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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="This represents an element of a group with basic operations that can be performed. This allows an FFT implementation (for example) to operate generically over either a field or elliptic curve group."><meta name="keywords" content="rust, rustlang, rust-lang, Group"><title>Group in halo2_proofs::arithmetic - Rust</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../normalize.css"><link rel="stylesheet" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../ayu.css" disabled><link rel="stylesheet" href="../../dark.css" disabled><link rel="stylesheet" href="../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../storage.js"></script><script defer src="sidebar-items.js"></script><script defer src="../../main.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../favicon.svg"><link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.10.0/dist/katex.min.css" integrity="sha384-9eLZqc9ds8eNjO3TmqPeYcDj8n+Qfa4nuSiGYa6DjLNcv9BtN69ZIulL9+8CqC9Y" crossorigin="anonymous">
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</head><body class="rustdoc trait"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="mobile-topbar"><button class="sidebar-menu-toggle">☰</button><a class="sidebar-logo" href="../../halo2_proofs/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><h2 class="location"></h2></nav><nav class="sidebar"><a class="sidebar-logo" href="../../halo2_proofs/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a><h2 class="location"><a href="#">Group</a></h2><div class="sidebar-elems"><section><h3><a href="#required-associated-types">Required Associated Types</a></h3><ul class="block"><li><a href="#associatedtype.Scalar">Scalar</a></li></ul><h3><a href="#required-methods">Required Methods</a></h3><ul class="block"><li><a href="#tymethod.group_add">group_add</a></li><li><a href="#tymethod.group_scale">group_scale</a></li><li><a href="#tymethod.group_sub">group_sub</a></li><li><a href="#tymethod.group_zero">group_zero</a></li></ul><h3><a href="#implementors">Implementors</a></h3></section><h2 class="location"><a href="index.html">In halo2_proofs::arithmetic</a></h2></div></nav><main><div class="width-limiter"><div class="sub-container"><nav class="sub"><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../wheel.svg"></a></div></div></form></nav></div><section id="main-content" class="content"><div class="main-heading"><h1 class="fqn">Trait <a href="../index.html">halo2_proofs</a>::<wbr><a href="index.html">arithmetic</a>::<wbr><a class="trait" href="#">Group</a><button id="copy-path" onclick="copy_path(this)" title="Copy item path to clipboard"><img src="../../clipboard.svg" width="19" height="18" alt="Copy item path"></button></h1><span class="out-of-band"><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class="inner">−</span>]</a></span></div><div class="item-decl"><pre class="rust trait"><code>pub trait Group: 'static + <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Copy.html" title="trait core::marker::Copy">Copy</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html" title="trait core::clone::Clone">Clone</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Send.html" title="trait core::marker::Send">Send</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Sync.html" title="trait core::marker::Sync">Sync</a> {
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type <a href="#associatedtype.Scalar" class="associatedtype">Scalar</a>: <a class="trait" href="trait.FieldExt.html" title="trait halo2_proofs::arithmetic::FieldExt">FieldExt</a>;
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fn <a href="#tymethod.group_zero" class="fnname">group_zero</a>() -> Self;
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<span class="item-spacer"></span> fn <a href="#tymethod.group_add" class="fnname">group_add</a>(&mut self, rhs: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self);
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<span class="item-spacer"></span> fn <a href="#tymethod.group_sub" class="fnname">group_sub</a>(&mut self, rhs: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self);
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<span class="item-spacer"></span> fn <a href="#tymethod.group_scale" class="fnname">group_scale</a>(&mut self, by: &Self::<a class="associatedtype" href="trait.Group.html#associatedtype.Scalar" title="type halo2_proofs::arithmetic::Group::Scalar">Scalar</a>);
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}</code></pre></div><details class="rustdoc-toggle top-doc" open><summary class="hideme"><span>Expand description</span></summary><div class="docblock"><p>This represents an element of a group with basic operations that can be
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performed. This allows an FFT implementation (for example) to operate
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generically over either a field or elliptic curve group.</p>
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</div></details><h2 id="required-associated-types" class="small-section-header">Required Associated Types<a href="#required-associated-types" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle method-toggle" open><summary><section id="associatedtype.Scalar" class="method has-srclink"><h4 class="code-header">type <a href="#associatedtype.Scalar" class="associatedtype">Scalar</a>: <a class="trait" href="trait.FieldExt.html" title="trait halo2_proofs::arithmetic::FieldExt">FieldExt</a></h4></section></summary><div class="docblock"><p>The group is assumed to be of prime order $p$. <code>Scalar</code> is the
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associated scalar field of size $p$.</p>
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</div></details></div><h2 id="required-methods" class="small-section-header">Required Methods<a href="#required-methods" class="anchor"></a></h2><div class="methods"><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.group_zero" class="method has-srclink"><h4 class="code-header">fn <a href="#tymethod.group_zero" class="fnname">group_zero</a>() -> Self</h4></section></summary><div class="docblock"><p>Returns the additive identity of the group.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.group_add" class="method has-srclink"><h4 class="code-header">fn <a href="#tymethod.group_add" class="fnname">group_add</a>(&mut self, rhs: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self)</h4></section></summary><div class="docblock"><p>Adds <code>rhs</code> to this group element.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.group_sub" class="method has-srclink"><h4 class="code-header">fn <a href="#tymethod.group_sub" class="fnname">group_sub</a>(&mut self, rhs: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self)</h4></section></summary><div class="docblock"><p>Subtracts <code>rhs</code> from this group element.</p>
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</div></details><details class="rustdoc-toggle method-toggle" open><summary><section id="tymethod.group_scale" class="method has-srclink"><h4 class="code-header">fn <a href="#tymethod.group_scale" class="fnname">group_scale</a>(&mut self, by: &Self::<a class="associatedtype" href="trait.Group.html#associatedtype.Scalar" title="type halo2_proofs::arithmetic::Group::Scalar">Scalar</a>)</h4></section></summary><div class="docblock"><p>Scales this group element by a scalar.</p>
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</div></details></div><h2 id="implementors" class="small-section-header">Implementors<a href="#implementors" class="anchor"></a></h2><div id="implementors-list"><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-Group-for-Ep" class="impl has-srclink"><a href="#impl-Group-for-Ep" class="anchor"></a><h3 class="code-header">impl <a class="trait" href="trait.Group.html" title="trait halo2_proofs::arithmetic::Group">Group</a> for Ep</h3></section></summary><div class="impl-items"><section id="associatedtype.Scalar-1" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.Scalar-1" class="anchor"></a><h4 class="code-header">type <a href="#associatedtype.Scalar" class="associatedtype">Scalar</a> = Fq</h4></section></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-Group-for-Eq" class="impl has-srclink"><a href="#impl-Group-for-Eq" class="anchor"></a><h3 class="code-header">impl <a class="trait" href="trait.Group.html" title="trait halo2_proofs::arithmetic::Group">Group</a> for Eq</h3></section></summary><div class="impl-items"><section id="associatedtype.Scalar-2" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.Scalar-2" class="anchor"></a><h4 class="code-header">type <a href="#associatedtype.Scalar" class="associatedtype">Scalar</a> = Fp</h4></section></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-Group-for-Fp" class="impl has-srclink"><a href="#impl-Group-for-Fp" class="anchor"></a><h3 class="code-header">impl <a class="trait" href="trait.Group.html" title="trait halo2_proofs::arithmetic::Group">Group</a> for Fp</h3></section></summary><div class="impl-items"><section id="associatedtype.Scalar-3" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.Scalar-3" class="anchor"></a><h4 class="code-header">type <a href="#associatedtype.Scalar" class="associatedtype">Scalar</a> = Fp</h4></section></div></details><details class="rustdoc-toggle implementors-toggle"><summary><section id="impl-Group-for-Fq" class="impl has-srclink"><a href="#impl-Group-for-Fq" class="anchor"></a><h3 class="code-header">impl <a class="trait" href="trait.Group.html" title="trait halo2_proofs::arithmetic::Group">Group</a> for Fq</h3></section></summary><div class="impl-items"><section id="associatedtype.Scalar-4" class="associatedtype trait-impl has-srclink"><a href="#associatedtype.Scalar-4" class="anchor"></a><h4 class="code-header">type <a href="#associatedtype.Scalar" class="associatedtype">Scalar</a> = Fq</h4></section></div></details></div><script src="../../implementors/pasta_curves/arithmetic/trait.Group.js" data-ignore-extern-crates="pasta_curves" async></script></section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="halo2_proofs" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (06f049a35 2022-10-17)" ></div></body></html> |