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{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-05T13:34:43","documenter_version":"1.7.0"}}
{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-13T14:05:35","documenter_version":"1.7.0"}}
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2₀₀₁
2₀₁₀
1
2₁₀₀</code></pre><h2 id="Magnetic-space-groups"><a class="docs-heading-anchor" href="#Magnetic-space-groups">Magnetic space groups</a><a id="Magnetic-space-groups-1"></a><a class="docs-heading-anchor-permalink" href="#Magnetic-space-groups" title="Permalink"></a></h2><p>Magnetic space groups are accessible via <a href="../api/#Crystalline.mspacegroup-Union{Tuple{D}, Tuple{Integer, Integer}, Tuple{Integer, Integer, Val{D}}} where D"><code>mspacegroup</code></a>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../operations/">« Symmetry operations</a><a class="docs-footer-nextpage" href="../irreps/">Irreps »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Thursday 5 September 2024 13:34">Thursday 5 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2₁₀₀</code></pre><h2 id="Magnetic-space-groups"><a class="docs-heading-anchor" href="#Magnetic-space-groups">Magnetic space groups</a><a id="Magnetic-space-groups-1"></a><a class="docs-heading-anchor-permalink" href="#Magnetic-space-groups" title="Permalink"></a></h2><p>Magnetic space groups are accessible via <a href="../api/#Crystalline.mspacegroup-Union{Tuple{D}, Tuple{Integer, Integer}, Tuple{Integer, Integer, Val{D}}} where D"><code>mspacegroup</code></a>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../operations/">« Symmetry operations</a><a class="docs-footer-nextpage" href="../irreps/">Irreps »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 13 September 2024 14:05">Friday 13 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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&quot;Γ₃&quot; =&gt; COMPLEX
&quot;Γ₄&quot; =&gt; COMPLEX
&quot;Γ₅&quot; =&gt; COMPLEX
&quot;Γ₆&quot; =&gt; COMPLEX</code></pre><p>The reality type can be computed ab initio via <a href="../api/#Crystalline.calc_reality-Union{Tuple{D}, Tuple{LGIrrep{D}, AbstractArray{SymOperation{D}, 1}}, Tuple{LGIrrep{D}, AbstractArray{SymOperation{D}, 1}, Union{Nothing, Vector{&lt;:Real}}}} where D"><code>calc_reality</code></a>, using the Frobenius criterion for <code>PGIrrep</code>s and <code>SiteIrrep</code>s and the Herring criterion for <code>LGIrrep</code>s.</p><h2 id="Data-sources"><a class="docs-heading-anchor" href="#Data-sources">Data sources</a><a id="Data-sources-1"></a><a class="docs-heading-anchor-permalink" href="#Data-sources" title="Permalink"></a></h2><p>Point group irreps are obtained from the Bilbao Crystallographic Server&#39;s <a href="https://www.cryst.ehu.es/cgi-bin/cryst/programs/representations_point.pl?tipogrupo=spg">Representations PG program</a> and little group irreps of space groups are obtained from <a href="https://stokes.byu.edu/iso/irtables.php">ISOTROPY&#39;s 2011 ISO-IR dataset</a>.</p><p>If these functionalities are used in published research, please cite the original publications (listed in associated function docstrings).</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-Inui"><a class="tag is-link" href="#citeref-Inui">Inui</a>Inui, Tanabe, &amp; Onodera, <em>Group Theory and its Applications in Physics</em>, Springer (1990). Section 11.9.</li><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>Cracknell, A.P., Davies, B.L., Miller, S.C., &amp; Love, W.F., <em>Kronecker Product Tables, Vol. 1. General Introduction and Tables of Irreducible Representations of Space Groups</em>, New York: IFI/Plenum (1979).</li><li class="footnote" id="footnote-2"><a class="tag is-link" href="#citeref-2">2</a>Koster, G.F., Dimmock, J.O., Wheeler, R.G., &amp; Statz, H., <em>Properties of the Thirty-two Point Groups</em>, Cambridge: MIT Press (1963).</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../groups/">« Groups</a><a class="docs-footer-nextpage" href="../bravais/">Bravais types &amp; bases »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Thursday 5 September 2024 13:34">Thursday 5 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
&quot;Γ₆&quot; =&gt; COMPLEX</code></pre><p>The reality type can be computed ab initio via <a href="../api/#Crystalline.calc_reality-Union{Tuple{D}, Tuple{LGIrrep{D}, AbstractArray{SymOperation{D}, 1}}, Tuple{LGIrrep{D}, AbstractArray{SymOperation{D}, 1}, Union{Nothing, Vector{&lt;:Real}}}} where D"><code>calc_reality</code></a>, using the Frobenius criterion for <code>PGIrrep</code>s and <code>SiteIrrep</code>s and the Herring criterion for <code>LGIrrep</code>s.</p><h2 id="Data-sources"><a class="docs-heading-anchor" href="#Data-sources">Data sources</a><a id="Data-sources-1"></a><a class="docs-heading-anchor-permalink" href="#Data-sources" title="Permalink"></a></h2><p>Point group irreps are obtained from the Bilbao Crystallographic Server&#39;s <a href="https://www.cryst.ehu.es/cgi-bin/cryst/programs/representations_point.pl?tipogrupo=spg">Representations PG program</a> and little group irreps of space groups are obtained from <a href="https://stokes.byu.edu/iso/irtables.php">ISOTROPY&#39;s 2011 ISO-IR dataset</a>.</p><p>If these functionalities are used in published research, please cite the original publications (listed in associated function docstrings).</p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-Inui"><a class="tag is-link" href="#citeref-Inui">Inui</a>Inui, Tanabe, &amp; Onodera, <em>Group Theory and its Applications in Physics</em>, Springer (1990). Section 11.9.</li><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>Cracknell, A.P., Davies, B.L., Miller, S.C., &amp; Love, W.F., <em>Kronecker Product Tables, Vol. 1. General Introduction and Tables of Irreducible Representations of Space Groups</em>, New York: IFI/Plenum (1979).</li><li class="footnote" id="footnote-2"><a class="tag is-link" href="#citeref-2">2</a>Koster, G.F., Dimmock, J.O., Wheeler, R.G., &amp; Statz, H., <em>Properties of the Thirty-two Point Groups</em>, Cambridge: MIT Press (1963).</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../groups/">« Groups</a><a class="docs-footer-nextpage" href="../bravais/">Bravais types &amp; bases »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 13 September 2024 14:05">Friday 13 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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<span class="sgr90"> └ 0 1 0 ╵ 0 ┘</span></code></pre><h2 id="Operator-inverses"><a class="docs-heading-anchor" href="#Operator-inverses">Operator inverses</a><a id="Operator-inverses-1"></a><a class="docs-heading-anchor-permalink" href="#Operator-inverses" title="Permalink"></a></h2><p>The operator inverse is defined as <span>$\{\mathbf{W}|\mathbf{w}\} = \{\mathbf{W}^{-1}|-\mathbf{W}^{-1}\mathbf{w}\}$</span> and can be computed via</p><pre><code class="language-julia hljs">inv(op1) # inv(3₁₁₁⁺)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">3₁₁₁⁻<span class="sgr90"> ──────────────────────────── (y,z,x)</span>
<span class="sgr90"> ┌ 0 1 0 ╷ -0 ┐</span>
<span class="sgr90"> │ 0 0 1 ┆ -0 │</span>
<span class="sgr90"> └ 1 0 0 ╵ -0 ┘</span></code></pre><h2 id="Action-of-symmetry-operators"><a class="docs-heading-anchor" href="#Action-of-symmetry-operators">Action of symmetry operators</a><a id="Action-of-symmetry-operators-1"></a><a class="docs-heading-anchor-permalink" href="#Action-of-symmetry-operators" title="Permalink"></a></h2><p>A <code>SymOperation</code> can act on vectors in direct (<a href="../api/#Crystalline.RVec-Union{Tuple{AbstractString}, Tuple{D}} where D"><code>RVec</code></a>) or reciprocal (<a href="../api/#Crystalline.KVec-Union{Tuple{AbstractString}, Tuple{D}} where D"><code>KVec</code></a>) space. When acting in reciprocal space, translation parts of a <code>SymOperation</code> have no effect.</p><h1 id="Magnetic-symmetry-operations"><a class="docs-heading-anchor" href="#Magnetic-symmetry-operations">Magnetic symmetry operations</a><a id="Magnetic-symmetry-operations-1"></a><a class="docs-heading-anchor-permalink" href="#Magnetic-symmetry-operations" title="Permalink"></a></h1><p>Magnetic symmetry operations that may incorporate composition with an anti-unitary time-reversal operation can be created via <a href="../api/#Crystalline.MSymOperation"><code>MSymOperation</code></a> (see also <a href="../api/#Crystalline.mspacegroup-Union{Tuple{D}, Tuple{Integer, Integer}, Tuple{Integer, Integer, Val{D}}} where D"><code>mspacegroup</code></a>).</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../groups/">Groups »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Thursday 5 September 2024 13:34">Thursday 5 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<span class="sgr90"> └ 1 0 0 ╵ -0 ┘</span></code></pre><h2 id="Action-of-symmetry-operators"><a class="docs-heading-anchor" href="#Action-of-symmetry-operators">Action of symmetry operators</a><a id="Action-of-symmetry-operators-1"></a><a class="docs-heading-anchor-permalink" href="#Action-of-symmetry-operators" title="Permalink"></a></h2><p>A <code>SymOperation</code> can act on vectors in direct (<a href="../api/#Crystalline.RVec-Union{Tuple{AbstractString}, Tuple{D}} where D"><code>RVec</code></a>) or reciprocal (<a href="../api/#Crystalline.KVec-Union{Tuple{AbstractString}, Tuple{D}} where D"><code>KVec</code></a>) space. When acting in reciprocal space, translation parts of a <code>SymOperation</code> have no effect.</p><h1 id="Magnetic-symmetry-operations"><a class="docs-heading-anchor" href="#Magnetic-symmetry-operations">Magnetic symmetry operations</a><a id="Magnetic-symmetry-operations-1"></a><a class="docs-heading-anchor-permalink" href="#Magnetic-symmetry-operations" title="Permalink"></a></h1><p>Magnetic symmetry operations that may incorporate composition with an anti-unitary time-reversal operation can be created via <a href="../api/#Crystalline.MSymOperation"><code>MSymOperation</code></a> (see also <a href="../api/#Crystalline.mspacegroup-Union{Tuple{D}, Tuple{Integer, Integer}, Tuple{Integer, Integer, Val{D}}} where D"><code>mspacegroup</code></a>).</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../groups/">Groups »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 13 September 2024 14:05">Friday 13 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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