<!DOCTYPE html><htmllang="en"><head><metacharset="utf-8"><metaname="viewport"content="width=device-width, initial-scale=1.0"><metaname="generator"content="rustdoc"><metaname="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."><metaname="keywords"content="rust, rustlang, rust-lang, Group"><title>Group in halo2_proofs::arithmetic - Rust</title><linkrel="preload"as="font"type="font/woff2"crossoriginhref="../../SourceSerif4-Regular.ttf.woff2"><linkrel="preload"as="font"type="font/woff2"crossoriginhref="../../FiraSans-Regular.woff2"><linkrel="preload"as="font"type="font/woff2"crossoriginhref="../../FiraSans-Medium.woff2"><linkrel="preload"as="font"type="font/woff2"crossoriginhref="../../SourceCodePro-Regular.ttf.woff2"><linkrel="preload"as="font"type="font/woff2"crossoriginhref="../../SourceSerif4-Bold.ttf.woff2"><linkrel="preload"as="font"type="font/woff2"crossoriginhref="../../SourceCodePro-Semibold.ttf.woff2"><linkrel="stylesheet"type="text/css"href="../../normalize.css"><linkrel="stylesheet"type="text/css"href="../../rustdoc.css"id="mainThemeStyle"><linkrel="stylesheet"type="text/css"href="../../ayu.css"disabled><linkrel="stylesheet"type="text/css"href="../../dark.css"disabled><linkrel="stylesheet"type="text/css"href="../../light.css"id="themeStyle"><scriptid="default-settings"></script><scriptsrc="../../storage.js"></script><scriptsrc="../../crates.js"></script><scriptdefersrc="../../main.js"></script>
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</a><h2class="location"><ahref="#">Trait Group</a></h2><divclass="sidebar-elems"><divclass="block items"><h3class="sidebar-title"><ahref="#associated-types">Associated Types</a></h3><divclass="sidebar-links"><ahref="#associatedtype.Scalar">Scalar</a></div><h3class="sidebar-title"><ahref="#required-methods">Required Methods</a></h3><divclass="sidebar-links"><ahref="#tymethod.group_add">group_add</a><ahref="#tymethod.group_scale">group_scale</a><ahref="#tymethod.group_sub">group_sub</a><ahref="#tymethod.group_zero">group_zero</a></div><h3class="sidebar-title"><ahref="#foreign-impls">Implementations on Foreign Types</a></h3><divclass="sidebar-links"><ahref="#impl-Group-for-Ep">Ep</a><ahref="#impl-Group-for-Eq">Eq</a><ahref="#impl-Group-for-Fp">Fp</a><ahref="#impl-Group-for-Fq">Fq</a></div><h3class="sidebar-title"><ahref="#implementors">Implementors</a></h3></div><h2class="location">Other items in<br><ahref="../index.html">halo2_proofs</a>::<wbr><ahref="index.html">arithmetic</a></h2><divid="sidebar-vars"data-name="Group"data-ty="trait"data-relpath=""></div><scriptdefersrc="sidebar-items.js"></script></div></nav><main><divclass="width-limiter"><divclass="sub-container"><aclass="sub-logo-container"href="../../halo2_proofs/index.html"><imgclass="rust-logo"src="../../rust-logo.svg"alt="logo"></a><navclass="sub"><divclass="theme-picker"><buttonid="theme-picker"aria-label="Pick another theme!"aria-haspopup="menu"title="themes"><imgwidth="18"height="18"alt="Pick another theme!"src="../../brush.svg"></button><divid="theme-choices"role="menu"></div></div><formclass="search-form"><divclass="search-container"><div>
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type <ahref="#associatedtype.Scalar"class="associatedtype">Scalar</a>: <aclass="trait"href="trait.FieldExt.html"title="trait halo2_proofs::arithmetic::FieldExt">FieldExt</a>;
}</code></pre></div><detailsclass="rustdoc-toggle top-doc"open><summaryclass="hideme"><span>Expand description</span></summary><divclass="docblock"><p>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.</p>
</div></details><h2id="associated-types"class="small-section-header">Associated Types<ahref="#associated-types"class="anchor"></a></h2><divclass="methods"><detailsclass="rustdoc-toggle"open><summary><divid="associatedtype.Scalar"class="method has-srclink"><divclass="rightside"></div><h4class="code-header">type <ahref="#associatedtype.Scalar"class="associatedtype">Scalar</a>: <aclass="trait"href="trait.FieldExt.html"title="trait halo2_proofs::arithmetic::FieldExt">FieldExt</a></h4></div></summary><divclass="docblock"><p>The group is assumed to be of prime order $p$. <code>Scalar</code> is the
associated scalar field of size $p$.</p>
</div></details></div><h2id="required-methods"class="small-section-header">Required methods<ahref="#required-methods"class="anchor"></a></h2><divclass="methods"><detailsclass="rustdoc-toggle"open><summary><divid="tymethod.group_zero"class="method has-srclink"><divclass="rightside"></div><h4class="code-header">fn <ahref="#tymethod.group_zero"class="fnname">group_zero</a>() -> Self</h4></div></summary><divclass="docblock"><p>Returns the additive identity of the group.</p>
</div></details><detailsclass="rustdoc-toggle"open><summary><divid="tymethod.group_add"class="method has-srclink"><divclass="rightside"></div><h4class="code-header">fn <ahref="#tymethod.group_add"class="fnname">group_add</a>(&mut self, rhs: <aclass="primitive"href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self)</h4></div></summary><divclass="docblock"><p>Adds <code>rhs</code> to this group element.</p>
</div></details><detailsclass="rustdoc-toggle"open><summary><divid="tymethod.group_sub"class="method has-srclink"><divclass="rightside"></div><h4class="code-header">fn <ahref="#tymethod.group_sub"class="fnname">group_sub</a>(&mut self, rhs: <aclass="primitive"href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self)</h4></div></summary><divclass="docblock"><p>Subtracts <code>rhs</code> from this group element.</p>
</div></details><detailsclass="rustdoc-toggle"open><summary><divid="tymethod.group_scale"class="method has-srclink"><divclass="rightside"></div><h4class="code-header">fn <ahref="#tymethod.group_scale"class="fnname">group_scale</a>(&mut self, by: &Self::<aclass="associatedtype"href="trait.Group.html#associatedtype.Scalar"title="type halo2_proofs::arithmetic::Group::Scalar">Scalar</a>)</h4></div></summary><divclass="docblock"><p>Scales this group element by a scalar.</p>
