Add `EnumeratorOfPartitionsSet`

[limakzi]

We have PartitionsSet, its memory expensive. There is no enumerator for that.

gap> memory_allocated;
0
gap> Ms := PartitionsSet([1..5]);
[ [ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ] ], [ [ 1 ], [ 2 ], [ 3 ], [ 4, 5 ] ], [ [ 1 ], [ 2 ], [ 3, 4 ], [ 5 ] ], [ [ 1 ], [ 2 ], [ 3, 4, 5 ] ],
  [ [ 1 ], [ 2 ], [ 3, 5 ], [ 4 ] ], [ [ 1 ], [ 2, 3 ], [ 4 ], [ 5 ] ], [ [ 1 ], [ 2, 3 ], [ 4, 5 ] ], [ [ 1 ], [ 2, 3, 4 ], [ 5 ] ],
  [ [ 1 ], [ 2, 3, 4, 5 ] ], [ [ 1 ], [ 2, 3, 5 ], [ 4 ] ], [ [ 1 ], [ 2, 4 ], [ 3 ], [ 5 ] ], [ [ 1 ], [ 2, 4 ], [ 3, 5 ] ],
  [ [ 1 ], [ 2, 4, 5 ], [ 3 ] ], [ [ 1 ], [ 2, 5 ], [ 3 ], [ 4 ] ], [ [ 1 ], [ 2, 5 ], [ 3, 4 ] ], [ [ 1, 2 ], [ 3 ], [ 4 ], [ 5 ] ],
  [ [ 1, 2 ], [ 3 ], [ 4, 5 ] ], [ [ 1, 2 ], [ 3, 4 ], [ 5 ] ], [ [ 1, 2 ], [ 3, 4, 5 ] ], [ [ 1, 2 ], [ 3, 5 ], [ 4 ] ],
  [ [ 1, 2, 3 ], [ 4 ], [ 5 ] ], [ [ 1, 2, 3 ], [ 4, 5 ] ], [ [ 1, 2, 3, 4 ], [ 5 ] ], [ [ 1, 2, 3, 4, 5 ] ], [ [ 1, 2, 3, 5 ], [ 4 ] ],
  [ [ 1, 2, 4 ], [ 3 ], [ 5 ] ], [ [ 1, 2, 4 ], [ 3, 5 ] ], [ [ 1, 2, 4, 5 ], [ 3 ] ], [ [ 1, 2, 5 ], [ 3 ], [ 4 ] ], [ [ 1, 2, 5 ], [ 3, 4 ] ],
  [ [ 1, 3 ], [ 2 ], [ 4 ], [ 5 ] ], [ [ 1, 3 ], [ 2 ], [ 4, 5 ] ], [ [ 1, 3 ], [ 2, 4 ], [ 5 ] ], [ [ 1, 3 ], [ 2, 4, 5 ] ],
  [ [ 1, 3 ], [ 2, 5 ], [ 4 ] ], [ [ 1, 3, 4 ], [ 2 ], [ 5 ] ], [ [ 1, 3, 4 ], [ 2, 5 ] ], [ [ 1, 3, 4, 5 ], [ 2 ] ],
  [ [ 1, 3, 5 ], [ 2 ], [ 4 ] ], [ [ 1, 3, 5 ], [ 2, 4 ] ], [ [ 1, 4 ], [ 2 ], [ 3 ], [ 5 ] ], [ [ 1, 4 ], [ 2 ], [ 3, 5 ] ],
  [ [ 1, 4 ], [ 2, 3 ], [ 5 ] ], [ [ 1, 4 ], [ 2, 3, 5 ] ], [ [ 1, 4 ], [ 2, 5 ], [ 3 ] ], [ [ 1, 4, 5 ], [ 2 ], [ 3 ] ],
  [ [ 1, 4, 5 ], [ 2, 3 ] ], [ [ 1, 5 ], [ 2 ], [ 3 ], [ 4 ] ], [ [ 1, 5 ], [ 2 ], [ 3, 4 ] ], [ [ 1, 5 ], [ 2, 3 ], [ 4 ] ],
  [ [ 1, 5 ], [ 2, 3, 4 ] ], [ [ 1, 5 ], [ 2, 4 ], [ 3 ] ] ]
gap> memory_allocated;
96304

[fingolfin]

As @limakzi already discovered, we do have IteratorOfPartitionsSet though. But of course that's still another thing.

@reiniscirpons might look into adding such an enumerator during the currently on going GAP Days in Porto. We'll see :-)