<?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 (CAP) - Chapter 14: Dummy implementations</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="chap14" 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 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href="chap14.html#X86A21A2379AA70E4" >14.1-1 IsDummyRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X7D89EFE77FC37A85" >14.1-2 IsDummyRingElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X87E7CFFB81611DED" >14.1-3 IsDummyCommutativeRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X79CB0F12853487F4" >14.1-4 IsDummyCommutativeRingElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X7F1159E287E0850B" >14.1-5 IsDummyField</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X7A227A6D7F366CDE" >14.1-6 IsDummyFieldElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X82B6E6F780AB19FA" >14.1-7 DummyRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X823C63568160007F" >14.1-8 DummyCommutativeRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X8675D79684AD56D0" >14.1-9 DummyField</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap14.html#X82A623E78640E822" >14.2 <span class="Heading" >Dummy categories</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X872B304F85971287" >14.2-1 IsDummyCategory</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X7FB7ED298101C4C5" >14.2-2 IsDummyCategoryObject</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X86ED2D2D84900225" >14.2-3 IsDummyCategoryMorphism</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X85EFD8FA7CA98ECB" >14.2-4 DummyCategory</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap14.html#X7D79D0478599BC12" >14.3 <span class="Heading" >Dummy homalg rings</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X83D2C38E849A65DC" >14.3-1 IsDummyHomalgRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X7A64A51C7B55BD18" >14.3-2 IsDummyHomalgRingElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X8170E18881CE3C03" >14.3-3 IsDummyCommutativeHomalgRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X7997E4157AB993E9" >14.3-4 IsDummyCommutativeHomalgRingElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X87E270D481736842" >14.3-5 IsDummyHomalgField</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X78E80ECF786AE153" >14.3-6 IsDummyHomalgFieldElement</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X830459217A01C164" >14.3-7 DummyHomalgRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X841685517C4CDC7A" >14.3-8 DummyCommutativeHomalgRing</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap14.html#X7CA21DAD784763AA" >14.3-9 DummyHomalgField</a></span >div ></div >div >span class="Heading" >Dummy implementations</span ></h3>any operation in this interface will simply signal an error. Hence, when using a dummy implementation, we can be sure that we only rely on the abstract interface but not on any implementation details , for the simple reason that there is no actual implementation. This is useful for testing or compilation against a generic implementation of a concept.</p>"X7B19E3AE7AB1B31B" name="X7B19E3AE7AB1B31B" ></a></p>span class="Heading" >Dummy rings</span ></h4>"X86A21A2379AA70E4" name="X86A21A2379AA70E4" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyRing</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of dummy rings.</p>"X7D89EFE77FC37A85" name="X7D89EFE77FC37A85" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyRingElement</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of elements of a dummy ring.</p>"X87E7CFFB81611DED" name="X87E7CFFB81611DED" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyCommutativeRing</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of dummy commutative rings.</p>"X79CB0F12853487F4" name="X79CB0F12853487F4" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyCommutativeRingElement</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of elements of a dummy commutative ring.</p>"X7F1159E287E0850B" name="X7F1159E287E0850B" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyField</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of dummy fields.</p>"X7A227A6D7F366CDE" name="X7A227A6D7F366CDE" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyFieldElement</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of elements of a dummy field.</p>"X82B6E6F780AB19FA" name="X82B6E6F780AB19FA" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ DummyRing</code >( )</td ><td class="tdright" >( function )</td ></tr ></table ></div >"X823C63568160007F" name="X823C63568160007F" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ DummyCommutativeRing</code >( )</td ><td class="tdright" >( function )</td ></tr ></table ></div >"X8675D79684AD56D0" name="X8675D79684AD56D0" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ DummyField</code >( )</td ><td class="tdright" >( function )</td ></tr ></table ></div >"X82A623E78640E822" name="X82A623E78640E822" ></a></p>span class="Heading" >Dummy categories</span ></h4>"X872B304F85971287" name="X872B304F85971287" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyCategory</code >( <var class="Arg" >arg</var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>strong class="pkg" >GAP</strong > category of a dummy CAP category.</p>"X7FB7ED298101C4C5" name="X7FB7ED298101C4C5" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyCategoryObject</code >( <var class="Arg" >arg</var > )</td ><td class="tdright" >( filter )</td ></tr ></table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>strong class="pkg" >GAP</strong > category of objects in a dummy CAP category.</p>"X86ED2D2D84900225" name="X86ED2D2D84900225" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyCategoryMorphism</code >( <var class="Arg" >arg</var > )</td ><td class="tdright" >( filter )</td ></tr table ></div >code class="keyw" >true</code > or <code class="keyw" >false</code ></p>strong class="pkg" >GAP</strong > category of morphisms in a dummy CAP category.</p>"X85EFD8FA7CA98ECB" name="X85EFD8FA7CA98ECB" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ DummyCategory</code >( <var class="Arg" >options</var > )</td ><td class="tdright" >( operation )</td ></tr ></table div >var class="Arg" >options</var >, which is a record passed on to <code class="func" >CategoryConstructor</code > (<a href="chap11.html#X8070F8B48111E8A7" ><span class="RefLink" >11.2-1</span ></a>). Note that the options <code class="code" >{category,object ,morphism}_filter</code > will be set to <code class="code" >IsDummyCategory{,Object ,Morphism}</code > and the options <code class="code" >{object ,morphism}_{constructor,datum}</code > and <code class="code" >create_func_*</code > will be set to dummy implementations (throwing errors when actually called). The dummy category will pretend to support empty limits by default.</p>"X7D79D0478599BC12" name="X7D79D0478599BC12" ></a></p>span class="Heading" >Dummy homalg rings</span ></h4>section require <code class="code" >MatricesForHomalg</code > to be loaded.</p>"X83D2C38E849A65DC" name="X83D2C38E849A65DC" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyHomalgRing</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of dummy homalg rings.</p>"X7A64A51C7B55BD18" name="X7A64A51C7B55BD18" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyHomalgRingElement</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of elements of a dummy homalg ring.</p>"X8170E18881CE3C03" name="X8170E18881CE3C03" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyCommutativeHomalgRing</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of dummy commutative homalg rings.</p>"X7997E4157AB993E9" name="X7997E4157AB993E9" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyCommutativeHomalgRingElement</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of elements of a dummy commutative homalg ring.</p>"X87E270D481736842" name="X87E270D481736842" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyHomalgField</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of dummy homalg fields.</p>"X78E80ECF786AE153" name="X78E80ECF786AE153" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ IsDummyHomalgFieldElement</code ></td ><td class="tdright" >( filter )</td ></tr ></table ></div >strong class="pkg" >GAP</strong > filter of elements of a dummy homalg field.</p>"X830459217A01C164" name="X830459217A01C164" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ DummyHomalgRing</code >( )</td ><td class="tdright" >( function )</td ></tr ></table ></div >"X841685517C4CDC7A" name="X841685517C4CDC7A" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ DummyCommutativeHomalgRing</code >( )</td ><td class="tdright" >( function )</td ></tr ></table ></div >"X7CA21DAD784763AA" name="X7CA21DAD784763AA" ></a></p>div class="func" ><table class="func" width="100%" ><tr ><td class="tdleft" ><code class="func" >‣ DummyHomalgField</code >( )</td ><td class="tdright" >( function )</td ></tr ></table ></div >div class="chlinkprevnextbot" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap13.html" >[Previous Chapter]</a> <a href="chap15.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="chapInd.html" >Ind</a> </div >hr />"foot" >generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc " >GAPDoc2HTML</a></p>body >html >quality 99%
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