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<!DOCTYPE html> <html lang="en"> <head> <title>Bertini input configuration -- a configuration option for a Bertini input file</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="software for numerical algebraic geometry" href="index.html">Bertini</a> :: <a title="a configuration option for a Bertini input file" href="___Bertini_spinput_spconfiguration.html">Bertini input configuration</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> <a href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">next</a> | <a href="___B_sq__Slice.html">previous</a> | <a href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">forward</a> | <a href="___B_sq__Slice.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>Bertini input configuration -- a configuration option for a Bertini input file</h1> <div> <div> <p>Refer to Appendix E of SIAM Bertini book for full details and list of options.</p> <p>MPType: Type of precision (0=double, 1=fixed higher, 2=adaptive).</p> <p>PRECISION: Precision, in bits, when used MPType=1. Precision is capitalized here to not conflict with Precision.</p> <p>ODEPredictor: Choice of predictor method (9 choices).</p> <p>TrackTolBeforeEG: Before endgame zone, Newton error must be less than this for success.</p> <p>TrackTolDuringEG: Same as previous, but during endgame.</p> <p>FinalTol: Path is deemed successful if final two endpoint approximations agree to FinalTol.</p> <p>MaxNorm: If SecurityLevel=0, path is truncated if two consecutive endpoint approximations exceed this value.</p> <p>MinStepSizeBeforeEG: Path is truncated if stepsize drops below this level before endgame.</p> <p>MinStepSizeDuringEG: Same as previous, but during endgame.</p> <p>ImagThreshold: Endpoint deemed real if infinity norm is smaller than this.</p> <p>CoeffBound: Useful only if MPType=2, bound on sum of coefficients of each polynomial.</p> <p>DegreeBound: Useful only if MPType=2, bound on degree of each polynomial.</p> <p>CondNumThreshold: Endpoint is deemed singular if multiple paths lead to it or condition number exceeds this.</p> <p>RandomSeed: Useful to repeat runs with the same random numbers.</p> <p>SingValZeroTol: Singular value is considered 0 if less than this value, when using fixed precision.</p> <p>EndGameNum: Choice of endgame (1=power series, 2=Cauchy, 3=trackback Cauchy).</p> <p>UseRegeneration: 1 to use regeneration for a zero-dimensional run.</p> <p>SecurityLevel: 1 to avoid truncation of possibly-infinite paths.</p> <p>ScreenOut: Level of output to the screen.</p> <p>OutputLevel: Level of output to files.</p> <p>StepsForIncrease: Number of consecutive Newton corrector successes before increase of stepsize.</p> <p>MaxNewtonIts: Newton corrector step deemed failed if no convergence prior to this number of iterations.</p> <p>MaxStepSize: Largest stepsize allowed.</p> <p>MaxNumberSteps: Max number of steps for entire path. Path failure if number of steps exceeds this.</p> <p>MaxCycleNum: Max cycle number considered during endgame.</p> <p>RegenStartLevel: Level at which regeneration begins.</p> <p>There are two recommended ways of using the optional arguments based on zero-dim solving and pos-dim solving.</p> <p>(1) Specify individual parameters in a function call:</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : CC[x,y]; F = {x^2-1,y^2-1};</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : bertiniZeroDimSolve(F,BertiniInputConfiguration=>{RandomSeed=>0,TrackTolBeforeEG=>1e-6,FinalTol=>1e-100}) o3 = {{1, 1}, {1, -1}, {-1, 1}, {-1, -1}} o3 : List</code></pre> </td> </tr> </table> <div> <p>(2) Store your frequently used favorites in an OptionTable and pass it as the last argument in each function call:</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i4 : opts = new OptionTable from {BertiniInputConfiguration=>{RandomSeed=>0,TrackTolBeforeEG=>1e-6,FinalTol=>1e-100}} o4 = OptionTable{BertiniInputConfiguration => {RandomSeed => 0, TrackTolBeforeEG => .000001, FinalTol => 1e-100}} o4 : OptionTable</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : G = {x^2+y^2-1};</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : bertiniPosDimSolve(G,opts) o6 = a "numerical variety" with components in dim 1: (dim=1,deg=2) o6 : NumericalVariety</code></pre> </td> </tr> </table> </div> <div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Bertini.m2:3373:0</span>.</p> </div> </div> </div> </body> </html>