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products/sources/formale Sprachen/GAP/pkg/cap/doc/ (Algebra von RWTH Aachen Version 4.15.1^©) Datei vom 22.8.2025 mit Größe 5 kB

Quelle _Chapter_Dummy_implementations.xml Sprache: XML

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


<Chapter Label="Chapter_Dummy_implementations">
<Heading>Dummy implementations</Heading>

<P/>
A dummy implementation of a concept seems to provide an interface for the concept, but calling 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.
<Section Label="Chapter_Dummy_implementations_Section_Dummy_rings">
<Heading>Dummy rings</Heading>

<ManSection>
  <Filt Name="IsDummyRing" />
<Description>
  The &GAP; filter of dummy rings.
</Description>
</ManSection>

<ManSection>
  <Filt Name="IsDummyRingElement" />
<Description>
  The &GAP; filter of elements of a dummy ring.
</Description>
</ManSection>

<ManSection>
  <Filt Name="IsDummyCommutativeRing" />
<Description>
  The &GAP; filter of dummy commutative rings.
</Description>
</ManSection>

<ManSection>
  <Filt Name="IsDummyCommutativeRingElement" />
<Description>
  The &GAP; filter of elements of a dummy commutative ring.
</Description>
</ManSection>

<ManSection>
  <Filt Name="IsDummyField" />
<Description>
  The &GAP; filter of dummy fields.
</Description>
</ManSection>

<ManSection>
  <Filt Name="IsDummyFieldElement" />
<Description>
  The &GAP; filter of elements of a dummy field.
</Description>
</ManSection>

<ManSection>
  <Func Arg="" Name="DummyRing" />
<Returns>a dummy ring
</Returns>
<Description>
<P/>
</Description>
</ManSection>

<ManSection>
  <Func Arg="" Name="DummyCommutativeRing" />
<Returns>a dummy commutative ring
</Returns>
<Description>
<P/>
</Description>
</ManSection>

<ManSection>
  <Func Arg="" Name="DummyField" />
<Returns>a dummy field
</Returns>
<Description>
<P/>
</Description>
</ManSection>

</Section>

<Section Label="Chapter_Dummy_implementations_Section_Dummy_categories">
<Heading>Dummy categories</Heading>

<ManSection>
  <Filt Arg="arg" Name="IsDummyCategory" Label="for IsCapCategory"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
  The &GAP; category of a dummy CAP category.
</Description>
</ManSection>

<ManSection>
  <Filt Arg="arg" Name="IsDummyCategoryObject" Label="for IsCapCategoryObject"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
  The &GAP; category of objects in a dummy CAP category.
</Description>
</ManSection>

<ManSection>
  <Filt Arg="arg" Name="IsDummyCategoryMorphism" Label="for IsCapCategoryMorphism"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
  The &GAP; category of morphisms in a dummy CAP category.
</Description>
</ManSection>

<ManSection>
  <Oper Arg="options" Name="DummyCategory" Label="for IsRecord"/>
<Returns>a category
</Returns>
<Description>
  Creates a dummy category subject to the options given via <A>options</A>, which is a record passed on to <Ref Oper="CategoryConstructor" Label="for IsRecord" />.
  Note that the options <Code>{category,object,morphism}_filter</Code> will be set to <Code>IsDummyCategory{,Object,Morphism}</Code> and the options <Code>{object,morphism}_{constructor,datum}</Code> and
  <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.
</Description>
</ManSection>

</Section>

<Section Label="Chapter_Dummy_implementations_Section_Dummy_homalg_rings">
<Heading>Dummy homalg rings</Heading>

The operations in this section require
<Code>MatricesForHomalg</Code> to be loaded.
<ManSection>
  <Filt Name="IsDummyHomalgRing" />
<Description>
  The &GAP; filter of dummy homalg rings.
</Description>
</ManSection>

<ManSection>
  <Filt Name="IsDummyHomalgRingElement" />
<Description>
  The &GAP; filter of elements of a dummy homalg ring.
</Description>
</ManSection>

<ManSection>
  <Filt Name="IsDummyCommutativeHomalgRing" />
<Description>
  The &GAP; filter of dummy commutative homalg rings.
</Description>
</ManSection>

<ManSection>
  <Filt Name="IsDummyCommutativeHomalgRingElement" />
<Description>
  The &GAP; filter of elements of a dummy commutative homalg ring.
</Description>
</ManSection>

<ManSection>
  <Filt Name="IsDummyHomalgField" />
<Description>
  The &GAP; filter of dummy homalg fields.
</Description>
</ManSection>

<ManSection>
  <Filt Name="IsDummyHomalgFieldElement" />
<Description>
  The &GAP; filter of elements of a dummy homalg field.
</Description>
</ManSection>

<ManSection>
  <Func Arg="" Name="DummyHomalgRing" />
<Returns>a dummy homalg ring
</Returns>
<Description>
<P/>
</Description>
</ManSection>

<ManSection>
  <Func Arg="" Name="DummyCommutativeHomalgRing" />
<Returns>a dummy commutative homalg ring
</Returns>
<Description>
<P/>
</Description>
</ManSection>

<ManSection>
  <Func Arg="" Name="DummyHomalgField" />
<Returns>a dummy homalg field
</Returns>
<Description>
<P/>
</Description>
</ManSection>

</Section>

</Chapter>

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