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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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<!-- 

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  MatrixOverGradedRing.xml     GradedRingForHomalg package documentation             Mohamed Barakat

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                                                                    Markus Lange-Hegermann

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         Copyright (C) 2010, Mohamed Barakat, University of Kaiserslautern

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                      Markus Lange-Hegermann, RWTH-Aachen University

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-->

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<Chapter Label="HomogeneousMatrices">

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  <Heading>Homogeneous Matrices</Heading>

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  The package &GradedRingForHomalg; defines the classes of graded

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  rings, ring elements and homogeneous matrices over such rings. These three

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  objects can be used as data structures defined in

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  &MatricesForHomalg; on which the &homalg; project can rely to do

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  homological computations over graded rings.

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  <P/>The graded rings most prominently can be used with methods known

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  from general &homalg; rings. The methods for doing the computations

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  are presented in the appendix (<Ref Appendix="FileOverview" />),

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  since they are not for external use. The new attributes and

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  operations are documented here.

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  <P/>Since the objects inplemented here are representations from

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  objects elsewhere in the &homalg; project

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  (i.e. &MatricesForHomalg;), we want to stress that there are many

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  other operations in &MatricesForHomalg;, which can be used in

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  connection with the ones presented here. A few of them can be found

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  in the examples and the appendix of this documentation.

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  <Section Label="HomogeneousMatrices:Category">

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    <Heading>Homogeneous Matrices: Category and Representations</Heading>

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    <#Include Label="IsHomalgMatrixOverGradedRingRep">

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  </Section>

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  <Section Label="Matrices:Constructors">

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    <Heading>Homogeneous Matrices: Constructors</Heading>

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    <#Include Label="MatrixOverGradedRing">

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  </Section>

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  <Section Label="HomogeneousMatrices:Attributes">

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    <Heading>Homogeneous Matrices: Attributes</Heading>

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    <#Include Label="DegreesOfEntries">

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    <#Include Label="NonTrivialDegreePerRow">

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    <#Include Label="NonTrivialDegreePerColumn">

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  </Section>

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  <Section Label="HomogeneousMatrices:Operations">

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    <Heading>Homogeneous Matrices: Operations and Functions</Heading>

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    <#Include Label="UnderlyingNonGradedRing:matrix">

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    <#Include Label="SetMatElm">

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    <#Include Label="AddToMatElm">

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    <#Include Label="MatElmAsString">

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    <#Include Label="MatElm">

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  </Section>

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</Chapter>

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