<Chapter Label="orbits">
  <Heading>
    Orbits
  </Heading>
  <Section><Heading>Looking for something in an orbit</Heading>
    The functions described in this section supplement the &Orb; package by
    providing methods for finding something in an orbit, with the possibility
    of continuing the orbit enumeration at some later point. 

    <#Include Label="EnumeratePosition">
    <#Include Label="LookForInOrb">
  </Section>
  <Section>
    <Heading>Strongly connected components of orbits</Heading>
    The functions described in this section supplement the &Orb; package by
    providing methods for operations related to strongly connected
    components of orbits.<P/>

    If any of the functions is applied to an open orbit, then the orbit is
    completely enumerated before any further calculation is performed. It is not
    possible to calculate the strongly connected components of an orbit of a
    semigroup acting on a set until the entire orbit has been found.

    <#Include Label="OrbSCC">
    <#Include Label="OrbSCCLookup">
    <#Include Label="OrbSCCTruthTable">
    <#Include Label="ReverseSchreierTreeOfSCC">
    <#Include Label="SchreierTreeOfSCC">
    <#Include Label="TraceSchreierTreeOfSCCBack">
    <#Include Label="TraceSchreierTreeOfSCCForward">
  </Section>
</Chapter>
