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class="divider" data-v-822684d1><div class="divider-line" data-v-822684d1></div></div></div><!----></header><!----><!----><div class="VPContent is-home" id="VPContent" data-v-a9a9e638 data-v-91765379><div class="VPHome" data-v-91765379 data-v-cbb6ec48><!--[--><!--]--><div class="VPHero VPHomeHero" data-v-cbb6ec48 data-v-955009fc><div class="container" data-v-955009fc><div class="main" data-v-955009fc><!--[--><!--]--><!--[--><h1 class="name" data-v-955009fc><span class="clip" data-v-955009fc>Hecke</span></h1><!----><p class="tagline" data-v-955009fc>Computational number theory for everyone</p><!--]--><!--[--><!--]--><div class="actions" data-v-955009fc><!--[--><div class="action" data-v-955009fc><a class="VPButton medium alt" href="/v0.33.8/start/" data-v-955009fc data-v-14206e74>Getting Started</a></div><div class="action" data-v-955009fc><a class="VPButton medium alt" href="/v0.33.8/manual/" data-v-955009fc data-v-14206e74>Manual</a></div><div class="action" data-v-955009fc><a 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It is written in julia and makes use of the computer algebra packages Nemo and AbstractAlgebra.</p><!----></article><!--]--></div></div><div class="grid-2 item" data-v-d0a190d7><div class="VPLink no-icon VPFeature" data-v-d0a190d7 data-v-f5e9645b><!--[--><article class="box" data-v-f5e9645b><!----><h2 class="title" data-v-f5e9645b>OSCAR</h2><p class="details" data-v-f5e9645b>Hecke is part of the [OSCAR](https://www.oscar-system.org/) system, which covers, in addition to number theory, also commutative algebra, algebraic geometry, group theory and polyhedral geometry.</p><!----></article><!--]--></div></div><!--]--></div></div></div><!--[--><!--]--><div class="vp-doc container" style="" data-v-cbb6ec48 data-v-7a48a447><!--[--><div style="position:relative;" data-v-cbb6ec48><div><h2 id="features" tabindex="-1">Features <a class="header-anchor" href="#features" aria-label="Permalink to &quot;Features&quot;">​</a></h2><ul><li><p>Number fields (absolute, relative, simple and non-simple)</p></li><li><p>Orders and ideals in number fields</p></li><li><p>Class and unit group computations of orders</p></li><li><p>Lattice enumeration</p></li><li><p>Sparse linear algebra</p></li><li><p>Class field theory</p></li><li><p>Abelian groups</p></li><li><p>Associative algebras</p></li><li><p>Ideals and orders in (semsimple) associative algebras</p></li><li><p>Locally free class groups of orders in semisimple algebras</p></li><li><p>Quadratic and Hermitian forms and lattices</p></li></ul><h2 id="Citing-Hecke" tabindex="-1">Citing Hecke <a class="header-anchor" href="#Citing-Hecke" aria-label="Permalink to &quot;Citing Hecke {#Citing-Hecke}&quot;">​</a></h2><p>If your research depends on computations done with Hecke, please consider giving us a formal citation:</p><ul><li>Claus Fieker, William Hart, Tommy Hofmann and Fredrik Johansson, <a href="https://doi.acm.org/10.1145/3087604.3087611" target="_blank" rel="noreferrer">Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language</a>. In: Proceedings of ISSAC &#39;17, pages 157–164, New York, NY, USA, 2017. ACM.</li></ul><div class="language-bib vp-adaptive-theme"><button title="Copy Code" class="copy"></button><span class="lang">bib</span><pre class="shiki shiki-themes github-light github-dark vp-code" tabindex="0"><code><span class="line"><span>@inproceedings{nemo,</span></span>
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