Issue with ClosureInverseMonoid

[ChristopherRussell]

4cef57f seems to have introduced a bug. I noticed an example where the IdempotentGeneratedSubsemigroup of a semigroup had an element that was not in the semigroup. @mtorpey helped me bisect the history to this commit but we were unsure how the changes were affecting this example.

gap> S := 
> InverseMonoid( [ PartialPerm( [ 1, 4 ], [ 1, 4 ] ), PartialPerm( [ 1, 3, 4, 5 ], [ 1, 6, 4, 2 ] ),
> PartialPerm( [ 1, 2, 4, 6 ], [ 1, 5, 4, 3 ] ), PartialPerm( [ 1, 4 ], [ 4, 1 ] ),
> PartialPerm( [ 1, 3, 4, 5 ], [ 1, 3, 4, 5 ] ), PartialPerm( [ 1, 2, 4, 6 ], [ 1, 2, 4, 6 ] ),
> PartialPerm( [ 1, 2, 3, 4, 5, 6, 7 ], [ 1, 2, 3, 4, 5, 6, 7 ] ) ] );
<inverse partial perm monoid of rank 7 with 7 generators>
gap> I := IdempotentGeneratedSubsemigroup(S);
<inverse partial perm monoid of rank 7 with 4 generators>
gap> I = Semigroup(Idempotents(S));
false
gap> Size(I); Size(Idempotents(S));
5
4
gap> Elements(S);
[ <identity partial perm on [ 1, 4 ]>, (1,4), <identity partial perm on [ 1, 3, 4, 5 ]>,
  [3,6][5,2](1)(4), <identity partial perm on [ 1, 2, 4, 6 ]>, [2,5][6,3](1)(4),
  <identity partial perm on [ 1, 2, 3, 4, 5, 6, 7 ]> ]
gap> Elements(I);
[ <identity partial perm on [ 1, 4 ]>, <identity partial perm on [ 1, 3, 4, 5 ]>,
  <identity partial perm on [ 1, 2, 4, 6 ]>, <identity partial perm on [ 1, 2, 3, 4, 5, 6 ]>,
  <identity partial perm on [ 1, 2, 3, 4, 5, 6, 7 ]> ]

[james-d-mitchell]

Thanks @ChristopherRussell and @mtorpey, I can't really investigate this this week, but will try next week. Unless you want to have a go at fixing it yourself @ChristopherRussell ?

[ChristopherRussell]

I have had a look.

IdempotentGeneratedSubsemigroup(S) calls the following:

InverseSemigroup(Idempotents( S ), rec(
    small := true,
    acting := false ));\

which returns the wrong result which I noted above.

However
InverseSemigroup(Idempotents( S ));
returns the right answer

Does this help?

[ChristopherRussell]

And the bug seems to arise in ClosureInverseMonoidOrSemigroupNC where S = One(coll) and coll is the subsemigroup which InverseSemigroup has been called on. The line coll := Filtered(coll, x -> not x in S); removes the identity element of coll and a potentially different element is added back in later because there are many possible identities for a collection of partial perms, in this case.

InstallMethod(ClosureInverseSemigroupOrMonoidNC,
"for a function, an inverse semigroup, finite list of mult. element, and rec",
[IsFunction,
 IsInverseSemigroup and IsGeneratorsOfInverseSemigroup,
 IsMultiplicativeElementCollection and IsFinite and IsList,
 IsRecord],
function(Constructor, S, coll, opts)
  local n, x, T, U, i;

  # EN_SEMI_CLOSURE copies the C++ semigroup if any whenever it is called, so
  # it is essential to filter coll to remove any elements that are already in S
  # here.
  coll := Filtered(coll, x -> not x in S);
  if IsEmpty(coll) then
    return S;
  fi;

  # opts must be copied and processed before calling this function
  # coll must be copied before calling this function

  # Make coll closed under inverses
  coll := Set(coll);
  n    := Length(coll);
  for i in [1 .. n] do
    x := coll[i] ^ -1;
    if not x in coll then
      AddSet(coll, x);
    fi;
  od;

  if Constructor = InverseMonoid and not One(coll) in coll then
    Error("ClosureInverseSemigroupOrMonoidNC2");    
    AddSet(coll, One(coll));
  fi;

[james-d-mitchell]

Think I fixed this @ChristopherRussell can you please comment on the PR?

[wilfwilson]

This was resolved by PR #436.