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___Ann__I__Fs_lp__Ideal_cm__Ring__Element_rp.html
<!DOCTYPE html> <html lang="en"> <head> <title>AnnIFs(Ideal,RingElement) -- the annihilating ideal of f^s for an arbitrary D-module</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="algorithms for b-functions, local cohomology, and intersection cohomology" href="index.html">BernsteinSato</a> :: <a title="the annihilating ideal of f^s for an arbitrary D-module" href="___Ann__I__Fs_lp__Ideal_cm__Ring__Element_rp.html">AnnIFs(Ideal,RingElement)</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="___B__Function.html">next</a> | <a href="___Ann__Fs.html">previous</a> | <a href="___B__Function.html">forward</a> | <a href="___Ann__Fs.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>AnnIFs(Ideal,RingElement) -- the annihilating ideal of f^s for an arbitrary D-module</h1> <ul> <li><span>Function: <a title="the annihilating ideal of f^s for an arbitrary D-module" href="___Ann__I__Fs_lp__Ideal_cm__Ring__Element_rp.html">AnnIFs</a></span></li> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">AnnIFs(I,f)</code></dd> </dl> </li> <li>Inputs: <ul> <li><span><span class="tt">I</span>, <span>an <a title="the class of all ideals" href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, that represents a holonomic D-module <em>A<sub>n</sub>/I</em> (the ideal is expected to be f-saturated; one may use <a title="Weyl closure of an ideal" href="___Weyl__Closure.html">WeylClosure</a> if it is not) </span></li> <li><span><span class="tt">f</span>, <span>a <a title="the class of all ring elements handled by the engine" href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, a polynomial in a Weyl algebra <em>A<sub>n</sub></em> (should contain no differential variables)</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>, the annihilating ideal of A_n[f^{-1},s] f^s tensored with A_n/I over the ring of polynomials</span></li> </ul> </li> </ul> <div> <h2>Description</h2> <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : W = QQ[x,dx, WeylAlgebra=>{x=>dx}] o1 = W o1 : PolynomialRing, 1 differential variable(s)</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : AnnIFs (ideal dx, x^2) o2 = ideal(x*dx - 2s) o2 : Ideal of QQ[x, dx, s]</code></pre> </td> </tr> </table> </div> <div> <h2>Caveat</h2> Caveats and known problems: The ring of f should not have any parameters: it should be a pure Weyl algebra. Similarly, this ring should not be a homogeneous Weyl algebra. </div> <div> <h2>See also</h2> <ul> <li><span><a title="differential annihilator of a polynomial in a Weyl algebra" href="___Ann__Fs.html">AnnFs</a> -- differential annihilator of a polynomial in a Weyl algebra</span></li> <li><span><a title="specify differential operators in the ring" href="../../Macaulay2Doc/html/_monoid_lp..._cm__Weyl__Algebra_eq_gt..._rp.html">WeylAlgebra</a> -- specify differential operators in the ring</span></li> <li><span><a title="Weyl closure of an ideal" href="___Weyl__Closure.html">WeylClosure</a> -- Weyl closure of an ideal</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use this method:</h2> <ul> <li><span><a title="the annihilating ideal of f^s for an arbitrary D-module" href="___Ann__I__Fs_lp__Ideal_cm__Ring__Element_rp.html">AnnIFs(Ideal,RingElement)</a> -- the annihilating ideal of f^s for an arbitrary D-module</span></li> </ul> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">BernsteinSato/DOC/annFs.m2:56:0</span>.</p> </div> </div> </div> </body> </html>
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