One Hat Cyber Team
Your IP :
216.73.216.135
Server IP :
194.44.31.54
Server :
Linux zen.imath.kiev.ua 4.18.0-553.77.1.el8_10.x86_64 #1 SMP Fri Oct 3 14:30:23 UTC 2025 x86_64
Server Software :
Apache/2.4.37 (Rocky Linux) OpenSSL/1.1.1k
PHP Version :
5.6.40
Buat File
|
Buat Folder
Eksekusi
Dir :
~
/
usr
/
share
/
doc
/
Macaulay2
/
BernsteinSato
/
html
/
Edit File:
_log__Cohomology_lp__Ring__Element_rp.html
<!DOCTYPE html> <html lang="en"> <head> <title>logCohomology(RingElement) -- logarithmic cohomology groups in two variables</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="logarithmic cohomology groups in two variables" href="_log__Cohomology_lp__Ring__Element_rp.html">logCohomology(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="_multiplier__Ideal_lp__Ideal_cm__Q__Q_rp.html">next</a> | <a href="___Loc__Strategy.html">previous</a> | <a href="_multiplier__Ideal_lp__Ideal_cm__Q__Q_rp.html">forward</a> | <a href="___Loc__Strategy.html">backward</a> | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>logCohomology(RingElement) -- logarithmic cohomology groups in two variables</h1> <ul> <li><span>Function: <a title="logarithmic cohomology groups in two variables" href="_log__Cohomology_lp__Ring__Element_rp.html">logCohomology</a></span></li> <li> <dl class="element"> <dt>Usage: </dt> <dd><code class="language-macaulay2">logCohomology f</code></dd> </dl> </li> <li>Inputs: <ul> <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>, polynomial in two variables</span></li> </ul> </li> <li>Outputs: <ul> <li><span><span>a <a title="the class of all hash tables" href="../../Macaulay2Doc/html/___Hash__Table.html">hash table</a></span>, with entries {VResolution, Input, TransferCycles, CohomologyGroups, PreCycles, OmegaRes, LocalizeMap, BFunction} </span></li> </ul> </li> </ul> <div> <h2>Description</h2> For a polynomial f in two variables executes the algorithm described in Castro-Jimenez and Takayama "The Computation of the Logarithmic Cohomology for Plane Curves" (arXiv:0712.0001). <table class="examples"> <tr> <td> <pre><code class="language-macaulay2">i1 : S=QQ[x,y];</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i2 : f=x*y*(x-y);</code></pre> </td> </tr> <tr> <td> <pre><code class="language-macaulay2">i3 : logCohomology(f) o3 = HashTable{BFunction => (s - 1) } 1 CohomologyGroups => HashTable{0 => QQ } 3 1 => QQ 2 2 => QQ Input => cokernel | xdx+ydy+3 xydy-y2dy+x-2y | LocalizeMap => LocMap 1 2 1 OmegaRes => (QQ[x..y, dx, dy]) <-- (QQ[x..y, dx, dy]) <-- (QQ[x..y, dx, dy]) <-- 0 0 1 2 3 PreCycles => HashTable{0 => | x | } | 1 | 1 => | -x -y 0 | | 0 0 -1 | | 0 0 0 | 2 => | -y -x | TransferCycles => HashTable{0 => | -x2y+xy2 | } 1 => | xy y2 -xy+y2 | | x2 xy 0 | 2 => | -y -x | 1 3 2 VResolution => (QQ[x..y, dx, dy]) <-- (QQ[x..y, dx, dy]) <-- (QQ[x..y, dx, dy]) <-- 0 0 1 2 3 o3 : HashTable</code></pre> </td> </tr> </table> </div> <div> <h2>See also</h2> <ul> <li><span><a title="deRham cohomology groups for the complement of a hypersurface" href="_de__Rham.html">deRham</a> -- deRham cohomology groups for the complement of a hypersurface</span></li> </ul> </div> <div> <div class="waystouse"> <h2>Ways to use this method:</h2> <ul> <li><span><a title="logarithmic cohomology groups in two variables" href="_log__Cohomology_lp__Ring__Element_rp.html">logCohomology(RingElement)</a> -- logarithmic cohomology groups in two variables</span></li> </ul> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">BernsteinSato/DOC/other.m2:107:0</span>.</p> </div> </div> </div> </body> </html>
Simpan