Incorrect multiplication tables

[flsmith]

When trying to get the multiplication table of a small semigroup, I can trigger this:

gap> S := AsSemigroup(IsTransformationSemigroup, SmallSemigroup(4, 18));
<transformation semigroup of size 4, degree 5 with 3 generators>
gap> sortedlist := AsSSortedList(S);;
gap> M := MultiplicationTable(S);;
gap> for i in [1 .. 4] do
> for j in [1 .. 4] do
> if not sortedlist[i] * sortedlist[j] = sortedlist[M[i][j]] then
> Error(i, j, M[i][j]);
> fi;
> od;
> od;
Error, 141 at *stdin*:40 called from
<function "unknown">( <arguments> )
 called from read-eval loop at *stdin*:43
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue

but the following is fine:

gap> S := Semigroup(GeneratorsOfSemigroup(S));
<transformation semigroup of degree 5 with 3 generators>
gap> sortedlist := AsSSortedList(S);;
gap> M := MultiplicationTable(S);;
gap> for i in [1 .. 4] do
> for j in [1 .. 4] do
> if not sortedlist[i] * sortedlist[j] = sortedlist[M[i][j]] then
> Error(i, j, M[i][j]);
> fi;
> od;
> od;
gap> 

[flsmith]

This is due to the following function in SmallSemi small.gi:

InstallMethod(IsomorphismTransformationSemigroup, [IsSmallSemigroup],
function(S)
  local table, map, T, iso;

  table := TransposedMat(MultiplicationTable(S));
  map   := x -> TransformationNC(Concatenation(table[x!.index], [x!.index]));

  T     := Semigroup(List(MinimalGeneratingSet(S), map));
  SetSize(T, Size(S));
  SetMultiplicationTable(T, MultiplicationTable(S));
  SetAsSSortedList(T, Set(S, map));
  SetIdSmallSemigroup(T, IdSmallSemigroup(S));
  UseIsomorphismRelation(S, T);

  iso := SemigroupHomomorphismByImagesNC(S, T, List(AsSSortedList(S), map));
  SetIsBijective(iso, true);

  return iso;
end);

Set can reorder the list so the line SetAsSSortedList(T, Set(S, map)); is incorrect.

[james-d-mitchell]

So, perhaps there will be a github version of Smallsemi sometime soon (@alex-konovalov), and then you could submit a PR there @flsmith ?

[james-d-mitchell]

I labelled this issue wontfix because we won't fix it here, but in Smallsemi itself.

[olexandr-konovalov]

With new GitHub feature, we will be able to transfer this issue to Smallsemi repo once it will be established.

[fingolfin]

So, is there a chance somebody will submit a fix to smallsemi, and a new release with this fixed will be released?

[james-d-mitchell]

Yes I intend to do this soon.

[olexandr-konovalov]

Fixed in #7 by @james-d-mitchell