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<!DOCTYPE html> <html lang="en"> <head> <title>isSNC -- whether the divisor is simple normal crossings</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="divisors" href="index.html">Divisor</a> :: <a title="whether the divisor is simple normal crossings" href="_is__S__N__C.html">isSNC</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="_is__Very__Ample_lp__Weil__Divisor_rp.html">next</a> | <a href="_is__Smooth_lp__Ideal_rp.html">previous</a> | <a href="_is__Very__Ample_lp__Weil__Divisor_rp.html">forward</a> | <a href="_is__Smooth_lp__Ideal_rp.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>isSNC -- whether the divisor is simple normal crossings</h1> <ul> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">isSNC( D )</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">D</span>, <span>an instance of the type <a title="the Types of divisors" href="___Basic__Divisor.html">BasicDivisor</a></span>, </span></li> </ul> </li> <li><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>: <ul> <li><span><span class="tt">IsGraded</span><span class="tt"> => </span><span>a <a title="the class of boolean values" href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, <span>default value false</span>, specify that we should do this computation on a projective algebraic variety</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>a <a title="the class of boolean values" href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, </span></li> </ul> </li> </ul> <div> <h2>Description</h2> <div> <p>This function returns <span class="tt">true</span> if the divisor is simple normal crossings, this includes checking that the ambient ring is regular.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : R = QQ[x, y, z] / ideal(x * y - z^2 );</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : D = divisor({1, -2}, {ideal(x, z), ideal(y, z)}) o2 = Div(x, z) + -2*Div(y, z) o2 : WeilDivisor on R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : isSNC( D ) o3 = false</code></pre> </td> </tr> </table> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i4 : R = QQ[x, y];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i5 : D = divisor(x*y*(x+y)) o5 = Div(x+y) + Div(y) + Div(x) o5 : WeilDivisor on R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i6 : isSNC( D ) o6 = false</code></pre> </td> </tr> </table> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i7 : R = QQ[x, y];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i8 : D = divisor(x*y*(x+1)) o8 = Div(y) + Div(x) + Div(x+1) o8 : WeilDivisor on R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i9 : isSNC( D ) o9 = true</code></pre> </td> </tr> </table> <div> <p>If <span class="tt">IsGraded</span> is set to <span class="tt">true</span> (default <span class="tt">false</span>), then the divisor is treated as if it is on the $Proj$ of the ambient ring. In particular, non-SNC behavior at the origin is ignored.</p> </div> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i10 : R = QQ[x, y, z] / ideal(x * y - z^2 );</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i11 : D = divisor({1, -2}, {ideal(x, z), ideal(y, z)}) o11 = -2*Div(y, z) + Div(x, z) o11 : WeilDivisor on R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i12 : isSNC( D, IsGraded => true ) o12 = true</code></pre> </td> </tr> </table> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i13 : R = QQ[x, y];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i14 : D = divisor(x*y*(x+y)) o14 = Div(y) + Div(x) + Div(x+y) o14 : WeilDivisor on R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i15 : isSNC( D, IsGraded => true ) o15 = true</code></pre> </td> </tr> </table> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i16 : R = QQ[x,y,z];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i17 : D = divisor(x*y*(x+y)) o17 = Div(x) + Div(x+y) + Div(y) o17 : WeilDivisor on R</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i18 : isSNC( D, IsGraded => true) o18 = false</code></pre> </td> </tr> </table> <div> <p>The output value of this function is stored in the divisor's cache with the value of the last <span class="tt">IsGraded</span> option. If you change the <span class="tt">IsGraded</span> option, the value will be recomputed.</p> </div> </div> <div> <div class="waystouse"> <h2>Ways to use <span class="tt">isSNC</span>:</h2> <ul> <li><kbd>isSNC(BasicDivisor)</kbd></li> </ul> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="whether the divisor is simple normal crossings" href="_is__S__N__C.html">isSNC</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function__With__Options.html">method function with options</a></span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Divisor.m2:4154:0</span>.</p> </div> </div> </div> </body> </html>
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