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<div class="ChapSects"><a href="chap9.html#X7E9BCB99816348F2">9 <span class="Heading">Module Elements</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X84A51EB87E054D3F">9.1 <span class="Heading">Module Elements: Category and Representations</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X784BBB2A782DB774">9.1-1 IsHomalgElement</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7BF482C77B68ED64">9.1-2 IsElementOfAModuleGivenByAMorphismRep</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7CFD0CF27A3FEB9D">9.2 <span class="Heading">Module Elements: Constructors</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X7BCBA7E780FE2B14">9.3 <span class="Heading">Module Elements: Properties</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X87FA282579406FC0">9.3-1 IsElementOfIntegers</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X80AE2D1C82A2059C">9.4 <span class="Heading">Module Elements: Attributes</span></a>
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<spanclass="ContSS"><br/>< class="nocss"> &;</span><a hrefchap9#X8769077379997D89>.5-1 HomalgRing/></span
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<h3<span class="Heading">odule</span></h3>

<p>

<><a id="X84A51EB87E054D3F" name="X84A51EB87E054D3F">/>/p>

<h4>9.1 <span class="Heading">Module Elements: Category and Representations</span></h4>

<p><a id="X784BBB2A782DB774" name=

<h51IsHomalgElement>

pidmathjaxlink=pcenter=".html"> on>
<p>Returns: <code class id ="X7E9BCB99816348F2">/<p

<p>The <strong class="pkg">GAP</strong> category of module elements.</p>

<p><a id="X7BF482C77B68ED64" name="X7BF482C77B68ED64"></a></p>

<h5>9.1-2 IsElementOfAModuleGivenByAMorphismRep

< class">tableclass"" width"0">>=tdleft"><codeclass"unc>#22 IsElementOfAModuleGivenByAMorphismRep( M )
( representation )

<p>Returns: <code class="code">true</code> or <code class="code">false</code></p>

<p>The <strong class="pkg">GAP</strong> representation of elements of modulesdiv/>

<p>(It is a subrepresentation of <code class="func">span>

<p><a id="X7CFD0CF27A3FEB9D" name="X7CFD0CF27A3FEB9D"></a></p>

<h4>9.2 <span class="Heading">Module Elements =""><br /< class>;  =html3</>span

<p><a id="X7BCBA7E780FE2B14" name="java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 7

<h4>9.3 <span class="Heading">Module Elements: Properties</span></h4>

<p/>

<<h5=ContSS /< class>nbsp;</><a ="chap9.#X8769077379997D89>.-

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ java.lang.StringIndexOutOfBoundsException: Range [0, 120) out of bounds for length 12
<p>: < class"true or class=code>/ode>/>

<p>Check if the <var class="Arg">m</var> is an element of the integers viewed as a module over itself


<div 
<span class="GAPprompt">gap></span> < class" := HomalgRingOfIntegers( );
Z class class"width10%>tr		code=func>#27 /> class"rg/ <> =tdrightcategory>t<table
<span class="GAPprompt">gapp>: < classtrue  <code=""></code>p
2
<span
true<p<a idX7BF482C77B68ED64 name="X7BF482C77B68ED64">/a></p>
<span="GAPprompt"gapgt/pan class="GAPinput>Z4 := zz/ 4;
Z<iv="func">< classfuncwidth00"
Arg">M</var )/tdtd class"">( representation;)</td</tr<table/div>
<span class"GAPprompt"gapgt/panspanclassGAPinputb:java.lang.StringIndexOutOfBoundsException: Range [123, 67) out of bounds for length 129
|[ 3 ]|
<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
false
</pre></div>

<p>h49 span ="">ModuleElementsConstructors/></>

<h4.4< classHeading"> Elements: Attributes/h4>

<pjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<h4>9.5 <span class="Heading">Module

<p><a id="X8769077379997D89" name="X8769077379997D89"></a></

<h5div class"table ="func"width"10%"tr>tdclass"tdleft class"&82;IsElementOfIntegersArg/ <td =tdrightnbsp;<tdtr></

<divpCheck the class><> is of  as over.</
 ="ring

<p>The


<div class="example"><pre>
<span class2
Z
<span class="GAPprompt">gap< class>><span< class>( a ;/span
2
<span="GAPprompt"gap;</span>span="APinput"IsIdenticalObjHomalgRing )<span
true
</pre></div>


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