resolutionAccess_GroupRing.xml~

<Section><Heading>The <K>HapLargeGroupResolution</K> Representation</Heading>

  The large group representation has one additional component called <C>groupring</C>.
  Elements of the modules in a resolution are represented by lists of group
  ring elements.
  <P/>
  
  All methods for the generic representation do also work for the large group
  representation. Some of them are wrappers for special methods which do only
  work for this representation.
  The following list only contains the methods which are not already present in
  the generic representation.
  <P/>
  Note that the input or the output of these functions does not comply
  with the standard representation.

<ManSection>
 <Meth Name="MultiplyGroupElts_LargeGroupRep" Arg="resolution x y" />
 <Meth Name="MultiplyGroupEltsNC_LargeGroupRep" Arg="resolution x y"/>
 <Returns>group element</Returns>
  <Description>
   Returns the product of <A>x</A> and <A>y</A>. The NC version does not check
   whether  <A>x</A> and <A>y</A> are actually elements of the group of
   <A>resolution</A>.
  </Description>
</ManSection>

<ManSection>
 <Meth Name="IsFreeZGLetter_LargeGroupRep" Arg="resolution term letter"/>
 <Returns>boolean</Returns>
  <Description>
   Returns <K>true</K> if and only if <A>letter</A> is a letter (a word of
   length 1) of the <A>term</A>th module of <A>resolution</A> in the
   <K>hapLargeGroupResolution</K> representation. I.e. it tests if
   <A>letter</A> is a pair consisting of an integer of the right size and a
   group element.
  </Description>
</ManSection>


<ManSection>
 <Meth Name="IsFreeZGWord_LargeGroupRep" Arg="resolution term word"/>
 <Returns>boolean</Returns>
  <Description>
    Tests if <A>word</A> is a list of letters in the large group resolution
    representation.
  </Description>
</ManSection>


<ManSection>
 <Meth Name="MultiplyFreeZGLetterWithGroupElt_LargeGroupRep" Arg="resolution
letter g"/>
 <Meth Name="MultiplyFreeZGLetterWithGroupEltNC_LargeGroupRep" Arg="resolution
letter g"/>
 <Returns>free ZG letter in large group representation (integer-group element pair)</Returns>
  <Description>
   Multiplies the letter <A>letter</A> with the group element <A>g</A> and
   returns the result. The NC version does not check whether <A>g</A> is an
   element of the group of <A>resolution</A> and <A>letter</A> can be a letter.
  </Description>
</ManSection>


<ManSection>
 <Meth Name="BoundaryOfFreeZGLetterNC_LargeGroupRep" Arg="resolution term
letter"/>
 <Meth Name="BoundaryOfFreeZGLetter_LargeGroupRep" Arg="resolution term letter"/>
 <Returns>free ZG word in large group representation</Returns>
  <Description>
   Calculates the boundary of the letter <A>letter</A> of the <A>term</A>th
   module of <A>resolution</A> in large group representation.
   The NC version does not check whether <A>letter</A> actually is a letter in
   the <A>term</A>th module.
  </Description>
</ManSection>


<ManSection>
 <Meth Name="BoundaryOfFreeZGWord_LargeGroupRep" Arg="resolution term word"/>
 <Returns>free ZG word in large group representation</Returns>
  <Description>
   Calculates the boundary of the element <A>word</A> of the <A>term</A>th
   module of <A>resolution</A> in large group representation.
   The NC version does not check whether <A>word</A> actually is a word (a list
   of letters) in the <A>term</A>th module.
  </Description>
</ManSection>


</Section>