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<div class="ChapSects"><a href="chap6_mj.html#X868F7BAB7AC2EEBC">6 <span class="Heading">Basics</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X7D9044767BEB1523">6.1 <span class="Heading">Global variables</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7CB459E282D621B2">6.1-1 HOMALG_TOOLS</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X7D03633A7D98026B">6.2 <span class="Heading">GAP Categories</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7E36B19C7FFEC100">6.2-1 IsStructureObjectOrObjectOrMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7A9BB94E7D9F3AB6">6.2-2 IsStructureObjectOrObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X85DC9C0A83ADB0C6">6.2-3 IsStructureObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7D2734947FBEB2EF">6.2-4 IsStructureObjectMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X8346DBCF876C70F7">6.2-5 IsHomalgRingOrModule</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X7C701DBF7BAE649A">6.3 <span class="Heading">Attributes</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X791768BD7815B343">6.3-1 RingFilter</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7CB137BC842F454F">6.3-2 RingElementFilter</a></span>
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<h3>6 <span class="Heading">Basics</span></h3>

<p><a id="X7D9044767BEB1523" name="X7D9044767BEB1523"></a></p>

<h4>6.1 <span class="Heading">Global variables</span></h4>

<p><a id="X7CB459E282D621B2" name="X7CB459E282D621B2"></a></p>

<h5>6.1-1 HOMALG_TOOLS</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&an style='color:turquoise'>#8227; HOMALG_TOOLS</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>A central place for configurations.</p>

<p><a id="X7D03633A7D98026B" name="X7D03633A7D98026B"></a></p>

<h4>6.2 <span class="Heading">GAP Categories</span></h4>

<p><a id="X7E36B19C7FFEC100" name="X7E36B19C7FFEC100"></a></p>

<h5>6.2-1 IsStructureObjectOrObjectOrMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&an style='color:turquoise'>#8227; IsStructureObjectOrObjectOrMorphism</code>( <var class="Arg">arg</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>This is the super super GAP-category which will include the GAP-categories IsStructureObjectOrObject and IsHomalgObjectOrMorphism</p>

<p><a id="X7A9BB94E7D9F3AB6" name="X7A9BB94E7D9F3AB6"></a></p>

<h5>6.2-2 IsStructureObjectOrObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&an style='color:turquoise'>#8227; IsStructureObjectOrObject</code>( <var class="Arg">arg</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>This is the super GAP-category which will include the GAP-categories IsHomalgRing, IsHomalgModule, IsHomalgRingOrModule and IsHomalgComplex</p>

<p><a id="X85DC9C0A83ADB0C6" name="X85DC9C0A83ADB0C6"></a></p>

<h5>6.2-3 IsStructureObject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&an style='color:turquoise'>#8227; IsStructureObject</code>( <var class="Arg">arg</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>This is the super GAP-category which will include the GAP-categories IsHomalgRing we need this GAP-category to define things like Hom(M,R) as easy as Hom(M,N) without distinguishing between structure objects (e.g. rings) and objects (e.g. modules)</p>

<p><a id="X7D2734947FBEB2EF" name="X7D2734947FBEB2EF"></a></p>

<h5>6.2-4 IsStructureObjectMorphism</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&an style='color:turquoise'>#8227; IsStructureObjectMorphism</code>( <var class="Arg">arg</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>This is the super GAP-category which will include the GAP-categories IsHomalgRingMap, etc.</p>

<p><a id="X8346DBCF876C70F7" name="X8346DBCF876C70F7"></a></p>

<h5>6.2-5 IsHomalgRingOrModule</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&an style='color:turquoise'>#8227; IsHomalgRingOrModule</code>( <var class="Arg">arg</var> )</td><td class="tdright">( filter )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> or <code class="keyw">false</code></p>

<p>this is the super GAP-category which will include the GAP-categories IsHomalgRing, IsHomalgModule:</p>

<p><a id="X7C701DBF7BAE649A" name="X7C701DBF7BAE649A"></a></p>

<h4>6.3 <span class="Heading">Attributes</span></h4>

<p><a id="X791768BD7815B343" name="X791768BD7815B343"></a></p>

<h5>6.3-1 RingFilter</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&an style='color:turquoise'>#8227; RingFilter</code>( <var class="Arg">ring</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>A filter inheriting from <code class="code">IsRing</code> which uniquely identifies the ring <var class="Arg">ring</var>. For example, the ring <code class="code">Integers</code> is identified by <code class="code">IsIntegers</code>. If no filter uniquely identifying the ring exists, the most special filter available should be chosen.</p>

<p><a id="X7CB137BC842F454F" name="X7CB137BC842F454F"></a></p>

<h5>6.3-2 RingElementFilter</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&an style='color:turquoise'>#8227; RingElementFilter</code>( <var class="Arg">ring</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>A filter inheriting from <code class="code">IsRingElement</code> which uniquely identifies elements of the ring <var class="Arg">ring</var>. For example, the elements of the ring <code class="code">Integers</code> are identified by <code class="code">IsInt</code>. If no filter uniquely identifying the elements of the ring exists, the most special filter available should be chosen.</p>


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