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<!DOCTYPE html> <html lang="en"> <head> <title>add -- Add Reduced Ideals</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="Miura curve arithmetic" href="index.html">Miura</a> :: <a title="Add Reduced Ideals" href="_add.html">add</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="_double.html">next</a> | <a href="index.html">previous</a> | <a href="_double.html">forward</a> | <a href="index.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>add -- Add Reduced Ideals</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">L=add(J,K)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">J</span>, an integral ideal</span></li> <li><span><span class="tt">K</span>, an integral ideal</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>an <a title="the class of all ideals" href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span></span></li> </ul> </li> </ul> <div> <h2>Description</h2> <p>The function add computes the reduced ideal of multiplication of two integral ideals. Each reduced ideal is a representative of its ideal class, and the addition is executed over the ideal class group.</p> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : setPolynomialRing(GF 13, {x,y}, {2,3}); setQuotientRing(y^2-x^3-7*x) o2 = QR o2 : QuotientRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : J=ideal(x, y); K=ideal(x-2, y-3); add(J, K) o3 : Ideal of QR o4 : Ideal of QR o5 = ideal (x + 3, y + 2) o5 : Ideal of QR</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : L=J*K; reduced(L) o6 : Ideal of QR o7 = ideal (x + 3, y + 2) o7 : Ideal of QR</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : setPolynomialRing(GF 5,{x,y,z},{4,6,5}) o8 = PR o8 : PolynomialRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i9 : setQuotientRing({y^2-x^3-1, z^2-x*y-1}) o9 = QR o9 : QuotientRing</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i10 : J=ideal(x-2,y-2,z) o10 = ideal (x - 2, y - 2, z) o10 : Ideal of QR</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i11 : K=ideal(x-4,y,z-1) o11 = ideal (x + 1, y, z - 1) o11 : Ideal of QR</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i12 : add(J, K) 2 o12 = ideal (z + 2x + 1, y + x + 1, x - x - 2) o12 : Ideal of QR</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="Compute Reduced Ideal" href="_reduced.html">reduced</a> -- Compute Reduced Ideal</span></li> <li><span><a title="Double Reduced Ideal" href="_double.html">double</a> -- Double Reduced Ideal</span></li> <li><span><a title="Add Reduced Ideal Multiple Times" href="_scalar__Multiplication.html">scalarMultiplication</a> -- Add Reduced Ideal Multiple Times</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">add</span>:</h2> <ul> <li><span><span class="tt">add(Ideal,Ideal)</span> (missing documentation)<!--tag: (add,Ideal,Ideal)--> </span></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="Add Reduced Ideals" href="_add.html">add</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">Miura.m2:176:0</span>.</p> </div> </div> </div> </body> </html>
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