Make free bands be acting semigroups

[james-d-mitchell]

It should be relatively straightforward to make free bands in the Semigroups package acting semigroups. This will involve the following:

• adding the filter IsActingSemigroup to IsFreeBandSubsemigroup, or at least, making it so that if IsFreeBandSubsemigroup holds then IsActingSemigroup does also
• Definitions of the functions in main/setup.gd for free bands:
  • ActionRank = content of a free band element
  • MinActionRank = full content
  • LambdaFunc = (ftol, suffix)
  • LambdaAct = if (ftol_1, suffix_1) is the lambda value, and (prefix, ltof, ftol_2, suffix_2) is the element, then return the LambdaFunc of (reverse suffix_1, ftol_1, ftol_1, suffix) * (prefix, ltof, ftol_2, suffix_2)
  • RhoAct + RhoFunc are the analogues of LambdaAct and LambdaFunc, given by (prefix, ltof).
  • LambdaOrbSeed + RhoOrbSeed should be some neutral lambda func.
  • LambdaRank + RhoRank is the content of the lambda value (output of lambda func).
  • LambdaInverse + RhoInverse @reiniscirpons please fill this in
  • LambdaBound + RhoBound should both be 1
  • LambdaIdentity + RhoIdentity should both be the identity permutation
  • LambdaPerm always returns the identity permutation.
  • LambdaConjugator always returns the identity permutation.
  • IdempotentTester always returns true
  • IdempotentCreator given the lamba value (prefix, ltof) and rho value (ftol, suffix) returns (prefix, ltof, ftol, suffix)
  • StablizerAction(x, p) returns x
  • SchutzenbergerGroupMembership returns true.
  • A hash function for elements of free bands.