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  GradedRing.xml     GradedRingForHomalg package documentation             Mohamed Barakat
                                                                    Markus Lange-Hegermann

         Copyright (C) 2010, Mohamed Barakat, University of Kaiserslautern
                      Markus Lange-Hegermann, RWTH-Aachen University
-->

<Chapter Label="GradedRing">
  
  <Heading>Graded Rings</Heading>
  
  The package &GradedRingForHomalg; defines the classes of graded
  rings, ring elements and matrices over such rings. These three
  objects can be used as data structures defined in
  &MatricesForHomalg; on which the &homalg; project can rely to do
  homological computations over graded rings.
  
  <P/>The graded rings most prominently can be used with methods known
  from general &homalg; rings. The methods for doing the computations
  are presented in the appendix (<Ref Appendix="FileOverview" />),
  since they are not for external use. The new attributes and
  operations are documented here.
  
  <P/>Since the objects inplemented here are representations from
  objects elsewhere in the &homalg; project
  (i.e. &MatricesForHomalg;), we want to stress that there are many
  other operations in &MatricesForHomalg;, which can be used in
  connection with the ones presented here. A few of them can be found
  in the examples and the appendix of this documentation.
  
  <Section Label="GradedRings:Category">

    <Heading>Graded Rings: Category and Representations</Heading>
    
    <#Include Label="IsHomalgGradedRingRep">
    
    <#Include Label="IsHomalgGradedRingElementRep">
    
  </Section>
  
  <Section Label="GradedRings:Constructors">
    
    <Heading>Graded Rings: Constructors</Heading>

    <#Include Label="HomalgGradedRingElement">
      
  </Section>

  <Section Label="GradedRings:Attributes">
    
    <Heading>Graded Rings: Attributes</Heading>
    
    <#Include Label="DegreeGroup">

    <#Include Label="CommonNonTrivialWeightOfIndeterminates">
    
    <#Include Label="WeightsOfIndeterminates">
    
    <#Include Label="MatrixOfWeightsOfIndeterminates">
    
  </Section>
  
  <Section Label="GradedRings:Operations">
    
    <Heading>Graded Rings: Operations and Functions</Heading>
      
    <#Include Label="UnderlyingNonGradedRing:ring">
    
    <#Include Label="UnderlyingNonGradedRing:element">
    
    <#Include Label="Name">
    
  </Section>
    
</Chapter>