Gedichte Musik Bilder Quellcodebibliothek Diashow Normaldarstellung
Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/homalg/doc/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 10.0.2024 mit Größe 44 kB image not shown  

Quelle  chap3.html   Sprache: HTML

 
 products/Sources/formale Sprachen/GAP/pkg/homalg/doc/chap3.html


<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
         "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<title>GAP (homalg) - Chapter 3: Objects</title>
<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
<meta name="generator" content="GAPDoc2HTML" />
<link rel="stylesheet" type="text/css" href="manual.css" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chap3"  onload="jscontent()">


<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chap7.html">7</a>  <a href="chap8.html">8</a>  <a href="chap9.html">9</a>  <a href="chap10.html">10</a>  <a href="chap11.html">11</a>  <a href="chap12.html">12</a>  <a href="chapA.html">A</a>  <a href="chapB.html">B</a>  <a href="chapC.html">C</a>  <a href="chapD.html">D</a>  <a href="chapE.html">E</a>  <a href="chapF.html">F</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap2.html">[Previous Chapter]</a>    <a href="chap4.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap3_mj.html">[MathJax on]</a></p>
<p><a id="X78497E777FB3E402" name="X78497E777FB3E402"></a></p>
<div class="ChapSects"><a href="chap3.html#X78497E777FB3E402">3 <span class="Heading">Objects</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7E3651DF87064E72">3.1 <span class="Heading">Objects: Category and Representations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7E610FA77A49B9EC">3.1-1 IsHomalgObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X79FC4A848517AF55">3.1-2 IsHomalgStaticObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7F1BC3F77949E779">3.1-3 IsFinitelyPresentedObjectRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X79ED26577A1C2E09">3.1-4 IsStaticFinitelyPresentedObjectOrSubobjectRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7B645ADA876153F2">3.1-5 IsStaticFinitelyPresentedObjectRep</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X837C31E38502E580">3.1-6 IsStaticFinitelyPresentedSubobjectRep</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7BD901538362C36E">3.2 <span class="Heading">Objects: Constructors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X810D3BFB7D9FE47E">3.2-1 Subobject</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7B3E8C797D15F0B7">3.3 <span class="Heading">Objects: Properties</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7CD2A77778432E7B">3.3-1 IsFree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7D49FC85781256AB">3.3-2 IsStablyFree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7EC041A77E7E46D2">3.3-3 IsProjective</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X84A8AB217E8F4611">3.3-4 IsProjectiveOfConstantRank</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7F065FD7822C0A12">3.3-5 IsInjective</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7FCE608683CCDC6B">3.3-6 IsInjectiveCogenerator</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8784F151844F01FA">3.3-7 FiniteFreeResolutionExists</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7A6A34C283332F60">3.3-8 IsReflexive</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X86D92DA17DCE22DD">3.3-9 IsTorsionFree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7D8F8A0B81EFD22A">3.3-10 IsArtinian</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X80C6B26284721409">3.3-11 IsTorsion</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7B894ED27D38E4B5">3.3-12 IsPure</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8373421F7E085763">3.3-13 IsCohenMacaulay</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X83CBA38E81DC4A72">3.3-14 IsGorenstein</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7E7AEFBE7801F196">3.3-15 IsKoszul</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7A20E4597A707218">3.3-16 HasConstantRank</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7CD026F185A5E41E">3.3-17 ConstructedAsAnIdeal</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X805B06828294072C">3.4 <span class="Heading">Objects: Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7E6C8ED2865B6F35">3.4-1 TorsionSubobject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X82BCEE867CBE84E5">3.4-2 TheMorphismToZero</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X85EFEC127CA408A1">3.4-3 TheIdentityMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8236B1D480ED04CD">3.4-4 FullSubobject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X81679BB58541E235">3.4-5 ZeroSubobject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C16CBCC78C56CDC">3.4-6 EmbeddingInSuperObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7ADC5B647C8E6D8C">3.4-7 SuperObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7FB9A7C3785D92DC">3.4-8 FactorObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7A23EAD67E6B85C1">3.4-9 UnderlyingSubobject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7FC5F0AF7CF5DC67">3.4-10 NatTrIdToHomHom_R</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X81889C777A22A5D3">3.4-11 Annihilator</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X809A7C3882912EFD">3.4-12 EndomorphismRing</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X85F3D7CF81E85423">3.4-13 UnitObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7E192147807E66DA">3.4-14 RankOfObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X84FDF25D797B874B">3.4-15 ProjectiveDimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X807BA3C583D3F1EB">3.4-16 DegreeOfTorsionFreeness</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7E32A9FC81E0E101">3.4-17 Grade</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X816186E587563E3F">3.4-18 PurityFiltration</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X8021C33D85444081">3.4-19 CodegreeOfPurity</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X84299BAB807A1E13">3.4-20 HilbertPolynomial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7BC36CC67CB09858">3.4-21 AffineDimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X82A1B55879AB1742">3.4-22 ProjectiveDegree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X791B772A7E368A88">3.4-23 ConstantTermOfHilbertPolynomialn</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7FC735717985B092">3.4-24 ElementOfGrothendieckGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X81024DAF8695083E">3.4-25 ChernPolynomial</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X79942F6187DF4434">3.4-26 ChernCharacter</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7B4D450B78A86F8B">3.5 <span class="Heading">Objects: Operations and Functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X87AEDF2985D65DCC">3.5-1 CurrentResolution</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X81FACFAC828CA2F9">3.5-2 UnderlyingObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X82AE15AF82136AE0">3.5-3 Saturate</a></span>
</div></div>
</div>

<h3>3 <span class="Heading">Objects</span></h3>

<p><a id="X7E3651DF87064E72" name="X7E3651DF87064E72"></a></p>

<h4>3.1 <span class="Heading">Objects: Category and Representations</span></h4>

<p><a id="X7E610FA77A49B9EC" name="X7E610FA77A49B9EC"></a></p>

<h5>3.1-1 IsHomalgObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsHomalgObject</code>( <var class="Arg">F</var> )</td><td class="tdright">( category )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>This is the super <strong class="pkg">GAP</strong>-category which will include the <strong class="pkg">GAP</strong>-categories <code class="func">IsHomalgStaticObject</code> (<a href="chap3.html#X79FC4A848517AF55"><span class="RefLink">3.1-2</span></a>), <code class="func">IsHomalgComplex</code> (<a href="chap6.html#X8166F9FD7BFDA207"><span class="RefLink">6.1-1</span></a>), <code class="func">IsHomalgBicomplex</code> (<a href="chap8.html#X80B7C45A850F4C3E"><span class="RefLink">8.1-1</span></a>), <code class="func">IsHomalgBigradedObject</code> (<a href="chap9.html#X795C082E83748032"><span class="RefLink">9.1-1</span></a>), and <code class="func">IsHomalgSpectralSequence</code> (<a href="chap10.html#X795DCCD88630BA47"><span class="RefLink">10.1-1</span></a>). We need this <strong class="pkg">GAP</strong>-category to be able to build complexes with *objects* being objects of <strong class="pkg">homalg</strong> categories or again complexes.</p>


<div class="example"><pre>
DeclareCategory( "IsHomalgObject",
        IsHomalgObjectOrMorphism and
        IsStructureObjectOrObject and
        IsAdditiveElementWithZero );
</pre></div>

<p><a id="X79FC4A848517AF55" name="X79FC4A848517AF55"></a></p>

<h5>3.1-2 IsHomalgStaticObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsHomalgStaticObject</code>( <var class="Arg">F</var> )</td><td class="tdright">( category )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>This is the super <strong class="pkg">GAP</strong>-category which will include the <strong class="pkg">GAP</strong>-categories <code class="code">IsHomalgModule</code>, etc.</p>


<div class="example"><pre>
DeclareCategory( "IsHomalgStaticObject",
        IsHomalgStaticObjectOrMorphism and
        IsHomalgObject );
</pre></div>

<p><a id="X7F1BC3F77949E779" name="X7F1BC3F77949E779"></a></p>

<h5>3.1-3 IsFinitelyPresentedObjectRep</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsFinitelyPresentedObjectRep</code>( <var class="Arg">M</var> )</td><td class="tdright">( representation )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>The <strong class="pkg">GAP</strong> representation of finitley presented <strong class="pkg">homalg</strong> objects.</p>

<p>(It is a representation of the <strong class="pkg">GAP</strong> category <code class="func">IsHomalgObject</code> (<a href="chap3.html#X7E610FA77A49B9EC"><span class="RefLink">3.1-1</span></a>), which is a subrepresentation of the <strong class="pkg">GAP</strong> representations <code class="code">IsStructureObjectOrFinitelyPresentedObjectRep</code>.)</p>


<div class="example"><pre>
DeclareRepresentation( "IsFinitelyPresentedObjectRep",
        IsHomalgObject and
        IsStructureObjectOrFinitelyPresentedObjectRep,
        [ ] );
</pre></div>

<p><a id="X79ED26577A1C2E09" name="X79ED26577A1C2E09"></a></p>

<h5>3.1-4 IsStaticFinitelyPresentedObjectOrSubobjectRep</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsStaticFinitelyPresentedObjectOrSubobjectRep</code>( <var class="Arg">M</var> )</td><td class="tdright">( representation )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>The <strong class="pkg">GAP</strong> representation of finitley presented <strong class="pkg">homalg</strong> static objects.</p>

<p>(It is a representation of the <strong class="pkg">GAP</strong> category <code class="func">IsHomalgStaticObject</code> (<a href="chap3.html#X79FC4A848517AF55"><span class="RefLink">3.1-2</span></a>).)</p>


<div class="example"><pre>
DeclareRepresentation( "IsStaticFinitelyPresentedObjectOrSubobjectRep",
        IsHomalgStaticObject,
        [ ] );
</pre></div>

<p><a id="X7B645ADA876153F2" name="X7B645ADA876153F2"></a></p>

<h5>3.1-5 IsStaticFinitelyPresentedObjectRep</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsStaticFinitelyPresentedObjectRep</code>( <var class="Arg">M</var> )</td><td class="tdright">( representation )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>The <strong class="pkg">GAP</strong> representation of finitley presented <strong class="pkg">homalg</strong> static objects.</p>

<p>(It is a representation of the <strong class="pkg">GAP</strong> category <code class="func">IsHomalgStaticObject</code> (<a href="chap3.html#X79FC4A848517AF55"><span class="RefLink">3.1-2</span></a>), which is a subrepresentation of the <strong class="pkg">GAP</strong> representations <code class="code">IsStaticFinitelyPresentedObjectOrSubobjectRep</code> and <code class="code">IsFinitelyPresentedObjectRep</code>.)</p>


<div class="example"><pre>
DeclareRepresentation( "IsStaticFinitelyPresentedObjectRep",
        IsStaticFinitelyPresentedObjectOrSubobjectRep and
        IsFinitelyPresentedObjectRep,
        [ ] );
</pre></div>

<p><a id="X837C31E38502E580" name="X837C31E38502E580"></a></p>

<h5>3.1-6 IsStaticFinitelyPresentedSubobjectRep</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsStaticFinitelyPresentedSubobjectRep</code>( <var class="Arg">M</var> )</td><td class="tdright">( representation )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>The <strong class="pkg">GAP</strong> representation of finitley presented <strong class="pkg">homalg</strong> subobjects of static objects.</p>

<p>(It is a representation of the <strong class="pkg">GAP</strong> category <code class="func">IsHomalgStaticObject</code> (<a href="chap3.html#X79FC4A848517AF55"><span class="RefLink">3.1-2</span></a>), which is a subrepresentation of the <strong class="pkg">GAP</strong> representations <code class="code">IsStaticFinitelyPresentedObjectOrSubobjectRep</code> and <code class="code">IsFinitelyPresentedObjectRep</code>.)</p>


<div class="example"><pre>
DeclareRepresentation( "IsStaticFinitelyPresentedSubobjectRep",
        IsStaticFinitelyPresentedObjectOrSubobjectRep and
        IsFinitelyPresentedObjectRep,
        [ ] );
</pre></div>

<p><a id="X7BD901538362C36E" name="X7BD901538362C36E"></a></p>

<h4>3.2 <span class="Heading">Objects: Constructors</span></h4>

<p><a id="X810D3BFB7D9FE47E" name="X810D3BFB7D9FE47E"></a></p>

<h5>3.2-1 Subobject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Subobject</code>( <var class="Arg">phi</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> subobject</p>

<p>A synonym of <code class="func">ImageSubobject</code> (<a href="chap4.html#X82FB6A4687E778D5"><span class="RefLink">4.4-7</span></a>).</p>

<p><a id="X7B3E8C797D15F0B7" name="X7B3E8C797D15F0B7"></a></p>

<h4>3.3 <span class="Heading">Objects: Properties</span></h4>

<p><a id="X7CD2A77778432E7B" name="X7CD2A77778432E7B"></a></p>

<h5>3.3-1 IsFree</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsFree</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is free.</p>

<p><a id="X7D49FC85781256AB" name="X7D49FC85781256AB"></a></p>

<h5>3.3-2 IsStablyFree</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsStablyFree</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is stably free.</p>

<p><a id="X7EC041A77E7E46D2" name="X7EC041A77E7E46D2"></a></p>

<h5>3.3-3 IsProjective</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsProjective</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is projective.</p>

<p><a id="X84A8AB217E8F4611" name="X84A8AB217E8F4611"></a></p>

<h5>3.3-4 IsProjectiveOfConstantRank</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsProjectiveOfConstantRank</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is projective of constant rank.</p>

<p><a id="X7F065FD7822C0A12" name="X7F065FD7822C0A12"></a></p>

<h5>3.3-5 IsInjective</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsInjective</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is (marked) injective.</p>

<p><a id="X7FCE608683CCDC6B" name="X7FCE608683CCDC6B"></a></p>

<h5>3.3-6 IsInjectiveCogenerator</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsInjectiveCogenerator</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is (marked) an injective cogenerator.</p>

<p><a id="X8784F151844F01FA" name="X8784F151844F01FA"></a></p>

<h5>3.3-7 FiniteFreeResolutionExists</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FiniteFreeResolutionExists</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> allows a finite free resolution. <br /> (no method installed)</p>

<p><a id="X7A6A34C283332F60" name="X7A6A34C283332F60"></a></p>

<h5>3.3-8 IsReflexive</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsReflexive</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is reflexive.</p>

<p><a id="X86D92DA17DCE22DD" name="X86D92DA17DCE22DD"></a></p>

<h5>3.3-9 IsTorsionFree</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsTorsionFree</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is torsion-free.</p>

<p><a id="X7D8F8A0B81EFD22A" name="X7D8F8A0B81EFD22A"></a></p>

<h5>3.3-10 IsArtinian</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsArtinian</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is artinian.</p>

<p><a id="X80C6B26284721409" name="X80C6B26284721409"></a></p>

<h5>3.3-11 IsTorsion</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsTorsion</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is torsion.</p>

<p><a id="X7B894ED27D38E4B5" name="X7B894ED27D38E4B5"></a></p>

<h5>3.3-12 IsPure</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsPure</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is pure.</p>

<p><a id="X8373421F7E085763" name="X8373421F7E085763"></a></p>

<h5>3.3-13 IsCohenMacaulay</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsCohenMacaulay</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is Cohen-Macaulay (depends on the specific Abelian category).</p>

<p><a id="X83CBA38E81DC4A72" name="X83CBA38E81DC4A72"></a></p>

<h5>3.3-14 IsGorenstein</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsGorenstein</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is Gorenstein (depends on the specific Abelian category).</p>

<p><a id="X7E7AEFBE7801F196" name="X7E7AEFBE7801F196"></a></p>

<h5>3.3-15 IsKoszul</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IsKoszul</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> is Koszul (depends on the specific Abelian category).</p>

<p><a id="X7A20E4597A707218" name="X7A20E4597A707218"></a></p>

<h5>3.3-16 HasConstantRank</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ HasConstantRank</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> has constant rank. <br /> (no method installed)</p>

<p><a id="X7CD026F185A5E41E" name="X7CD026F185A5E41E"></a></p>

<h5>3.3-17 ConstructedAsAnIdeal</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ConstructedAsAnIdeal</code>( <var class="Arg">J</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>Check if the <strong class="pkg">homalg</strong> subobject <var class="Arg">J</var> was constructed as an ideal. <br /> (no method installed)</p>

<p><a id="X805B06828294072C" name="X805B06828294072C"></a></p>

<h4>3.4 <span class="Heading">Objects: Attributes</span></h4>

<p><a id="X7E6C8ED2865B6F35" name="X7E6C8ED2865B6F35"></a></p>

<h5>3.4-1 TorsionSubobject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TorsionSubobject</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> subobject</p>

<p>This constructor returns the finitely generated torsion subobject of the <strong class="pkg">homalg</strong> object <var class="Arg">M</var>.</p>

<p><a id="X82BCEE867CBE84E5" name="X82BCEE867CBE84E5"></a></p>

<h5>3.4-2 TheMorphismToZero</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TheMorphismToZero</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> map</p>

<p>The zero morphism from the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> to zero.</p>

<p><a id="X85EFEC127CA408A1" name="X85EFEC127CA408A1"></a></p>

<h5>3.4-3 TheIdentityMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TheIdentityMorphism</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> map</p>

<p>The identity automorphism of the <strong class="pkg">homalg</strong> object <var class="Arg">M</var>.</p>

<p><a id="X8236B1D480ED04CD" name="X8236B1D480ED04CD"></a></p>

<h5>3.4-4 FullSubobject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FullSubobject</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> subobject</p>

<p>The <strong class="pkg">homalg</strong> object <var class="Arg">M</var> as a subobject of itself.</p>

<p><a id="X81679BB58541E235" name="X81679BB58541E235"></a></p>

<h5>3.4-5 ZeroSubobject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ZeroSubobject</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> subobject</p>

<p>The zero subobject of the <strong class="pkg">homalg</strong> object <var class="Arg">M</var>.</p>

<p><a id="X7C16CBCC78C56CDC" name="X7C16CBCC78C56CDC"></a></p>

<h5>3.4-6 EmbeddingInSuperObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ EmbeddingInSuperObject</code>( <var class="Arg">N</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> map</p>

<p>In case <var class="Arg">N</var> was defined as a subobject of some object <span class="SimpleMath">L</span> the embedding of <var class="Arg">N</var> in <span class="SimpleMath">L</span> is returned.</p>

<p><a id="X7ADC5B647C8E6D8C" name="X7ADC5B647C8E6D8C"></a></p>

<h5>3.4-7 SuperObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SuperObject</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> object</p>

<p>In case <var class="Arg">M</var> was defined as a subobject of some object <span class="SimpleMath">L</span> the super object <span class="SimpleMath">L</span> is returned.</p>

<p><a id="X7FB9A7C3785D92DC" name="X7FB9A7C3785D92DC"></a></p>

<h5>3.4-8 FactorObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FactorObject</code>( <var class="Arg">N</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> object</p>

<p>In case <var class="Arg">N</var> was defined as a subobject of some object <span class="SimpleMath">L</span> the factor object <span class="SimpleMath">L/</span><var class="Arg">N</var> is returned.</p>

<p><a id="X7A23EAD67E6B85C1" name="X7A23EAD67E6B85C1"></a></p>

<h5>3.4-9 UnderlyingSubobject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UnderlyingSubobject</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> subobject</p>

<p>In case <var class="Arg">M</var> was defined as the object underlying a subobject <span class="SimpleMath">L</span> then <span class="SimpleMath">L</span> is returned. <br /> (no method installed)</p>

<p><a id="X7FC5F0AF7CF5DC67" name="X7FC5F0AF7CF5DC67"></a></p>

<h5>3.4-10 NatTrIdToHomHom_R</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ NatTrIdToHomHom_R</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> morphism</p>

<p>The natural evaluation morphism from the <strong class="pkg">homalg</strong> object <var class="Arg">M</var> to its double dual <code class="code">HomHom</code><span class="SimpleMath">(</span><var class="Arg">M</var><span class="SimpleMath">)</span>.</p>

<p><a id="X81889C777A22A5D3" name="X81889C777A22A5D3"></a></p>

<h5>3.4-11 Annihilator</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Annihilator</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> subobject</p>

<p>The annihilator of the object <var class="Arg">M</var> as a subobject of the structure object.</p>

<p><a id="X809A7C3882912EFD" name="X809A7C3882912EFD"></a></p>

<h5>3.4-12 EndomorphismRing</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ EndomorphismRing</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> object</p>

<p>The endomorphism ring of the object <var class="Arg">M</var>.</p>

<p><a id="X85F3D7CF81E85423" name="X85F3D7CF81E85423"></a></p>

<h5>3.4-13 UnitObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UnitObject</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: a Chern character</p>

<p><var class="Arg">M</var> is a <strong class="pkg">homalg</strong> object.</p>

<p><a id="X7E192147807E66DA" name="X7E192147807E66DA"></a></p>

<h5>3.4-14 RankOfObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ RankOfObject</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a nonnegative integer</p>

<p>The projective rank of the <strong class="pkg">homalg</strong> object <var class="Arg">M</var>.</p>

<p><a id="X84FDF25D797B874B" name="X84FDF25D797B874B"></a></p>

<h5>3.4-15 ProjectiveDimension</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ProjectiveDimension</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a nonnegative integer</p>

<p>The projective dimension of the <strong class="pkg">homalg</strong> object <var class="Arg">M</var>.</p>

<p><a id="X807BA3C583D3F1EB" name="X807BA3C583D3F1EB"></a></p>

<h5>3.4-16 DegreeOfTorsionFreeness</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ DegreeOfTorsionFreeness</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a nonnegative integer of infinity</p>

<p>Auslander's degree of torsion-freeness of the homalg object M. It is set to infinity only for M=0.



<p><a id="X7E32A9FC81E0E101" name="X7E32A9FC81E0E101"></a></p>

<h5>3.4-17 Grade</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Grade</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a nonnegative integer of infinity</p>

<p>The grade of the <strong class="pkg">homalg</strong> object <var class="Arg">M</var>. It is set to infinity if <var class="Arg">M</var><span class="SimpleMath">=0</span>. Another name for this operation is <code class="code">Depth</code>.</p>

<p><a id="X816186E587563E3F" name="X816186E587563E3F"></a></p>

<h5>3.4-18 PurityFiltration</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ PurityFiltration</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> filtration</p>

<p>The purity filtration of the <strong class="pkg">homalg</strong> object <var class="Arg">M</var>.</p>

<p><a id="X8021C33D85444081" name="X8021C33D85444081"></a></p>

<h5>3.4-19 CodegreeOfPurity</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CodegreeOfPurity</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a list of nonnegative integers</p>

<p>The codegree of purity of the <strong class="pkg">homalg</strong> object <var class="Arg">M</var>.</p>

<p><a id="X84299BAB807A1E13" name="X84299BAB807A1E13"></a></p>

<h5>3.4-20 HilbertPolynomial</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ HilbertPolynomial</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a univariate polynomial with rational coefficients</p>

<p><var class="Arg">M</var> is a <strong class="pkg">homalg</strong> object.</p>

<p><a id="X7BC36CC67CB09858" name="X7BC36CC67CB09858"></a></p>

<h5>3.4-21 AffineDimension</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AffineDimension</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a nonnegative integer</p>

<p><var class="Arg">M</var> is a <strong class="pkg">homalg</strong> object.</p>

<p><a id="X82A1B55879AB1742" name="X82A1B55879AB1742"></a></p>

<h5>3.4-22 ProjectiveDegree</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ProjectiveDegree</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a nonnegative integer</p>

<p><var class="Arg">M</var> is a <strong class="pkg">homalg</strong> object.</p>

<p><a id="X791B772A7E368A88" name="X791B772A7E368A88"></a></p>

<h5>3.4-23 ConstantTermOfHilbertPolynomialn</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ConstantTermOfHilbertPolynomialn</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: an integer</p>

<p><var class="Arg">M</var> is a <strong class="pkg">homalg</strong> object.</p>

<p><a id="X7FC735717985B092" name="X7FC735717985B092"></a></p>

<h5>3.4-24 ElementOfGrothendieckGroup</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ElementOfGrothendieckGroup</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: an element of the Grothendieck group of a projective space</p>

<p><var class="Arg">M</var> is a <strong class="pkg">homalg</strong> object.</p>

<p><a id="X81024DAF8695083E" name="X81024DAF8695083E"></a></p>

<h5>3.4-25 ChernPolynomial</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ChernPolynomial</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: a Chern polynomial with rank</p>

<p><var class="Arg">M</var> is a <strong class="pkg">homalg</strong> object.</p>

<p><a id="X79942F6187DF4434" name="X79942F6187DF4434"></a></p>

<h5>3.4-26 ChernCharacter</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ChernCharacter</code>( <var class="Arg">M</var> )</td><td class="tdright">( property )</td></tr></table></div>
<p>Returns: a Chern character</p>

<p><var class="Arg">M</var> is a <strong class="pkg">homalg</strong> object.</p>

<p><a id="X7B4D450B78A86F8B" name="X7B4D450B78A86F8B"></a></p>

<h4>3.5 <span class="Heading">Objects: Operations and Functions</span></h4>

<p><a id="X87AEDF2985D65DCC" name="X87AEDF2985D65DCC"></a></p>

<h5>3.5-1 CurrentResolution</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ CurrentResolution</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> complex</p>

<p>The computed (part of a) resolution of the static object <var class="Arg">M</var>.</p>

<p><a id="X81FACFAC828CA2F9" name="X81FACFAC828CA2F9"></a></p>

<h5>3.5-2 UnderlyingObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UnderlyingObject</code>( <var class="Arg">M</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> object</p>

<p>In case <var class="Arg">M</var> was defined as a subobject of some object <span class="SimpleMath">L</span> the object underlying the subobject <span class="SimpleMath">M</span> is returned.</p>

<p><a id="X82AE15AF82136AE0" name="X82AE15AF82136AE0"></a></p>

<h5>3.5-3 Saturate</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Saturate</code>( <var class="Arg">K</var>, <var class="Arg">J</var> )</td><td class="tdright">( operation )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> ideal</p>

<p>Compute the saturation ideal <span class="SimpleMath"><var class="Arg">K</var>:<var class="Arg">J</var>^∞</span> of the ideals <var class="Arg">K</var> and <var class="Arg">J</var>.</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">zz := HomalgRingOfIntegers( );</span>
Z
<span class="GAPprompt">gap></span> <span class="GAPinput">Display( zz );</span>
<An internal ring>
<span class="GAPprompt">gap></span> <span class="GAPinput">m := LeftSubmodule( "2", zz );</span>
<A principal (left) ideal given by a cyclic generator>
<span class="GAPprompt">gap></span> <span class="GAPinput">Display( m );</span>
[ [  2 ] ]

A (left) ideal generated by the entry of the above matrix
<span class="GAPprompt">gap></span> <span class="GAPinput">J := LeftSubmodule( "3", zz );</span>
<A principal (left) ideal given by a cyclic generator>
<span class="GAPprompt">gap></span> <span class="GAPinput">Display( J );</span>
[ [  3 ] ]

A (left) ideal generated by the entry of the above matrix
<span class="GAPprompt">gap></span> <span class="GAPinput">I := Intersect( J, m^3 );</span>
<A principal (left) ideal given by a cyclic generator>
<span class="GAPprompt">gap></span> <span class="GAPinput">Display( I );</span>
[ [  24 ] ]

A (left) ideal generated by the entry of the above matrix
<span class="GAPprompt">gap></span> <span class="GAPinput">Im := SubobjectQuotient( I, m );</span>
<A principal (left) ideal of rank 1 on a free generator>
<span class="GAPprompt">gap></span> <span class="GAPinput">Display( Im );</span>
[ [  12 ] ]

A (left) ideal generated by the entry of the above matrix
<span class="GAPprompt">gap></span> <span class="GAPinput">I_m := Saturate( I, m );</span>
<A principal (left) ideal of rank 1 on a free generator>
<span class="GAPprompt">gap></span> <span class="GAPinput">Display( I_m );</span>
[ [  3 ] ]

A (left) ideal generated by the entry of the above matrix
<span class="GAPprompt">gap></span> <span class="GAPinput">I_m = J;</span>
true
</pre></div>


<div class="example"><pre>
InstallMethod( Saturate,
        "for homalg subobjects of static objects",
        [ IsStaticFinitelyPresentedSubobjectRep, IsStaticFinitelyPresentedSubobjectRep ],
        
  function( K, J )
    local quotient_last, quotient;
    
    quotient_last := SubobjectQuotient( K, J );
    
    quotient := SubobjectQuotient( quotient_last, J );
    
    while not IsSubset( quotient_last, quotient ) do
        quotient_last := quotient;
        quotient := SubobjectQuotient( quotient_last, J );
    od;
    
    return quotient_last;
    
end );


InstallMethod( \-, ## a geometrically motivated definition
        "for homalg subobjects of static objects",
        [ IsStaticFinitelyPresentedSubobjectRep, IsStaticFinitelyPresentedSubobjectRep ],
        
  function( K, J )
    
    return Saturate( K, J );
    
end );
</pre></div>


<div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap2.html">[Previous Chapter]</a>    <a href="chap4.html">[Next Chapter]</a>   </div>


<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a>  <a href="chap1.html">1</a>  <a href="chap2.html">2</a>  <a href="chap3.html">3</a>  <a href="chap4.html">4</a>  <a href="chap5.html">5</a>  <a href="chap6.html">6</a>  <a href="chap7.html">7</a>  <a href="chap8.html">8</a>  <a href="chap9.html">9</a>  <a href="chap10.html">10</a>  <a href="chap11.html">11</a>  <a href="chap12.html">12</a>  <a href="chapA.html">A</a>  <a href="chapB.html">B</a>  <a href="chapC.html">C</a>  <a href="chapD.html">D</a>  <a href="chapE.html">E</a>  <a href="chapF.html">F</a>  <a href="chapBib.html">Bib</a>  <a href="chapInd.html">Ind</a>  </div>

<hr />
<p class="foot">generated by <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>

100%


¤ Dauer der Verarbeitung: 0.32 Sekunden  ¤

*© Formatika GbR, Deutschland




Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.