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<!DOCTYPE html> <html lang="en"> <head> <title>LocalRings : Table of Contents</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="Localizations of polynomial rings at prime ideals" href="index.html">LocalRings</a> :: <a href="toc.html">Table of Contents</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> next | previous | forward | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <h1>LocalRings : Table of Contents</h1> <ul> <li><span><a title="Localizations of polynomial rings at prime ideals" href="index.html">LocalRings</a> -- Localizations of polynomial rings at prime ideals</span> <ul> <li><span><a title="The class of all local rings" href="___Local__Ring.html">LocalRing</a> -- The class of all local rings</span> <ul> <li><span><a title="Constructor for local rings" href="_local__Ring.html">localRing</a> -- Constructor for local rings</span></li> <li><span><a title="Lifts various objects over R_P to R." href="_lift__Up.html">liftUp</a> -- Lifts various objects over R_P to R.</span></li> <li><span><a title="produce the ring from which a ring was formed" href="_base__Ring_lp__Local__Ring_rp.html">baseRing(LocalRing)</a> -- produce the ring from which a ring was formed</span></li> <li><span><a title="get the characteristic of the ring or field" href="_char_lp__Local__Ring_rp.html">char(LocalRing)</a> -- get the characteristic of the ring or field</span></li> <li><span><a title="get the coefficient ring" href="_coefficient__Ring_lp__Local__Ring_rp.html">coefficientRing(LocalRing)</a> -- get the coefficient ring</span></li> <li><span><a title="the length of the degree vector" href="_degree__Length_lp__Local__Ring_rp.html">degreeLength(LocalRing)</a> -- the length of the degree vector</span></li> <li><span><a title="degrees of generators" href="_degrees_lp__Local__Ring_rp.html">degrees(LocalRing)</a> -- degrees of generators</span></li> <li><span><a title="compute the Krull dimension" href="_dim_lp__Local__Ring_rp.html">dim(LocalRing)</a> -- compute the Krull dimension</span></li> <li><span><a title="construct a fraction field" href="_frac_lp__Local__Ring_rp.html">frac(LocalRing)</a> -- construct a fraction field</span></li> <li><span><a title="the list of generators of a ring" href="_generators_lp__Local__Ring_rp.html">generators(LocalRing)</a> -- the list of generators of a ring</span></li> <li><span><a title="whether a ring is commutative" href="_is__Commutative_lp__Local__Ring_rp.html">isCommutative(LocalRing)</a> -- whether a ring is commutative</span></li> <li><span><a title="whether a local ring is well defined" href="_is__Well__Defined_lp__Local__Ring_rp.html">isWellDefined(LocalRing)</a> -- whether a local ring is well defined</span></li> <li><span><a title="number of generators of a polynomial ring" href="_numgens_lp__Local__Ring_rp.html">numgens(LocalRing)</a> -- number of generators of a polynomial ring</span></li> </ul> </li> </ul> </li> <li><span><a title="Computes the Hilbert-Samuel Function of Modules over Local Rings" href="_hilbert__Samuel__Function.html">hilbertSamuelFunction</a> -- Computes the Hilbert-Samuel Function of Modules over Local Rings</span></li> <li><span><a href="_replacements_spfor_spfunctions_spfrom_spversion_sp1.0.html">replacements for functions from version 1.0</a></span> <ul> <li><span><a title="set the maximal ideal for local ring methods" href="_set__Max__Ideal.html">setMaxIdeal</a> -- set the maximal ideal for local ring methods</span></li> <li><span><a title="find the splitting of the target of a map" href="_local__Complement.html">localComplement</a> -- find the splitting of the target of a map</span></li> <li><span><a title="find syzygies" href="_localsyz.html">localsyz</a> -- find syzygies</span></li> <li><span><a title="finds a minimal set of generators" href="_local__Mingens.html">localMingens</a> -- finds a minimal set of generators</span></li> <li><span><a title="find the pre-image (pullback) of image of a map over a local ring" href="_local__Modulo.html">localModulo</a> -- find the pre-image (pullback) of image of a map over a local ring</span></li> <li><span><a title="find a minimal presentation" href="_local__Prune.html">localPrune</a> -- find a minimal presentation</span></li> <li><span><a title="find a resolution over a local ring" href="_local__Resolution.html">localResolution</a> -- find a resolution over a local ring</span></li> </ul> </li> </ul> </body> </html>