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<!DOCTYPE html> <html lang="en"> <head> <title>sendra -- the system sendra</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="examples of polynomial systems" href="index.html">ExampleSystems</a> :: <a title="the system sendra" href="_sendra.html">sendra</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="_trinks.html">next</a> | <a href="_rose.html">previous</a> | <a href="_trinks.html">forward</a> | <a href="_rose.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>sendra -- the system sendra</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">sendra(kk)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">kk</span>, <span>a <a title="the class of all rings" href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, the coefficient ring</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>a <a title="the class of all lists -- {...}" href="../../Macaulay2Doc/html/___List.html">list</a></span>, of polynomials in the system</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>This system was solved in May 2020, using <a title="solve a system of polynomial equations" href="../../NumericalAlgebraicGeometry/html/_solve__System_lp__List_rp.html">solveSystem</a> in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.</p> <p>There were 46 solutions found in 0.111 seconds (with a Bezout bound of 49).</p> <p>Reference: PoSSo test suite.</p> <p>See also: http://homepages.math.uic.edu/~jan/Demo/sendra.html.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : sendra(QQ) 4 3 4 3 7 6 5 2 4 3 o1 = {- 270x y - 314x*y - 689x*y + 1428, 36x + 417x y - 422x y - 270x y ------------------------------------------------------------------------ 3 4 2 5 6 6 5 4 2 3 3 + 1428x y - 1475x y + 510x*y - 200x - 174x y - 966x y + 529x y + ------------------------------------------------------------------------ 2 4 5 6 4 2 3 4 5 4 269x y + 49x*y - 267y + 529x y + 1303x y - 314x*y + 262y + 36x - ------------------------------------------------------------------------ 2 2 3 4 788x y - 689x*y + 177y } o1 : List</code></pre> </td> </tr> </table> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">sendra</span>:</h2> <ul> <li><kbd>sendra(Ring)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="the system sendra" href="_sendra.html">sendra</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function.html">method function</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">ExampleSystems/sendra.m2:38:0</span>.</p> </div> </div> </div> </body> </html>