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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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

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<!-- This is an automatically generated file. -->

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<Chapter Label="Chapter_Category_of_Matrices">

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<Heading>Category of Matrices</Heading>

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<Section Label="Chapter_Category_of_Matrices_Section_Constructors">

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<Heading>Constructors</Heading>

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<ManSection>

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  <Attr Arg="F" Name="MatrixCategory" Label="for IsFieldForHomalg"/>

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 <Returns>a category

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</Returns>

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 <Description>

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The argument is a homalg field <Math>F</Math>.

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The output is the matrix category over <Math>F</Math>.

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Objects in this category are non-negative integers.

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Morphisms from a non-negative integer <Math>m</Math> to a non-negative integer <Math>n</Math> are given by

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<Math>m \times n</Math> matrices.

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 </Description>

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</ManSection>

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<ManSection>

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  <Oper Arg="S, M, R" Name="VectorSpaceMorphism" Label="for IsVectorSpaceObject, IsHomalgMatrix, IsVectorSpaceObject"/>

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 <Returns>a morphism in <Math>\mathrm{Hom}(S,R)</Math>

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</Returns>

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 <Description>

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The arguments are an object <Math>S</Math> in the category of matrices over a

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homalg field <Math>F</Math>, a homalg matrix <Math>M</Math> over <Math>F</Math>, and another object <Math>R</Math>

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in the category of matrices over <Math>F</Math>.

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The output is the morphism <Math>S \rightarrow R</Math> in the category

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of matrices over <Math>F</Math> whose underlying matrix is given by <Math>M</Math>.

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 </Description>

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</ManSection>

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<ManSection>

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  <Oper Arg="d, F" Name="VectorSpaceObject" Label="for IsInt, IsFieldForHomalg"/>

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 <Returns>an object

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</Returns>

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 <Description>

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The arguments are a non-negative integer <Math>d</Math>

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and a homalg field <Math>F</Math>.

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The output is an object in the category of

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matrices over <Math>F</Math> of dimension <Math>d</Math>.

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 </Description>

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</ManSection>

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</Section>

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<Section Label="Chapter_Category_of_Matrices_Section_GAP_Categories">

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<Heading>GAP Categories</Heading>

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<ManSection>

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  <Filt Arg="object" Name="IsVectorSpaceMorphism" Label="for IsCapCategoryMorphism and IsCellOfSkeletalCategory"/>

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 <Returns><C>true</C> or <C>false</C>

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</Returns>

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 <Description>

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The GAP category of morphisms in the category

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of matrices of a field <Math>F</Math>.

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 </Description>

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</ManSection>

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<ManSection>

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  <Filt Arg="object" Name="IsVectorSpaceObject" Label="for IsCapCategoryObject and IsCellOfSkeletalCategory"/>

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 <Returns><C>true</C> or <C>false</C>

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</Returns>

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 <Description>

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The GAP category of objects in the category

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of matrices of a field <Math>F</Math>.

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 </Description>

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</ManSection>

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</Section>

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<Section Label="Chapter_Category_of_Matrices_Section_Attributes">

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<Heading>Attributes</Heading>

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<ManSection>

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  <Attr Arg="alpha" Name="UnderlyingFieldForHomalg" Label="for IsVectorSpaceMorphism"/>

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 <Returns>a homalg field

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</Returns>

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 <Description>

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The argument is a morphism <Math>\alpha</Math> in the matrix category over a

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homalg field <Math>F</Math>.

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The output is the field <Math>F</Math>.

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 </Description>

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</ManSection>

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<ManSection>

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  <Attr Arg="alpha" Name="UnderlyingMatrix" Label="for IsVectorSpaceMorphism"/>

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 <Returns>a homalg matrix

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</Returns>

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 <Description>

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The argument is a morphism <Math>\alpha</Math> in a matrix category.

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The output is its underlying matrix <Math>M</Math>.

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 </Description>

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</ManSection>

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<ManSection>

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  <Attr Arg="A" Name="UnderlyingFieldForHomalg" Label="for IsVectorSpaceObject"/>

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 <Returns>a homalg field

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</Returns>

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 <Description>

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The argument is an object <Math>A</Math> in the matrix category over a

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homalg field <Math>F</Math>.

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The output is the field <Math>F</Math>.

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 </Description>

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</ManSection>

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<ManSection>

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  <Attr Arg="A" Name="Dimension" Label="for IsVectorSpaceObject"/>

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 <Returns>a non-negative integer

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</Returns>

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 <Description>

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The argument is an object <Math>A</Math> in a matrix category.

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The output is the dimension of <Math>A</Math>.

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 </Description>

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</ManSection>

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</Section>

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</Chapter>

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