Quelle chap9_mj.html
Sprache: unbekannt
<?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 >
<
script type=
"text/javascript"
src=
"https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML " >
</
script >
<
title >GAP (Modules) - Chapter
9 : Module Elements</
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=
"chap9" onload=
"jscontent()" >
<
div class=
"chlinktop" ><
span class=
"chlink1" >Goto Chapter: </
span ><
a href=
"chap0_mj.html" >Top<
/a > <a href="chap1_mj.html" >1 </a > <a href="chap2_mj.html" >2 </a > <a href="chap3_mj.html" >3 </a > <a href="chap4_mj.html" >4 </a > <a href="chap5_mj.html" >5 </a > <a href="chap6_mj.html" >6 </a > <a href="chap7_mj.html" >7 </a > <a href="chap8_mj.html" >8 </a > <a href="chap9_mj.html" >9 </a > <a href="chap10_mj.html" >10 </a a href="chap11_mj.html" >11 </a > <a href="chap12_mj.html" >12 </a > <a href="chap13_mj.html" >13 </a > <a href="chapA_mj.html" >A </a > <a href="chapB_mj.html" >B </a > <a href="chapC_mj.html" >C</a > <a href="chapBib_mj.html" >Bib</a > <a href="chapInd_mj.html" >Ind</a > </div >div class="chlinkprevnexttop" > <a href="chap0_mj.html" >[Top of Book]</a > <a href="chap0_mj.html#contents" >[Contents]</a > <a href="chap8_mj.html" >[Previous Chapter]</a > <a href="chap10_mj.html" >[Next Chapter]</a > </div >p id="mathjaxlink" class="pcenter" ><a href="chap9.html" >[MathJax off]</a ></p >p ><a id="X7E9BCB99816348F2" name="X7E9BCB99816348F2" ></a ></p >div class="ChapSects" ><a href="chap9_mj.html#X7E9BCB99816348F2" >9 <span class="Heading" >Module Elements</span ></a >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X84A51EB87E054D3F" >9 .1 <span class="Heading" >Module Elements: Category and Representations</span ></a >span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X784BBB2A782DB774" >9 .1 -1 IsHomalgElement</a ></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X7BF482C77B68ED64" >9 .1 -2 IsElementOfAModuleGivenByAMorphismRep</a ></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X7CFD0CF27A3FEB9D" >9 .2 <span class="Heading" >Module Elements: Constructors</span ></a >span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X7BCBA7E780FE2B14" >9 .3 <span class="Heading" >Module Elements: Properties</span ></a >span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X87FA282579406FC0" >9 .3 -1 IsElementOfIntegers</a ></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X80AE2D1C82A2059C" >9 .4 <span class="Heading" >Module Elements: Attributes</span ></a >span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap9_mj.html#X813DF977812C06B6" >9 .5 <span class="Heading" >Module Elements: Operations and Functions</span ></a >span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap9_mj.html#X8769077379997D89" >9 .5 -1 HomalgRing</a ></span >div ></div >div >9 <span class="Heading" >Module Elements</span ></h3>p >An element of a module <span class="SimpleMath" >\(M\)</span > is internally represented by a module map from the (distinguished) rank 1 free module to the module <span class="SimpleMath" >\(M\)</span >. In particular, the data structure for module elements automatically profits from the intrinsic realization of morphisms in the <strong class="pkg" >homalg</strong > project.</p >p ><a id="X84A51EB87E054D3F" name="X84A51EB87E054D3F" ></a ></p >9 .1 <span class="Heading" >Module Elements: Category and Representations</span ></h4>p ><a id="X784BBB2A782DB774" name="X784BBB2A782DB774" ></a ></p >9 .1 -1 IsHomalgElement</h5>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >&#an style='color: green'>8227; IsHomalgElement</code >( <var class="Arg" >M</var > )</td ><td class="tdright" 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 > category of module elements.</p >p ><a id="X7BF482C77B68ED64" name="X7BF482C77B68ED64" ></a ></p >9 .1 -2 IsElementOfAModuleGivenByAMorphismRep</h5>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >&#an style='color: green'>8227; IsElementOfAModuleGivenByAMorphismRep</code >( <var class="Arg" 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 elements of modules.</p >p >(It is a subrepresentation of <code class="func" >IsElementOfAnObjectGivenByAMorphismRep</code > (<a href="https://homalg-project.github.io/homalg_project/homalg/doc/chap5_mj.html#X87F3740E85E9AA51 " ><span class="RefLink" >homalg: IsElementOfAnObjectGivenByAMorphismRep</span ></a >).)</p >p ><a id="X7CFD0CF27A3FEB9D" name="X7CFD0CF27A3FEB9D" ></a ></p >9 .2 <span class="Heading" >Module Elements: Constructors</span ></h4>p ><a id="X7BCBA7E780FE2B14" name="X7BCBA7E780FE2B14" ></a ></p >9 .3 <span class="Heading" >Module Elements: Properties</span ></h4>p ><a id="X87FA282579406FC0" name="X87FA282579406FC0" ></a ></p >9 .3 -1 IsElementOfIntegers</h5>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >&#an style='color: green'>8227; IsElementOfIntegers</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 <var class="Arg" >m</var > is an element of the integers viewed as a module over itself.</p >div class="example" ><pre >span class="GAPprompt" >gap></span > <span class="GAPinput" >zz := HomalgRingOfIntegers( );</span >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" >IsElementOfIntegers( a );</span >span class="GAPprompt" >gap></span > <span class="GAPinput" >Z4 := zz / 4 ;</span >4 )span class="GAPprompt" >gap></span > <span class="GAPinput" >b := HomalgElement( HomalgMap( "[[-1]]" , 1 * Z4, 1 * Z4 ) );</span >3 ]|span class="GAPprompt" >gap></span > <span class="GAPinput" >IsElementOfIntegers( b );</span >pre ></div >p ><a id="X80AE2D1C82A2059C" name="X80AE2D1C82A2059C" ></a ></p >9 .4 <span class="Heading" >Module Elements: Attributes</span ></h4>p ><a id="X813DF977812C06B6" name="X813DF977812C06B6" ></a ></p >9 .5 <span class="Heading" >Module Elements: Operations and Functions</span ></h4>p ><a id="X8769077379997D89" name="X8769077379997D89" ></a ></p >9 .5 -1 HomalgRing</h5>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >&#an style='color: green'>8227; 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 >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 >pre ></div >div class="chlinkprevnextbot" > <a href="chap0_mj.html" >[Top of Book]</a > <a href="chap0_mj.html#contents" >[Contents]</a > <a href="chap8_mj.html" >[Previous Chapter]</a > <a href="chap10_mj.html" >[Next Chapter]</a > </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0_mj.html" >Top</a > <a href="chap1_mj.html" >1 </a > <a href="chap2_mj.html" >2 </a > <a href="chap3_mj.html" >3 </a > <a href="chap4_mj.html" >4 </a > <a href="chap5_mj.html" >5 </a > <a href="chap6_mj.html" >6 </a > <a href="chap7_mj.html" >7 </a > <a href="chap8_mj.html" >8 </a > <a href="chap9_mj.html" >9 </a > <a href="chap10_mj.html" >10 </a a href="chap11_mj.html" >11 </a > <a href="chap12_mj.html" >12 </a > <a href="chap13_mj.html" >13 </a > <a href="chapA_mj.html" >A </a > <a href="chapB_mj.html" >B </a > <a href="chapC_mj.html" >C</a > <a href="chapBib_mj.html" >Bib</a > <a href="chapInd_mj.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 > Messung V0.5 in Prozent C=100 H=100 G=100
[zur Elbe Produktseite wechseln0.14QuellennavigatorsAnalyse erneut starten2026-09-04]
2026-08-25
Neuigkeiten Aktuelles Motto des Tages Open Source Software
Jenseits des Üblichen ....
Besucherstatistik
Statistik #Sources=1019547 #Domains=890699
