<?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" "https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML " >script >title >GAP (MatricesForHomalg) - Chapter 6: Ring Relations</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="chap6" 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="chapA_mj.html" >A</a> <a href="chapB_mj.html" >B</a> <a href="chapC_mj.html" >C</a> <a href="chapD_mj.html" >D</a> <a href="chapE_mj.html" >E</a> <a href="chapF_mj.html" >F</a> <a href="chapBib_mj.html" >Bib</a> <a href="chapInd_mj.html" div >div class="chlinkprevnexttop" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap5_mj.html" >[Previous Chapter]</a> <a href="chapA_mj.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap6.html" >[MathJax off]</a></p>"X8163F0658017F220" name="X8163F0658017F220" ></a></p>div class="ChapSects" ><a href="chap6_mj.html#X8163F0658017F220" >6 <span class="Heading" >Ring Relations</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X7EB7C20C78788C69" >6.1 <span class="Heading" >Ring Relations: Categories and Representations</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7D50E3AD82087AE6" >6.1-1 IsHomalgRingRelations</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7DECADD683403C65" >6.1-2 IsHomalgRingRelationsAsGeneratorsOfLeftIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X78746A217FEEB058" >6.1-3 IsHomalgRingRelationsAsGeneratorsOfRightIdeal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X86CA83A081B8C8EA" >6.1-4 IsRingRelationsRep</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X81D1405F81B86E4B" >6.2 <span class="Heading" >Ring Relations: Constructors</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X7FFB5DE07BB77319" >6.3 <span class="Heading" >Ring Relations: Properties</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X835DF250790EF863" >6.3-1 CanBeUsedToDecideZero</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6_mj.html#X7B9398827AEEA2E6" >6.3-2 IsInjectivePresentation</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X849ED71B8164D1C2" >6.4 <span class="Heading" >Ring Relations: Attributes</span ></a>span >div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6_mj.html#X7ABFB8F982EBD7F8" >6.5 <span class="Heading" >Ring Relations: Operations and Functions</span ></a>span >div >div >span class="Heading" >Ring Relations</span ></h3>"X7EB7C20C78788C69" name="X7EB7C20C78788C69" ></a></p>span class="Heading" >Ring Relations: Categories and Representations</span ></h4>"X7D50E3AD82087AE6" name="X7D50E3AD82087AE6" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsHomalgRingRelations</code >( <var class="Arg" >rel</var > )</td ><td class="tdright" >( category )</td ></tr table ></div >code class="code" >true</code > or <code class="code" >false</code ></p>strong class="pkg" >GAP</strong > category of <strong class="pkg" >homalg</strong > ring relations.</p>"X7DECADD683403C65" name="X7DECADD683403C65" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsHomalgRingRelationsAsGeneratorsOfLeftIdeal</code >( <var class="Arg" >rel</var > )</td ><td class="tdright" td ></tr ></table ></div >code class="code" >true</code > or <code class="code" >false</code ></p>strong class="pkg" >GAP</strong > category of <strong class="pkg" >homalg</strong > ring relations as generators of a left ideal.</p>strong class="pkg" >GAP</strong > category <code class="code" >IsHomalgRingRelations</code >.)</p>"X78746A217FEEB058" name="X78746A217FEEB058" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsHomalgRingRelationsAsGeneratorsOfRightIdeal</code >( <var class="Arg" >rel</var > )</td ><td class="tdright" >( category )</td ></tr ></table ></div >code class="code" >true</code > or <code class="code" >false</code ></p>strong class="pkg" >GAP</strong > category of <strong class="pkg" >homalg</strong > ring relations as generators of a right ideal.</p>strong class="pkg" >GAP</strong > category <code class="code" >IsHomalgRingRelations</code >.)</p>"X86CA83A081B8C8EA" name="X86CA83A081B8C8EA" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsRingRelationsRep</code >( <var class="Arg" >rel</var > )</td ><td class="tdright" >( representation )</td tr ></table ></div >code class="code" >true</code > or <code class="code" >false</code ></p>strong class="pkg" >GAP</strong > representation of a finite set of relations of a <strong class="pkg" >homalg</strong > ring.</p>strong class="pkg" >GAP</strong > category <code class="func" >IsHomalgRingRelations</code > (<a href="chap6_mj.html#X7D50E3AD82087AE6" ><span class="RefLink" >6.1-1</span ></a>))</p>"X81D1405F81B86E4B" name="X81D1405F81B86E4B" ></a></p>span class="Heading" >Ring Relations: Constructors</span ></h4>"X7FFB5DE07BB77319" name="X7FFB5DE07BB77319" ></a></p>span class="Heading" >Ring Relations: Properties</span ></h4>"X835DF250790EF863" name="X835DF250790EF863" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ CanBeUsedToDecideZero</code >( <var class="Arg" >rel</var > )</td ><td class="tdright" >( property )</td ></tr table ></div >code class="code" >true</code > or <code class="code" >false</code ></p>strong class="pkg" >homalg</strong > set of relations <var class="Arg" >rel</var > can be used for normal form reductions. <br /> (no method installed)</p>"X7B9398827AEEA2E6" name="X7B9398827AEEA2E6" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsInjectivePresentation</code >( <var class="Arg" >rel</var > )</td ><td class="tdright" >( property )</td ></tr ></table ></div >code class="code" >true</code > or <code class="code" >false</code ></p>strong class="pkg" >homalg</strong > set of relations <var class="Arg" >rel</var > has zero syzygies.</p>"X849ED71B8164D1C2" name="X849ED71B8164D1C2" ></a></p>span class="Heading" >Ring Relations: Attributes</span ></h4>"X7ABFB8F982EBD7F8" name="X7ABFB8F982EBD7F8" ></a></p>span class="Heading" >Ring Relations: Operations and Functions</span ></h4>div class="chlinkprevnextbot" > <a href="chap0_mj.html" >[Top of Book]</a> <a href="chap0_mj.html#contents" >[Contents]</a> <a href="chap5_mj.html" >[Previous Chapter]</a> <a href="chapA_mj.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span ><a href="chap0_mj.html" 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