Quelle semigroupfactorization.gi Sprache: unbekannt

############################################################################
##
#W  semigroupfactorization.gi           Manuel Delgado <mdelgado@fc.up.pt>
#W                                      Jose Morais    <josejoao@fc.up.pt>
##
##
#Y  Copyright (C)  2005,  CMUP, Universidade do Porto, Portugal
##
##
###########################################################################
InstallGlobalFunction(SemigroupFactorization, function(S, elements)
  local  semigroupFactorization_with_semigroups_pkg,
         semigroupFactorization_without_semigroups_pkg, sgp, old;

  # main function below...

  ## local functions

  semigroupFactorization_with_semigroups_pkg := function()
    local  gens, L, list, l, fact;

    gens := GeneratorsOfSemigroup(sgp);

    if IsList(elements) then
      L := ShallowCopy(elements);
    else
      L := [elements];
    fi;

    list := [];
    for l in L do
#      fact := MinimalFactorization(sgp, l);
      fact := Factorization(sgp, l);
      ## the problem caused by having the identity transformation as a factor does not occur using MinimalFactorization, but this function had to be declared (unless the semigroups package had already been read)
      if (Length(fact)) > 1 and (1 in fact) then
        Unbind(fact[Position(fact,1)]);
        fact := Compacted(fact);
      fi;
      ##
      Add(list,List(fact, g -> gens[g]));
    od;
    return list;
  end;

  ##
  semigroupFactorization_without_semigroups_pkg := function()
    local  S, L, path2fact, iso, M, gens2, gensx, gens, el, els, els_len, cg, G,
           L_len, L_vis, L_pos, p, T, a, q, p1, visited, path, fact, i,
           current, current2, v;

    S := StructuralCopy(sgp);
    L := ShallowCopy(elements);

    path2fact := function(p)
      local f, i, len;

      f := [];
      len := Length(p);
      for i in [1..len-1] do
        Add(f, gens[T[p[i]][p[i+1]]]);
      od;
      return(f);
    end;
    ## End of path2fact()  --

    if not (IsSemigroup(S) or IsMonoid(S)) then
      Error("The first argument must be a semigroup");
    fi;
    if not IsTransformationSemigroup(S) then
      Print("I will work with an isomorphic transformation semigroup instead\n");
      iso := IsomorphismTransformationSemigroup(S);
      S := Range(iso);
      S := Semigroup(ReduceNumberOfGenerators(GeneratorsOfSemigroup(S)));
      L := List(L, x->ImageElm(iso,x));
    fi;

    if MultiplicativeNeutralElement(S) = fail then
      M := Monoid(Set(GeneratorsOfSemigroup(S)));
      gens2 := GeneratorsOfMonoid(M);
    else
      gens2 := Set(GeneratorsOfSemigroup(S));
      gensx := Difference(gens2,[IdentityTransformation]);

      if gensx = [] then
        gensx := [ShallowCopy(MultiplicativeNeutralElement(S))];
      fi;
      M := Monoid(gensx);
      gens2 := GeneratorsOfMonoid(M);
    fi;

    gens := [];
    for el in gens2 do
      if not el = MultiplicativeNeutralElement(M) then
        Add(gens, el);
      fi;
    od;

    els := Elements(M);
    els_len := Size(M);
    if not IsList(L) then
      L := [L];
    fi;
    if L = [] then
      return([]);
    fi;
    if ForAny(L, x -> not x in els) then
      Error("The second argument must be a list of elements of the given semigroup");
    fi;

    cg := RightCayleyGraphAsAutomaton(M);
    G := UnderlyingGraphOfAutomaton(cg);

    L_len := Length(L);
    L_vis := 0;
    L_pos := Set(List(L, x -> Position(els, x)));
    if MultiplicativeNeutralElement(M) in L then
      L_len := L_len - 1;
      p := Position(els, MultiplicativeNeutralElement(M));
      RemoveSet(L_pos, p);
    fi;

    T := NullMat(els_len, els_len);
    for a in [1..cg!.alphabet] do
      for q in [1..cg!.states] do
        T[q][cg!.transitions[a][q]] := a;
      od;
    od;

    p1 := Position(els, MultiplicativeNeutralElement(M));

    visited := [];
    path := [];
    fact := [];
    for i in [1..els_len] do
      visited[i] := false;
    od;
    path[p1] := [p1];
    fact[p1] := [MultiplicativeNeutralElement(M)];

    current := [[p1, G[p1]]];
    while L_vis < L_len do
      current2 := [];
      for el in current do
        for v in el[2] do
          if not visited[v] then
            visited[v] := true;
            path[v] := ShallowCopy(path[el[1]]);
            Add(path[v],v);
            if v in L_pos then
              L_vis := L_vis + 1;
            fi;
            Add(current2, [v, G[v]]);
          fi;
        od;
      od;
      current := current2;
    od;

    for i in L_pos do
      fact[i] := path2fact(path[i]);
    od;
    return(List(L, x -> fact[Position(els, x)]));
  end;

  #main function
  # to face the fact that semigroups behave differently depending on the use or not of the "semigroups" package, a fresh object is created
  if IsMonoid(S) then
    sgp := Monoid(GeneratorsOfMonoid(S));
  elif IsSemigroup(S) then
    sgp := Semigroup(GeneratorsOfSemigroup(S));
  else
    Error("The first argument must be a semigroup");
  fi;

  old := InfoLevel(InfoWarning); #to be removed (after a fix in the semigroups pkg)
  SetInfoLevel(InfoWarning,0);#to be removed (after a fix in the semigroups pkg)
  if TestPackageAvailability("semigroups") = true then
    return semigroupFactorization_with_semigroups_pkg();
  else
    return semigroupFactorization_without_semigroups_pkg();
  fi;
  SetInfoLevel(InfoWarning,old);#to be removed (after a fix in the semigroups pkg)

end);

Quelle semigroupfactorization.gi Sprache: unbekannt

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