Anforderungen  |   Konzepte  |   Entwurf  |   Entwicklung  |   Qualitätssicherung  |   Lebenszyklus  |   Steuerung
 
 
 
 

products/Sources/formale Sprachen/GAP/pkg/hap/doc/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 19.6.2025 mit Größe 24 kB image not shown  

Quelle  chap8.html   Sprache: HTML

 
 products/Sources/formale Sprachen/GAP/pkg/hap/doc/chap8.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 (HAP commands) - Chapter 8:  Functors</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="chap8"  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="chap13.html">13</a>  <a href="chap14.html">14</a>  <a href="chap15.html">15</a>  <a href="chap16.html">16</a>  <a href="chap17.html">17</a>  <a href="chap18.html">18</a>  <a href="chap19.html">19</a>  <a href="chap20.html">20</a>  <a href="chap21.html">21</a>  <a href="chap22.html">22</a>  <a href="chap23.html">23</a>  <a href="chap24.html">24</a>  <a href="chap25.html">25</a>  <a href="chap26.html">26</a>  <a href="chap27.html">27</a>  <a href="chap28.html">28</a>  <a href="chap29.html">29</a>  <a href="chap30.html">30</a>  <a href="chap31.html">31</a>  <a href="chap32.html">32</a>  <a href="chap33.html">33</a>  <a href="chap34.html">34</a>  <a href="chap35.html">35</a>  <a href="chap36.html">36</a>  <a href="chap37.html">37</a>  <a href="chap38.html">38</a>  <a href="chap39.html">39</a>  <a href="chap40.html">40</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="chap7.html">[Previous Chapter]</a>    <a href="chap9.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap8_mj.html">[MathJax on]</a></p>
<p><a id="X78D1062D78BE08C1" name="X78D1062D78BE08C1"></a></p>
<div class="ChapSects"><a href="chap8.html#X78D1062D78BE08C1">8 <span class="Heading"> Functors</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8.html#X7CFDEEC07F15CF82">8.1 <span class="Heading">  </span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X81BA486D7E532469">8.1-1 ExtendScalars</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X788F3B5E7810E309">8.1-2 HomToIntegers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7E0216028756963B">8.1-3 HomToIntegersModP</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X81FED0E9858E413A">8.1-4 HomToIntegralModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7F5BAB35811AB0D1">8.1-5 TensorWithIntegralModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7CF7B8A3842D498B">8.1-6 HomToGModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7D686D5D78FEF5C9">8.1-7 InduceScalars</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X8456E06D7E76707B">8.1-8 LowerCentralSeriesLieAlgebra</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X83BA99787CBE2B7D">8.1-9 TensorWithIntegers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X829DD3868410FE2E">8.1-10 FilteredTensorWithIntegers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7A0B33D085067A38">8.1-11 TensorWithTwistedIntegers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X8122D25786C83565">8.1-12 TensorWithIntegersModP</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X873096CB823BFD1B">8.1-13 TensorWithTwistedIntegersModP</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X809BA8A87F61EEDA">8.1-14 TensorWithRationals</a></span>
</div></div>
</div>

<h3>8 <span class="Heading"> Functors</span></h3>

<p><a id="X7CFDEEC07F15CF82" name="X7CFDEEC07F15CF82"></a></p>

<h4>8.1 <span class="Heading">  </span></h4>

<p><a id="X81BA486D7E532469" name="X81BA486D7E532469"></a></p>

<h5>8.1-1 ExtendScalars</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ ExtendScalars</code>( <var class="Arg">R</var>, <var class="Arg">G</var>, <var class="Arg">EltsG</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a <span class="SimpleMath">ZH</span>-resolution <span class="SimpleMath">R</span>, a group <span class="SimpleMath">G</span> containing <span class="SimpleMath">H</span> as a subgroup, and a list <span class="SimpleMath">EltsG</span> of elements of <span class="SimpleMath">G</span>. It returns the free <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">(R ⊗_ZH ZG)</span>. The returned resolution <span class="SimpleMath">S</span> has S!.elts:=EltsG. This is a resolution of the <span class="SimpleMath">ZG</span>-module <span class="SimpleMath">(Z ⊗_ZH ZG)</span>. (Here <span class="SimpleMath">⊗_ZH</span> means tensor over <span class="SimpleMath">ZH</span>.)</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X788F3B5E7810E309" name="X788F3B5E7810E309"></a></p>

<h5>8.1-2 HomToIntegers</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ HomToIntegers</code>( <var class="Arg">X</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs either a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">X=R</span>, or an equivariant chain map <span class="SimpleMath">X = (F:R ⟶ S)</span>. It returns the cochain complex or cochain map obtained by applying <span class="SimpleMath">HomZG( _ , Z)</span> where <span class="SimpleMath">Z</span> is the trivial module of integers (characteristic 0).</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap1.html">1</a></span> , <span class="URL"><a href="../tutorial/chap7.html">2</a></span> , <span class="URL"><a href="../tutorial/chap8.html">3</a></span> , <span class="URL"><a href="../tutorial/chap10.html">4</a></span> , <span class="URL"><a href="../tutorial/chap13.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCohomologyRings.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutSpaceGroup.html">7</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutIntro.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTorAndExt.html">9</a></span> </p>

<p><a id="X7E0216028756963B" name="X7E0216028756963B"></a></p>

<h5>8.1-3 HomToIntegersModP</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ HomToIntegersModP</code>( <var class="Arg">R</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">R</span> and returns the cochain complex obtained by applying <span class="SimpleMath">HomZG( _ , Z_p)</span> where <span class="SimpleMath">Z_p</span> is the trivial module of integers mod <span class="SimpleMath">p</span>. (At present this functor does not handle equivariant chain maps.)</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap8.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutSpaceGroup.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutIntro.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTorAndExt.html">4</a></span> </p>

<p><a id="X81FED0E9858E413A" name="X81FED0E9858E413A"></a></p>

<h5>8.1-4 HomToIntegralModule</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ HomToIntegralModule</code>( <var class="Arg">R</var>, <var class="Arg">f</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">R</span> and a group homomorphism <span class="SimpleMath">f:G ⟶ GL_n(Z)</span> to the group of <span class="SimpleMath">n×n</span> invertible integer matrices. Here <span class="SimpleMath">Z</span> must have characteristic 0. It returns the cochain complex obtained by applying <span class="SimpleMath">HomZG( _ , A)</span> where <span class="SimpleMath">A</span> is the <span class="SimpleMath">ZG</span>-module <span class="SimpleMath">Z^n</span> with <span class="SimpleMath">G</span> action via <span class="SimpleMath">f</span>. (At present this function does not handle equivariant chain maps.)</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap7.html">1</a></span> , <span class="URL"><a href="../tutorial/chap13.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTwistedCoefficients.html">3</a></span> </p>

<p><a id="X7F5BAB35811AB0D1" name="X7F5BAB35811AB0D1"></a></p>

<h5>8.1-5 TensorWithIntegralModule</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorWithIntegralModule</code>( <var class="Arg">R</var>, <var class="Arg">f</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">R</span> and a group homomorphism <span class="SimpleMath">f:G ⟶ GL_n(Z)</span> to the group of <span class="SimpleMath">n×n</span> invertible integer matrices. Here <span class="SimpleMath">Z</span> must have characteristic 0. It returns the chain complex obtained by tensoring over <span class="SimpleMath">ZG</span> with the <span class="SimpleMath">ZG</span>-module <span class="SimpleMath">A=Z^n</span> with <span class="SimpleMath">G</span> action via <span class="SimpleMath">f</span>. (At present this function does not handle equivariant chain maps.)</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap7.html">1</a></span> </p>

<p><a id="X7CF7B8A3842D498B" name="X7CF7B8A3842D498B"></a></p>

<h5>8.1-6 HomToGModule</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ HomToGModule</code>( <var class="Arg">R</var>, <var class="Arg">A</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">R</span> and an abelian G-outer group A. It returns the G-cocomplex obtained by applying <span class="SimpleMath">HomZG( _ , A)</span>. (At present this function does not handle equivariant chain maps.)</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap6.html">1</a></span> , <span class="URL"><a href="../tutorial/chap7.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCrossedMods.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutGouter.html">4</a></span> </p>

<p><a id="X7D686D5D78FEF5C9" name="X7D686D5D78FEF5C9"></a></p>

<h5>8.1-7 InduceScalars</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ InduceScalars</code>( <var class="Arg">R</var>, <var class="Arg">hom</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a <span class="SimpleMath">ZQ</span>-resolution <span class="SimpleMath">R</span> and a surjective group homomorphism <span class="SimpleMath">hom:G→ Q</span>. It returns the unduced non-free <span class="SimpleMath">ZG</span>-resolution.</p>

<p><strong class="button">Examples:</strong></p>

<p><a id="X8456E06D7E76707B" name="X8456E06D7E76707B"></a></p>

<h5>8.1-8 LowerCentralSeriesLieAlgebra</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LowerCentralSeriesLieAlgebra</code>( <var class="Arg">G</var> )</td><td class="tdright">( function )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ LowerCentralSeriesLieAlgebra</code>( <var class="Arg">f</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a pcp group <span class="SimpleMath">G</span>. If each quotient <span class="SimpleMath">G_c/G_c+1</span> of the lower central series is free abelian or p-elementary abelian (for fixed prime p) then a Lie algebra <span class="SimpleMath">L(G)</span> is returned. The abelian group underlying <span class="SimpleMath">L(G)</span> is the direct sum of the quotients <span class="SimpleMath">G_c/G_c+1</span> . The Lie bracket on <span class="SimpleMath">L(G)</span> is induced by the commutator in <span class="SimpleMath">G</span>. (Here <span class="SimpleMath">G_1=G</span>, <span class="SimpleMath">G_c+1=[G_c,G]</span> .)</p>

<p>The function can also be applied to a group homomorphism <span class="SimpleMath">f: G ⟶ G' . In this case the induced homomorphism of Lie algebras L(f):L(G) ⟶ L(G')</span> is returned.</p>

<p>If the quotients of the lower central series are not all free or p-elementary abelian then the function returns fail.</p>

<p>This function was written by Pablo Fernandez Ascariz</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap7.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutIntro.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutLie.html">3</a></span> </p>

<p><a id="X83BA99787CBE2B7D" name="X83BA99787CBE2B7D"></a></p>

<h5>8.1-9 TensorWithIntegers</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorWithIntegers</code>( <var class="Arg">X</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs either a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">X=R</span>, or an equivariant chain map <span class="SimpleMath">X = (F:R ⟶ S)</span>. It returns the chain complex or chain map obtained by tensoring with the trivial module of integers (characteristic 0).</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap1.html">1</a></span> , <span class="URL"><a href="../tutorial/chap3.html">2</a></span> , <span class="URL"><a href="../tutorial/chap6.html">3</a></span> , <span class="URL"><a href="../tutorial/chap7.html">4</a></span> , <span class="URL"><a href="../tutorial/chap10.html">5</a></span> , <span class="URL"><a href="../tutorial/chap11.html">6</a></span> , <span class="URL"><a href="../tutorial/chap13.html">7</a></span> , <span class="URL"><a href="../tutorial/chap14.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutArithmetic.html">9</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutArtinGroups.html">10</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutAspherical.html">11</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutParallel.html">12</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPerformance.html">13</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCocycles.html">14</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPersistent.html">15</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPoincareSeries.html">16</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">17</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">18</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPolytopes.html">19</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoxeter.html">20</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutRosenbergerMonster.html">21</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutDavisComplex.html">22</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutDefinitions.html">23</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutSimplicialGroups.html">24</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutExtensions.html">25</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutSpaceGroup.html">26</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutFunctorial.html">27</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutGraphsOfGroups.html">28</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutIntro.html">29</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTorAndExt.html">30</a></span> </p>

<p><a id="X829DD3868410FE2E" name="X829DD3868410FE2E"></a></p>

<h5>8.1-10 FilteredTensorWithIntegers</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ FilteredTensorWithIntegers</code>( <var class="Arg">R</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">R</span> for which "filteredDimension" lies in NamesOfComponents(R). (Such a resolution can be produced using TwisterTensorProduct(), ResolutionNormalSubgroups() or FreeGResolution().) It returns the filtered chain complex obtained by tensoring with the trivial module of integers (characteristic 0).</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap10.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPersistent.html">2</a></span> </p>

<p><a id="X7A0B33D085067A38" name="X7A0B33D085067A38"></a></p>

<h5>8.1-11 TensorWithTwistedIntegers</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorWithTwistedIntegers</code>( <var class="Arg">X</var>, <var class="Arg">rho</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs either a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">X=R</span>, or an equivariant chain map <span class="SimpleMath">X = (F:R ⟶ S)</span>. It also inputs a function <span class="SimpleMath">rho: G→ Z</span> where the action of <span class="SimpleMath">g ∈ G</span> on <span class="SimpleMath">Z</span> is such that <span class="SimpleMath">g.1 = rho(g)</span>. It returns the chain complex or chain map obtained by tensoring with the (twisted) module of integers (characteristic 0).</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap3.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoveringSpaces.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutCoverinSpaces.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTwistedCoefficients.html">4</a></span> </p>

<p><a id="X8122D25786C83565" name="X8122D25786C83565"></a></p>

<h5>8.1-12 TensorWithIntegersModP</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorWithIntegersModP</code>( <var class="Arg">X</var>, <var class="Arg">p</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs either a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">X=R</span>, or a characteristics 0 chain complex, or an equivariant chain map <span class="SimpleMath">X = (F:R ⟶ S)</span>, or a chain map between characteristic 0 chain complexes, together with a prime <span class="SimpleMath">p</span>. It returns the chain complex or chain map obtained by tensoring with the trivial module of integers modulo <span class="SimpleMath">p</span>.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap1.html">1</a></span> , <span class="URL"><a href="../tutorial/chap10.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutArithmetic.html">3</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPerformance.html">4</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPersistent.html">5</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutPoincareSeries.html">6</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutDefinitions.html">7</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutExtensions.html">8</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTorAndExt.html">9</a></span> </p>

<p><a id="X873096CB823BFD1B" name="X873096CB823BFD1B"></a></p>

<h5>8.1-13 TensorWithTwistedIntegersModP</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorWithTwistedIntegersModP</code>( <var class="Arg">X</var>, <var class="Arg">p</var>, <var class="Arg">rho</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs either a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">X=R</span>, or an equivariant chain map <span class="SimpleMath">X = (F:R ⟶ S)</span>, and a prime <span class="SimpleMath">p</span>. It also inputs a function <span class="SimpleMath">rho: G→ Z</span> where the action of <span class="SimpleMath">g ∈ G</span> on <span class="SimpleMath">Z</span> is such that <span class="SimpleMath">g.1 = rho(g)</span>. It returns the chain complex or chain map obtained by tensoring with the trivial module of integers modulo <span class="SimpleMath">p</span>.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../www/SideLinks/About/aboutTwistedCoefficients.html">1</a></span> </p>

<p><a id="X809BA8A87F61EEDA" name="X809BA8A87F61EEDA"></a></p>

<h5>8.1-14 TensorWithRationals</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ TensorWithRationals</code>( <var class="Arg">R</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a <span class="SimpleMath">ZG</span>-resolution <span class="SimpleMath">R</span> and returns the chain complex obtained by tensoring with the trivial module of rational numbers.</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap10.html">1</a></span> , <span class="URL"><a href="../tutorial/chap13.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutExtensions.html">3</a></span> </p>


<div class="chlinkprevnextbot"> <a href="chap0.html">[Top of Book]</a>   <a href="chap0.html#contents">[Contents]</a>    <a href="chap7.html">[Previous Chapter]</a>    <a href="chap9.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="chap13.html">13</a>  <a href="chap14.html">14</a>  <a href="chap15.html">15</a>  <a href="chap16.html">16</a>  <a href="chap17.html">17</a>  <a href="chap18.html">18</a>  <a href="chap19.html">19</a>  <a href="chap20.html">20</a>  <a href="chap21.html">21</a>  <a href="chap22.html">22</a>  <a href="chap23.html">23</a>  <a href="chap24.html">24</a>  <a href="chap25.html">25</a>  <a href="chap26.html">26</a>  <a href="chap27.html">27</a>  <a href="chap28.html">28</a>  <a href="chap29.html">29</a>  <a href="chap30.html">30</a>  <a href="chap31.html">31</a>  <a href="chap32.html">32</a>  <a href="chap33.html">33</a>  <a href="chap34.html">34</a>  <a href="chap35.html">35</a>  <a href="chap36.html">36</a>  <a href="chap37.html">37</a>  <a href="chap38.html">38</a>  <a href="chap39.html">39</a>  <a href="chap40.html">40</a>  <a href="chapInd.html">Ind</a>  </div>

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

100%


¤ Dauer der Verarbeitung: 0.3 Sekunden  (vorverarbeitet)  ¤

*© 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.





                                                                                                                                                                                                                                                                                                                                                                                                     

Neuigkeiten

     Aktuelles
     Motto des Tages

Software

     Produkte
     Quellcodebibliothek

Aktivitäten

     Artikel über Sicherheit
     Anleitung zur Aktivierung von SSL

Muße

     Gedichte
     Musik
     Bilder
Jenseits des Üblichen ....

Besucherstatistik

Besucherstatistik

Monitoring

Montastic status badge