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Mister Spy & Souheyl Bypass Shell

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#W  ghompcgs.gd                 GAP library                      Bettina Eick
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#Y  Copyright (C)  1997,  Lehrstuhl D für Mathematik,  RWTH Aachen, Germany
#Y  (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y  Copyright (C) 2002 The GAP Group
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#R  IsGroupGeneralMappingByPcgs(<map>)
##
##  <#GAPDoc Label="IsGroupGeneralMappingByPcgs">
##  <ManSection>
##  <Filt Name="IsGroupGeneralMappingByPcgs" Arg='map' Type='Representation'/>
##
##  <Description>
##  is the representations for mappings that map a pcgs to images and thus
##  may use exponents to decompose generators.
##  </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareRepresentation( "IsGroupGeneralMappingByPcgs",
      IsGroupGeneralMappingByImages,
      [ "generators", "genimages", "sourcePcgs", "sourcePcgsImages" ] );

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#R  IsPcGroupGeneralMappingByImages(<map>)
#R  IsPcGroupHomomorphismByImages(<map>)
##
##  <#GAPDoc Label="IsPcGroupGeneralMappingByImages">
##  <ManSection>
##  <Filt Name="IsPcGroupGeneralMappingByImages" Arg='map' Type='Representation'/>
##  <Filt Name="IsPcGroupHomomorphismByImages" Arg='map' Type='Representation'/>
##
##  <Description>
##  is the representation for mappings from a pc group
##  </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareRepresentation( "IsPcGroupGeneralMappingByImages",
      IsGroupGeneralMappingByPcgs,
      [ "generators", "genimages", "sourcePcgs", "sourcePcgsImages" ] );
DeclareSynonym("IsPcGroupHomomorphismByImages",
  IsPcGroupGeneralMappingByImages and IsMapping);

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#R  IsToPcGroupGeneralMappingByImages( <map>)
#R  IsToPcGroupHomomorphismByImages( <map>)
##
##  <#GAPDoc Label="IsToPcGroupGeneralMappingByImages">
##  <ManSection>
##  <Filt Name="IsToPcGroupGeneralMappingByImages" Arg='map' Type='Representation'/>
##  <Filt Name="IsToPcGroupHomomorphismByImages" Arg='map' Type='Representation'/>
##
##  <Description>
##  is the representation for mappings to a pc group
##  </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareRepresentation( "IsToPcGroupGeneralMappingByImages",
      IsGroupGeneralMappingByImages,
      [ "generators", "genimages", "rangePcgs", "rangePcgsPreimages" ] );
DeclareSynonym("IsToPcGroupHomomorphismByImages",
  IsToPcGroupGeneralMappingByImages and IsMapping);

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#O  NaturalIsomorphismByPcgs( <grp>, <pcgs> ) . . presentation through <pcgs>
##
##  <ManSection>
##  <Oper Name="NaturalIsomorphismByPcgs" Arg='grp, pcgs'/>
##
##  <Description>
##  </Description>
##  </ManSection>
##
DeclareOperation( "NaturalIsomorphismByPcgs", [ IsGroup, IsPcgs ] );


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#R  IsNaturalHomomorphismPcGroupRep . . . . . . . . natural hom in a pc group
##
##  <ManSection>
##  <Filt Name="IsNaturalHomomorphismPcGroupRep" Arg='obj' Type='Representation'/>
##
##  <Description>
##  </Description>
##  </ManSection>
##
DeclareRepresentation( "IsNaturalHomomorphismPcGroupRep",
      IsGroupHomomorphism and IsSurjective and IsSPGeneralMapping and
      IsAttributeStoringRep,
      [ "sourcePcgs", "rangePcgs" ] );

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#R  IsPcgsToPcgsGeneralMappingByImages(<obj>)
##
##  <ManSection>
##  <Filt Name="IsPcgsToPcgsGeneralMappingByImages" Arg='obj' Type='Representation'/>
##
##  <Description>
##  </Description>
##  </ManSection>
##
DeclareRepresentation( "IsPcgsToPcgsGeneralMappingByImages",
      IsPcGroupGeneralMappingByImages and IsToPcGroupGeneralMappingByImages,
      [ "generators", "genimages", "sourcePcgs", "sourcePcgsImages",
        "rangePcgs", "rangePcgsPreimages" ] );
DeclareSynonym( "IsPcgsToPcgsHomomorphism",
  IsPcgsToPcgsGeneralMappingByImages and IsMapping);


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#E