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Documenter.jl committed Jun 28, 2024
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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-06-27T15:11:40","documenter_version":"1.4.1"}}
{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-06-28T19:25:46","documenter_version":"1.4.1"}}
2 changes: 1 addition & 1 deletion dev/Example/index.html
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3*q[1]^4*q[4]^2</code></pre><pre><code class="language-julia hljs">julia&gt; feynman_integral_branch_type(F, a)
6*q[1]^4*q[4]^2</code></pre><pre><code class="language-julia hljs">julia&gt; feynman_integral_degree(F, 3)
6*q[1]^4*q[2]^2 + 6*q[1]^4*q[3]^2 + 6*q[1]^4*q[4]^2 + 18*q[1]^2*q[2]^4 + 6*q[1]^2*q[2]^2*q[3]^2 + 6*q[1]^2*q[2]^2*q[4]^2 + 18*q[1]^2*q[3]^4 + 6*q[1]^2*q[3]^2*q[4]^2 + 18*q[1]^2*q[4]^4</code></pre><pre><code class="language-julia hljs">julia&gt; substitute(feynman_integral_sum(F, 8))
20640*q[1]^16 + 9996*q[1]^14 + 4320*q[1]^12 + 1650*q[1]^10 + 456*q[1]^8 + 90*q[1]^6 + 6*q[1]^4</code></pre></article><nav class="docs-footer"><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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Thursday 27 June 2024 15:11">Thursday 27 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
20640*q[1]^16 + 9996*q[1]^14 + 4320*q[1]^12 + 1650*q[1]^10 + 456*q[1]^8 + 90*q[1]^6 + 6*q[1]^4</code></pre></article><nav class="docs-footer"><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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Friday 28 June 2024 19:25">Friday 28 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/Feynman Integral/Feynman/index.html
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We compute the Feynman integral over all the partitions of the degree d of graph G for all vertex ordering.
</code></pre><p>jldoctest graph julia&gt; feynman<em>integral</em>degree(F,3) # here d=3 6<em>q[1]^4</em>q[2]^2 + 6<em>q[1]^4</em>q[3]^2 + 6<em>q[1]^4</em>q[4]^2 + 18<em>q[1]^2</em>q[2]^4 + 6<em>q[1]^2</em>q[2]^2<em>q[3]^2 + 6</em>q[1]^2<em>q[2]^2</em>q[4]^2 + 18<em>q[1]^2</em>q[3]^4 + 6<em>q[1]^2</em>q[3]^2<em>q[4]^2 + 18</em>q[1]^2*q[4]^4</p><pre><code class="nohighlight hljs">
We compute the sum of coefficients.
</code></pre><p>julia&gt; sum<em>of</em>coeff( feynman<em>integral</em>degree(F,3)) 90 ```</p></article><nav class="docs-footer"><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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Thursday 27 June 2024 15:11">Thursday 27 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
</code></pre><p>julia&gt; sum<em>of</em>coeff( feynman<em>integral</em>degree(F,3)) 90 ```</p></article><nav class="docs-footer"><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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Friday 28 June 2024 19:25">Friday 28 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/Gromov/index.html
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3*q[1]^4*q[4]^2</code></pre><pre><code class="language-julia hljs">julia&gt; feynman_integral_branch_type(F, a)
6*q[1]^4*q[4]^2</code></pre><pre><code class="language-julia hljs">julia&gt; feynman_integral_degree(F, 3)
6*q[1]^4*q[2]^2 + 6*q[1]^4*q[3]^2 + 6*q[1]^4*q[4]^2 + 18*q[1]^2*q[2]^4 + 6*q[1]^2*q[2]^2*q[3]^2 + 6*q[1]^2*q[2]^2*q[4]^2 + 18*q[1]^2*q[3]^4 + 6*q[1]^2*q[3]^2*q[4]^2 + 18*q[1]^2*q[4]^4</code></pre><pre><code class="language-julia hljs">julia&gt; substitute(q,feynman_integral_sum(F, 8))
20640*q[1]^16 + 9996*q[1]^14 + 4320*q[1]^12 + 1650*q[1]^10 + 456*q[1]^8 + 90*q[1]^6 + 6*q[1]^4</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Hurwitz/">« Examples Hurwitz numbers.</a><a class="docs-footer-nextpage" href="../Overview/">Functions »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Thursday 27 June 2024 15:11">Thursday 27 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
20640*q[1]^16 + 9996*q[1]^14 + 4320*q[1]^12 + 1650*q[1]^10 + 456*q[1]^8 + 90*q[1]^6 + 6*q[1]^4</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../Hurwitz/">« Examples Hurwitz numbers.</a><a class="docs-footer-nextpage" href="../Overview/">Functions »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Friday 28 June 2024 19:25">Friday 28 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/Hurwitz/index.html
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128*q[2]^4*q[3]^2*q[6]^2</code></pre><p>The Feynman Integral branch type for all ordering is</p><pre><code class="language-julia hljs">julia&gt; feynman_integral_branch_type(F, a)
256*q[2]^4*q[3]^2*q[6]^2</code></pre><p>also we can compute Feynman Integral of degree 3</p><pre><code class="language-julia hljs">julia&gt; f = feynman_integral_degree(F, 3)
288*q[1]^6 + 32*q[1]^4*q[2]^2 + 32*q[1]^4*q[3]^2 + 32*q[1]^4*q[5]^2 + 32*q[1]^4*q[6]^2 + 8*q[1]^2*q[2]^2*q[5]^2 + 8*q[1]^2*q[2]^2*q[6]^2 + 8*q[1]^2*q[3]^2*q[5]^2 + 8*q[1]^2*q[3]^2*q[6]^2 + 24*q[2]^6 + 152*q[2]^4*q[3]^2 + 8*q[2]^4*q[5]^2 + 8*q[2]^4*q[6]^2 + 152*q[2]^2*q[3]^4 + 32*q[2]^2*q[3]^2*q[5]^2 + 32*q[2]^2*q[3]^2*q[6]^2 + 32*q[2]^2*q[4]^4 + 8*q[2]^2*q[4]^2*q[5]^2 + 8*q[2]^2*q[4]^2*q[6]^2 + 8*q[2]^2*q[5]^4 + 32*q[2]^2*q[5]^2*q[6]^2 + 8*q[2]^2*q[6]^4 + 24*q[3]^6 + 8*q[3]^4*q[5]^2 + 8*q[3]^4*q[6]^2 + 32*q[3]^2*q[4]^4 + 8*q[3]^2*q[4]^2*q[5]^2 + 8*q[3]^2*q[4]^2*q[6]^2 + 8*q[3]^2*q[5]^4 + 32*q[3]^2*q[5]^2*q[6]^2 + 8*q[3]^2*q[6]^4 + 288*q[4]^6 + 32*q[4]^4*q[5]^2 + 32*q[4]^4*q[6]^2 + 24*q[5]^6 + 152*q[5]^4*q[6]^2 + 152*q[5]^2*q[6]^4 + 24*q[6]^6</code></pre><p>Finally we substitute all <span>$q$</span> variables by <span>$q_{1}$</span> after computing the sum of all Feynman Integral of degree up to 8.</p><pre><code class="language-julia hljs">julia&gt; substitute(q,feynman_integral_degree_sum(F,8))
10246144*q[1]^16 + 3294720*q[1]^14 + 886656*q[1]^12 + 182272*q[1]^10 + 25344*q[1]^8 + 1792*q[1]^6 + 32*q[1]^4</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../SmallExample/">« First example</a><a class="docs-footer-nextpage" href="../Gromov/">Examples Gromov-Witten invariants »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Thursday 27 June 2024 15:11">Thursday 27 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
10246144*q[1]^16 + 3294720*q[1]^14 + 886656*q[1]^12 + 182272*q[1]^10 + 25344*q[1]^8 + 1792*q[1]^6 + 32*q[1]^4</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../SmallExample/">« First example</a><a class="docs-footer-nextpage" href="../Gromov/">Examples Gromov-Witten invariants »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.4.1 on <span class="colophon-date" title="Friday 28 June 2024 19:25">Friday 28 June 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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