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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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  GradedRing.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="GradedRing">

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  <Heading>Graded Rings</Heading>

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  The package &GradedRingForHomalg; defines the classes of graded

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  rings, ring elements and 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="GradedRings:Category">

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    <Heading>Graded Rings: Category and Representations</Heading>

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    <#Include Label="IsHomalgGradedRingRep">

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    <#Include Label="IsHomalgGradedRingElementRep">

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  </Section>

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  <Section Label="GradedRings:Constructors">

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    <Heading>Graded Rings: Constructors</Heading>

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    <#Include Label="HomalgGradedRingElement">

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  </Section>

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  <Section Label="GradedRings:Attributes">

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    <Heading>Graded Rings: Attributes</Heading>

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    <#Include Label="DegreeGroup">

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    <#Include Label="CommonNonTrivialWeightOfIndeterminates">

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    <#Include Label="WeightsOfIndeterminates">

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    <#Include Label="MatrixOfWeightsOfIndeterminates">

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  </Section>

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  <Section Label="GradedRings:Operations">

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    <Heading>Graded Rings: Operations and Functions</Heading>

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    <#Include Label="UnderlyingNonGradedRing:ring">

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    <#Include Label="UnderlyingNonGradedRing:element">

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    <#Include Label="Name">

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  </Section>

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</Chapter>

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