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{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-06-28T19:25:46","documenter_version":"1.4.1"}}
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Feynman Integral · GromovWitten.jl</title><meta name="title" content="Feynman Integral · GromovWitten.jl"/><meta property="og:title" content="Feynman Integral · GromovWitten.jl"/><meta property="twitter:title" content="Feynman Integral · GromovWitten.jl"/><meta name="description" content="Documentation for GromovWitten.jl."/><meta property="og:description" content="Documentation for GromovWitten.jl."/><meta property="twitter:description" content="Documentation for GromovWitten.jl."/><meta property="og:url" content="https://singular-gpispace.github.io/GromovWitten.git/Feynman Integral/Feynman/"/><meta property="twitter:url" content="https://singular-gpispace.github.io/GromovWitten.git/Feynman Integral/Feynman/"/><link rel="canonical" href="https://singular-gpispace.github.io/GromovWitten.git/Feynman Integral/Feynman/"/><script data-outdated-warner 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href="../../SmallExample/">First example</a></li></ul></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../../Hurwitz/">Examples Hurwitz numbers.</a></li><li><a class="tocitem" href="../../Gromov/">Examples Gromov-Witten invariants</a></li></ul></li><li><a class="tocitem" href="../../Overview/">Functions</a></li><li><a class="tocitem" href="../../quasimodular/">Quasimodular</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Feynman Integral</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Feynman Integral</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/singular-gpispace/GromovWitten" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/singular-gpispace/GromovWitten/blob/main/docs/src/Feynman Integral/Feynman.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Feynman-Integral"><a class="docs-heading-anchor" href="#Feynman-Integral">Feynman Integral</a><a id="Feynman-Integral-1"></a><a class="docs-heading-anchor-permalink" href="#Feynman-Integral" title="Permalink"></a></h1><h2 id="Graph"><a class="docs-heading-anchor" href="#Graph">Graph</a><a id="Graph-1"></a><a class="docs-heading-anchor-permalink" href="#Graph" title="Permalink"></a></h2><p>A Feynman graph is a (non-metrized) graph Γ without ends with n vertices which are labeled <span>$x_1, . . . , x_n$</span> and with labeled edges <span>$q_1, . . . , q_r$</span>. The graph <span>$G$</span> is represented as a collection of vertices <span>$V$</span> and edges <span>$E$</span>. Each edge is a pair <span>$(v,w)$</span> where both <span>$v$</span> and <span>$w$</span> are elements of the set of vertices <span>$V$</span>.</p><pre><code class="language-julia-repl hljs">julia&gt; ve=[(1, 1), (1, 2), (2, 3), (3, 1)]
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Feynman Integral · GromovWitten.jl</title><meta name="title" content="Feynman Integral · GromovWitten.jl"/><meta property="og:title" content="Feynman Integral · GromovWitten.jl"/><meta property="twitter:title" content="Feynman Integral · GromovWitten.jl"/><meta name="description" content="Documentation for GromovWitten.jl."/><meta property="og:description" content="Documentation for GromovWitten.jl."/><meta property="twitter:description" content="Documentation for GromovWitten.jl."/><meta property="og:url" content="https://singular-gpispace.github.io/GromovWitten.git/Feynman Integral/Feynman/"/><meta property="twitter:url" content="https://singular-gpispace.github.io/GromovWitten.git/Feynman Integral/Feynman/"/><link rel="canonical" href="https://singular-gpispace.github.io/GromovWitten.git/Feynman Integral/Feynman/"/><script data-outdated-warner 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data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../../">GromovWitten.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><span class="tocitem">Home</span><ul><li><a class="tocitem" href="../../">GromovWitten</a></li><li><a class="tocitem" href="../../Installation/">Installation</a></li><li><a class="tocitem" href="../../SmallExample/">First example</a></li></ul></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../../Hurwitz/">Examples Hurwitz numbers.</a></li><li><a class="tocitem" href="../../Gromov/">Examples Gromov-Witten invariants</a></li></ul></li><li><a class="tocitem" href="../../Overview/">Functions</a></li><li><span class="tocitem">Quasimodular</span><ul><li><a class="tocitem" href="../../quasimodular/">Quasimodular</a></li><li><a class="tocitem" href="../../quasimodular_psi/">Quasimodular</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Feynman Integral</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Feynman Integral</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/singular-gpispace/GromovWitten" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/singular-gpispace/GromovWitten/blob/main/docs/src/Feynman Integral/Feynman.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Feynman-Integral"><a class="docs-heading-anchor" href="#Feynman-Integral">Feynman Integral</a><a id="Feynman-Integral-1"></a><a class="docs-heading-anchor-permalink" href="#Feynman-Integral" title="Permalink"></a></h1><h2 id="Graph"><a class="docs-heading-anchor" href="#Graph">Graph</a><a id="Graph-1"></a><a class="docs-heading-anchor-permalink" href="#Graph" title="Permalink"></a></h2><p>A Feynman graph is a (non-metrized) graph Γ without ends with n vertices which are labeled <span>$x_1, . . . , x_n$</span> and with labeled edges <span>$q_1, . . . , q_r$</span>. The graph <span>$G$</span> is represented as a collection of vertices <span>$V$</span> and edges <span>$E$</span>. Each edge is a pair <span>$(v,w)$</span> where both <span>$v$</span> and <span>$w$</span> are elements of the set of vertices <span>$V$</span>.</p><pre><code class="language-julia-repl hljs">julia&gt; ve=[(1, 1), (1, 2), (2, 3), (3, 1)]
4-element Vector{Tuple{Int64, Int64}}:
(1, 1)
(1, 2)
Expand All @@ -25,4 +25,4 @@
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="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>
</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><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="Wednesday 30 October 2024 10:48">Wednesday 30 October 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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