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedDiv.html" title="trait alga::general::operator::ClosedDiv">ClosedDiv</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedNeg.html" title="trait alga::general::operator::ClosedNeg">ClosedNeg</a>, </span></code><a href='#impl-AffineTransformation%3CE%3E-1' class='anchor'></a><a class='srclink' href='../src/alga/linear/transformation.rs.html#328-372' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Rotation-1' class="type"><code id='Rotation.t-1'>type <a href='../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Rotation' class="type">Rotation</a> = <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code></h4><div class='docblock'><p>Type of the first rotation to be applied.</p>
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</div><h4 id='associatedtype.NonUniformScaling-1' class="type"><code id='NonUniformScaling.t-1'>type <a href='../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.NonUniformScaling' class="type">NonUniformScaling</a> = R</code></h4><div class='docblock'><p>Type of the non-uniform scaling to be applied.</p>
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</div><h4 id='associatedtype.Translation-1' class="type"><code id='Translation.t-1'>type <a href='../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Translation' class="type">Translation</a> = <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>></code></h4><div class='docblock'><p>The type of the pure translation part of this affine transformation.</p>
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</div><h4 id='method.decompose-1' class="method hidden"><code id='decompose.v-1'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.decompose' class='fnname'>decompose</a>(<br> &self<br>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a><a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>, <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>>, R, <a class="struct" href="../nalgebra/struct.Id.html" title="struct nalgebra::Id">Id</a><<a class="struct" href="../alga/general/operator/struct.Multiplicative.html" title="struct alga::general::operator::Multiplicative">Multiplicative</a>><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#339-341' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation. <a href="../alga/linear/transformation/trait.AffineTransformation.html#tymethod.decompose">Read more</a></p>
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</div><h4 id='method.append_translation-1' class="method hidden"><code id='append_translation.v-1'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.append_translation' class='fnname'>append_translation</a>(&self, &<R as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::transformation::AffineTransformation::Translation">Translation</a>) -> R</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#344-346' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Appends a translation to this similarity.</p>
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</div><h4 id='method.prepend_translation-1' class="method hidden"><code id='prepend_translation.v-1'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.prepend_translation' class='fnname'>prepend_translation</a>(&self, &<R as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::transformation::AffineTransformation::Translation">Translation</a>) -> R</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#349-351' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Prepends a translation to this similarity.</p>
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</div><h4 id='method.append_rotation-1' class="method hidden"><code id='append_rotation.v-1'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.append_rotation' class='fnname'>append_rotation</a>(&self, &<R as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::transformation::AffineTransformation::Rotation">Rotation</a>) -> R</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#354-356' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Appends a rotation to this similarity.</p>
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</div><h4 id='method.prepend_rotation-1' class="method hidden"><code id='prepend_rotation.v-1'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.prepend_rotation' class='fnname'>prepend_rotation</a>(&self, &<R as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::transformation::AffineTransformation::Rotation">Rotation</a>) -> R</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#359-361' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Prepends a rotation to this similarity.</p>
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</div><h4 id='method.append_scaling-1' class="method hidden"><code id='append_scaling.v-1'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.append_scaling' class='fnname'>append_scaling</a>(<br> &self, <br> s: &<R as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.NonUniformScaling" title="type alga::linear::transformation::AffineTransformation::NonUniformScaling">NonUniformScaling</a><br>) -> R</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#364-366' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Appends a scaling factor to this similarity.</p>
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</div><h4 id='method.prepend_scaling-1' class="method hidden"><code id='prepend_scaling.v-1'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#tymethod.prepend_scaling' class='fnname'>prepend_scaling</a>(<br> &self, <br> s: &<R as <a class="trait" href="../alga/linear/transformation/trait.AffineTransformation.html" title="trait alga::linear::transformation::AffineTransformation">AffineTransformation</a><E>>::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.NonUniformScaling" title="type alga::linear::transformation::AffineTransformation::NonUniformScaling">NonUniformScaling</a><br>) -> R</code><a class='srclink' href='../src/alga/linear/transformation.rs.html#369-371' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Prepends a scaling factor to this similarity.</p>
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</div><h4 id='method.append_rotation_wrt_point-1' class="method hidden"><code id='append_rotation_wrt_point.v-1'>fn <a href='../alga/linear/transformation/trait.AffineTransformation.html#method.append_rotation_wrt_point' class='fnname'>append_rotation_wrt_point</a>(&self, r: &Self::<a class="type" href="../alga/linear/transformation/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::transformation::AffineTransformation::Rotation">Rotation</a>, p: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#84-95' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Appends to this similarity a rotation centered at the point <code>p</code>, i.e., this point is left invariant. <a href="../alga/linear/transformation/trait.AffineTransformation.html#method.append_rotation_wrt_point">Read more</a></p>
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</div></div><h3 id='impl-Scaling%3CE%3E-1' class='impl'><code class='in-band'>impl<R, E> <a class="trait" href="../alga/linear/transformation/trait.Scaling.html" title="trait alga::linear::transformation::Scaling">Scaling</a><E> for R <span class="where fmt-newline">where<br> E: <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a><RealField = R>,<br> R: <a class="trait" href="../nalgebra/trait.RealField.html" title="trait nalgebra::RealField">RealField</a> + <a class="trait" href="../alga/general/subset/trait.SubsetOf.html" title="trait alga::general::subset::SubsetOf">SubsetOf</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedMul.html" title="trait alga::general::operator::ClosedMul">ClosedMul</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedDiv.html" title="trait alga::general::operator::ClosedDiv">ClosedDiv</a><R>,<br> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../alga/general/operator/trait.ClosedNeg.html" title="trait alga::general::operator::ClosedNeg">ClosedNeg</a>, </span></code><a href='#impl-Scaling%3CE%3E-1' class='anchor'></a><a class='srclink' href='../src/alga/linear/transformation.rs.html#374-399' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.to_real-1' class="method hidden"><code id='to_real.v-1'>fn <a href='../alga/linear/transformation/trait.Scaling.html#method.to_real' class='fnname'>to_real</a>(&self) -> <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::vector::EuclideanSpace::RealField">RealField</a></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#381-383' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Converts this scaling factor to a real. Same as <code>self.to_superset()</code>.</p>
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</div><h4 id='method.from_real-1' class="method hidden"><code id='from_real.v-1'>fn <a href='../alga/linear/transformation/trait.Scaling.html#method.from_real' class='fnname'>from_real</a>(r: <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::vector::EuclideanSpace::RealField">RealField</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><R></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#386-388' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Attempts to convert a real to an element of this scaling subgroup. Same as <code>Self::from_superset()</code>. Returns <code>None</code> if no such scaling is possible for this subgroup. <a href="../alga/linear/transformation/trait.Scaling.html#method.from_real">Read more</a></p>
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</div><h4 id='method.powf-3' class="method hidden"><code id='powf.v-3'>fn <a href='../alga/linear/transformation/trait.Scaling.html#method.powf' class='fnname'>powf</a>(&self, n: <E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::vector::EuclideanSpace::RealField">RealField</a>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><R></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#391-393' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>Raises the scaling to a power. The result must be equivalent to <code>self.to_superset().powf(n)</code>. Returns <code>None</code> if the result is not representable by <code>Self</code>. <a href="../alga/linear/transformation/trait.Scaling.html#method.powf">Read more</a></p>
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</div><h4 id='method.scale_between-1' class="method hidden"><code id='scale_between.v-1'>fn <a href='../alga/linear/transformation/trait.Scaling.html#method.scale_between' class='fnname'>scale_between</a>(<br> a: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a>, <br> b: &<E as <a class="trait" href="../alga/linear/vector/trait.EuclideanSpace.html" title="trait alga::linear::vector::EuclideanSpace">EuclideanSpace</a>>::<a class="type" href="../alga/linear/vector/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::vector::EuclideanSpace::Coordinates">Coordinates</a><br>) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><R></code><a class='srclink' href='../src/alga/linear/transformation.rs.html#396-398' title='goto source code'>[src]</a></h4><div class='docblock hidden'><p>The scaling required to make <code>a</code> have the same norm as <code>b</code>, i.e., <code>|b| = |a| * norm_ratio(a, b)</code>. <a href="../alga/linear/transformation/trait.Scaling.html#method.scale_between">Read more</a></p>
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