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<h1>ToolsForHomalg</h1>


<h2>Special methods and knowledge propagation tools</h2>

<p>
    2025.05-01</p>

<p>
    2 May 2025
  </p>

</div>
<p><b>
    Mohamed Barakat




  </b>
<br />Email: <span class="URL"><a href="mailto:mohamed.barakat@uni-siegen.de">mohamed.barakat@uni-siegen.de</a></span>
<br />Homepage: <span class="URL"><a href="https://mohamed-barakat.github.io">https://mohamed-barakat.github.io</a></span>
<br />Address: <br />Walter-Flex-Str. 3<br /> 57072 Siegen<br /> Germany<br />
</p><p><b>
    Sebastian Gutsche




  </b>
<br />Email: <span class="URL"><a href="mailto:gutsche@mathematik.uni-siegen.de">gutsche@mathematik.uni-siegen.de</a></span>
<br />Homepage: <span class="URL"><a href="https://sebasguts.github.io">https://sebasguts.github.io</a></span>
<br />Address: <br />Department Mathematik<br /> Universität Siegen<br /> Walter-Flex-Straße 3<br /> 57072 Siegen<br /> Germany<br />
</p><p><b>
    Markus Lange-Hegermann




  </b>
<br />Email: <span class="URL"><a href="mailto:markus.lange.hegermann@rwth-aachen.de">markus.lange.hegermann@rwth-aachen.de</a></span>
<br />Homepage: <span class="URL"><a href="http://wwwb.math.rwth-aachen.de/~markus/">http://wwwb.math.rwth-aachen.de/~markus/</a></span>
<br />Address: <br />Markus Lange-Hegermann<br /> Lehrstuhl B fuer Mathematik, RWTH Aachen<br /> Templergraben 64<br /> 52062 Aachen<br /> Germany<br />
</p>

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<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1.html#X7A42AF337F0F3EAE">1 <span class="Heading">Caches</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X824C0CC579E8DD7F">1.1 <span class="Heading">Object constructors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E14EE657C553EDB">1.1-1 CachingObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X85F7EEE385E58EBB">1.1-2 CachingObject</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7F4F8C2380D95C03">1.2 <span class="Heading">Setters, getters</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7FA41BDA822790B2">1.2-1 CacheValue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X81D3DA3881F54824">1.2-2 SetCacheValue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X828F425478CE6FF1">1.2-3 IsEqualForCache</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X7CAF0DB27B3836F9">1.3 <span class="Heading">Managing functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E2443877886AEFD">1.3-1 SetCachingObjectCrisp</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7E1E50AD7FE9BE4D">1.3-2 SetCachingObjectWeak</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B68A31E806C85A2">1.3-3 DeactivateCachingObject</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X8791224B7C97F0CF">1.4 <span class="Heading">Install functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7CC147407A5963AF">1.4-1 InstallMethodWithCache</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X867A71918020901E">1.4-2 InstallMethodWithCrispCache</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X7B148C2280708F41">1.4-3 InstallMethodWithCacheFromObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1.html#X8154383B83B3A992">1.4-4 FunctionWithCache</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap2.html#X83F0437887B743C6">2 <span class="Heading">Lazy arrays</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7D03633A7D98026B">2.1 <span class="Heading">GAP categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X863831C4843545B3">2.1-1 IsLazyArray</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X86EC0F0A78ECBC10">2.2 <span class="Heading">Constructors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7F49E56781DF539E">2.2-1 LazyArrayWithValues</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3.html#X833D807C81E07ABC">3 <span class="Heading">Lazy homogeneous lists</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X7D03633A7D98026B">3.1 <span class="Heading">GAP categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C320F5A879A7FD8">3.1-1 IsLazyHList</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3.html#X86EC0F0A78ECBC10">3.2 <span class="Heading">Constructors</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3.html#X7C4EDA327FA79326">3.2-1 LazyHList</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4.html#X7AE60B0886355B92">4 <span class="Heading">Lists with attributes</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7D03633A7D98026B">4.1 <span class="Heading">GAP categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X831B2B37870A29FD">4.1-1 IsListWithAttributes</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X86EC0F0A78ECBC10">4.2 <span class="Heading">Constructors</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X794FB63684D26A64">4.2-1 TypedListWithAttributes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X870B67E178BEA1B6">4.2-2 ListWithAttributes</a></span>
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</div>
<div class="ContChap"><a href="chap5.html#X7B4028057844FD6B">5 <span class="Heading">ToDo-list</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X849630B07F560FF5">5.1 <span class="Heading">Blueprints</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8627840881B04F30">5.1-1 ToDoListEntryToMaintainEqualAttributes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X83C3ABAA78446811">5.1-2 ToDoListEntryToMaintainFollowingAttributes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X829D3C967A146C7B">5.1-3 ToDoListEntry</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X84032B267EDC4FAC">5.1-4 ToDoList_this_object</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X87779438810212EE">5.1-5 ToDoListEntryToMaintainEqualAttributesBlueprint</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7FFB4C148359E579">5.1-6 ToDoListEntryToMaintainFollowingAttributesBlueprint</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7A7B0E87843AF435">5.1-7 ToDoListEntryBlueprint</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X86137045808AF035">5.2 <span class="Heading">ToDo-list entries</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7EB7863D7F4DC75E">5.2-1 AddToToDoList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X876F23977AA5C19E">5.2-2 SourcePart</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X86B9FC7A78FF9347">5.2-3 TargetPart</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7F63A94D7B43B880">5.2-4 ProcessAToDoListEntry</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7DF4A87E7E84F14F">5.2-5 ToDoListEntry</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7FAFD188845D6FA6">5.2-6 ToDoListEntry</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X8041DC118358A5CD">5.2-7 SetTargetValueObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X793216E3836F177C">5.2-8 SetTargetObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X804F847184D6908B">5.2-9 ToDoListEntryWithContraposition</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X81E733C27D96F9C8">5.2-10 DescriptionOfImplication</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X83F78A1D7DF72241">5.2-11 ToDoListEntryForEqualAttributes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7F1C9BF878D60312">5.2-12 ToDoListEntryForEquivalentAttributes</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7D9151158577E272">5.3 <span class="Heading">Category</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X86D2B9E180E01856">5.3-1 IsToDoList</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7ABF649E831D4D8E">5.4 <span class="Heading">Constructor</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7A46917986B3374A">5.4-1 NewToDoList</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7B69858A7C5DD48B">5.5 <span class="Heading">This is the magic</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X788F2635833587F8">5.5-1 Process_A_ToDo_List_Entry</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7AD403197873FE42">5.5-2 ProcessToDoList</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X844D8E5879757C61">5.6 <span class="Heading">Methods for all objects</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X87B1AEB986DECB11">5.6-1 ToDoList</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X7AB979547B1614FD">5.7 <span class="Heading">Proof tracking</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X86E9744B84BB30D1">5.7-1 TraceProof</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5.html#X8716E6D386B3DF40">5.8 <span class="Heading">Maintainance</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X83B49FF387DDD845">5.8-1 ActivateToDoList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7D3ECBE97AF4EC11">5.8-2 ActivateToDoList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X7946D5AC84D7ACBD">5.8-3 DeactivateToDoList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X824248897F4F4759">5.8-4 DeactivateToDoList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X82A37E2D78476607">5.8-5 ActivateWhereInfosInEntries</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5.html#X82089CAA87F9930B">5.8-6 DeactivateWhereInfosInEntries</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap6.html#X868F7BAB7AC2EEBC">6 <span class="Heading">Basics</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7D9044767BEB1523">6.1 <span class="Heading">Global variables</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7CB459E282D621B2">6.1-1 HOMALG_TOOLS</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7D03633A7D98026B">6.2 <span class="Heading">GAP Categories</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7E36B19C7FFEC100">6.2-1 IsStructureObjectOrObjectOrMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7A9BB94E7D9F3AB6">6.2-2 IsStructureObjectOrObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X85DC9C0A83ADB0C6">6.2-3 IsStructureObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7D2734947FBEB2EF">6.2-4 IsStructureObjectMorphism</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X8346DBCF876C70F7">6.2-5 IsHomalgRingOrModule</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7C701DBF7BAE649A">6.3 <span class="Heading">Attributes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X791768BD7815B343">6.3-1 RingFilter</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6.html#X7CB137BC842F454F">6.3-2 RingElementFilter</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap7.html#X81C68E82799A72EA">7 <span class="Heading">Pointers</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X86D963DC7968899B">7.1 <span class="Heading">Weak pointer objects</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7AF6D36B86EF4FBD">7.1-1 IsContainerForWeakPointers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X78528671799AA08D">7.1-2 ContainerForWeakPointers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X81A9F7857F8526B2">7.1-3 UpdateContainerOfWeakPointers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E59DD5B8396C63B">7.1-4 _AddElmWPObj_ForHomalg</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7E229DC980597F0D">7.1-5 _AddTwoElmWPObj_ForHomalg</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7FD47F2B820F45E1">7.1-6 _ElmWPObj_ForHomalg</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7.html#X7D48F98C7CA131A2">7.2 <span class="Heading">Pointer objects</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X820FC040793F6725">7.2-1 IsContainerForPointers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7B40EDC784E11197">7.2-2 ContainerForPointers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X79FC60458580DCAB">7.2-3 UpdateContainerOfPointers</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X81EB136386E98806">7.2-4 _AddElmPObj_ForHomalg</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X7C77C0C384F45C0C">7.2-5 _AddTwoElmPObj_ForHomalg</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap7.html#X854EF9EA85DB1E4F">7.2-6 _ElmPObj_ForHomalg</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap8.html#X8508AEF8845565A1">8 <span class="Heading">Tools</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8.html#X86FA580F8055B274">8.1 <span class="Heading">Functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7F85CB6A7CAA6BBF">8.1-1 homalgTotalRuntimes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X828ACDE1848695B1">8.1-2 AddLeftRightLogicalImplicationsForHomalg</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7DBCB2087D46555D">8.1-3 LogicalImplicationsForOneHomalgObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7821595B7D6C985E">8.1-4 LogicalImplicationsForTwoHomalgBasicObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X87595FE07BB2D793">8.1-5 InstallLogicalImplicationsForHomalgBasicObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7B9DE98E8174793E">8.1-6 LeftRightAttributesForHomalg</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X85A284627F1B7BF9">8.1-7 InstallLeftRightAttributesForHomalg</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X79A7303E87C290EE">8.1-8 MatchPropertiesAndAttributes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X857BE9A3866F724E">8.1-9 InstallImmediateMethodToPullPropertyOrAttribute</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X80C82B2178A64870">8.1-10 InstallImmediateMethodToConditionallyPullPropertyOrAttribute</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7C553A4986E5420F">8.1-11 InstallImmediateMethodToPullPropertyOrAttributeWithDifferentName</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7B57C37A7B535381">8.1-12 InstallImmediateMethodToPullPropertiesOrAttributes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7C9F11D27AEB0202">8.1-13 InstallImmediateMethodToPullTrueProperty</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X84075C2F827EE9FC">8.1-14 InstallImmediateMethodToConditionallyPullTrueProperty</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7F103C9D809C6A2E">8.1-15 InstallImmediateMethodToPullTruePropertyWithDifferentName</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7A5A1B0186115AC0">8.1-16 InstallImmediateMethodToPullTrueProperties</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X821062A186F7D13F">8.1-17 InstallImmediateMethodToPullFalseProperty</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7AEEA30384AFABED">8.1-18 InstallImmediateMethodToConditionallyPullFalseProperty</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X82B3D84386DB7F67">8.1-19 InstallImmediateMethodToPullFalsePropertyWithDifferentName</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7C25ACB185A071E8">8.1-20 InstallImmediateMethodToPullFalseProperties</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X81EA2ECA82E03EBC">8.1-21 InstallImmediateMethodToPushPropertyOrAttribute</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X8459EC487E871B85">8.1-22 InstallImmediateMethodToConditionallyPushPropertyOrAttribute</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7BF8B06F826A0EFD">8.1-23 InstallImmediateMethodToPushPropertyOrAttributeWithDifferentName</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X8295EE2C7FDC1F73">8.1-24 InstallImmediateMethodToPushPropertiesOrAttributes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X8396EFF27E644EF0">8.1-25 InstallImmediateMethodToPushTrueProperty</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7B176145841326DC">8.1-26 InstallImmediateMethodToPushTruePropertyWithDifferentName</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X847108CD829E1632">8.1-27 InstallImmediateMethodToPushTrueProperties</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X82840F9D82789DCD">8.1-28 InstallImmediateMethodToPushFalseProperty</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X8567A6F582543395">8.1-29 InstallImmediateMethodToPushFalsePropertyWithDifferentName</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7C7B82D3812F3D1A">8.1-30 InstallImmediateMethodToPushFalseProperties</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X80BBA5FF81CA093E">8.1-31 DeclareAttributeWithCustomGetter</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7FC6DE90801EC0D3">8.1-32 AppendToAhomalgTable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X80BD423678C01BE8">8.1-33 homalgNamesOfComponentsToIntLists</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7B1C91077BEF9BD5">8.1-34 IncreaseExistingCounterInObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X78DDBC728516654B">8.1-35 IncreaseExistingCounterInObjectWithTiming</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X797F5F0A7840EBD8">8.1-36 IncreaseCounterInObject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X818E23CC81FC0355">8.1-37 MemoryToString</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X861CC82A8236E488">8.1-38 PrimePowerExponent</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7960EFE481EB7D7D">8.1-39 ViewList</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7C4259BE7D66F63A">8.1-40 homalgLaTeX</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X810CE8C27E769247">8.1-41 IdenticalPosition</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7C03CAC285CC3734">8.1-42 PositionsOfMaximalObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7B9807D581A928C0">8.1-43 MaximalObjects</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7F5EB34C835F5EA5">8.1-44 CollectEntries</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X85DB89C57A37721C">8.1-45 MakeShowable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X81B5CF5380CE2021">8.1-46 MakeShowableWithLaTeX</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7EF0700882F21FD8">8.1-47 ReplacedStringViaRecord</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7FED6864832055C4">8.1-48 StartTimer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7F11AC1E7EF7D799">8.1-49 StopTimer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X836482F57C4B757F">8.1-50 ResetTimer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X796292DF861A07AE">8.1-51 DisplayTimer</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7F6543E78601EC4A">8.1-52 ListImpliedFilters</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7B82900C85ABA1C8">8.1-53 Breakpoint</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X87CE4AC7811FC3E5">8.1-54 ReadPackageOnce</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8.html#X86F60B7B826FA61E">8.2 <span class="Heading">Example functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X7A0A10B585C49632">8.2-1 ExamplesForHomalg</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8.html#X8041FC897BF996CB">8.2-2 ExamplesForHomalg</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap9.html#X82EAC5E57CAA5FC5">9 <span class="Heading">Trees</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9.html#X82EAC5E57CAA5FC5">9.1 <span class="Heading">Trees</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7ACE7DC5811BC3E6">9.1-1 IsTree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7F3BD31F8167E2AD">9.1-2 Content</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X87364E1880BAFD86">9.1-3 ListOfSuccessors</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7963601778389D55">9.1-4 Predecessor</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7DBFDC727BD18391">9.1-5 ListOfSentinels</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X82C8BE577AF4389D">9.1-6 RemoveHead</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X81853D90786ACF86">9.1-7 Tree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X822ED357788C5AE8">9.1-8 Tree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X7C9C3B5F81D1B816">9.1-9 Add</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X874C552787D43D73">9.1-10 ContentListFromSentinelToHead</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9.html#X851053447BC5684C">9.1-11 PostOrder</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap10.html#X7BE235988693C72F">10 <span class="Heading">Z-functions</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10.html#X85BDA2257D22C617">10.1 <span class="Heading">Gap categories for Z functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X824F514F847A353D">10.1-1 IsZFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7F33D8E781560FA8">10.1-2 IsZFunctionWithInductiveSides</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10.html#X8416D8F37C19C23D">10.2 <span class="Heading">Creating Z-functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7F11AE5C829E0465">10.2-1 VoidZFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7D65928287AA2E78">10.2-2 AsZFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X860B41867880891C">10.2-3 UnderlyingFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X78F26197785091E3">10.2-4 ZFunctionValue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X79F5AA977A75B664"><code>10.2-5 <span>\</span>[<span>\</span>]</code></a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X867DAC087866CD8C">10.2-6 ZFunctionWithInductiveSides</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7F50565B78308CB0">10.2-7 UpperFunction</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X8553572B7B5E58D9">10.2-8 StableUpperValue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X846C56B882566639">10.2-9 IndexOfStableUpperValue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X839E578D86B98DFD">10.2-10 SetStableUpperValue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7C607DDE786591AC">10.2-11 StableLowerValue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7D5F7C4D80091041">10.2-12 IndexOfStableLowerValue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7E01C0927F9B5AC7">10.2-13 SetStableLowerValue</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X863225F9798BD2CC">10.2-14 Reflection</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X80EB63EC828CE582">10.2-15 ApplyShift</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X8308ACDA78E96FC5">10.2-16 ApplyMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7AC919EC8734B869">10.2-17 ApplyMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7E943C6E7B5784CD">10.2-18 BaseZFunctions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X7A7795C883285A22">10.2-19 AppliedMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X854A6DE682EAADB3">10.2-20 CombineZFunctions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap10.html#X83D1892185F38BDA">10.2-21 Replace</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapInd.html"><span class="Heading">Index</span></a></div>
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