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<!DOCTYPE html> <html lang="en"> <head> <title>Oscillators : Table of Contents</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="generation and analysis of oscillator steady states for small graphs" href="index.html">Oscillators</a> :: <a href="toc.html">Table of Contents</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> next | previous | forward | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <h1>Oscillators : Table of Contents</h1> <ul> <li><span><a title="generation and analysis of oscillator steady states for small graphs" href="index.html">Oscillators</a> -- generation and analysis of oscillator steady states for small graphs</span></li> <li><span><a title="Compute all unique principal minors of a given matrix" href="_all__Unique__Principal__Minors.html">allUniquePrincipalMinors</a> -- Compute all unique principal minors of a given matrix</span></li> <li><span><a title="generating all SCT graphs on n vertices" href="___Checking_spthe_spcodimension_spand_spirreducible_spdecomposition_spof_spthe_sp__I__G_spideal.html">Checking the codimension and irreducible decomposition of the IG ideal</a> -- generating all SCT graphs on n vertices</span></li> <li><span><a title="example 4.1 in arXiv 2312.16069" href="___Example_sp4.1_co_spunique_spgraph_spon_sp8_spvertices_spwith_spexotic_spsolutions_spand_spno_spinduced_spcycle_spof_splength_spat_spleast_sp5.html">Example 4.1: unique graph on 8 vertices with exotic solutions and no induced cycle of length at least 5</a> -- example 4.1 in arXiv 2312.16069</span></li> <li><span><a title="example 4.2 in arXiv 2312.16069" href="___Example_sp4.2_co_spa_sp__K5_spand_sppentagon_spglued_spalong_span_spedge.html">Example 4.2: a K5 and pentagon glued along an edge</a> -- example 4.2 in arXiv 2312.16069</span></li> <li><span><a title="example 4.3 in arXiv 2312.16069" href="___Example_sp4.3_co_spexamples_spof_spgluing_sptwo_spcycles_spalong_span_spedge.html">Example 4.3: examples of gluing two cycles along an edge</a> -- example 4.3 in arXiv 2312.16069</span></li> <li><span><a title="example 4.4 in arXiv 2312.16069" href="___Example_sp4.4_co_sp__The_spsquare_spwithin_spa_spsquare.html">Example 4.4: The square within a square</a> -- example 4.4 in arXiv 2312.16069</span></li> <li><span><a title="find real solutions, at least one per component for well-conditioned systems" href="_find__Real__Solutions.html">findRealSolutions</a> -- find real solutions, at least one per component for well-conditioned systems</span></li> <li><span><a title="generating all SCT graphs on n vertices" href="___Generation_spof_spall_sp__S__C__T_sp_lpsimple_cm_spconnected_cm_sp2-connected_rp_spgraphs_spon_spsmall_spnumbers_spof_spvertices.html">Generation of all SCT (simple, connected, 2-connected) graphs on small numbers of vertices</a> -- generating all SCT graphs on n vertices</span></li> <li><span><a title="Compute angles from a list of solutions" href="_get__Angles.html">getAngles</a> -- Compute angles from a list of solutions</span></li> <li><span><a title="Compute linearly stable solutions for the Kuramoto oscillator system associated to a graph" href="_get__Linearly__Stable__Solutions.html">getLinearlyStableSolutions</a> -- Compute linearly stable solutions for the Kuramoto oscillator system associated to a graph</span></li> <li><span><a title="Arxiv 2312.16069 reference" href="___Harrington-__Schenck-__Stillman.html">Harrington-Schenck-Stillman</a> -- Arxiv 2312.16069 reference</span></li> <li><span><a title="Identify the stability of a list of eigenvalues, or of potential solutions to the oscillator system" href="_identify__Stability.html">identifyStability</a> -- Identify the stability of a list of eigenvalues, or of potential solutions to the oscillator system</span></li> <li><span><a title="Check if a given solution is stable for the Kuramoto oscillator system" href="_is__Stable__Solution.html">isStableSolution</a> -- Check if a given solution is stable for the Kuramoto oscillator system</span></li> <li><span><a title="create the Jacobian for the oscillator system associated to a graph" href="_osc__Jacobian.html">oscJacobian</a> -- create the Jacobian for the oscillator system associated to a graph</span></li> <li><span><a title="find the homogeneous quadrics in the homogeneous Kuramoto ideal" href="_osc__Quadrics.html">oscQuadrics</a> -- find the homogeneous quadrics in the homogeneous Kuramoto ideal</span></li> <li><span><a title="create a polynomial ring for a given graph or number of oscillators" href="_osc__Ring.html">oscRing</a> -- create a polynomial ring for a given graph or number of oscillators</span></li> <li><span><a title="the ideal of the reduced equilibrium points of a dynamical system of oscillators" href="_osc__System.html">oscSystem</a> -- the ideal of the reduced equilibrium points of a dynamical system of oscillators</span></li> <li><span><a title="finding graphs of small size with exotic solutions" href="___S__C__T_spgraphs_spwith_spexotic_spsolutions.html">SCT graphs with exotic solutions</a> -- finding graphs of small size with exotic solutions</span></li> <li><span><a title="Display exotic solutions: linearly stable solutions which are not all-in-phase solution" href="_show__Exotic__Solutions.html">showExoticSolutions</a> -- Display exotic solutions: linearly stable solutions which are not all-in-phase solution</span></li> <li><span><a title="find the "standard solutions" for the oscillator system associated to a graph" href="_standard__Sols.html">standardSols</a> -- find the "standard solutions" for the oscillator system associated to a graph</span></li> <li><span><a title="computes the vertex spanning polynomial" href="_vertex__Spanning__Polynomial.html">vertexSpanningPolynomial</a> -- computes the vertex spanning polynomial</span></li> </ul> </body> </html>