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<title>GAP (Modules) - Chapter 9: Module
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<div class>9.1-1 </h5

< id="" class""><a hrefchap9_mjhtml[MathJax]</a></p>
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<spanclassContSSbr>span="nocss">nbspnbsp;</span><a href"chap9.html#X87FA282579406FC0">9.31 IsElementOfIntegers/a</>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X813DF977812C06B6">9.5 <span class="Heading">Module Elements: Operations and Functions</span></a>
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<h3>9 <span class="Heading">Module Elements</span></h3>

<p>An element of a module <span class="SimpleMath">M</span> is internally represented byReturnscode="code>"falsepjava.lang.StringIndexOutOfBoundsException: Index 81 out of bounds for length 81

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

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

<p><aspan="GAPinput"zz HomalgRingOfIntegers

<h5>9.1-1 IsHomalgElement</h5>

<div="func"><table="func ="00"<>		"< class""&827;IsHomalgElementrg">M )tdclass"">(  )

<p>eturnscode="code"></code> or classcode>false>/>

<p>The <strong class="pkg">GAP

>="X7BF482C77B68ED64"name><

<h5 class>&;<s> <span"":  

< class>table="" ="10"tr">">&27 (< class="Arg>)/><td=tdright; >/><><div
<p>Returns: <code class="code">true</code> or ="&; < class=""> = HomalgElement( HomalgMap( "[[-1]]", 1 * Z4, 1 * Z4 ) );

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

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

<p><a id

<h4>92<spanclassHeadingModule : Constructors<spanh4

<p><a id>9.4 span=""Module/>/h4

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

<p><a id="X87FA282579406FC0" name="X87FA282579406FC0"></a></

<h5>9.3-1 IsElementOfIntegers</h5>

<div="func"< classfunc =10"<> ="><code="func">#27 /> < class">m)/td>		">(&;property )/td>

<p>Returns: <code

<p>Check ifthe <var="Arg"><var an element the integersviewed a module itself</>


<div class="

Returns: a pkg>homalg>ring>
<span class="GAPprompt">gap></span> <span class="GAPinput">zz := HomalgRingOfIntegers( );</span>
Z
<span class="java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
span="GAPprompt"gap;/> span="GAPinput"IsElementOfIntegers)<span>
true class>>/span>< class"APinput>IsIdenticalObj( zz, HomalgRing( a ))
<spanjava.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 4
Z/( 4 )
<span class="GAPprompt">gap></span> <span class="GAPinput">b := HomalgElement( HomalgMap( "[[-1]]", 1 * Z4 class; =">[Top of Book]  >Contents;  &;<a hrefchap8[ Chapter<a>   <a href="chap10.html">[Next Chapter]</a>   </div>
|  ]
<span class="GAPprompt">gap></span> <span class="GAPinput">IsElementOfIntegers( b );</span
false
</pre></div>

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<h4>9.4 <span class="Heading">Module Elements: Attributes</span></h4>

<p><a id="X813DF977812C06B6" name="X813DF977812C06B6"></a></p>

<h4>9.5 <span class="Heading">Module Elements: Operations and Functions</span></h4>

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

<h5>9.5-1 HomalgRing</h5>

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

<p>The <strong class="pkg">homalg</strong> ring of the <strong class="pkg">homalg</strong> module element <var class="Arg">m</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">a := HomalgElement( HomalgMap( "[[2]]", 1 * zz, 1 * zz ) );</span>
2
<span class="GAPprompt">gap></span> <span class="GAPinput">IsIdenticalObj( zz, HomalgRing( a ) );</span>
true
</pre></div>


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