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products/Sources/formale Sprachen/GAP/pkg/toolsforhomalg/doc/ (Algebra von RWTH Aachen Version 4.15.1^©) Datei vom 2.4.2025 mit Größe 3 kB

Quelle _Chapter_Basics.xml Sprache: XML

<?xml version="1.0" encoding="UTF-8"?>


<Chapter Label="Chapter_Basics">
<Heading>Basics</Heading>

<Section Label="Chapter_Basics_Section_Global_variables">
<Heading>Global variables</Heading>

<ManSection>
  <Var Name="HOMALG_TOOLS" />
<Description>
A central place for configurations.
</Description>
</ManSection>

</Section>

<Section Label="Chapter_Basics_Section_GAP_Categories">
<Heading>GAP Categories</Heading>

<ManSection>
  <Filt Arg="arg" Name="IsStructureObjectOrObjectOrMorphism" Label="for IsAttributeStoringRep"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
This is the super super GAP-category which will
include the GAP-categories IsStructureObjectOrObject and IsHomalgObjectOrMorphism
</Description>
</ManSection>

<ManSection>
  <Filt Arg="arg" Name="IsStructureObjectOrObject" Label="for IsStructureObjectOrObjectOrMorphism"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
This is the super GAP-category which will include the GAP-categories
IsHomalgRing, IsHomalgModule, IsHomalgRingOrModule and IsHomalgComplex
</Description>
</ManSection>

<ManSection>
  <Filt Arg="arg" Name="IsStructureObject" Label="for IsStructureObjectOrObject"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
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)
</Description>
</ManSection>

<ManSection>
  <Filt Arg="arg" Name="IsStructureObjectMorphism" Label="for IsAttributeStoringRep"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
This is the super GAP-category which will include the GAP-categories
IsHomalgRingMap, etc.
</Description>
</ManSection>

<ManSection>
  <Filt Arg="arg" Name="IsHomalgRingOrModule" Label="for IsStructureObjectOrObject"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
this is the super GAP-category which will include the GAP-categories
IsHomalgRing, IsHomalgModule:
</Description>
</ManSection>

</Section>

<Section Label="Chapter_Basics_Section_Attributes">
<Heading>Attributes</Heading>

<ManSection>
  <Attr Arg="ring" Name="RingFilter" Label="for IsRing"/>
<Description>
A filter inheriting from <Code>IsRing</Code> which uniquely identifies the ring <A>ring</A>.
For example, the ring <Code>Integers</Code> is identified by <Code>IsIntegers</Code>.
If no filter uniquely identifying the ring exists,
the most special filter available should be chosen.
</Description>
</ManSection>

<ManSection>
  <Attr Arg="ring" Name="RingElementFilter" Label="for IsRing"/>
<Description>
A filter inheriting from <Code>IsRingElement</Code> which uniquely identifies elements of the ring <A>ring</A>.
For example, the elements of the ring <Code>Integers</Code> are identified by <Code>IsInt</Code>.
If no filter uniquely identifying the elements of the ring exists,
the most special filter available should be chosen.
</Description>
</ManSection>

</Section>

</Chapter>

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