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#W  pairs-cong.xml
#Y  Copyright (C) 2015                                      Michael Torpey
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##  Licensing information can be found in the README file of this package.
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<#GAPDoc Label="AsLookupTable">
  <ManSection> 
    <Attr Name="AsLookupTable" Arg="cong"/>
    <Returns>A list.</Returns>
    <Description>
      This attribute describes the semigroup congruence <A>cong</A> as a list of
      positive integers with length the size of the semigroup over which
      <A>cong</A> is defined.<P/>

      Each position in the list corresponds to an element of the semigroup (in
      the order defined by <C>SSortedList</C>) and the integer at that position
      is a unique identifier for that element's congruence class under
      <A>cong</A>.  Hence, two elements are congruent if and only if they have
      the same number at their two positions in the list.<P/>
      <Example><![CDATA[
gap> s := Monoid( [ Transformation( [ 1, 2, 2 ] ),
>                   Transformation( [ 3, 1, 3 ] ) ] );;
gap> cong := SemigroupCongruence( s,
>       [Transformation([1,2,1]),Transformation([2,1,2])] );;
gap> AsLookupTable(cong);
[ 1, 2, 3, 4, 5, 6, 3, 2, 1, 6, 5, 1 ]]]></Example>
    </Description>
  </ManSection>
<#/GAPDoc>
